Manasreh, III-Nitride Semiconductors - Electrical, Structural and Defects Properties 0444506306 Elsevier 2000)

V

Preface

Research advances in Ill-nitride semiconductor materials and device have led to an exponential increase in activity directed towards electronic and optoelectronic applications. There is also great scientific interest in this class of materials because they appear to form the first semiconductor system in which extended defects do not severely affect the optical properties of devices. This volume consists of chapters written by a number of leading researchers in nitride materials and device technology with the emphasis on the dopants incorporation, impurities identifications, defects engineering, defects characterization, ion implantation, irradiation-induced defects, residual stress, structural defects, and phonon confinement. This unique volume provides a comprehensive review and introduction of defects and structural properties of GaN and related compounds for newcomers to the field and stimulus to further advances for experienced researchers.

Given the current level of interest and research activity directed towards nitride materials and devices, the publication of this volume is particularly timely. Early pioneering work by Pankove and co-workers in the 1970s yielded a metal-insulator-semiconductor GaN light-emitting diode (LED), but the difficulty of producing p-type GaN precluded much further effort. The current level of activity in nitride semiconductors was inspired largely by the results of Akasaki and co-workers and of Nakamura and co-workers in the late 1980s and early 1990s in the development of p-type doping in GaN and the demonstration of nitride-based LEDs at visible wavelengths. These advances were followed by the successful fabrication and commercialization of nitride blue laser diodes by Nakamura et al at Nichia. The chapters contained in this volume constitutes a mere sampling of the broad range of research on nitride semiconductor materials and defect issues currently being pursued in academic, government, and industrial laboratories worldwide.

I would like to thank all authors of the chapters, whose excellent efforts have made this volume possible.

M.O. MANASREH

University of New Mexico

August 2000

VII

List of Contributors

ED. Auret

M. Babiker

C.R. Bennett

J.C. Culbertson

Nora V. Edwards

M. Eatemi

S.A. Goodman

R.L. Henry

H.X. Jiang

M. Kamiriska

D.D. Koleske

J.Y. Lin

Physics Department, University^ of Pretoria, Pretoria 0002, South Africa. E-mail: [email protected]

Department of Physics, University of Essex, Colchester C04 3SQ, Engeland

Department of Physics, University of Essex, Colchester C04 3SQ, Engeland

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA

Department of Physics and Measurement Technology, Materials Science, Linkopings Universitet, S-58183 Linkoping, Sweden. E-mail: [email protected]


Physics Department, University of Pretoria, Pretoria 0002, South Africa


Department of Physics, Kansas State University, Manhattan, KS 66506, USA. E-mail: [email protected]

Institute of Experimental Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland


Department of Physics, Kansas State University, Manhattan, KS 66506, USA. E-mail: [email protected]

VIII List of Contributors

M. Omar Manasreh

M. Palczewska

Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131-1356, USA. E-mail: [email protected]

Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland, E-mail: [email protected]

Bemd Rauschenbach Universitdt Augsburg, Institut fUr Physik Universitdtsstrasse 1, D-86135 Augsburg, Germany. E-mail: [email protected]

B.K. Ridley

S. Ruvimov

K. Saarinen

John T. Torvik

M.E. Twigg

A.E. Wickenden

N.A. Zakhleniuk

Department of Electronic Systems Engineering, University of Essex, Colchester C04 3SQ, Engeland

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. E-mail: [email protected]

Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 Hut, Finland. E-mail: [email protected]

Astralux, Inc., 2500 Central Ave., Boulder, CO 80301, USA. E-mail: [email protected]

Electronics Science and Technology Division, Naval Research Laboratory, Washington, DC 20375-5320, USA. E-mail: [email protected]


Department of Electronic Systems Engineering, University of Essex, Colchester C04 3SQ, Engeland. E-mail: [email protected]

III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B.V. All rights reserved

CHAPTER 1

Introduction to defects and structural properties of Ill-nitride semiconductors

M.O. Manasreh

1. Introduction

GaN and related compounds attracted tremendous interest for their applications to blue/green diode lasers and LEDs, high-temperature electronics, high-density optical data storage, and electronics for aerospace and automobiles. There is also great scientific interest in this class of materials because they appear to form the first semiconductor system in which extended defects do not severely affect the optical properties of devices. This volume is focused on the defects and structural properties of Ill-nitrides featuring chapters written by experts in the field. This unique volume provides a comprehensive review and introduction of defects and structural properties of GaN and related compounds for newcomers to the field and stimulus to further advances for experienced researchers. This introductory chapter is constructed based on the input and information reported by the authors of the technical chapters. Hence it provides some ideas about each chapter and the topics discussed by the authors.

When Maruska and Titjen succeeded in growing GaN on sapphire substrates in the late 1960s using chemical vapor deposition [1], it quickly became obvious that doping and defects would play a vital role in the future development of GaN. The early unintentionally doped GaN was invariably n-type, which at the time was believed due to nitrogen vacancies. The high n-type background carrier concentration on the order of 10^^ cm~^ proved difficult to minimize and the absence of a shallow acceptor dinmied the prospects of a production-scale GaN-based device effort. Nevertheless, the early work using zinc-compensation led to the first demonstrations of blue, green, yellow and red metal-insulating-n-type GaN light emitting diodes (LEDs) [2], but further device development was still stifled by the seemingly insurmountable problem of making conducting p-type GaN. The search for p-type GaN was not successful until Akasaki and Amano demonstrated this feat in 1989 [3]. This remarkable achievement was actually a result of two significant milestones. First, the crystalline quality and the background n-type carrier density in unintentionally doped GaN films was significantly reduced by the use of a low temperature AIN buffer layer [4,5]. Second, p-type GaN was demonstrated with Mg-doping followed by an ex situ low energy electron beam irradiation (LEEBI) treatment. Conducting p-type GaN had previously remained elusive despite other Mg-doping efforts because it was found that hydrogen passivates the Mg-acceptors [6], similar to the effect of hydrogen on acceptors in Si [7]. Thus, it was theorized that the LEEBI treatment, which was accidentally discovered while studying

2 Ch. 1 M.O. Manasreh

the cathodoluminescence of a Mg-doped sample, disassociated the H-Mg complex allowing the Mg to form a quasi-shallow acceptor level. This theory was later confirmed by producing p-GaN by annealing GaNiMg in a hydrogen-free ambient such as N2 [8]. The process was also reversible rendering GaN:Mg insulating by annealing in a hydrogen-rich environment such as ammonia (NH3). These remarkable discoveries eventually led to the demonstration of a variety of bipolar devices, such as blue and green p-n junction LEDs and violet laser diodes (for examples see ref. [9]), solar-blind and ultraviolet sensitive p-i-n photodiodes [10-13] and high-power, high-temperature bipolar transistors [14,15].

Even though much progress has been made in doping GaN, there still exists significant challenges; especially with p-type doping. The low hole mobility and low achievable free hole concentration result in large sheet resistance preventing the fabrication of reliable Ohmic contacts with low contact resistivities. These material challenges have prevented the use of the AlGaN/GaN system to its full potential in electronic applications such as microwave heterojunction bipolar transistors (HBTs). Furthermore, the immature p-type doping technology has led to degradation (lifetime) problems and required that InGaN laser diodes operate at a higher than expected bias voltage.

The ten technical chapters in this volume are focused on various aspects of dopants, impurities, defects, electrical and structural properties. The chapters are treating different aspects of Ill-nitrides as described in the following sections.

2. Dopants and defect engineering

The aim of chapter two is to describe the state-of-the-art undoped and doped GaN by comparing select optical and electronic properties. The results reported in this chapter show that N-type doping of GaN using Si is well-understood, as Si readily incorporates on a Ga-site forming a single shallow donor with an activation energy of 12-15 meV leading to near complete donor ionization at room temperature. The growth is largely controlled over a wide range of densities from low-10^^ to mid-10^^ cm~^, although some structural problems occur in thick and heavily doped films. On the other hand, P-type doping remains a major challenge, as Mg forms a 'quasi-shallow' acceptor level located more than 170 meV above the valence band edge. The deep nature of the acceptor level leads to poor acceptor ionization of several percent at room temperature. Excessively high Mg concentrations are therefore needed to produce p-type films above mid-10^^ cm~^, which often results in resistive films.

The near-band edge optical transitions are well understood in GaN, and thus, low temperature photoluminescence spectroscopy is a valuable tool in characterizing nominally undoped GaN. On the other hand, the origins of various defect-related transitions such as the ever-present yellow PL are still hotly debated and will require further investigations to unambiguously identify. The broad defect-related PL signatures observed well below the intrinsic optical band edge tends to dominate the spectra and often limit the useful information that can be extracted from PL measurements on heavily doped material. PL can generally be used to identify the presence of and to extract the binding energies for common dopants such as Mg and Si in low and medium doped GaN.

Properties of Ill-nitride semiconductors Ch. 1 3

The Hall-effect measurement is a useful tool to determine the carrier concentration, mobility and resistively in conducting GaN and temperature-dependent measurements yield info regarding the thermal activation energies. However, caution should be placed on equating the thermal activation energy to the actual location of the donor/acceptor levels responsible for electron/hole conduction with respect to the band edges. The electrical measurements can substantially underestimate the location of the donor/acceptor levels as heavily doped material is most often used, which causes potential fluctuations in the lattice leading to significant band-tailing. A comparison with PL measurements on modestly doped material can often clarify the situation. This is particularly true for Mg-doped GaN as shown in chapter two.

Diffusion as a doping technique is impractical for GaN due to the vanishing small diffusivities at temperatures below 1 lOO 'C. Ion implantation is more promising for both conductivity modulation and optical purposes, but further work is required to optimize activation and minimize residual implantation damage. The process compatibility of implantation is limited due to the high annealing temperatures needed above 1500°C to repair implantation-induced damage. Nevertheless, implantation can possibly be used in areas of the device that is removed from critical (minority) carrier flow such for creating heavily doped contact layers facilitating tunneling contacts with low resistivities. In situ doping is therefore the doping technique of choice due to the above-mentioned challenges. Tricks such as piezoelectric enhanced superlattice doping can create p-layers with low resistivities, but is not practical for vertical carrier conduction. Molecular doping of paired donors and acceptors is another alternative that deserves further exploration.

How does the current status of dopants in GaN impact the future device efforts? It is clear that devices will continue to exhibit large series resistances and contact problems until the above-mentioned fundamental p-type doping problem is solved. The most glaring examples are the high operating voltages and lifetime problems associated with GaN-based lasers and the absence of microwave operation in HBTs. The fundamental problems can be circumvented on an individual basis by clever device design using techniques such as re-growth, selective growth, implantation, superlattice doping, deep-sub-micron lithography and wafer bonding with a penalty in increased processing costs. However, a general and fundamental solution to the p-type doping problem GaN and the related alloy system (Al-In-Ga-N) has tremendous potential for both optoelectronic and electronic devices due to superior materials parameters such as a wide and direct bandgap energy, high breakdown fields, high saturated electron velocity and adequate electron mobility and thermal conductivity.

Chapter three reviews the common crystallographic defects observed in the GaN and related Ill-nitride systems based on the electron microscopy results. All foreign substrates available for the GaN epitaxy have a high mismatch in lattice parameters, thermal expansion and chemical composition with the GaN layer. Among a large number of different foreign substrates tested for the GaN deposition [16], sapphire and 6H silicon carbide have demonstrated the best results in terms of the layer quality. The mismatch in lattice parameters and thermal expansion coefficients between the GaN and these substrates is high. It leads to a generation of the high density of defects at the epi-layer-substrate interface. The lattice mismatch between the GaN and SiC is about


2%, but it is even higher in case of the GaN layers grown on sapphire being about 16 and 30% for c- or a-facet of sapphire, respectively. However, the defect densities in the GaN layers grown by metal-organic vapor phase epitaxy (MOVPE) on SiC and sapphire substrates were found to be comparable [17]. This could be explained taking into account that defect density in the GaN layer is controlled by structure of the buffer layer and its roughness, in particular.

Defect generation and annihilation discussed in chapter three were shown to be mainly growth-related processes. Because of the very low dislocation mobility in the GaN, the high misfit stress relaxes mainly at earlier growth stages resulting in the high defect density at the interface with the substrate. On the other hand, the low dislocation mobility is favorable for long lifetime of the GaN-based optoelectronic devices. The majority of defects are generated at the interfaces with the substrate and the buffer layer. The dislocation annihilation also occurs mainly in the buffer layer and in the area close to it by the lateral overgrowth of some grains over the others. The proper preparation of substrate surface and optimization of the buffer layer enhancing the lateral overgrowth is essential for the reduction of the defects in the GaN layer. The structural quality of the GaN layer can be controlled by the growth conditions, especially during the first growth stages.

3. Identification and characterization of defects

Several characterization tools were employed in this volume to identify and characterize defects in Ill-nitride semiconductors. For example, magnetic resonance, which is the subject of chapter four, is a very useful technique in solid state physics. The term 'magnetic resonance' means: resonance absorption of electromagnetic radiation at microwave (radiofrequency) range, by paramagnetic defect center present in investigated crystal, with magnetic field of values characteristic for the center applied as well. Basic advantage of wide family of methods based on the magnetic resonance is that they provide information about microscopic nature of paramagnetic defects. Simultaneously, the sensitivity of magnetic resonance methods is much higher than that of most other techniques leading to understand a microscopic picture of investigated centers.

The classical magnetic resonance method is electron spin resonance (ESR), which has been developing very rapidly since 1945 [18]. Electron spin resonance means resonant absorption of microwave power by electronic levels of magnetic ion or defect, in applied magnetic field. These electronic levels originate from the ground state of magnetic center, splitted by Zeeman effect. Electron spin resonance experiments are performed in order to determine the nature, symmetry and environment of paramagnetic defects in crystals. They have been successfully used for many years to study defects in different semiconductors [19-22], providing considerable information about the ground states of paramagnetic centers introduced intentionally, as well as present as unintentional contamination. In ESR, sensitivities even of the order of 10 ^ spins (ions) can be achieved in some cases.

The other magnetic resonance technique, called optically detected magnetic resonance (ODMR), allows studying excited states of defects. It can essentially provide similar information about investigated defects as ESR technique, i.e. determine their


nature and symmetry. The idea of ODMR experiment consists in detection of emission changes due to microwave absorption at the excited states in applied magnetic field. Samples are irradiated with light that causes emission, and are subject to microwave radiation. In such an arrangement, magnetic resonance of defects in excited state can lead to changes in emission intensity. Increase or decrease of sample irradiation intensity is viewed either in polarized light or as changes of total emission. ODMR technique has been successfully used to study defects in different semiconductors, like II-VI, III-V, amorphous Si [23].

In general, the analysis of ESR or ODMR spectra is the same and can provide similar information about defect center. However, in the case of ODMR the line widths are typically substantially broader than in ESR spectra. Therefore, the determination of resonance parameters is more difficult and less accurate from ODMR spectra. On the other hand, the great advantage of optical method is its sensitivity, which increases to about three orders of magnitude over conventional ESR. Another advantage of ODMR is the possibility of directly linking a resonance with a particular emission process.

Another magnetic resonance technique is electrically detected magnetic resonance (EDMR). In analogy to ODMR, in EDMR method the magnetic resonance is observed through spin-dependent electrical properties (optical in ODMR) of sample. Such measurements give great enhancement in sensitivity in comparison with ESR as well as they allow to observe centers participating in electrical processes, not necessary paramagnetic under thermal equilibrium conditions [24]. EDMR studies have been mainly performed on devices, especially in case of GaN-based materials. The results of EDMR experiments on GaN-based devices are not a subject of this book, but and can be found elsewhere [25].

In chapter four, a review of magnetic resonance studies of defects in nitrides is given. Results of research performed by different scientific groups are sunmiarized. The investigated crystals were grown by different techniques: bulk material by high pressure method [26], epitaxial layers by molecular organic chemical vapor deposition (MOCVD) [27] and microcrystalline powder by ammonothermal method [28]. An attempt was made in this chapter to present the main achievements of magnetic resonance studies on defects in nitride compounds. In spite of huge amount of work performed on nitrides, especially in the last 5 years, not too much has been clarified in the area of defect identification. One of the main reasons is the difficulty to obtain bulk nitride crystals, the best materials for ESR studies. The ESR signal due to shallow donor characteristic for MOCVD grown GaN is well established in chapter four. Its parameters are the same for undoped n-type as well as Si-doped layers. However, it has not been definitively proven that Si is the main shallow donor defect in MOCVD-grown GaN. Signal coming from shallow donor in bulk GaN of slightly different parameters has also been identified. In this case, oxygen nature should be strongly considered as possible origin, since bulk GaN suffers from oxygen contamination. On the other hand, quite clear situation is in the area of two main acceptors of GaN, namely Mg and Zn. Their magnetic resonance spectra have been positively identified and found to follow the well know process of hydrogen passivation and its diffusion out of acceptor centers. Transition metal impurities, common trace impurities of many semiconductors, are far from being known in GaN when it comes to their magnetic resonance properties. Up


to now, ESR spectra of only manganese Mn^^ (3d^), iron Fe^+ (3d^), nickel Ni + (3d^) and recently erbium Er^+ (4f^^) have been published. The studies of electron-irradiated GaN have not come up to expectations and have not led to positive identification of any of hoped-for simple native defects.

For mixed AUGai_;cN (0 < JC < 0.26) layers ESR signal of shallow donor has also been reported in chapter four, but the origin of this donor remains still unknown. ESR spectrum observed for polycrystalline AIN ceramics, containing intentional Cr impurities, has been attributed to Cr " (3d^). Finally, in some studies, nitrogen vacancy related ESR defects have been suggested in AIN and BN materials. Since it seems that intentional doping of nitrides and studies of such materials have just started, one can expect much more yet to come in the area of defect identification in nitride compounds in the coming years.

Traditionally the experimental information on point defects has been obtained by electrical and optical characterization techniques, such as Hall measurements and infrared absorption. Although the defects can be detected in these experiments, their atomic structures remain very often unresolved. The methods based on ESR (as discussed in chapter four) are more sensitive to the structure of defects, but so far these techniques have given only limited information in GaN materials. An experimental technique is thus needed for the unambiguous defect identification. This goal is reached for vacancy-type defects by utilizing the positron annihilation spectroscopy as discussed thoroughly in chapter five. Thermalized positrons in solids get trapped by the vacant lattice sites. The reduced electron density at the vacancies increases positron lifetime and narrows the positron-electron momentum distribution. The detection of these quantities yields direct information on the vacancy defects in solids. Positron lifetime measurements can be used to probe homogeneous defect distributions in semiconductor substrates. This technique is relatively simple to implement, but yet very powerful in identifying the atomic structure of the defect, its charge state and concentration. Defects in the near-surface region 0-3 ixm can be studied by a monoenergetic positron beam. This technique is well suited for the defect studies of epitaxial semiconductor materials. The information provided by positron experiments is especially useful when combined with those of other spectroscopies. The correlation of positron measurements with electrical and optical methods enables quantitative studies of technologically important phenomena, such as electrical compensation, light absorption and photoluminescence.

In chapter five, the author presented positron annihilation spectroscopy technique, which was used to identify vacancy defects in GaN epitaxial layers. It yields quantitative information on vacancy concentrations in the range 10^^-10^° cm"^. Positron experiments detect Ga vacancies as native defects in GaN bulk crystals. It is reported in this chapter that the concentration of Voa decreases with increasing Mg doping, as expected from the behavior of their formation energy as a function of the Fermi level. The trapping of positrons at the hydrogenic state around negative ions gives evidence that most of the Mg atoms are negatively charged. This suggests that Mg doping converts n-type GaN to semi-insulating mainly due to the electrical compensation of O^ donors by MgQ^ acceptors.

Ga vacancies are observed as native defects in various n-type GaN overlayers grown by MOCVD on sapphire. Their concentration is >10^^ cm~^ in nominally undoped


material, which show n-type conductivity due to residual oxygen. When similar doping is done with Si impurities and less oxygen is present, the concentration of Ga vacancies is lower by at least an order of magnitude. No Ga vacancies are observed in p-type or semi-insulating layers doped with Mg. These trends agree well with the theoretical calculations, which predict that the formation energy of Ga vacancy is high in p-type and semi-insulating material, but greatly reduced in n-type GaN, and even further reduced due to the formation of Voa-ON complexes.

In addition to doping, the presence of open-volume defects in GaN layers depends on the growth conditions. The concentrations of Ga vacancies increases strongly when more N-rich stoichiometry is applied in the MOCVD growth. On the other hand, the lattice mismatch and associated dislocation density seem to have less influence on the formation of point defects than doping and stoichiometry — at least at distances >0.5 |xm from the layer/substrate interface. This suggests that the formation of point defect in both epitaxial layers and bulk crystals follows mainly the trends expected for defects in thermal equilibrium.

Due to their wide band gaps, effects of deep level centers on the Ill-nitride materials and devices are expected to be more pronounced than in narrower band gap materials. Indeed, deep level centers and the associated persistent photoconductivity (PPC) effect described in chapter six have been observed in a wide variety of Ill-nitride materials and structures. Their presence indicates possible charge trapping (or charge freeze out) effects in Ill-nitride devices, which could cause instabilities in such devices and hence have significant influences on the device performance. For example, there is evidence that the presence of deep level impurities are responsible for the current-voltage characteristic collapse seen in Ill-nitride field effect transistors (FETs) [29-31]. The prolonged carrier capture time in the PPC state was also shown to affect the photocurrent transient behaviors in AlGaN/GaN heterojunction UV detectors [32]. The research to determine the origin of PPC in Ill-nitrides has been driven not only by its peculiar and interesting physical properties, but more importantly by its relevance for device applications, i.e. an understanding of the physics as well as the control of PPC and the associated deep level centers is necessary in order to further optimize Ill-nitride devices.

PPC is the light-enhanced conductivity that persists for a long period of time after the removal of photoexcitation and has been observed in many semiconductor materials and structures. At low temperatures, the PPC decay times become extremely long (of the order of minutes to years) and incompatible with normal lifetime-limiting recombination processes in semiconductor materials. Earlier work on conventional III-V and II-VI semiconductors has shown that understanding of the PPC phenomena can provide mechanisms for carrier generation and relaxation. It is also known that the PPC has a profound effect on device operations, e.g. it is detrimental to the operation of AlGaAs/GaAs modulation doped heterojunction field effect transistors (MOD-FETs) [33-37]. On the other hand, PPC is useful for adjusting the density of the two-dimensional electron gas (2DEG) at a semiconductor interface[38] and for possible device applications such as memory device and optical gratings [39,40]. It can also be utilized to probe the profile of the impurities [41], properties of metal-insulator transition [42], and transport properties of the tail states in the density of states in semiconductor alloys [43,44].


The aim of chapter six is to review the PPC in Ill-nitrides and to provide an overview on such an effect in these materials. The PPC characteristics including its buildup and decay behaviors, evidence of DX-like centers as well as the nature of defects, and implications on PPC mechanisms, effects of PPC on Ill-nitride devices including FETs and photodetectors, and possible uses of PPC are discussed in this chapter. As shown in this chapter, our understandings of the properties of PPC and associated deep level centers in Ill-nitrides have built on the early studies on AlGaAs alloys. Studies of PPC in Ill-nitrides, just as any other topics in this field, are driven primarily by technological developments and needs. This trend will be continued. Current devices in the Ill-nitrides all take advantages of heterostructures and quantum wells. In this sense, understanding and control of PPC as well as the associated deep level centers and their effects on devices based heterostructures and quantum wells will become more and more important. As the nitride materials quality further improves, the nature of deep level center as well as their characteristics can be identified. With the insights from theoretical calculations, the detailed information regarding the energy levels as well as their atomic configurations in Ill-nitride lattices will be understood.

4. Ion implantation and radiation effects

Ion implantation has become a highly developed tool for modifying the structure and properties of semiconductors. The energetic implants are applied in the doping of semiconductor material, the formation of insulator regions to isolate the active regions of circuits, in the fabrication of optical active regions and also in the device application. According to chapter seven, the advantages of the ion implantation are: • An accurate dose control is possible by measurement of the ion current. • The depth distribution of the injected dopants and the introduced lattice disorder are

directly related to the ion energy and the masses of the target material and ion. By variation of the ion energy and dose the concentration profile of the impurities and also the structural changes can be tailored.

• In contrast to high temperature processing, the ion implantation is an intrinsic low temperature process, although subsequent annealing is generally necessary. In this respect, it differs greatly from the diffusion approach, where high temperatures during doping may lead to decomposition of the near surface region.

• Ion implantation is insensitive to the lattice structure, lattice defects and the presence of impurities.

• The implantation process is not constrained by thermodynamic considerations. This means, that any species of ion may be implanted into any host. A wide concentration range can be achieved with the upper limit generally set by the sputtering yield rather than by equilibrium solubility.

• Ion implantation can be included in the semiconductor process technology and implantation machines can be designed for specific applications. To understand and to control the electrical and optical properties of group Ill-nitride

is one of the great challenges associated with the development of semiconductors. It is well-known that wide band gap semiconductors are difficult to dope by ion implantation due to the native defects and the high resistance against the damage recovery. As the

Properties oflll-nitride semiconductors Ch. 1 9

quality of epitaxial GaN layers continues to improve, ion implantation is considered to be a promising doping technology. Recent progress has been made in this field such as the controlled p-type doping, damage annealing, implant isolation, implantation induced optical activation as well as device fabrication. The main disadvantage of the ion implantation in semiconductors is related to the lattice disorder caused by implanted ions. Because of the high background electron concentration of the as-growth GaN, ion implantation with high concentrations of acceptors is generally needed to compensate the native electron background and to realize the transition to p-type. However, the crystalline structure is diminished by implantation induced damage after implantation with high dopant concentrations. Consequently, a precise control of implantation conditions such as ion energy, temperature during implantation, ion dose, etc., and an optimal annealing process are essential to successful doping by ion implantation.

The purpose of chapter seven is to present an introduction into and a review of the state of ion implantation in GaN and related III-V materials. Although significant progress has been reported for doping and isolation of wide band gap semiconductors, there are still many problems to be solved before an extensive application of ion implantation in device fabrication can be realized. In recent years several excellent review papers have appeared addressing various aspects of the implantation technology of group Ill-nitrides [45-47]. This chapter is devoted to the implantation induced damage and the defect annealing. The realization of the controlled n-type and p-type doping by ion implantation is discussed with the main emphasis on the results of GaN. Then, the impurity luminescence and isolation by ion implantation are discussed.

During several semiconductor-processing steps, for example particle irradiation for lifetime tailoring [48,49] dry etching [50,51], metallization [52,53] and device isolation [54,55] the semiconductor is intentionally or unintentionally exposed to a variety of particles with energies ranging from a few eV to several MeV. When these particles impinge on the semiconductor, they enter into it, transfer energy to the semiconductor lattice and introduce defects. These defects can have a profound influence on the semiconductor properties and on the characteristics of devices fabricated on it, which may be either beneficial or deleterious, depending on the application. Chapter eight is presenting the latest research efforts on radiation-induced defects in GaN.

In order to avoid the deleterious effects of some of these particle-induced defects and utilize the beneficial effects of others, depending on the application, it is imperative to understand the effect of radiation on electronic materials and devices fabricated on them as discussed in chapter eight. To achieve this, it is essential that the electronic properties and concentration of radiation induced defects should be known, allowing calculation of their effect on the properties of electronic materials and devices. In addition, the structure, introduction rate, introduction mechanism and thermal stability of the defects should be determined, so that they can be reproducibly introduced, avoided or eliminated, depending on the application. Regarding electrical techniques for defect characterization, deep level transient spectroscopy (DLTS), which allows independent studies of different defect species in the same semiconductor, has played a key role in providing most of this information. Hall effect measurements have also contributed a fair deal to our understanding of radiation-induced defects and its effect on carrier mobility and donor and acceptor concentration. As far as the electrical


characterization of simple devices are concerned, current-voltage (/-V) and capacitance (C-V) measurements have traditionally been used to evaluate the effect of defects on diode performance and the free carrier density of semiconductors, respectively.

Since growth-induced defects have an inhibiting effect on the detection of process induced defects, chapter eight describes which defects are present in GaN grown by different epitaxial techniques. This should not be seen as a complete review of growth induced defects, but rather as a guideline as to which defects can be expected in epitaxially grown GaN when attempting to characterize process induced defects in it. High energy particle irradiation introduces several electron traps in n-GaN, as shown in this chapter, with energy levels between 0.06 and 0.95 eV below the conduction band. Some controversy surrounds the nature of the most frequently observed level at 0.20 eV. It has recently been shown that the DLTS signal of this level can be deconvoluted into at least two levels. One of these is a shallow donor at EQ —0.06 eV which has previously been assigned to the VN- The origin of the deeper lying defects is not clear yet. All the observed high energy irradiation induced defects anneal out at 700 K.

Resistive (joule) evaporation and electrodeposition of metals do not introduce defects in semiconductors according to chapter eight. However, two other metallization processes, E-beam and sputter deposition, were shown to introduce electrically active defects in GaN. Both of these processes introduce a defect with a level similar to that of ER3, believed to be related to the nitrogen vacancy. In addition, each of these processes introduces defects characteristic to the process. The concentration of these process induced defects can be minimized by optimizing the deposition conditions as discussed in chapter eight. For sputter deposition, this can be achieved by minimizing the deposition power and maximizing the plasma pressure. In the case of E-beam evaporation, the geometry of the e-gun with respect to the sample position should also be taken into account. Finally, the thermal stability of these metallization induced defects has not yet been reported. This, in conjunction with the thermal stability of the Schottky contacts, is required to assess whether or not post-deposition annealing can remove the defects responsible for diode degradation.

5. Stress, structural and phonon properties

One of the preliminary goals of chapter nine is to show that residual stresses have a profound effect on nitride optical data. And since these materials are being heavily developed for optoelectronic applications, the presumption is that anything affecting nitride optical properties to such a large extent should be investigated, at the very least so that such perturbations can be eventually eliminated or exploited to improve nitride-based LED and laser diode performance. Such an investigation will naturally center around the fundamental ways that stress affects the optical properties of a material, but we will also be concemed with the materials and growth parameters that produce such stresses in the first place. Chapter nine will also examine the extent to which it has been possible to manipulate residual stresses in these materials, with the goal of improving optical properties. The focus in this chapter is on GaN films and will largely ignore the non-negligible role that defects and impurities (readers interested in this topic should see, for example [56]) play in this study. This is justified for the simple


reason that the strain states of even the most rudimentary GaN heterostructures are not at all well-understood and that we must master the simplest case before proceeding to more complex combinations of materials.

Chapter nine demonstrates with a collection of selected GaN low temperature reflectance lineshapes [57] obtained from films grown under a variety of conditions. Prior to proceeding with the optical data, this chapter examines the physical structure of the samples that are being measured. Because much has been learned lately about nitride physical properties and growth mechanisms since the first reflectance data were taken by R. Dingle and coworkers in 1971 [58]. Indeed, during the course of this chapter, we shall see that a lack of information about the physical properties of the material has been the source of considerable misunderstanding about strain behavior in the GaN literature.

There are several examples of phenomenological strategies to manage strain in nitride heterostructures; one of the most successful is the Lateral Epitaxial Overgrowth technique [59]. Here, briefly, GaN is deposited on an underlying GaN layer through the windows of an Si02 mask. The deposited material first grows vertically on top of the mask then proceeds to grow laterally over the mask (and vertically as well) until the growth fronts from all of the windows coalesce into a continuous layer. What is remarkable about GaN films grown by this technique is the dramatic reduction in threading dislocation density observed in the films: the usual 10^-10^^ cm"- in the area beside the mask and less than 10" cm~^ in the area above it. Since dislocations have their origins in lattice mismatch and are detrimental to device operation, the technique is an excellent example of engineering stress in order to enhance device performance. Indeed, the threshold current of Ill-nitride lasers is substantially reduced using LEO 'substrates' and these lasers experience a corresponding and dramatic increase in lifetime [60].

Unfortunately a simple look at the thermal and lattice mismatch behavior of nitride materials still cannot neatly explain the wide range of stress-related phenomena observed, even for simple heterostructures. Not surprisingly the majority of unexplained issues are related to the failure of classical Matthews-Blakeslee thin film relaxation models. Some examples involve stresses formed by the coalescence of two dimensional islands, stresses that cause growth mode changes and then in turn exert stresses, and the observation of what appears to be multiple slip systems in simple structures. These appear to play an important but as of yet unclarified role in the relief of residual stress in GaN films in a way that transcend simple lattice mismatch. Again, this tells us that though impressive optoelectronic devices have been demonstrated and commercialized in recent years, it has been done with only a rudimentary and indeed merely phenomenological understanding of stress. The big implication is that the work is not yet finished with regard to relaxation phenomena in this materials system. Though much has been achieved with this phenomenological 'understanding', far more could be achieved if relaxation phenomena were thoroughly understood (and controlled) even in simple nitride heterostructures.

Chapter ten is focused on the structural defects in nitride heterojunctions. Because of the difficulty in growing sufficiently large GaN substrates, GaN films must be grown heteroepitaxially on a variety of alternative substrates. Despite large differences in lattice parameters and thermal expansion coefficients, technologically ômising GaN thin films have been grown on c-plane (i.e. {0001}) sapphire, a-plane {1120} sapphire.


and {0001} SiC. As a consequence of heteroepitaxy, however, the resulting film suffers from a large density of extended defects. Differences in lattice parameter and coefficient of thermal expansion necessarily lead to large dislocation densities, whereas differences in surface and interfacial energies often lead to the formation of islands and planar defects. Heteroepitaxial c-axis growth of a polar material like GaN also introduces the problem of inversion domain boundaries (IDBs), as well as the possibility that the deposited film may have one of two polarities: Ga-terminated or N-terminated.

Properly optimized MOVPE growth of GaN has succeeded in producing GaN films with dislocation densities between 10^ and 10^/cm^. Advances in the understanding of the effects of substrate nitridation and vicinality, reactor pressure, and dislocation filtering have led to strategies for reducing dislocation density and increasing grain size. These strategies, in turn, have contributed to the growth of uniform GaN films with properties suitable for electronic and electro-optic devices.

Extended defects, which are thoroughly discussed in chapter ten, in heteroepitaxial GaN films grown by MOVPE scatter carriers, resulting in lower mobility, and appear to surround themselves with point defects and impurities which act to compensate dopants. It also appears that point defects may be able to compensate dopants without associating with extended defects; the SIMS and TEM study of carbon in GaN films deposited by variable pressure growth supports this contention. In particular, it is interesting to consider carbon as a point defect involved in compensation, since it is an inevitable by-product of the MOVPE process which can be controlled, to some degree, by altering the reactor pressure.

According to chapter ten, reactor pressure influences grain size as well as carbon concentration and there appears to be a reactor-dependent optimal pressure for growing grains that are large without the onset of faceting, or the onset of associated lattice tilting and twist boundaries. These reactor parameters for growing a film with the minimum extended defect density on a nucleation layer is similar to growth via LEO in that the lateral growth rate must be as large as possible without the onset of faceting. There is also reason to believe that both LEO and conventional growth can be optimized by the use of vicinal c-plane SiC or a-plane sapphire substrates, in order to improve grain alignment and thereby reduce the edge dislocation density occurring at grain boundaries.

The role of the nucleation layer in heteroepitaxial GaN growth and the procedures for optimizing this layer are still not well understood. For some reactors, at least, it appears that the optimal nucleation layer goes down with a significant fraction of the film consisting of the zinc blende polymorph, which then transforms into the wurtzite phase upon annealing. Although there has been a preliminary effort to explain these structural constraints; there is not yet a sufficiently general understanding to guide a grower in achieving a good nucleation layer. There is some indication that optimizing the nucleation layer results in defining a specific film polarity (i.e. Ga-terminated) and that this desirable result may be achieved by reducing the oxygen composition and thereby eliminate oxygen-rich inversion domain boundaries in the nucleation layer. It also appears that achieving a film with no inversion boundaries is frustrated by a rough substrate morphology.

In chapter eleven, the authors systematize the theory underlying the dispersive continuum model and apply it to describe the lattice vibrations in layered heterostructures.

Properties of lll-nitride semiconductors Ch. 1 13

with particular emphasis on heterostructures based on III-V nitride materials. The nitride-based heterostructures have, in general, very special dynamical properties which distinguish them from the more traditional GaAs/AlAs heterostructures. The differences in properties between the two types of heterostructure are so significant that a more in-depth analysis of macroscopic lattice dynamics is required to deal correctly with the situation in nitride-based heterostructures. Another important question that chapter eleven has addressed concerns the mechanical boundary conditions. It turns out that the only rigorous self-consistent route to arrive at physically acceptable boundary conditions is to start from the microscopic mechanical equations, which describe the vibrations of the separate ions and then carefully proceed to obtain the continuum limit. This is done in this chapter using the Keating model approach [61].

Chapter eleven presents a brief description of the essential features of bulk nitride materials, particularly in relation to lattice vibrations and dielectric properties and a treatment of the quantum field theory of dispersive polar optical (PO) continuum modes in bulk nitrides, emphasizing the additional features introduced by the incorporation of spatial dispersion. This rigorous theory is presented in this chapter for the first time and applied in the context of electron-phonon interactions in the bulk. This chapter also presents the application of the dispersive continuum theory to the situation in a heterostructure. Once more the inclusion of dispersion in the theory makes this section an original account presented here for the first time. The microscopic origin of the continuum theory of PO phonons in heterostructures is also presented in this chapter. In particular, the authors seek to shed some light on how the boundary conditions to be satisfied by PO modes at interfaces between different media emerge from a microscopic treatment when the continuum limit is carefully applied. Descriptions of results emerging from the hybrid models, the double hybrid and extended hybrid models, in the context of electron-PO phonon interactions in double heterostructures and superlattices based on GaN systems are also shown in chapter eleven. The existence of a sum-rule which holds whenever one is concerned with total contributions from the entire spectrum of allowed modes is discussed for the first time. The relationship between the dispersive continuum theory (in its hybrid model form) and the DC model is clarified. Section 8 of chapter eleven contains a brief summary of optical phonons and their interaction in nitride-based heterostructures. However, the authors found that the task would have been incomplete without a presentation of a quantum field theory of the dispersive continuum model of optical phonons in the bulk and in heterostructures. The treatment is presented in this chapter for the first time and it completes the picture of the continuum description of dispersive polar optical modes and their interaction with electrons in heterostructures. The issues of boundary conditions have also been explored in depth in this chapter from a microscopic point of view and the application of the theory to double heterostructures and superlattices has been presented. One important conclusion that has been reached is the existence of a sum-rule, which applies whenever the interaction of electrons with phonons involves the full set of optical phonons irrespective of the model that has been used to describe the PO modes in the heterosystem.

14 Ch. 1 M.O. Manas re h

6. Conclusion

This introductory chapter summarized the subjects and issues discussed thoroughly in the ten technical chapters. The focus of this volume is directed toward dopants incorporation, impurities identifications, defects engineering, defects characterization, ion implantation, irradiation-induced defects, residual stress, structural defects, and phonon confinement in Ill-nitride semiconductors. There is also great scientific interest in this class of materials because they appear to form the first semiconductor system in which extended defects do not severely affect the optical properties of devices. This unique volume provides a comprehensive review and introduction of defects and structural properties of GaN and related compounds for newcomers to the field and stimulus to further advances for experienced researchers.

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CHAPTER 2

Dopants in GaN

John T. Torvik

1. Introduction

GaN and the related alloy system (Al-In-Ga-N) has tremendous potential for both optoelectronic and electronic devices due to superior materials parameters such as a wide and direct bandgap energy, high breakdown fields, high saturated electron velocity and adequate electron mobility and thermal conductivity. However, when Maruska and Titjen succeeded in growing GaN on sapphire substrates in the late 1960s using chemical vapor deposition [1], it quickly became obvious that doping and defects would play a vital role in the future development of GaN. The early unintentionally doped GaN was invariably n-type, which at the time was believed due to nitrogen vacancies. The high n-type background carrier concentration on the order of 10 ^ cm~^ proved difficult to minimize and the absence of a shallow acceptor dimmed the prospects of a production-scale GaN-based device effort. Nevertheless, the early work using zinc-compensation led to the first demonstrations of blue, green, yellow and red metal-insulating-n-type GaN light-emitting diodes (LEDs) [2] but, further device development was still stifled by the seemingly insurmountable problem of making conducting p-type GaN. The search for p-type GaN was not successful until Akasaki and Amano demonstrated this feat in 1989 [3]. This remarkable achievement was actually a result of two significant milestones. First, the crystalline quality and the background n-type carrier density in unintentionally doped GaN films was significantly reduced by the use of a low temperature AIN buffer layer [4,5]. Second, p-type GaN was demonstrated with Mg-doping followed by an ex situ low energy electron beam irradiation (LEEBI) treatment. Conducting p-type GaN had previously remained elusive despite other Mg-doping efforts because it was found that hydrogen passivates the Mg-acceptors [6], similar to the effect of hydrogen on acceptors in Si [7]. Thus, it was theorized that the LEEBI treatment, which was accidentally discovered while studying the cathodoluminescence of a Mg-doped sample, disassociated the H-Mg complex allowing the Mg to form a quasi-shallow acceptor level. This theory was later confirmed by producing p-GaN by annealing GaN:Mg in a hydrogen-free ambient such as N2 [8]. The process was also reversible rendering GaNiMg insulating by annealing in a hydrogen-rich environment such as ammonia (NH3). These remarkable discoveries eventually led to the demonstration of a variety of bipolar devices such as blue and green pn junction LEDs and violet laser diodes (for example, see [9]), solar-blind and ultraviolet sensitive p-i~n photodiodes [10-13] and high-power, high-temperature bipolar transistors [14,15].

18 Ch. 2 J.T. Torvik

Even though much progress has been made in doping GaN there still exists significant challenges; especially with p-type doping. The low hole mobility and low achievable free hole concentration result in large sheet resistance preventing the fabrication of reliable Ohmic contacts with low contact resistivities. These material challenges have prevented the use of the AlGaN/GaN system to its full potential in electronic applications such as microwave heterojunction bipolar transistors (HBTs). Furthermore, the immature p-type doping technology has led to degradation (lifetime) problems and required that InGaN laser diodes operate at a higher than expected bias voltage.

The aim of this chapter is to describe the state-of-the-art undoped and doped GaN by comparing select optical and electronic properties. This is not an attempt to exhaustively cover all material properties or varieties, but rather to compare fundamental phenomena, such as luminescence, absorption, and conduction. Furthermore, we explore the electrical and optical characteristics using relatively simple and inexpensive measurement techniques, which are readily available in most semiconductor laboratories.

2. Background

Doping control is a prerequisite for the fabrication of most optical and electrical devices. For example, n- and p-type layers are the basic building blocks for bipolar devices, such as light-emitting diodes, laser diodes, photodiodes, and bipolar transistors, while undoped (or high resistivity) layers are needed for field effect transistors and photodiodes. Ideally, one should be able to grow intrinsic GaN prior to intentionally introducing dopants into GaN for conductivity modulation. However, as previously mentioned, unintentionally doped GaN tends to be n-type, which has been attributed to nitrogen vacancies [1,16] and residual oxygen [17] impurities. Recent electron irradiation experiments suggests that the background electron concentration cannot be due to nitrogen vacancies as this defect forms a level at 65 meV below the conduction band edge [18]. For comparison, the thermal activation energy(s) of electrons from the donor level(s) to the conduction band edge in unintentionally doped GaN is typically less than 37 meV [19]. Another challenge with GaN growth is the lack of a cheap and lattice matched substrate. C-plane (0001) sapphire and a-SiC are the most conmmon substrates with a lattice mismatch of 16 and 3%, respectively [20]. The resulting strain necessitates the use of GaN or AIN nucleation (buffer) layers prior to growth of high quality GaN epitaxial layers with high electron mobility, specular surface morphology and low background electron concentration.

Conductivity modulation can be achieved in GaN by doping with donors such as Si, O and Ge or with acceptors such as Mg, Zn and Be. Si and Mg are primarily the n-type and p-type dopants of choice, respectively. Si-doping has been successfully used to produce films with free electron concentrations from the low 10 ^ to the mid 10^^ cm~^ with almost complete room temperature donor activation. Furthermore, Si-doped GaN can routinely be grown with a bulk electron mobility above 300 cm^/V-s at modest doping densities. However, cracking of thicker films (>1 |xm) has been observed in heavily Si-doped films when the doping density exceeds 10 ^ cm~^. The cracking has been attributed to the smaller ionic radius of Si" (0.41 A) compared to Ga^ (0.62 A) [19]. Unfortunately, the story is less encouraging for p-type GaN. The

Dopants in GaN Ch.2 19

maximum reproducible hole concentration achieved in p-GaN with conventional doping techniques barely exceeds 10 ^ cm~^ without compromising the surface morphology. Furthermore, the deep nature of the Mg acceptor (Ey > 170 meV) leads to a poor room temperature hole activation of several percent. This leads to the use of excessively high Mg-concentrations above the mid 10 ^ cm~^ for heavy p-doping. The high Mg concentration degrades the hole mobility; often to below 10 cm^/V-s. This results in quite resistive (typically >2 ^-cm) p-GaN epilayers and devices exhibiting large series resistances and poor contacts.

3. Experiment

It is important to understand both the electrical and optical properties of GaN, due to the tremendous potential for GaN in both the electronic and optoelectronic arena. The optical and electronic properties of undoped, n-type and p-type GaN are therefore discussed in detail in this chapter. The discussion relies heavily on Hall-effect measurements and photoluminescence and photoconductivity spectroscopy, which are relatively simple and powerful measurements techniques and as shown in this chapter can yield a wealth of information regarding GaN.

3.1, Characterization

Photoluminescence (PL) spectroscopy has been the workhorse of the optical characterization techniques due to its non-destructive nature and ability to yield valuable information about both intrinsic and extrinsic transitions. The latter is important since both defect-related and near bandgap transitions are frequently observed in GaN. The photoluminescence measurements presented in this chapter are performed using single-pass 0.5 m prism monochromator or a 0.32 m grating monochromator. The detectors used were a photomultiplier tube for the visible and UV, while a thermoelectrically cooled InGaAs detector was used for the IR part of the spectrum. The temperature-dependent measurements were performed using a closed-cycle He-cooled cryostat equipped with quartz windows. The UV excitation sources used include a HeCd laser operating at 325 nm, a UV line from an Ar-ion laser at 351.1 nm, and a pulsed (sub ns) N2 laser operating at 337 nm. The IR excitation source (for the Er-doped section) was an InGaAs laser diode operating at 983 nm or a tunable Ti: sapphire laser. The laser spot size diameters were < 1 mm. The PL signals were detected using the lock-in technique and recorded using a computer.

Photoconductivity (PC) spectroscopy is another sensitive and non-destructive optical characterization tool. In PC spectroscopy, one measures the change in conductivity between two Ohmic contacts in response to optical illumination. PC measurements can therefore be sensitive to defect-related absorption allowing the investigation of the defect distribution in the 'forbidden' energy gap as well as the absorption near and above the bandgap energy [21]. The PC measurement was performed using co-planar indium contacts spaced about 1 mm apart or interdigitated finger contacts (Ni/Au for p-GaN and Ti/Al for n-GaN) with finger spacing of 3 |xm. Up to 50 V was applied across the samples and the photocurrent was measured across a variable load using a


lock-in amplifier and recorded by a computer. The light source was a tungsten-lamp (GE 1493) or a deuterium light source dispersed by a the prism monochromater and focused onto the samples using quartz optics.

The Hall measurement can give useful information about the electrical properties of GaN films such as sheet resistance, carrier concentration and mobility (for example, see [22]). Furthermore, the ionization energy of shallow dopants can be extracted from temperature dependent measurements. The only materials quantity needed is the film thickness assuming uniform transport within the film. However, it is worth pointing out that the experimental setup and contact geometry is important [23,24]. The GaN samples used for the Hall-effect measurement were ~ 5 x 5 mm^ squares with indium contacts at the comers. The Ohmic contacts were checked using current-voltage measurements assuring linearity to avoid depletion effects associated with Schottky contacts. The temperature-dependent Hall data presented in this chapter are obtained using a computer-controlled Hall system equipped with a magnet typically operated at 3500 Gauss. This system is capable of scanning from 80 to 400 K.

3.2. Samples

The GaN samples described in this chapter can broadly placed into four categories; unintentionally doped. Si-doped, Mg-doped, and Er-doped.

The unintentionally doped GaN includes samples grown by MOCVD and HVPE. Details on the growth and substrate pre-treatments of the 57-74 |xm-thick GaN samples produced by a chloride-transport HVPE are given elsewhere [25]. One of the samples grown by MOCVD is a free-standing unintentionally doped ~100-|xm-thick GaN sample grown using epitaxial lateral overgrowth [26,27]. The sample was semi-insulating and we were therefore unable to determine the carrier concentration and mobility by Hall measurements. The GaN was made free-standing by polishing off the sapphire substrate. These samples typically have a threading dislocation density between 10^ and 10 cm~^. 'Conventional' 2-|xm-thick GaN films grown by atmospheric pressure MOCVD using GaN buffer layers on sapphire substrates were used for comparison [28]. These films have a typical threading dislocation density of > 10^ cm~^.

The Mg- and Si-doped GaN samples used were grown by MOCVD (Mg), MBE (Mg and Si) and bulk platelets (Mg) grown at high temperatures and pressures. The bulk Mg-doped GaN samples used in this study were grown under N2 pressures of 10-20 kbar at temperatures ranging from 1400 to 1700°C from a Ga solution containing 0.1-0.5 at.% Mg [29,30]. The Mg concentration is ^ 10^ cm"^ and the thickness is ^ 1 0 0 |JLm. SIMS measurements show a typical background oxygen concentration of 10^^-10^^ cm"^. The bulk-GaN typically exhibits a threading dislocation density of <10 cm"- . Furthermore, the bulk crystals exhibit good crystalline quality as determined by X-ray diffraction rocking curves with a full-width-at-half-maximum of 20 arc seconds (0004). MOCVD-grown Mg-doped (p = 2 x 10 ^ cm"^ and p = 6 x 10 ^ cm"^) GaN films grown on sapphire substrates were used for comparison [28,31]. Both Mg and Si-doped samples grown by the ECR-MBE method [32] were used in this study. These samples were 0.5 jxm {p = 10 ^ cm~^) and 3.5 |xm ( z = 2 — 3 x 10 ' cm~^), respectively. Detailed descriptions of the growth is given elsewhere [21,32].

Dopants in GaN Ch. 2 21

Er-doped samples were fabricated using ion implantation [33,34] of GaN films grown using HVPE. The GaN was implanted with 10 ^ Er^"^/cm^ at 350 keV and co-doped with 10 ^ Q-^/cm^ at 80 keV. A post implant anneal at 800-900°C for 45 min in flowing NH3 was performed to repair the implantation-induced crystal damage. All samples are grown on C-plane (0001) sapphire if not stated otherwise.

The next sections will detail both optical and electrical characterization of the samples described above.

4. Results and discussion

4.1. Optical properties

As previously mentioned, photoluminescence spectroscopy has been extensively used to characterize doped and undoped GaN. Photoluminescence measurements have become particularly useful in the last decade when unintentionally doped GaN with a background n-type carrier concentration in the low 10^^ cm"- has become available. One can resolve a forest of near bandgap exciton-related PL lines using low temperature measurements due to the increased quality and purity of GaN specimen. In this section on optical properties, unintentionally doped GaN is discussed first, before investigating the effects of common donors, acceptors, compensating defects and other common dopants in GaN.

4.1.1. Unintentionally doped GaN 4.1.1.1. Near-band edge transitions. Two typical photoluminescence spectra of high quality unintentionally doped GaN grown by HVPE and measured a room temperature and at 6 K are shown in Fig. 1.

As seen in Fig. 1, the PL spectrum changes drastically when going from 300 to 6 K. The most apparent differences are the temperature dependence of the optical bandgap energy and the thermal broadening. At 6 K (solid line), well-resolved PL peaks appear near the intrinsic optical bandgap energy. The strongest peak at 3.473 eV is attributed to bound exciton recombination. More specifically, this exciton recombination is associated with a neutral donor (D^X), since unintentionally doped GaN invariably is n-type. The bound excitons are typically observed up to approximately 100 K, were the bound excitons thermally dissociate, leaving the free exciton recombination to dominate the spectrum [35]. Thus, the main PL peak observed at room temperature (broken line) at 3.404 eV is attributed free A-exciton recombination. The various free excitons (A, B, and C) and their origin will be discussed later. Unfortunately, little fine structure is resolved at room temperature due to thermal broadening. The binding energy of the free A-exciton has been extracted from Arrhenius plots of the PL intensity at approximately 27 meV [36], compared to a value of about 26 meV extracted from a comparison with the spectral location of the A-exciton's excited (n = 2) state [37]. The free exciton binding energy measurement places the lowest bandgap energy at ~3.504 eV at 2 K. Furthermore, the donor-bound exciton binding energy is approximately 6 meV, as determined by measuring the energy difference between the bound and free exciton (n = l) lines [38].


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Several near-bandgap low temperature PL peaks are often observed in addition to the exciton peaks in high-quality unintentionally doped GaN. For example, one can frequently observe donor and acceptor-related luminescence. Phonon replicas of the above-mentioned PL lines also often appear in the low temperature spectra of GaN. To illustrate this, we compare the near-band edge emission at 6 K from samples with different background carrier concentrations as shown in Fig. 2.

The PL spectrum from unintentionally doped GaN with low background carrier concentration (n = 7 x 10 ^ cm~^ at 300 K) grown by HVPE is shown using a solid line in Fig. 2. This sample exhibits a strong bound exciton (D^X) peak at 3.473 eV accompanied by the LO phonon replica located at 3.381 eV approximately 92 meV lower in energy. Another characteristic feature in this spectrum is the shoulder on the low energy side of the main (zero phonon) D^X peak. This shoulder is attributed to donor-bound exciton recombination, but with the donor left in its excited (n = 2) state [35]. The origin of the PL peak at 3.334 eV is uncertain, but it has been attributed to Mg-impurities by other authors [39].

The PL from the sample with low background doping is contrasted by a spectrum from an unintentionally doped sample grown by MOCVD with a higher background carrier concentration of n = 3 x 10 ^ cm~ . This spectrum is shown using the broken line in Fig. 2. The sample with the higher background electron concentration exhibits a drastically different set of satellite peaks. The main D^X peak is located slightly lower in energy at 3.496 eV, which is a common effect of the higher electron concentration [40]. The strongest satellite peak located at 3.282 eV from the sample with higher doping density is attributed to donor-acceptor (DÂ ) pair recombination [41] with the two peaks at lower energy being the ILO and 2LO phonon replicas, respectively. The donor level associated with this PL has been attributed to O on a N site with a binding energy


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3.1 3.3 Photon Energy (eV)

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Fig. 2. Photoluminescence spectra of unintentionally doped GaN measured 6 K comparing two samples with low (n = 7 X 10'^ cm~^ at 300 K) and medium (3 x 10^^ cm~^ at 300 K) background n-type carrier concentration.

of about 32-37 meV [19]. The acceptor involved has not yet been positively identified, but several theories including C on a N site [42] and acceptor-hke native defects have been proposed [43]. Even though the origin is unknown, the acceptor level appears to have a binding energy of about 220-225 meV [44].

From an optical standpoint, the highest quality unintentionally doped GaN has been produced by homoepitaxial growth. Homoepitaxial growth eliminates much of the structural defects generated by growth on lattice mismatched substrates such as sapphire or SiC even with the use of use of buffer (nucleation) layers. Unfortunately, only small bulk GaN platelets (~100 nmi^) grown under high temperatures and pressures are presently available [45]. Nevertheless, both MOCVD and IVIBE growth on such substrates led to high quality epitaxial GaN exhibiting bound exciton linewidths as narrow as 0.5 meV [46,47]. These optical characteristics were recently improved using optimized homoepitaxial MOCVD growth on similar GaN platelets [48]. The GaN was grown on the polished and CAIBE-etched Ga-face of the GaN substrate. The resulting optical quality of the film was remarkably improved over conventional GaN films exhibiting a minimum bound exciton linewidth (FWHM) of 95 |xeV at 2 K as shown in Fig. 3.

Furthermore, the fine structure revealed up to five donor-bound exciton peaks in the 3.4701-3.4720 spectral range. It is important to note that the exact spectral location of the exciton peaks strongly depends on the residual strain in the GaN layer, and can vary several tens of meV depending on growth and substrate. In this case, the estimated lattice mismatch between the GaN film and bulk GaN substrate is small at Aa/a <2 X 10"" and is attributed to the large difference in carrier concentrations between the homoepitaxial layer and substrate.

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Fig. 4. PC spectrum of free-standing and undoped GaN grown using epitaxial lateral overgrowth with MOCVD. The sample is 100 ixm thick, semi-insulating, and has the original sapphire substrate polished off.

As shown in Fig. 3, one can clearly observe both the neutral donor-bound excitons (D^X) and neutral acceptor-bound excitons (A^X). The free excitons are also clearly observed in the 3.48-3.50 eV range. A reflectance measurement is a powerful way to distinguish between the bound and the free excitons. In the reflectance spectrum shown in Fig. 3 one can clearly see the free A, B and C excitons (labeled as XA, XB, XC and n = 1) and their excited states (ji = 2). The three different free exciton peaks involve holes from the three valence bands of symmetry r9, Fy (upper) and Fy (lower) and electrons in the lowest conduction band (Fy) [49].

Free exciton peaks are also observed in photoconductivity spectra from GaN. The electric field dissociates the excitons, thereby producing free carriers detected in the PC measurement. A PC spectrum of a semi-insulating GaN sample grown using the epitaxial lateral overgrowth method is shown in Fig. 4.

As shown in Fig. 4, the PC spectrum of high-quality undoped GaN typically exhibits an abrupt spectral cutoff below the optical bandgap energy indicating few shallow defects in this relatively pure GaN sample. Furthermore, the relatively flat PC response above bandgap suggests that there is negligible surface recombination, i.e. the as-grown surface is passivated. The free exciton peak is clearly observed at 3.404 eV at room temperature, which is similar to the spectral location in the PL spectrum (Fig. 1). Although the strongest PC peak is dominated by the A-exciton, it probably contains contributions by the B-exciton, which is located approximately 5 meV higher in energy [50]. The peak approximately 20-40 meV higher in photon energy is tentatively attributed to the excited state of the A-exciton (n = 2) with possible contribution from the C-exciton. This part of the spectrum is magnified and plotted on a linear scale inset for clarity. Interestingly, the free exciton peaks are not typically observed in PC spectra from other unintentionally doped GaN or AlGaN possibly due to a higher background carrier concentration [21,51,52].


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Fig. 5. A comparison of room temperature PL spectra from unintentionally doped GaN grown by MOCVD and HVPE.

4.1.1.2. Defect-related transitions. The near band-edge luminescence in unintentionally doped GaN is often accompanied by broad defect-related luminescence. This is clearly illustrated in Fig. 5 showing three typical PL spectra obtained from GaN grown by MOCVD on C-plane (0001) sapphire and HVPE on C-plane and R-plane (ll02) sapphire.

All the samples in Fig. 5 exhibit broad defect-related PL well below the optical bandgap energy. Furthermore, it is interesting to note that the broad defect related peaks at the low photon energies vary from about 1.8 to 2.2 eV. The most frequently observed defect-related luminescence is the often referred to as the 'yellow band' due to the spectral location at about 2.2 eV. The origin of the yellow luminescence has been extensively debated for several decades, with no positive identification to date. It has been attributed to transitions of free (or weakly bound) electrons from the conductions band edge (or a shallow donor level) to a deep acceptor level located about 860 meV above the valence band edge [53]. This theory was later supported by pressure-dependent PL measurements [54]. It was further suggested that the donor level is carbon-related and the acceptor level is due to gallium-vacancies [53]. Recently, theoretical investigations have provided support for the gallium-vacancy theory, but suggest the shallow donor level is associated with oxygen [55] and that the presence of carbon is merely coincidental [56]. Further support for the gallium-vacancy involvement in the defect-related PL is provided by experiments demonstrating that the yellow PL can be suppressed in GaN grown under gallium-rich conditions [57]. Other proposed alternative origins of the deep acceptor include the nitrogen anti-site (on the gallium site) defect [58]. For completeness, the yellow PL has also been attributed to transitions between a deep donor to a shallow acceptor [59] and a shallow donor to a deep double-donor [60]. The reason the spectral location of the defect-related PL varies in


Fig. 5 is attributed to different impurities since the samples are grown by different laboratories. Note that the 1.8 eV peak is not to be confused with the red defect-related PL often observed from the sapphire substrate. Since the 1/e absorption depth of He-Cd laser light at 325 nm is ~0.1 jxm and GaN film is ~10 ixm thick virtually no pump light can reach the substrate. Similar red luminescence has been observed from HVPE-GaN on c-plane sapphire [61].

It is well documented that the yellow PL seems present in most n-type GaN, but what are the ramifications? For device applications it is important to determine if the defect responsible for the yellow PL is a fast non-radiative recombination center. Fortunately, the defect is radiative in nature with a long decay time [60] and, thus, is a relatively benign defect in terms of minority carrier recombination. Historically, the ratio of the magnitude of the yellow PL peak to the near-band edge PL peak is often used as a quality measure of GaN. It should be noted that such a comparison is complicated by different pump power dependencies of the PL in the two spectral ranges [62].

4.1.2. Si-doping Silicon is the n-type dopant of choice for GaN since it effectively incorporates on the gallium site and forms a single shallow donor level. The PL spectra of Si-doped GaN typically exhibits similar near-bandgap emission compared to that of unintentionally doped GaN. Two typical PL spectra are compared in Fig. 6.

As shown in Fig. 6, the donor bound exciton (D^X) peak in Si-doped GaN (solid line) peaks at 3.47 eV, which is similar to that of an unintentionally doped GaN sample with similar background carrier concentration. The FWHM of about 30 meV is slightly larger

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that expected for Si-doped GaN grown by ECR-MBE at this donor concentration [32], while the unintentionally doped samples exhibits a FWHM of ^11 meV. Curiously, the donor-acceptor peaks (and their LO phonon replicas), which are present in the PL spectra from the unintentionally doped sample, are not observed in this Si-doped GaN grown by MBE. This indicates that the residual acceptor background concentration is quite low. Si-doping typically has two effect on the PL spectra: (1) broadening of the D^X peak at carrier concentrations above n > 10 ^ cm~^; and (2) the near band-edge PL red-shifts to lower photon energies. The doping-induced broadening of the PL peak has been attributed to band-tailing due to doping-induced potential fluctuations [63] or band filling resulting in a FWHMpL that scales with the electron concentration as a n^^^ for samples with 10 ^ cm"- < n <2x 10^^ cm"^ [64].

The position of the Si donor level with respect to the conduction band edge was extracted from low temperature PL measurements on Si-doped GaN [65]. Two separate PL peaks were attributed to recombination from the conduction band and the Si-donor level to the same acceptor (Mg) level, respectively. The energy difference between these peaks placed the Si-donor level at 22 meV below the conduction band edge.

4.1.3. Mg-doping Conducting p-GaN is always heavily Mg-doped due to the deep nature of the Mg level, which leads to incomplete room temperature acceptor ionization of several percent. The heavy doping tends to mask information regarding intrinsic transitions in p-type GaN. However, PL spectroscopy can be a valuable tool anyway as the Mg-related defect levels exhibit characteristic PL signatures. For example, strong blue luminescence is generally observed in ]Vlg-doped GaN. Typical PL spectra from a Mg-doped GaN sample grown by MOCVD are shown in Fig. 7.

As shown in Fig. 7, the PL spectra from Mg-doped GaN exhibits strong and broad defect-related blue peak centered at about 2.75 eV at room temperature similar to that reported by other authors [66]. Both the magnitude and spectral location exhibit a significant temperature dependence as illustrated by the shift of the peak from 2.75 eV at room temperature to about 2.9 eV at 6 K. The origin of this broad Mg-related luminescence in p-type GaN has been widely discussed similarly to the ongoing debate on the yellow defect related PL in n-type GaN. As with the yellow PL, there is no clear consensus in the literature on the origin of this PL. However, it has been established that when Mg substitutes for Ga in the GaN lattice, it leads to the quasi-shallow level responsible for most of the hole activation [67]. On the other hand, the blue PL is most likely due to transitions from the conduction band edge to deeper Mg-related levels or complexes involving Mg [68]. Thus, the lattice location of the radiative Mg-related defect is also unknown. Interestingly, the optical ionization energies for separate Mg-related levels were determined at 290 and 550 meV, respectively [68]. As will be discussed later in this chapter, these optical ionization energies are significantly larger than the electrical activation energy ('^l 10-200 meV) of the Mg-related acceptor level responsible for the majority of the hole activation.

Another a PL peak located at about 3.26 eV is observed in Mg-doped GaN at low temperature as shown in Fig. 7. This PL peak was also observed in unintentionally doped GaN as shown in Fig. 2. As previously discussed, this peak is attributed to


1.0

29

2.5 3.0 Photon Energy (eV)

Fig. 7. PL spectra measured at 6 K from a Mg-doped GaN sample grown by MOCVD. This particular sample has a room temperature hole concentration of /? = 4 x 10^^ cm~^.

a donor-acceptor (DÂ^) transition as it has been shown that the magnitude of the donor-acceptor PL peak is greatly increased with enhanced Mg-doping [69]. Lastly, the bound or free exciton peaks are not observed in this heavily doped sample, but the near bandgap PL is frequently observed in lightly doped samples [70]. Furthermore, the near band edge PL spectra in lightly Mg-doped samples are most often dominated by acceptor-bound exciton recombination as opposed to the donor-bound exciton recombination observed in n-type GaN.

It is evident that Mg-doping has a significant effect upon the emission spectra in GaN. As we will now explore, the Mg-doping also affects the absorption spectra as measured by photoconductivity spectroscopy [71]. To illustrate this, we first compare the PC spectra from a heavily Mg-compensated and insulating bulk GaN sample with the PC spectrum from a conducting p-type Mg-doped epi-layer grown by MOCVD in Fig. 8a.

It is evident from Fig. 8a that as a UV detector, the visible rejection ratio is more than three orders of magnitude better in the bulk sample compared to the heavily dislocated MOCVD-grown thin films. Note that this is not due to the presence of Mg since both the samples are heavily and comparably doped. For example, the p-type GaN film has a free carrier concentration of 7 x 10^ cm~^, indicating that the Mg concentration is roughly 100 times higher due to incomplete ionization at room temperature. However, the structural properties are quite different in the bulk and epitaxial GaN. The bulk GaN:Mg is nearly free of threading dislocations (<10 cm'^), while the MOCVD-films typically have a threading dislocation density of >10^ cm~^. The dramatic increase in rejection ratio is therefore at least partly attributed to the absence of threading dislocations in the bulk GaN:Mg. It can also be attributed to molecular doping of paired Mg-acceptors and residual 0-donors with subsequent removal of gap states [72].

30 Ch. 2 J.T Torvik

1 2 3 4 Photon Energy (eV)

1 2 3 4 Photon Energy (eV)

Fig. 8. Photoconductivity spectra comparing: (a) lOO-jJim-thick free standing bulk GaN:Mg and epitaxial ~2-|jim-thick GaN:Mg film grown on sapphire; and (b) the same bulk GaN.Mg and 100-|xm-thick semi-insulating unintentionally doped GaN grown using epitaxial lateral overgrowth.

To investigate the effect heavy Mg-doping has on the PC spectra in GaN, we compared the PC responses of GaN with and without Mg-doping. Samples with low defect densities were used to minimize the above-mentioned parasitic effect of threading dislocations. The PC responses from the bulk GaN:Mg and the unintentionally doped free-standing GaN film are shown in Fig. 8b. It is evident that the spectral cutoff is much sharper in the unintentionally doped GaN. The sharp spectral cutoff is attributed to the absence of a high density of Mg-impurities perturbing the crystal structure. As expected, their rejection ratios are similar since both samples contain low threading dislocation densities and fewer gap states.

4.1.4. Zn-doping Much work was devoted to Zn-doping during the search for conducting p-type GaN using both implantation [73] and in situ doping during growth [74]. Unfortunately, p-type conduction was not achieved as Zn does not form sufficiently shallow acceptor levels. At least four deep Zn-related levels have been identified in GaN at 370, 650, 1070 and 1430 meV above the valance band edge, respectively [75]. The shallowest level at 370 meV is attributed to the divalent Zn dopant occupying the Ga (column III) site forming a single acceptor. The three deeper levels are attributed to Zn substituting on the N site (column V) forming a triple acceptor.

The first visible metal-insulating-n-type (m-i-n) light-emitting diodes were made using Zn-doped GaN since Zn effectively compensates for the residual background electron concentration. Electroluminescence ranging from red to blue was obtained in these diodes depending on doping conditions as shown in Fig. 9 [74].


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Zn-doping also found a use in the in the early commercial double heterostructure AlGaN/InGaN blue and blue-green LEDs that were used in applications such as traffic lights and full color displays [76]. The InGaN active layers were Zn-doped and co-doped with Si {n = 10 ^ cm~^) resulting in LEDs exhibiting a maximum output power of 3 mW with an external quantum efficiency of 5.4% at a forward current of 20 mA. A typical EL spectrum from these LEDs peaked at 450 nm with a FWHM of 70 nm at 20 mA.

4.1.5. Rare-earth doping Ironically, GaN (and it alloys Al-In-Ga-N), which now is established as the semiconductor of choice for short wavelength green-UV applications, has also been considered for longer wavelength applications in the IR using rare-earth (RE) doping. The rare-earths elements can emit light ranging from the IR to the UV [77]. The radiation is due to dipole-forbidden intra-4/-shell transitions, which become allowed transitions when the element is under the influence of a perturbing crystal field such as encountered in a semiconductor. For example, the much-heralded Er^"^-related L54 |xm emission corresponds to a transition from the first excited state C Ii3/2) to the ground state C Ii5/2). Obviously, Er-doped insulators have had much success culminating in products such as Er-doped fiber amplifiers and lasers. The idea of using the recombination radiation from a semiconductor host to excite REs was first proposed in 1963 [78]. However, rare earth-related luminescence was not reported until the late 1970s and early 1980s from various elements such as Sm, Yb, Er in Si, GaAs, InP, GaP hosts [79,80].

The initial focus using the Ill-nitrides was on Er-doped GaN and the 1.54 |xm emission for optical communication purposes. Er was implanted into GaN in 1976 [81], but Er-related 1.54 |xm luminescence was first reported in 1994 (PL) [82] and 1995 (CL) [83]. A recent flurry of reports of other rare earth dopants such as Nd [84], Eu [85], Tm

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[87], Pr [86] using both ion implantation and in situ during growth has broadened scope to include red, green and blue emitters and monolithically integrated full-color displays [87].

Historically, the main challenges with RE-doped semiconductors have been the characteristic thermal PL/EL quenching and the low solubility limit observed in 'low-bandgap' semiconductors. However, the wide bandgap semiconductors have negligible Er-related PL intensity temperature dependence [88] and possibly increased solubility above 10^^ cm~^ [89]. For comparison, the solubility limit was estimated at 1.7 x 10 ^ cm-^ in Si [90].

Several groups have confirmed the minimal temperature dependence by reporting strong Er-signatures at room temperatures around 1.54 ^.m using GaN [82,83,91-94]. Typical PL and EL spectra measured at 77 K and at room temperature are shown in Fig. 10.

Typically, in Er-doped GaN one observes a decrease in the integrated PL intensity of <50% when going from 77 K to room temperature. For comparison, Er-related luminescence is reduced by several orders of magnitude over the same temperature range when using Si or GaAs hosts [88]. Furthermore, the peak emission wavelength at 1.54 |jLm remains stable over the same temperature range within the spectral resolution of 5 A due to the atomic nature (inner 4/-shell transition) of the emission process.

The possibility of electrical excitation is the single most important reason for doping Er into GaN (as opposed to an insulator). A typical room temperature Er-related EL spectrum from a metal-insulator-n-type GaN LED [95] is shown in Fig. 10. Interestingly, the electrical excitation cross section was measured at 4.8 x 10~^^ cm^, which is 4-5


1

33

1 1 } 0 1 2 3 4 5 6 7 8

Time (ms)

Fig. 11. PL and EL decay traces from GaN:Er,0 measured at room temperature.

orders of magnitude larger that the optical equivalent. This value is in good agreement with earlier estimates for Er in Si (6 x 10"^^ cm^) [96]. The large electrical excitation cross section serves as a big motivation to pursue electrically pumped Er-doped GaN devices.

The luminescence lifetime can serve as an indicator of the material quality since ion implantation is often employed at high concentrations. A long excited state (" 113/2) lifetime as observed in sufficiently annealed material suggests minimal non-radiative channels due to implantation damage. Single exponential PL and EL decay traces exhibiting 1/e lifetime of 2.33 and 1.74 ms, respectively, are shown in Fig. 11.

These long lifetimes have been confirmed in GaN:Er grown by HVPE [92]. The fact that the lifetime is long is a characteristic of the dipole-forbidden intra-4/-shell transition and for comparison the 1.54 |xm Er-related PL decay is between 900 and 300 |xs in Si [97] 3 and 5 ms in sulfate glass [98], and 10 ms in silica glass [99].

Sample preparation is a critical issue as the Er's lattice location apparently plays a critical role in making it optically active. Site selective PL was performed by identifying four distinct Er sites in implanted and annealed GaN [100], clearly demonstrating that different Er sites are sensitive to different optical pump wavelengths. Apparently, between 90.0 and 99.9% of the Er ions are situated on Ga sites and only pumped with below bandgap excitation (direct 4/-shell absorption) [101]. This leaves preciously few Er ions susceptible to the desired above bandgap excitation (electron-hole pair mediated excitation). This has serious implications for a potential forward biased GaN:Er LED, where the Er excitation will presumably be facilitated by e-h pairs.

Recently, a flurry of activity has emerged within RE-doped GaN for visible light emitter [84-87]. Red, green, and blue electroluminescence was demonstrated using Eu (621 nm) or Pr (650 nm), Er (537 and 558 nm), and Tm (447 nm), respectively [102]. RE doping was demonstrated using both ion implantation and in situ incorporation during


MBE-growth with solid RE-sources. The demonstration of all the primary colors in GaN substrates opens up the possibility of full planar color displays with the use of selective implantation. The electroluminescence was stimulated using Schottky diodes made with either aluminum or indium-tin oxide contacts. Unfortunately, the diodes are typically operated at large voltages >20 V, although, the RE-luminescence appears strong based on the signal-to-noise ratio. The authors suggest that the growth and fabrication of RE-doped GaN diodes is simpler than for the commercial InGaN HJ diodes. However, GaN-based RE-doped p-n junction LEDs have not yet been demonstrated and a detailed study of the quantum efficiencies are needed to determine the commercial potential of the RE-approach. Furthermore, the RE's are known to getter free carriers, however, little information is available regarding the electrical characteristics of RE-doped GaN films.

4.1.6. Other dopants Thirty-five elements were implanted into GaN in an early and extensive study in search of p-type GaN [81]. The background doping density was 3 x 10^^ cm"^ and the implant density was calibrated to yield a dopant density of 5 x 10^ cm~^. The implantation damage was partially repaired by post-implantation anneals at 1050°C in an ammonia ambient. Several of the samples implanted with Mg, P, Zn, Cd, Ca, As, Hg, and Ag exhibited characteristic photoluminescence signatures as shown in Fig. 12, although none of the samples became p-type.

In retrospect, the high-temperature anneal in an ammonia ambient to repair the implantation-induced damage to the GaN lattice made p-type conduction impossible for the Mg-doped sample because NH3 would introduce compensating hydrogen.

4.2. Electrical properties

The ability to intentionally induce conductivity modulation by doping allows for the fabrication of various electronic and optoelectronic devices. More specifically, n- and p-type layers are needed for bipolar devices, while ultra-pure undoped layers with high mobility are needed for various transistor and detector structures. Furthermore, semi-insulating substrates are needed for high-frequency devices. Precise doping control is therefore a prerequisite for optimizing device design and allowing production of devices with consistent performance parameters. In this section on electrical properties, we first discuss the electronic properties of unintentionally doped GaN, and subsequently investigate Si- and Mg-doped GaN.

4.2.1. Unintentionally doped GaN Defect-free and ultra-pure GaN has proven elusive by any conventional growth method such as MOCVD, MBE or HVPE due to a combination of reasons such as the lack of a lattice matched substrate, the high growth temperatures required, and the high vapor pressure of nitrogen over GaN (at the high growth temperatures). From an electrical standpoint, the highest quality unintentionally doped GaN produced to date typically exhibits an n-type background carrier concentration in the mid-to-low 10^^ cm~^. However, it is important to note that a low carrier concentration is not necessarily a quality measure since residual contaminants can create deep defect levels


Fig. 12. Photoluminescence spectra of implanted and annealed (1050°C in NH3) GaN measured at 78 K (Reprinted after [82] with permission from AIR)

that effectively scavenge free carriers producing resistive films of poor electrical quality. Thus, the mobility has typically been used as the electrical figure of merit for GaN films. GaN films with an electron mobility above 300-400 cm^/V-s at room temperature are generally considered of high electrical quality.

The highest reported bulk electron mobilities for unintentionally doped GaN are ~900 cm^/V-s at room temperature for films grown by HVPE [25] and MOCVD [103]. Unfortunately, such high electron mobilities have not yet been demonstrated in MBE-grown GaN, possibly due to the lower growth temperatures resulting in incomplete buffer layer re-crystallization [104]. The highest reported room temperature bulk electron mobility for GaN grown MBE is ~560 cm^/V-s [105]. However, before MBE is dismissed as an inferior technique for III-V nitride growth, it should be noted that MBE has successfully been used to grow Alo.12Gao.88N/GaN heterostructures on MOCVD-GaN substrates with a record a 2DEG mobility of 20,000 cm^/V-s and a sheet carrier density of 5 x 10 ^ cm'^ at 12 K [106].

As previously mentioned, HVPE-growth has produced some of the highest quality undoped GaN as determined by electronic measurements. To illustrate, the resistivity, mobility and carrier concentration of an HVPE-grown unintentionally doped 70-|xm-thick GaN sample are shown in Fig. 13.

36

10000

E

1*1000 J

o E

J

] (a) 1 -|

^ \ « J \ i 1 i B

H B 1 1 1 • J B

•j

"1

4n17 _ 10 1

1 n

E o '*•' c o f? is c ^ c i o o im

.2 'i^ CO

o

C/z. 2 7.7: Torvil

^^ - ^

\ n^ ^ \ / ^ -^—^ ^

X A \ A—• \ X I \ V ^ \ i f ^ • \ . . . r '^ to

^ • . ^ 1 0 ^ N ^mme^ ¥ •

_ i 1

^^ E V 2

-0.1 .$* > -« fO 'w 0)

a --

10 100 1000 0 5 10 15 Temperature (K) 1000/T (1000/K)

100

Fig. 13. (a) Mobility vs. temperature for a 70-|xm-thick undoped HVPE-grown GaN sample, (b) Resistivity (open circles) and carrier concentration (solid circles) vs. reciprocal temperature for the same sample.

This undoped HVPE-sample exhibits a high electron mobility of 780 cm^/V-s at room temperature and reaches a maximum value of 2070 cm^/V-s at 115 K as shown in Fig. 13. However, the interpretation of the Hall-effect data is complicated by the existence of a degenerate n-type layer at the GaN/sapphire interface [107]. Apparently, when GaN is grown on GaCl-pretreated sapphire a ~0.2-|xm-thick and highly defective interface layer, which mainly consists of stacking faults, exists at the interface [108]. Taking this into account it was later shown that the bulk carrier concentration and mobility can be accurately extracted by using a two-layer Hall-effect model [109,110]. By correcting the mobility data using a two-layer Hall model leads to somewhat higher mobility of 890 cm^/V-s at room temperature for this sample. Interestingly, when GaN is grown on ZnO-pretreated sapphire, there is no evidence of the same defective interface layer, but the resulting GaN film exhibits a continuous reduction of defect density with increasing film thickness [111].

The thermal activation energy of electrons from the donor level responsible for the background carrier concentration to the conduction band can generally be extracted from a plot of the carrier concentration vs. reciprocal temperature. As discussed above, the two-layer Hall model was used to fit the temperature-dependent Hall-effect data yielding a single donor level with an activation energy of 18.6 meV [110].

4.2.2. Si-doping Several column IV elements such as Si, Ge, Sn have been investigated as candidates for n-type doping of GaN. Of the three choices, silicon is the most commonly used and it effectively incorporates on a Ga (column III) site thereby donating one electron per Si atom. Si-doping is advantageous because it forms a relatively shallow donor


1000

£

o E

"Jo X

100 10 100 1000

Temperature (K) 5 10

1000/T(1000/K) 15

Fig. 14. (a) Mobility vs. temperature for a 3.5-|xm-thick Si-doped GaN sample grown by MBE. (b) Resistivity (open circles) and carrier concentration (solid circles) vs. reciprocal temperature of the same sample.

level as discussed below, and thus, allows for almost complete donor activation at room temperature.

The electronic properties of Si in GaN can readily be determined by temperature dependent Hall-effect measurements as shown in Fig. 14.

This n-type GaN sample exhibits a maximum electron mobility of about 250 cm^/V-s at room temperature and 303 cm^/V-s at 180 K. These numbers are somewhat lower than expected in MOCVD-grown GaN:Si, but typical for MBE-grown material [104]. The thermal activation energy for electrons from the Si-donor level to the conduction band edge was extracted from the carrier concentration vs. reciprocal temperature plot. A fit to the linear region of the n vs. 1/T region yields a single donor level with an activation energy of 14 meV. This corresponds nicely with other measurements on Si-doped GaN grown both by MOCVD [108] and by MBE [112]. For comparison, the position of the Si donor level was measured at 22 meV below the conduction band edge as determined by low temperature PL measurements [65]. To the best of our knowledge, there have not been any reports of a degenerate interface layer to complicate matters as with HVPE-grown material. At least not in GaN grown using AIN or GaN buffer/nucleation layers. There have also been reports on temperature dependent Hall-effect measurements suggesting that there are two dominating donor levels in Si-doped n-type GaN. These measurements were performed on material grown by MOCVD using a silane (SiH4) precursor for Si-doping [19]. The shallowest donor level was the Si-related level discussed above. However, to generate accurate fits to the temperature dependent Hall-effect data, these authors had to include a second and slightly deeper level located at 32-37 meV due to a residual contaminant. The density of this second donor was ^ 3-6 x 10^ cm~^ in these particular samples and independent of


Si concentration. The origin was tentatively attributed to oxygen impurities introduced by the ammonia gas during growth.

The shallow nature of the Si donor level leads to almost complete room temperature activation even at modest doping densities. In fact, this has been confirmed using SIMS measurements [19,113]. It was also demonstrated that at a high Si doping density of 2 X 10^ cm"^, the resulting electron concentration remains constant with temperature from ~100 to 500 K. This indicates that when the Si density is sufficiently high, it causes potential fluctuations in the lattice forming band tails and impurity band broadening, which in turn reduces the donor activation energy.

4.2.3. Mg-doping Several divalent elements including Mg, Be, Zn, have been investigated for p-type doping of GaN. Unfortunately, none of these elements form a desired shallow acceptor level needed for efficient hole activation. Mg is the most commonly used acceptor and it forms a single 'quasi-shallow' acceptor level when incorporated on a Ga (column III) site. The relatively deep nature of the Mg acceptor level is the primary reason p-type doping technology is not nearly as advanced as n-type doping. However, this problem is not unique to GaN as all known p-type dopants in SiC form acceptor levels more than 200 meV above the valence band maximum [114]. Al is the p-dopant of choice with the shallowest known acceptor level located approximately 220 meV above the valance band edge of 6H-SiC. The approach to obtain highly p-type SiC has been to increase the doping density sufficiently forming band tails and impurity band broadening to reduce the acceptor activation energy. To date, commercial vendors can supply SiC epi-layers with a free hole concentration up to 2 x 10 ^ cm~^ without a degraded surface morphology (for example, see [115]). Furthermore, Al implantation of SiC and subsequent flash-lamp annealing has successfully been used to activate a room temperature free hole concentration up to 5 x 10^° cm~^ [116]. This 'brute force' approach has not been effective for Mg-doped GaN as the maximum hole concentration produced on a consistent basis in GaN is typically ten times lower at 2-3 x 10 ^ cm~^. However, a lowering of the Mg-related effective activation energy from 190 to 112 meV was observed when increasing the Mg concentration from 1.6 x 10 ^ cm"^ to 3 x 10 ^ cm-^[117].

The electronic properties of a heavily Mg-doped GaN sample as determined by temperature dependent Hall-effect measurements are shown in Fig. 15.

Fig. 15 illustrates the high free hole concentration that can be activated in GaN grown by MBE without the use of post-growth processing. This thin p-type GaN sample exhibits a free hole concentration of nearly 1 x 10 ^ cm~^ at room temperature. Unfortunately, the hole mobility at room temperature is low at 0.95 cm^/V-s which is common for highly Mg-doped p-type GaN [19,32]. An interesting feature observed in Fig. 15 is the increase in hole concentration below --190 K (1000/190 K = 5.3 K"^). This effect is accompanied by a rapid decrease in mobility and therefore attributed to hopping conduction. This particular sample was quite thin at 0.4 jxm, which in addition to the low hole mobility, results in a large resistivity of < 10 ^-cm.

The thermal activation energy for holes from the Mg-acceptor level to the valance band edge was extracted from the carrier concentration vs. reciprocal temperature


E o

o E To X

0.1

o 0

o

o

• r ^

-t 100

1000

E y a

*>

o cc

10 100 1000 Temperature (K)

- I 1 T"

3 4 5 6 7 1000/T(1000/K)

Fig. 15. Left: mobility vs. temperature for a 0.45-(xm-thick 'as-grown' Mg-doped GaN sample grown by ECR-assisted MBE. Right: resistivity (open triangles) and carrier concentration (solid circles) vs. reciprocal temperature for the same sample.

data. A fit to the linear region of the p vs. 1/T region yields a single acceptor level with an activation energy of ~ 110 meV. Although, other authors have reported values of approximately 170 meV [118], this value is consistent with the activation energy reported at high Mg-concentrations discussed above [117].

After discussing both the electrical and optical properties of p-GaN, it is instructive to compare the results. The most obvious feature is the discrepancy between the activation energy measured for the Mg-level responsible for hole conduction (110-200 meV) and the optically determined binding energies (<250 meV) for Mg-related levels deduced from PL measurements. As described in the section on optical characterization, the most common Mg PL signatures are the blue peak at ^^2.75 eV and neutral donor-acceptor recombination at 3.26 eV. The optical ionization energies measured for the 'shallowest' Mg level range from 210 meV [119] to 290 meV [68]. The reason the electrical activation energies appears smaller than the optical equivalent is that conducting p-GaN is heavily doped, which causes broadening of the bands. This is consistent with the report of an activation energy lowering with increased Mg-concentration [117]. For completeness, the blue PL was attributed to transitions from the conduction band edge to deeper Mg-related levels or complexes involving Mg [68].

Hydrogen passivation is another difficulty with Mg-doping of GaN. Hydrogen is incorporated interstitially during MOCVD growth, which results in the formation of a H-Mg complex rendering the Mg-dopant electrically inactive. A post-growth annealing process in an inert gas ambient (or vacuum) or a LEEBI treatment is subsequently required to dissociate the H-Mg complex allowing the Mg to become electrically active. The growth method of choice is therefore an important issue for p-type doping of GaN.

40 Ch. 2 IT. Torvik

The UHV environment of MBE is inherently advantageous for Mg-doped GaN growth by minimizing residual hydrogen incorporation. Avoiding hydrogen incorporation in MOCVD growth is virtually impossible since anmionia (NH3) is the most frequently used nitrogen precursor. MBE is a proven technique to routinely produce p-GaN with a high free carrier concentration above 10 ^ cm"^ without post-growth processing [11,32]. ECR-assisted MBE has been used under optimized conditions to demonstrate p-GaN with a free hole density up to 10 ^ cm~^ at room temperature [120]. For comparison, MOCVD growth has also been used to grow heavily p-doped GaN with a free hole concentration up to 7 x 10^^ cm~^ after a LEEBI treatment [121]. Due to the lower growth temperature (and unresolved buffer layer technology) in MBE, there seems to be a general consensus that the structural quality as measured by threading dislocation density generally favors the MOCVD-grown material [104].

4.3. Doping techniques

The success of doping techniques other than in-situ doping during growth is unfortunately limited for GaN and its alloys. The reasons include the high temperatures required to repair the implantation-induced lattice damage and low diffusivities of impurities. The highlights of the various doping techniques are briefly explored in the next three sections.

4.3.1. Diffusion Doping by diffusion is a powerful technique used effectively in Si processing. Unfortunately, diffusion of donors and acceptors is not a practical doping technique for GaN due to the vanishing small diffusion coefficients for such elements at practical temperatures [122]. Zolper et al. studied the redistribution of donors (Si and O) and acceptors (Be, Mg, Zn and Ca) by ion implantation and subsequent rapid thermal annealing [123]. Only Mg was found to move slighdy (50 nm in 15 s) when annealed at 1100*^0. The diffusivity of Mg was estimated at 1.7 x 10"^^ cm^/s. The upshot of the low diffusivity is that no significant Mg redistribution is observed during MOCVD growth up to 1060°C [124].

4.3.2. Ion implantation Ion implantation is another widely used doping technique for both electrical and optical applications. With implantation one can precisely control the spatial distribution of the impurities by using photolithographically defined masks, which is convenient for applications such as integrated circuits and lateral devices. Furthermore, using implantation one avoids surface segregation, residual contaminants from doping sources, and memory effects in gas lines and growth chamber. However, creating thick uniformly doped layers requires multiple mid-to-high energy implants (keV to several MeV), which are costly and create severe implantation damage. Implanted samples must therefore be annealed at elevated temperatures up to 1600°C [125] to sufficiently repair the lattice damage. Even so, ion implantation has successfully been used to modify the optical [126] and electrical [127,128] characteristics of GaN. For electrical purposes, most of the work has focused on Si and Mg implantation. Pearton et al. reported that


D

ID

10

10*

10

- • D—Mg*/P - • - s r - A - M g * —T— Unimplanted

700 800 900 1000 1100

Anneal Temperature (°C)

Fig. 16. Sheet resistance of undoped. Si"*"-, Mg"^-, Mg"*'/P-implanted GaN subjected to different annealing temperatures. (Reprinted after [128] with permission from AIR)

Si^-implanted GaN exhibited a dramatic decrease in sheet resistance when annealed above 1050°C indicating significant donor activation as shown in Fig. 16 [127].

At this annealing temperature, the electron mobility did not recover from its pre-implantation value indicating residual implantation damage. In more recent work, the same group reported on Si"^-implantation (100 keV) of GaN using optimized anneals up to 1500°C [128]. Protective AIN cap layers were in this latter case used to prevent decomposition at elevated temperatures. The results indicate over 90% donor activation at a dose of 5 x 10 ^ cm~^ resulting in a free carrier concentration of nearly 5 x 10 ^ cm~^. The obvious application for such highly doped layers are for contact purposes, and a separate effort using Si-implantation has led to contacts with a specific contact resistivity as low as 3.6 x 10"^ ^cm^^ [129]. Implantations for p-type conduction have been less successful than for n-type. Even so, there have been reports of p-type GaN created with Mg-implantation exhibiting an acceptor activation of 62% when co-implanting with P [127]. The conversion from n-type to p-type was achieved at an annealing temperature of 1050-1100°C as shown in Fig. 16.

4.3.3. Doping during growth The doping of GaN has primarily been performed in situ during growth due to challenges facing diffusion and implantation as discussed above. Doping during growth is fundamentally advantageous compared to diffusion and implantation for vertical device structures because thick/thin and buried (doped) layers with abrupt interfaces can be grown without interruption. Furthermore, implantation damage is avoided, although post-growth annealing has proven essential when electrically activating Mg-dopants when grown in a hydrogen-rich environment such as MOCVD. A rigorous treatment of in-situ doping during growth is beyond the scope of this chapter and is left to several excellent reviews [9,25,32]. Instead, this section will explore the two interesting concepts of composition modulation (superlattice) enhanced doping and molecular doping.

42 Ch. 2 J.T Torvik

1

1 :

0.1-

r

1 ^ • • D

1 T

1

AIGaN L = 20A L = 37A L = 68A L = 88A

• • •

1 1

—D—

•

^ , - ^ — , , 1

EA = 238 m e V ^ ^^-^^^ ft j

/ ^ T E A = 228 meV

^^--^^^^- 173 meV 1

EA=16meV D • D

W T ^ EA-OmeV

, , , 1000 1050 1100 Position (A)

1150 1200 1.5 2.0 3.5 2.5 3.0 1000/T (1000/K)

Fig. 17. Left: valence band diagram for Mg-doped Alo.2Gao.8N/GaN superlattices with L = 30 A shown with (bottom) and without (top) polarization effects included in calculation. Right: Arrhenius plots of resistivity measurements. (Reprinted after [132] with permission from AIR)

4.3.3.1. Composition modulation (superlattice) enhanced doping. Schubert et al. proposed a novel superlattice structure to circumvent the fundamental problem of low acceptor activation in the III-V nitrides [130]. The proposed structure consists of a uniformly doped superlattice formed by spatially modulating the alloy composition. This creates a periodic oscillation in the valance band due to the valance band offsets between adjacent layers. The enhancement in the acceptor activation occurs by efficient hole ionization from the deep acceptors in the larger bandgap material into the valance band of the lower bandgap material. More recently, calculations accompanied by experimental verification on Alo.iGao.gN/GaN superlattices by Kozodoy et al. [131] show that the large polarization fields present in the nitrides further enhances the valance band oscillation causing a greater hole ionization than previously anticipated. The calculated valence band diagram for the Mg-doped Alo.2Gao.8N/GaN superlattice is shown in Fig. 17 illustrating the dramatic effect of the polarization fields induced by the piezoelectric effect and spontaneous polarization.

In this superlattice structure the ionized holes accumulate where the Fermi energy is close to the valance band edge resulting in parallel sheets of holes. The spatially averaged three-dimensional density of holes is substantially larger (about 10 x) than in the bulk film. The average room temperature hole concentration in the Mg-doped Alo.2Gao.8N/GaN superlattice peaked at 2 x 10^ cm~^ with a lateral resistivity as low as 0.2 ^-cm.

4.3.3.2. Molecular doping. It has long been known from the work of Reiss et al. [132] that co-doping with donors and acceptors increases the solubility of both impurities beyond the solubility limit of either single impurity in the given semiconductor. Reiss et al. demonstrated this phenomenon for Li (donor) and Ga (acceptor) co-doped Ge. More recently, Withrow et al. co-implanted and annealed Ga (donor) and As (acceptor) in Si and found their solubility to increase sevenfold compared to the solubility of Ga or As alone in Si [133]. Most recently, Brandt et al. doped GaN with Be and O and showed


1.0

43

Photon Energy (eV)

Fig. 18. UV reflection spectra of MgO (broken line) and bulk GaN:MgO (solid line).

that this molecular doping greatly increased the mobility of holes to 150 cm^/V-s in p-type cubic GaN [134]. The large hole mobility was attributed to BeO forming a dipole with a lower scattering cross-section for holes than the usual Coulomb scattering of a monopolar acceptor. A similar effect was postulated for Mg and O, if they combine to form molecular doping with a binding energy larger than the binding energy of Ga to N in GaN. The energy levels attributable to MgO would reside outside the energy gap of GaN. In other words, Mg would scavenge the residual donors in GaN and remove their donor levels from the bandgap of GaN. The bandgap of MgO is in the energy range of 7.3-7.7 eV [135-137], more than twice that of GaN (3.4 eV). As a molecular impurity, the states attributable to O will appear in the conduction band while those of Mg will appear in the valence band. UV reflection spectrometry in combination with photoconductivity measurements show that the simultaneous presence of Mg and O in GaN makes the GaN insulating and renders the GaN more solar-blind than MgO-free GaN [72]. The improved solar blindness is tentatively attributed to molecular doping by MgO with the benefit that Mg scavenges 0-donors that contribute to gap states. Supporting evidence for the molecular doping concept appears as a peak at 6.7 eV and an exciton peak at 7.6 eV in both MgO and GaN.MgO as shown in Fig. 18.

Molecular doping been explored theoretically by Yamamoto et al., with the conclusion that co-doping donors and acceptors can allow increased solubility of acceptors [138,139].

5. Summary

N-type doping of GaN using Si is well-understood, as Si readily incorporates on a Ga-site forming a single shallow donor with an activation energy of 12-15 meV

44 Ch. 2 J.T Torvik

leading to near complete donor ionization at room temperature. The growth is largely controlled over a wide range of densities from low-10^^ to mid-10^^ cm"^, although some structural problems occur in thick and heavily doped films. P-type doping remains a major challenge, as Mg forms a 'quasi-shallow' acceptor level located more than 170 meV above the valence band edge. The deep nature of the acceptor level leads to poor acceptor ionization of several percent at room temperature. Excessively high Mg concentrations are therefore needed to produce p-type films above mid-10^^ cm~^, which often results in resistive films.

The near-band edge optical transitions are well understood in GaN, and thus, low temperature photoluminescence spectroscopy is a valuable tool in characterizing nominally undoped GaN. On the other hand, the origins of various defect-related transitions such as the ever-present yellow PL are still hotly debated and will require further investigations to unambiguously identify. The broad defect-related PL signatures observed well below the intrinsic optical band edge tends to dominate the spectra and often limit the useful information that can be extracted from PL measurements on heavily doped material. PL can generally be used to identify the presence of and to extract the binding energies for common dopants such as Mg and Si in low and medium doped GaN.

The Hall-effect measurement is a useful tool to determine the carrier concentration, mobility and resistivity in conducting GaN and temperature-dependent measurements yield info regarding the thermal activation energies. However, caution should be placed on equating the thermal activation energy to the actual location of the donor/acceptor levels responsible for electron/hole conduction with respect to the band edges. The electrical measurements can substantially underestimate the location of the donor/acceptor levels as heavily doped material is most often used, which causes potential fluctuations in the lattice leading to significant band-tailing. A comparison with PL measurements on modestly doped material can often clarify the situation. This is particularly true for Mg-doped GaN.

Diffusion as a doping technique is impractical for GaN due to the vanishing small diffusivities at temperatures below 1100°C. Ion implantation is more promising for both conductivity modulation and optical purposes, but further work is required to optimize activation and minimize residual implantation damage. The process compatibility of implantation is limited due to the high annealing temperatures needed above 1500°C to repair implantation-induced damage. Nevertheless, implantation can possibly be used in areas of the device that is removed from critical (minority) carrier flow such for creating heavily doped contact layers facilitating tunneling contacts with low resistivities. In situ doping is therefore the doping technique of choice due to the above-mentioned challenges. Tricks such as piezoelectric enhanced superlattice doping can create p-layers with low resistivities, but is not practical for vertical carrier conduction. Molecular doping of paired donors and acceptors is another alternative that deserves further exploration.

How does the current status of dopants in GaN impact the future device efforts? It is clear that devices will continue to exhibit large series resistances and contact problems until the above-mentioned fundamental p-type doping problem is solved. The most glaring examples are the high operating voltages and lifetime problems


associated with GaN-based lasers and the absence of microwave operation in HBTs. The fundamental problems can be circumvented on an individual basis by clever device design using techniques such as re-growth, selective growth, implantation, superlattice doping, deep-sub-micron lithography and wafer bonding with a penalty in increased processing costs. However, a general and fundamental solution to the p-type doping problem is preferable.

Acknowledgements

The author would like to thank J.I. Pankove for patient and continuous tutelage over the last decade in addition to a critical review of this work. Furthermore, he would like to acknowledge R. Krutsinger, T. Wangensteen, C.H. Qiu, M. Leksono and J.L. Torvik for significant input and valuable discussions. The author also owes thanks to S.J. Pearton, P. Kozodoy and C. Kirchner for supplying figures, preprints or other data. He is also indebted to R.J. Molnar for supplying HVPE-GaN and reviewing the interpretation of the data collected from these samples. As always, T.D. Moustakas has generously supplied high quality GaN samples. Collaborators on the Er-doped work include R. Feuerstein and F. Namavar. Other GaN samples have generously been supplied by I. Akasaki and H. Amano, S. Nakamura, I. Grzegory, and S. Porowski.

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CHAPTER 3

Defect engineering in Ill-nitrides epitaxial systems

S. Ruvimov

1. Introduction

In recent years, GaN and related compounds have attracted a lot of scientific interest due to their application in optoelectronics [1-4]. Within a short period of time, visible light-emitting diodes (LEDs) [1-4], blue lasers [3,4] and metal-semiconductor field-effect transistors [5] have been successfully fabricated based on GaN and related Ill-nitrides. Surprisingly, good optical characteristics of GaN-based LEDs and lasers have been achieved despite high dislocation density in the GaN epitaxial layers [4]. On the other hand, the lifetime of laser diodes under continuous wavelength operation appears to be limited by the presence of crystallographic defects. So the reduction of defect density is still one of the major problems in the GaN technology. The optimization of the GaN growth requires the knowledge of the atomic structure of crystallographic defects in GaN and mechanisms of their generation and annihilation.

Due to the lack of the substrates with similar lattice parameters and thermal expansion coefficients, the GaN epitaxial layers usually contain numerous crystalline defects. The typical dislocation density reported [6-15] for GaN-based heterostructures ranges from 10^ to 10^ cm~^. Besides dislocations, the major defects in the GaN epitaxial layer include stacking faults (SFs) [13-15], small angle grain boundaries [10-12] and nanopipes [7,12-15]. The defect formation appears to depend on a number of factors including growth conditions [10,16], a level of doping [11,12], type of impurities, substrate and buffer layer [15-22]. Recently, epitaxial lateral overgrowth (ELOG) technique has been shown to drastically reduce the defect density in the GaN grown on (0001) sapphire [23,24] and 6H-SiC substrates [25,26].

The present chapter reviews the common crystallographic defects observed in the GaN and related Ill-nitride systems based on the electron microscopy results that the author obtained during his work at LBNL and on the literature data. The major focuses are the structure of defects in the wurtzite GaN and the factors that control their formation.

2. Experimental details

TEM studies have been performed on a variety of GaN samples grown either by molecular-beam epitaxy (MBE) [20] or metal-organic vapor phase epitaxy (MOVPE) [27]. The growth details are described elsewhere [20,27]. The (0001) or (1120) planes

52 Ch. 3 S. Ruvimov

of sapphire and (0001) plane of SiC were used as substrates for MOVPE growth of GaN layers. Low-temperature (LT) GaN or AIN were used as buffer layers. MBE growth of the GaN was performed on (0001) sapphire substrates using Riber 1000 system [20]. LT GaN was used as a buffer layer. Some GaN samples were grown without the buffer layer.

High-resolution electron microscopy (HREM) observations were obtained using Top-con 002 and ARM nndcroscopes operated at 200 and 800 kV, respectively. Conventional transmission electron microscopy (TEM) was carried out on JEOL 200CX microscope operated at 200 kV. The in-situ heating experiments (up to 1000°C) were performed on 1.5 MV electron microscope. Cross-sectional specimens for TEM were prepared either by mechanical polishing followed by dimpling and Argon ion milling or by cleaving along the {1100} crystallographic planes of the GaN. The cleaved samples were mounted on a copper grid for TEM inspection. Convergent beam electron diffraction experiments were employed to determine the polarity of the GaN layers. The two-beam gb analysis was employed to determine the Burgers vectors of dislocations.

3. Structure of the GaN epitaxially grown on the foreign substrate

A pseudomorphic epitaxial growth of Ill-nitride layers on the GaN monocrystalline substrates would be a natural way to obtain defect-free material for device application. The GaN layers grown either by MBE [28] or MOVPE [29,30] on the bulk platelets have demonstrated good optical properties and low density of defects if the proper substrate cleaning and growth conditions were adopted. The defects, generated occasionally during the homoepitaxial growth of the GaN layers, result from the presence of impurities on the substrate surface [28]. The defect formation in the homoepitaxial GaN layers has been shown to exhibit a strong dependence on the polarity of the (0001) substrate surface [29,30]. The majority of GaN layers and related compounds were grown on the foreign substrates, because bulk GaN crystals are still too small and expensive to be of commercial interest as substrates.

All foreign substrates available for the GaN epitaxy have a high mismatch in lattice parameters, thermal expansion and chemical composition with the GaN layer. Among a large number of different foreign substrates tested for the GaN deposition [31], sapphire and 6H silicon carbide have demonstrated the best results in terms of the layer quality. The mismatch in lattice parameters and thermal expansion coefficients between the GaN and these substrates is high. It leads to a generation of the high density of defects at the epi-layer-substrate interface. The lattice mismatch between the GaN and SiC is about 2%, but it is even higher in case of the GaN layers grown on sapphire being about 16 and 30% for c- or a-facet of sapphire, respectively. However, the defect densities in the GaN layers grown by MOVPE on SiC and sapphire substrates were found to be comparable [18]. This could be explained taking into account that defect density in the GaN layer is controlled by structure of the buffer layer and its roughness, in particular.

Fig. 1 shows a typical defect distribution in the epitaxial GaN layers grown on sapphire with AIN buffer layer. The dislocation density is high in the AIN buffer layer and at the GaN/AIN interface, then drastically decreases over 0.2 |xm toward the GaN top surface. This dislocation distribution being typical for other GaN samples indicates

Defect engineering in Ill-nitrides epitaxial systems Ch. 3 53

KIH

' ^ ^ - 4Ni?*fe#H

40 nm F/g. 7. Defect distribution in the GaN layer grown by MOVPE on (0001) sapphire substrate with AIN buffer layer (cross-sectional TEM image).

that the majority of threading dislocations originates and annihilates during the eariy growth stages of the AIN and GaN layers. Some dislocations form the half-loops at the AlN/GaN interface and do not further propagate into the GaN layer (see Fig. 1). The formation of these loops is linked to the mechanisms of defect generation and annihilation in the layer [18]. The half-loops are likely to be formed during the growth of the layer, at earlier growth stages as a result of the lateral overgrowth [16].

The atomic structure of the AIN buffer layer (Fig. 2) suggests that a high density of small coherent hexagonal AIN nuclei are formed at first stages of the growth. The 3D growth mode of the buffer layers results from a high mismatch in lattice parameters and chemistry with the substrate. The further deposition of the AIN leads to growth of the islands and their coalescence [17]. As a result, the AIN buffer layer has a columnar structure consisting of small crystalline subgrains (Fig. 2). The subgrains in the layers are typically misoriented around the c-axis, but almost perfectly oriented in the c-plane. Threading dislocations formed at vertical merging boundaries accommodate to the misorientation between the adjacent subgrains. The AlN/sapphire interface contains a high density of misfit dislocations, which release almost all the misfit between their crystalline lattices at the growth temperature [11,18,32]. The threading dislocations in the AIN layer are generated at the interface with the substrate during coalescence of 3D AIN islands.

The growth of the GaN layer also starts in a 3D fashion due to the high lattice mismatch. The threading dislocations in the GaN layer appear at the points where the misfit dislocation network is disturbed, for example, by the presence of atomic steps at the interface or at merging points of adjacent islands. Some dislocations propagate from the AIN buffer layer as well (see Fig. 2).

54 Ch. 3 S. Ruvimov

i nm sapjfliire Fr^. 2. Structure of LT AIN buffer layer grown by MOVPE on (0001) sapphire substrate (cross-sectional

HREM image).

The formation of subgrain boundaries in the AIN buffer and generation of threading dislocations in the GaN layer were often observed above sites of interface deterioration (Fig. 3) [18]. The deterioration is associated with oxygen outdiffusion from sapphire that may cause defect generation in the GaN layer. The optimal growth of the AIN buffer layer reduces possible deterioration of sapphire and the interface roughness. As a result, it reduces a number of threading dislocations and effects their arrangement in the GaN layer. Thus, the structure of the buffer layer and the roughness of the interfaces with substrate and the buffer layer have a significant effect on defect density in the GaN layer.

Fig- 3. face).

Deterioration of the sapphire substrate (cross-sectional HREM image of the AlN/sapphire inter-


Fig. 4. Cross-sectional TEM image of the GaN layer grown by MOVPE on (0001) SiC substrate with AIN buffer layer.

Similar observations was made for the GaN layers grown on SiC with the AIN buffer layer (Fig. 4) [18]. The AIN buffer layer on the cross-sectional TEM image of Fig. 3 consists of pyramidal islands faceted by {0001}, {1101} and {1100} crystallographic planes. As a result, a row of pinholes facetted by {1101} crystallographic planes was formed during coalescence of the AIN islands. The threading dislocations were often generated at merging points of adjacent islands (Fig. 4) [10]. This suggests that the structure of the buffer layer is an important factor that controls the defect generation in the GaN layer.

The GaN and sapphire differ in the crystalline structure: the structure of sapphire is trigonal (space group R3c) while the GaN has a hexagonal symmetry (space group P63mc). Fig. 5 shows the GaN lattice in the [0001] projection. The orientation relationship between the AIN buffer and sapphire substrate, (0001)AIN//(0001)AI2O3.

[1100]AIN//[1120]AI2O3» provides the best match between their crystalline lattices, but the mismatch still remains high. The orientation relationship results in a_6 to 7 'magic' ratio between crystalline lattices of AIN and sapphire: every 6 planes ([1100] or [1120]) of AIN fits to 7 planes ([1120] or [1100], respectively) of sapphire with an error of about 2% (Fig. 6).

The period of 1.65 nm for the contrast oscillations observed at the AlN/sapphire interface (Fig. 7) fits well to this 'magic' value. The coincidence site lattice for adjacent Al layers (two-dimensional lattices of Al atoms) in crystaUine AIN and sapphire (Fig. 8) has a period of 3.3 nm in the [1100] AIN direction. The areas of 'good' match between these two-dimensional lattices of Al atoms are divided by the areas of a poor match, which are, in fact, misfit dislocations with delocalized cores. Periodic arrangement of misfit dislocations at the AlN/sapphire interface (Fig. 8) corresponds to the periodical oscillation contrast (Fig. 7) so that any disturbance in the observed oscillations reflects the disturbance in the arrangement of misfit dislocations.

The defect distribution in the GaN layer (Fig. 1) is Hnked to the mechanisms of their generation and annihilation. The mechanisms, which are typical for other III-V epitaxial systems (such as AlGaAs, GaAs/Si, etc.), might not play an important role in Ill-nitrides. The preferential mechanisms of dislocation generation depend on the

56 Ch. 3 S. Ruvimov

Fig. 5. Atomic structure of GaN in the [0001] projection.

• • = tsF «<=" tP *P *^ • = •<> if «•= » - •<^ «" ^

o ^ , s , o , o , o ô ^z ô , e , 0 ^. , o , o ^

t OOOlsap

1120 sap

Fig. 6. Atomic structure of the AlN/sapphire interface in cross-section (simplified model).

growth mode, the mechanical properties of the materials of layer and substrate, and the stress level in the epitaxial system developed during growth and post-growth cooling. It is known that the GaN epitaxial layers may exhibit stress up to 1.5 GPa [32].

The generation of a dislocation includes two steps, the nucleation and the propagation of the dislocation into a layer. Typically dislocations in III-V epitaxial systems either propagate from the substrate or nucleate at internal interfaces or at the surface of growing layer. The dislocation may further multiplicate or annihilate depending on the reactions between dislocations. In the Ill-nitride epitaxial layers the nucleation of dislocations at the interface dominates other mechanisms.

In order to improve the structural quality of the epitaxial layers the two-step growth


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is used for highly mismatched epitaxial systems [16]. A typical example is the GaAs/Si system that is comparable with GaN/SiC in terms of the lattice mismatch. In the case of GaAs/Si a thin low temperature GaS layer was deposited on (001) Si substrate prior to the growth of the main GaAs layer in order to reduce the dislocation density. The structural quality of the GaAs layer was found to depend on a number of factors including the substrate orientation, treatment of Si surface prior to the GaAs deposition,

58 Ch. 3 S. Ruvimov

thickness of the buffer layer, growth parameters of the buffer and main layers, etc. The defect density was typically high at the GaAs/Si interface and gradually decreased toward the top surface of the layer. The growth proceeds first in the three dimensional fashion resulting in the formation of 3D islands. The further deposition of GaAs leads to island growth followed by their coalescence and formation of a crystalline layer with smooth surface. Consequently, the growth mode converts into two-dimensional, layer-by-layer growth. Misfit dislocations generated at island edges release the misfit stress associated with the mismatch in lattice parameters between GaAs layer and Si substrate. The threading dislocations are mainly generated during island coalescence to accommodate the misfit between the merging islands. The misfit stress is typically relaxed at growth temperature so that the residual stress in the layer results from the difference in thermal expansion coefficients between the layer and substrate. Depending on the post-growth cooling conditions, the thermal stress could be partially relaxed. Dislocations could also be generated from the surface. This process may involve the dislocation generation at the surface of the layer, followed by their propagation toward the layer-substrate interface to accommodate the residual thermal stress.

In contrast to GaAs, the dislocation mobility in GaN and other Ill-nitrides appears to be very low even at growth temperatures [33]. The dislocation mobility in GaN at room temperature was estimated to be 10~^^-10"^^ times lower than that of GaAs [33]. The calculated activation energies for the dislocation glide in GaN, InGaN and AlGaN are 2.1, 2.0 and 2.3 eV, respectively [33]. The dislocation climb in GaN could be also insignificant, because the dislocations in GaN-related materials do not act as nonradiative recombination centers [34]. The low dislocation mobility in the GaN could be one of the reasons for the remarkably long lifetime of GaN based LEDs despite of the high defect density [33].

The dislocation velocities in the GaN increase with the temperature and become comparable to those of GaAs under current injection at about 400°C [33]. The dislocation motion was observed in the GaN layer grown on sapphire, during the heating at a temperature above 350°C directly in the column of a high voltage electron microscope [35]. Some dislocation segments have moved for a short distance ranging from 0.2 to 0.5 |xm under the exposure to a focused electron beam, but the majority of dislocations remained immobile. This indicates the possibility of the partial relaxation of a thermal stress developed during the cooling, as it was suggested earlier [11]. However, the residual thermal stress in the GaN layer seems to be mostly controlled by the deposition temperature, thickness and structure of the buffer layer [20,21,32]. The majority of as-grown dislocations in the GaN layer are immobile during post-growth cooling. As a result, the dislocation generation, propagation and annihilation appear to be mainly growth-related processes and, hence, can be controlled by the growth conditions, especially during the first growth stages. The dislocation distribution in the GaN layer is, to a large extent, frozen after the layer growth and, hence, reflects the growth process itself. This explains the fact that the defects in the GaN crystals are primarily elongated in the growth direction, i.e. parallel to c- and a-directions in case of the GaN epilayer and the bulk platelet, respectively [36]. The structural quality of the GaN layer appears to depend on the growth evolution [16]. Because of the low mobility of dislocations in the GaN, the probability for their interaction and annihilation is also low compared


with other III-V materials such as GaAs. The defect density in GaN layers can be significantly reduced by optimization of growth conditions [10,15,16].

3.1. The structure of the buffer layer

A low temperature buffer layer was typically deposited prior the growth of the GaN layer aims to reduce a number of defects and obtain a single crystalline layer with a flat surface. The major role of the buffer layer is to provide a high density of nuclei for the growth of the main GaN layer at a high temperature and to promote the lateral growth of GaN [16]. A LT buffer layer also releases the stress, decreases the defect density, and helps to maintain a certain crystallographic orientation and the polarity of the layer [15,30]. Growth and subsequent coalescence of GaN islands finally leads to a quasi-two-dimensional (2D) growth and formation of the layer with a smooth top surface [2,17].

The optimization of the buffer layer appeared to be the focus of many studies [10,16,19-22,37]. It has been shown that the low temperature buffer layer such as AIN [16] or GaN [37] dramatically improves the surface morphology and the crystalline quality of GaN layer subsequently grown at high temperatures. Before the LT buffer deposition, the sapphire surface is usually exposed a nitrogen-containing gas flow for nitridation at high temperature [15,16,20,21]. This annealing under a nitrogen rich atmosphere provides a cleaning and uniform chemical termination of the sapphire surface. The optimal conditions for both nitridation and deposition of the low temperature buffer layer appear to be essential for the reduction of dislocation density in the main GaN layer.

The nitridation depends on the nitrogen source, the partial pressure of nitrogen or anmioniac, the temperature and time of the nitridation [15]. The (0001) sapphire surface has complex structure and contains a mixture of O and Al atoms [38]. The nitrogen diffuses into sapphire and reacts with the Al atoms replacing the oxygen [39]. The AlON compound or its mixture with the AIN could be formed on the sapphire surface depending on the nitridation conditions. Rouviere et al. [15] have reported a cubic phase of AlON compound at the sapphire/buffer layer interface. One to a few monolayers of AIN under the amorphous-like AINO layer was observed by high-resolution electron microscopy after nitridation of sapphire in our study [39]. It has been found that the nitridation and growth conditions of buffer layer effects the polarity and morphology of the growing GaN layer [15]. The nucleation and growth of GaN under Ga-rich conditions have been found to result in improved structural, electrical and optical properties with smoother surface morphologies as compared to N-rich growth [15,20]. The difference in surface morphology has been linked to the presence of inversion domains [40], which originated in the nucleation layer [21,40]. It was suggested that the nitrogen-rich growth and growth under atomic hydrogen enhanced the growth rate of inversion domains with respect to the surrounding matrix. The growth under Ga-rich conditions seems to result in a closer equal growth rate and, hence, in a smoother surface morphology. The inhomogeneous nitridation on the sapphire substrate due to a remnant high-energy ion content in the nitrogen flux from the rf-plasma source was suggested as a possible cause of the inversion domains [40].

50 Ch. 3 S. Ruvimov

The LT buffer layer was found to transform during the temperature ramp/anneal with an increase of average grain size and surface roughness [19-21]. The growth evolution can be affected by a number of parameters including the thickness of LT buffer, the temperatures for LT and HT growth, growth rate, Ga/N flux ratio, gas ambient, etc. The surface morphology of the GaN layer has been shown to improve by increasing ramping time for temperature rising from 550 to 1100**C [19]. The ramping process effects the structure of the LT GaN buffer layer leading to its recrystallization. In addition to small grains, Ga droplets were observed on the surface of the buffer layer after 10 min annealing at 950°C resulting from the decomposition of GaN and evaporation of nitrogen from the LT GaN buffer layer [19]. The critical temperature for the GaN decomposition depends on growth conditions. In our in-situ heating experiments, the decomposition of the GaN layer has been observed at 850°C [33].

The following scenario could be suggested for the buflfer layer transformation during the ramping and first growth stages for the GaN layer [19,21]. The small crystalline nuclei that are initially formed on the substrate during the LT buffer deposition are covered with amorphous-like material. If these nuclei grow fast enough to be exposed to the surface of the buffer layer during the temperature rise they become suitable nuclei for the growth of GaN layers. The transformation of the buffer layer depends on the ramping parameters (temperature, time, Ga/N ratio, gas pressure, etc.) [19]. As an example, if the ramping time is too short, the crystalline nuclei may not grow not to be large enough so that the amorphous layer will still covers them. The misoriented nuclei for the GaN growth would be formed on the surface of LT buffer layer, giving rise for a high defect density in the growing layer. At an optimal ramping process the single crystals would protrude out of the surrounding amorphous layers. During the high temperature growth these crystals would grow laterally over the amorphous layer [21]. If the ramping time is too long, the number of large crystals would increase so the number of dislocations associated with island coalesce [19].

3.1.1. Lateral overgrowth The lateral overgrowth in Ill-nitrides is based on the difference in growth rates of the GaN in different crystallographic directions. It seems to be an important mechanism for the defect annihilation in the GaN epitaxial layers [16,18]. Fig. 2 shows that the subgrain size increases in the growth direction. The GaN subgrains are larger than the AIN subgrains, and the AIN subgrains at the GaN/AlN interface are larger then those at the AlN/sapphire interface. Such evolution of the subgrain size is caused by lateral overgrowth of some of the AIN and GaN subgrains. The growth conditions for various grains are locally different because the islands differ in their initial size and strain distribution within each island. Therefore, larger islands with lower strain will grow faster than other ones. As a result, these islands will laterally overgrow the others leaving them buried near the interface. Some of the AIN subgrains in Fig. 2 have buried smaller subgrains under them. The threading dislocations that accommodate the misorientation between adjacent AIN grains are forced by this lateral overgrowth to bend into basal planes interact with other dislocations and often annihilate. Schematically it is shown in Fig. 9. This process leads to the formation of many half loops in the AIN buffer and in the first 0.2 |xm of the GaN observed in Fig. 1 and in the decrease of overall

Defect engineering in lU-nitrides epitaxial systems Ch. 3 61

dislocations

/1 \ \ disiocation

> loops

buffer layer

Fig. 9. Lateral overgrowth of islands during the early growth stages (schematic drawing) Note the formation of the half-loops at the interface with substrate by the lateral overgrowth of some grains over the others.

dislocation density in the growing GaN layer. The efficiency of this process depends on both thickness and structure of the buffer layer, and on the growth conditions [16].

Some impurities may enhance the lateral overgrowth while the others suppress it. This may explain the effect of doping on the density and distribution of the dislocations in GaN layers. For example, Si-doping was found to reduce the dislocation density while Mg doping seems to increase it [18]. A high density of horizontal dislocation segments in the Si-doped GaN layers [11] increases the probability of dislocation interaction and annihilation. The formation of such horizontal segments suggests a higher probability of the lateral overgrowth for Si-doped GaN compared to that of Mg-doped layers [18].

The epitaxial lateral overgrowth technique has been proven recently to drastically reduce the defect density in GaN grown on sapphire [23,24] and 6H-SiC [25,26]. This techniques involves the growth of GaN through the windows of a Si02 mask on a patterned GaN buffer layer. The microstructure of ELOG GaN layer on the mask design and, in particular, on the orientation of the strips. The width of the oxide strips was typically ranging from 3 to 5 |xm. The defect density has been reported to be lower by over two orders of magnitude as compared to that in the GaN layers grown on unpattemed substrate. Consequently, the lifetime of laser diodes based on the ELOG GaN has been significantly improved [23].

4. Crystallographic defects in GaN

The defects in crystals are typically classified by dimension. Zero-dimension (OD) or point defects include intrinsic point defects such as vacancies, interstitials, antisite defects and impurity-point defect complexes. Extended defects include linear defects (dislocations) and planar defects (grain boundaries, interfaces, stacking faults and micro-cracks). The three dimension (3D) defects include precipitates, holes (including nanopipes) and surface hillocks and pits (so called pinholes).

The density of the intrinsic point defects in GaN could be very high and they may significantly effect the physical properties of the material [32]. The common extended defects in GaN and related compounds are dislocations and stacking faults. Their structure being determined by crystallography is similar to that in other III~V and II-VI

62 Ch. 3 S. Ruvimov

' ( III

Fig. 10. Plan view TEM image of the GaN layer grown by MOVPE on (0001) sapphire substrate with AIN buffer layer.

compounds and, to some extent, to the defect structure in hexagonal close-packed (HCP) metals [41].

4.1. Dislocations and small angle grain boundaries

Both perfect and partial dislocations were observed in the GaN layer. [6-15] The are three major Burgers vectors of perfect dislocations are 1/3<1120>, <0001> and 1/3<1123> [41]. Typically, they correspond to edge, screw and mixed type of dislocations because the majority of dislocations in GaN epitaxial layers extend along the c-growth axis. The mixed dislocation with Burgers vector of 1/3 <1123> can be considered as a sum of the edge and screw dislocations with Burgers vectors of 1/3<1120> and <0001>. The majority of dislocations in GaN epitaxial layers are typically edge dislocations with Burgers vector of 1/3 <1120> (Fig. 10). The fraction of screw and mixed dislocations ranges from 5 to 40% depending on the growth conditions and buffer layer.

The threading dislocations of high density are typically arranged in small angle boundaries dividing crystalline layer into domains (Fig. 11) [10,11]. Depending on the type of threading dislocations the small angle boundaries may have tilt and twist components of misorientation. The diffraction analysis evidences that the majority of the threading dislocations are edge dislocations with b = a/3 <1120> lying in c-plane. Therefore, grains were mainly misoriented around the c-axis being almost perfectly oriented in the c-plane. As a result, a full width at half maximum (FWHM) for a symmetric (0002) X-ray rocking curve from the GaN layer is typically much smaller than the width of asynmietric X-ray rocking curve.


Fig. 11. Dissociation of threading dislocations in the GaN layer grown by MOVPE on (0001) sapphire substrate with AIN buffer layer (cross-sectional TEM image, dark field, weak beam). Fringe contrast is associated with stacking faults.

The_ Burgers vectors of partial dislocations are l /3<l l00>, 1/2<0001> or l/6<2203> [41]. The partial dislocations are associated with stacking faults. If the Burgers vector of the dislocation is lying in the plane of stacking fault the dislocation is Shockley partial. If the Burgers vector is perpendicular to the stacking fault plane the dislocation is Frank partial. Shockley partials are typically formed by a slip in the crystal while Frank partial require condensation of point defects and can move by a climb. Because the energy of a dislocation is proportional to the square of the Burgers vector magnitude it can be energetically favorable for perfect dislocations to dissociate into partials. Common reaction for the dislocation dissociation is 1/3 <1120> = 1 / 3 <1010> + 1/3<0110>. Such dissociation has been frequently observed in epitaxial layers in both basal and prism planes (see Fig. 12) [11,18].

4.2. Planar defects

The planar defects observed in GaN-based epitaxial structures include the grain boundaries and interfaces, stacking faults, inversion domain boundaries and micro-cracks.

4.2.1. Stacking faults Stacking faults are common defects in Ill-nitrides. Structure of stacking faults in wurtzite crystals was extensively studied by conventional electron microscopy about 30 years ago [42-44], in particular by the group of Dr. S. Amelinckx [42,43]. Recently, the planar defects in Ill-nitride crystals have been studied using advanced electron microscopy techniques (HREM, CBED, etc.) [12-15,29,30,45,46] and theoretical calculations [47-49] of their atomic structure. The majority of stacking faults in GaN is basal

64 Ch. 3 S. Ruvimov

Fig. 12. Small angle (dislocation) grain boundary in the GaN layer (plan view TEM image).

Table 1. Planar defects in GaN

Defect type

Basal SF, Ij Basal SF, h Basal SF, E Prismatic SF Stacking mismatch boundary Inversion domain boundary

p= l/3<liOO>;c = <0001>;

Plane

(0001) (0001) (0001) (1120) (1100) (1100)

I is inversion operation.

Displacement vector

P+V2C

P V2C V2P

p-hV2C I-hV2C

Energy (meV/A^)

1.1 [47] 2.5 [47] 3.9 [47] 72 [49] 105 [49] 25 [49]

Stacking faults (BSF) lying in a basal (0001) plane. The prismatic stacking faults (PSF) lying in (1120) and (1100) prism planes and inversion domain boundaries (IDB) with (1100) habit planes were also observed in the GaN layers. The characteristics of planar defects observed in GaN are summarized in Table 1.

A high density of basal stacking faults was typically observed in Ill-nitride epitaxial layers near the interface with the substrate [10-12,15]. There are three types (Ii, h and E) of basal stacking faults observed in GaN with one (b), two (c) and three (d) cubic bilayers, respectively (Fig. 13) [41]. Formation of BSFs in GaN can be considered as a wurtzite-sphalerite transition within a few atomic layers. Thus the stacking fault energy can be estimated based on bulk calculations for polytypes [47]. Ab initio calculations


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resulted in close energy values for the stacking faults [48]. SFs in GaN have lower energy than in InN and much lower than in AIN.

The energy of SFs in wurtzite Ill-nitrides, y, is roughly proportional to the number of cubic bilayers [47,48]: yn =l/2yi2 =l/3yE similar to that for hexagonal metals [41]. Among the basal stacking faults, the fault Ii has a lowest energy. It is also the one most frequently found in the MOVPE grown GaN [18]. However its formation requires the removal of a basal double GaN layer followed by slip of l/3<liOO>. Therefore, the fault II cannot be generated as a result of a strain relaxation, but must be growth related. This also applies to the extrinsic SF, E, which can be produced by inserting an extra plane. Stacking faults are bounded by partial dislocations being a part of faulted dislocation loop or end at internal interfaces (for example, at grain boundaries). The nature (vacancy or interstitial) of stacking fault can be determined by analyses of partial dislocations based on their high-resolution microscopy images or diffraction contrast. SFs in the AIN buffer and in the GaN epitaxial layers were found to result from both growth mistakes and movement of partial dislocations [18]. Stacking faults can also be formed by condensation of intrinsic point defects, vacancies or interstitials.

56 Ch. 3 S. Ruvimov

The fault 12 that contains two cubic layers (Fig. 13) has the second lowest energy. In contrast to the faults II and E, the fault 12 can be produced by a simple shear in a basal plane and hence, can result from strain relaxation in the growing layer. Another shear by I /3 < 1 iOO> in the adjacent basal plane would lead to the formation of a pair of two faults II separated by the layer of a wurtzite structure. This configuration appears to have even a lower energy than the fault 12 as it has been shown by ab initio calculations [48]. It has been suggested that this configuration is a new type of stacking faults. The multiple shearing in adjacent basal planes can produce a variety of faults II separated by different numbers of wurtzite layers. One can easily imagine that the n consequent shears in n adjacent basal planes would result in of two cubic layers (two faults II) separated by (n-1) wurtzite layers. Such process could be also a result of growth mistakes in conjunction with stress relaxation during the coalescence of the small islands at initial growth stages.

Based on the electronic structure of stacking faults derived from the ab initio calculations Stampf et al. [48] have concluded that stacking faults can lead to luminescence transition acting like a quantum well of cubic material embedded in wurtzite matrix. A similar model has been earlier proposed by Albrecht et al. [49] who observed that GaN samples with a high density of stacking faults exhibit a luminescence line at 3.40 eV.

Prismatic stacking faults lying either in {1100} or {1120} crystallographic planes were occasionally observed in GaN grown on SiC and sapphire substrates. The {lIOO} fault is also called as stacking mismatch boundary because its formation has been linked to the atomic steps at the substrate surface [49]. These faults could be a part of closed faulted domains in the GaN layer with a low energy SF II in a basal plane or may propagate through the entire layer. Such closed domains have been earlier reported for other wurtzite crystals [42,44]. The formation energy of the {1120} prismatic SF is less than that of {1100} fault (see Table 1). They also differ by their displacement vectors. The {1120} fault has extra shear by l /6<l l00> so its displacement vector is equal to R = l/3<liOO> -h l /6<l i00> = l /2<l i00> according to Drum (Fig. 14) [44]_. Fig. 15 shows the experimental high resolution electron microscopy images of the {1120} stacking fault that was found in GaN layer grown by MBE on sapphire substrate. Inserted is the simulated high-resolution image based on the Drum's model [44].

4.2.2. Inversion domain boundaries The inversion domain boundaries (IDBs) are typical defects for non-centrosymmetric crystals. The IDBs lying on {1100} planes (Figs. 16 and 17) seem to be even more common defects in the GaN epitaxial layers as compared to prismatic SFs because their energy is much lower than the energy of prismatic SFs (see Table 1) [49]. The most stable structure of IDB involves the shear by 1/2<0001> in the {1100} habit plane (see Fig. 18). The extra shear in c-direction compared to the classical IDB model removes the wrong bonding between Ga and N atoms at the boundary plane [49]. This shear significantly reduces the boundary energy. Because IDB in the basal plane would have a very high energy these defects usually propagate through the entire layer from the substrate [21]. Typically, the inversion domains in the GaN layers are hexagonal prim bounded by {1100} crystallographic planes, but the closed domains at the sapphire interface were also reported. IDBs were observed in the GaN layers grown by both MOVPE and MBE growth techniques on the SiC and sapphire substrates. The formation


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of IDBs was linked to the surface chemistry of the sapphire, which could be terminated either by aluminum or oxygen [10]. Consequently, the GaN may start to grow either with a gallium or nitrogen layer. Although this model simplifies the real process, it gives an idea of possible alternating of polarity of the growing layer. Because the sapphire substrate is usually exposed to the nitrogen prior to the deposition of the buffer layer, the formation of a thin AIN layer at the interface with sapphire substrate is expected even in the case of GaN buffer layer. Depending on the conditions for the nitridation and deposition of the buffer layer, this AIN interfacial layer may have small domains with opposite polarity giving rise for IDE formation.

IVlore often IDBs were found in the GaN layers grown by MBE on sapphire substrates [21]. Dislocations were often lying within IDBs, which form prism-shaped domains of 15-30 nm in diameter (Fig. 16) bounded by the {1100} planes. Dislocations and IDBs originated at the interface with sapphire and propagated up to the layer surface. Some of dislocations form half loops at the interface and don not propagate further into the GaN layer.

68 Ch. 3 S. Ruvimov

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Fig. 16. Inversion domains in GaN grown by MBE on (0001) sapphire substrate with LT GaN buffer layer (plan view TEM image).

Defect engineering in Ill-nitrides epitaxial systems Ch, 3 69

Fig. 17. Inversion domains in GaN grown by MBE on (0001) sapphire substrate with LT GaN buffer layer (cross-sectional HREM image).

The GaN/sapphire interface on the image of Fig. 17 is almost atomically abrupt, but contains the steps of about 1-2 monolayer height. The formation of IDBs was often associated with specific defects at the interface with a substrate. A white contrast often appears under the IDBs (Fig. 17) suggesting that AIN might locally change the polarity and might give rise for the formation of IDBs. IDBs are likely to originate at earlier growth stages, during or just after the buffer layer deposition. IDBs were observed in the GaN buffer layer before and after the high temperature ramp/anneal. Prior to annealing, the buffer layer often contained a fraction of cubic phase (not shown) that transforms

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into hexagonal structure during the high temperature ramp/anneal. Fig. 19 shows a typical HREM image of IDB in the GaN layer.

4.2.3. Microcracks The microcracks were usually observed as a result of a stress relaxation during the post-growth cooling or annealing. The cracking typically occur in the samples which were under the tensile residual stress after the growth, i.e. primarily in the GaN layers grown on SiC substrate. The cracks usually start at the epilayer-substrate interface and propagate in vertical directions parallel to [1100] crystallographic planes. In some cases, the cracks propagate in the horizontal directions resulting in pilling the layer off the substrate. The cracks typically originate at certain areas of a higher stress such as Ga-rich micro-inclusions. The networks of the microcracks were also observed at sample edges.

4.3. Nanotubes and pinholes in the GaN

Nanopipes or nanotubes are hollow tube-shaped defects often observed in the GaN crystals (Fig. 20) [15,51-53]. They are typically oriented along the [0001] growth direction and often associated with the dislocations. The nanotubes are generally hexagonal and often exhibit a nail-like or funnel-like shape with its wider crater at the top. If the nanotube is close to the surface of GaN layer its wider crater usually ends at the GaN free surface. The crater is either hexagonal or circular. The nano-tubes ended at free surface were also called pinholes. Both defects are openings in the material. The openings in the GaN layer can also be as large as a few microns and propagate through entire epitaxial layer from the substrate. The nature and the formation mechanism of these defects were discussed by a number of researches [15,51-53].


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Similar defects, called micropipes, were previously observed in 6H silicon carbide that also has a wurtzite structure [53]. While the effect of nanotubes on the electrical properties of GaN is still under discussion, the micropipes in SiC are known to degrade the properties of SiC-based diodes. The quality of SiC crystals can be significantly improved by seaUng the micropipes or growing micropipe-free material.

In contrast to GaN, where the nanotubes usually are a few nanometers in diameter, the diameter of hollow tubes in SiC ranges from a few ten nanometers to several ten micrometers. While the nanotube in the GaN are typically a few nanometers long, the micropipes in SiC can penetrate the whole crystal. It is interesting to note that micropipes often occur in the materials showing polytypism, i.e. a superlattice stacking with a large period. In most cases the axis of micropipe is parallel to the polytype direction. Although GaN typically grows with either cubic or wurtzite structure, it may potentially show polytypism under certain growth conditions.

Because the micropipes in SiC were often observed at the centers of growth spirals

72 Ch. 3 S. Ruvimov

Fig. 20. Nanotubes in the GaN (cross-sectional HREM images in [1120] projection).

which are typically associated with screw dislocations, the micropipes were interpreted as open core *giant' screw dislocations [15,51,53] in accordance with Frank's theory [54]. The existence of hollow core dislocation is based on the assumption that the total energy associated with dislocation can be reduced by removal of the material at the dislocation core. Frank derived a relationship between Burgers vector b of the dislocation and the hollow core radius ro assuming that the reduction of the dislocation energy compensates the formation energy of the internal surface of the hollow core. This would give the following expression for the equilibrium radius for a stable micropipe:

r = ixbVSTT Y

where |x and y denote the shear modulus and the surface energy, respectively.

(1)


The attempts to estimate the surface energy of the hollow core, based on the expression (1) and known values of the shear modulus of the material, Burgers vector of dislocation, and the diameter of the micro-tube, give very low values and lead to contradictory results [52].

The fact that the nano-tubes may exist in the GaN crystal without any dislocation indicates that their formation results from the depressions in the growth surface rather than stress relaxation by opening the dislocation core. The dislocation may or may not be further attracted by the hollow tube that could stabilize it during the growth. The dislocations could also cause depressions in the growth surface and, hence, provoke the formation of hollow tubes. Recent ab initio calculations of energy of the dislocations in GaN based on local-density functional cluster method and a density functional tight binding method evidence the possible existence of a open core for screw dislocation in the GaN crystal. The estimated equilibrium diameter of the open core is about 0.72 nm. In contrast to screw dislocations, the edge dislocations in the GaN did not show any energy gain by opening their cores and, thus, should exist with a full core. This result supports the growth-related model for the nanotube formation in the GaN.

It is interesting that the threading dislocations in the GaN, both screw and edge ones, seem to be electrically inactive [55]. However, the dislocation stress fields seem to be large enough to trap the impurities and intrinsic defects during the growth. For example, trapping the Ga vacancy O complex by dislocations may give rise for the Yellow luminescence in the n-type GaN.

Pinholes at GaN layer surfaces were observed in almost all samples while nanopipes were mostly observed in GaN:Mg layers. The density of pinholes was found to increase with doping and impurity concentration in the layer (in particular, oxygen). Both pinholes and nanopipes were often associated with threading dislocations, but some were formed inside the GaN layer, far from dislocations. This observation suggests that both types of defects related to a local instability of growth possibly caused by impurity segregation on the growth front. Such segregation is often associated with dislocations, which explains the frequent attachment of nanopipes to dislocations. The density of pinholes was also found to be much lower in samples grown on SiC compared with the samples grown on sapphire. This observation supports an idea that pinhole density correlates with impurity level (in particular with oxygen concentration) in the GaN layer [52].

5. Conclusions

In conclusion, defect generation and annihilation were shown to be mainly growth-related processes. Because of the very low dislocation mobility in the GaN, the high misfit stress relaxes mainly at earlier growth stages resulting in the high defect density at the interface with the substrate. On the other hand, the low dislocation mobility is favorable for long lifetime of the GaN-based opto-electronic devices.

The majority of defects are generated at the interfaces with the substrate and the buffer layer. The dislocation annihilation also occurs mainly in the buffer layer and in the area close to it by the lateral overgrowth of some grains over the others. The proper preparation of substrate surface and optimization of the buffer layer enhancing

74 Ch. 3 S. Ruvimov

the lateral overgrowth is essential for the reduction of the defects in the GaN layer. The structural quality of the GaN layer can be controlled by the growth conditions, especially during the first growth stages.

Acknowledgements

This work was partly supported by the Director, Office of Energy Research, U.S. Department of Energy under Contract No. DE-AC03-76SF00098 and partly by BMDO (Dr. K. Wu) monitored by the US Army Space and Strategic Defense Command. The author is greatly thankful to Dr. Z. Liliental-Weber for the pleasure of working in her group at LBNL. The use of the facilities at National Center for Electron Microscopy and assistance of W. Swider for sample preparation are appreciated. The author wants to thank Dr. H. Amano, Dr. I. Akasaki, Dr. S. Nakamura, Dr. Y. Yang, Dr. J. Baranowski, Dr. T. Suski, Dr. B. McDermott, and Dr. J. Redwing for providing the GaN samples, and Dr. Z. Liliental-Weber, Dr. E.R. Weber, Dr. J.W. Ager III, and Dr. J. Washburn for the fruitful discussions.

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Sugimoto, T. Kozaki, H. Unemoto, M. Sano, K. Chocho, Appl. Phys. Lett. 72 (1998). [25] T.S. Zeleva, O.-H. Nam, M. Bremser and R.F. Davis, Appl. Phys. Lett. 71, 2472 (1997). [26] O.-H. Nam, M. Bremser, T.S. Zeleva and R.F. Davis, Appl. Phys. Lett. 71, 2638 (1997). [27] I. Akasaki, et al. J. Crystal Growth 98, 209 (1989). [28] A. Gassmann, T. Suski, N. Newman, Ch. Kisielowski, E. Jones, E.R. Weber, Z. Liliental-Weber, M.

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Gassmann, X. Liu, L. Schloss, E.R. Weber, L Grzegory, M. Bockowski, J. Jun, T. Suski, K. Pakula, J. Baranowski, S. Porowski, H. Amano, I. Akasaki and W. Imler, Mat. Res. Soc. Symp. Proc. 395, 351 (1996).

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CHAPTER 4

Magnetic resonance studies of defects in GaN and related compounds

M. Palczewska and M. Kamiriska

1. Introduction

Magnetic resonance is a very useful technique of solid state investigation. The term 'magnetic resonance' means: resonance absorption of electromagnetic radiation at microwave (radiofrequency) range, by paramagnetic defect center present in investigated crystal, with magnetic field of values characteristic for the center applied as well. Basic advantage of wide family of methods based on the magnetic resonance is that they provide information about microscopic nature of paramagnetic defects. Simultaneously, the sensitivity of magnetic resonance methods is much higher than that of most other techniques leading to understand a microscopic picture of investigated centers.

The very classical magnetic resonance method is electron spin resonance (ESR), which has been developing very rapidly since 1945, the moment of discovery of this resonance [1]. ESR means resonant absorption of microwave power by electronic levels of magnetic ion or defect, in applied magnetic field. These electronic levels originate from the ground state of magnetic center, splitted by Zeeman effect. ESR experiments are performed in order to determine the nature, symmetry and environment of paramagnetic defects in crystals. They have been successfully used for many years to study defects in different semiconductors [2-7], providing considerable information about the ground states of paramagnetic centers introduced intentionally, as well as present as unintentional contamination. In ESR, sensitivities even of the order of 10 ^ spins (ions) can be achieved in some cases.

The other magnetic resonance technique, called optically detected magnetic resonance (ODMR), allows studying excited states of defects. It can essentially provide similar information about investigated defects as ESR technique, i.e. determine their nature and symmetry. The idea of ODMR experiment consists in detection of emission changes due to microwave absorption at the excited states in applied magnetic field. Samples are irradiated with light that causes emission, and are subject to microwave radiation. In such an arrangement, magnetic resonance of defects in excited state can lead to changes in emission intensity. Increase or decrease of sample irradiation intensity is viewed either in polarized light or as changes of total emission.

ODMR technique has been successfully used to study defects in different semiconductors, like II-VI, III-V, amorphous Si [8].

In general, the analysis of ESR or ODMR spectra is the same and can provide similar information about defect center. However, in the case of ODMR the line widths are

78 Ch. 4 M, Palczewska and M. Kaminska

typically substantially broader than in ESR spectra. Therefore, the determination of resonance parameters is more difficult and less accurate from ODMR spectra. On the other hand, the great advantage of optical method is its sensitivity, which increases to about three orders of magnitude over conventional ESR. Another advantage of ODMR is the possibility of directly linking a resonance with a particular emission process [8].

Another magnetic resonance technique is electrically detected magnetic resonance (EDMR). In analogy to ODMR, in EDMR method the magnetic resonance is observed through spin dependent electrical properties (optical in ODMR) of sample. Such measurements give great enhancement in sensitivity in comparison with ESR as well as they allow to observe centers participating in electrical processes, not necessary paramagnetic under thermal equilibrium conditions [9]. EDMR studies have been mainly performed on devices, especially in case of GaN-based materials. The results of EDMR experiments on GaN-based devices are not a subject of this article and can be found elsewhere [10].

Both ESR and ODMR methods have been applied for investigations of defects in nitride compounds. However, the number of identified centers is up to now much lower than for silicon, GaAs or other III-V compounds. The main problem deterring magnetic resonance studies of nitrides is lack of proper samples. Bulk material, which is the most convenient for such studies, is very difficult to obtain because of huge technological problems.

In the presented chapter a review of magnetic resonance studies of defects in nitrides is given. Results of research performed by different scientific groups are summarized. The investigated crystals were grown by different techniques: bulk material by high pressure method [11], epitaxial layers by Molecular Organic Chemical Vapor Deposition (MOCVD) [12] and microcrystalline powder by ammonothermal method [13].

At the beginning, the idea of magnetic resonance technique and the ways of its realization are given. This is followed by the description of crystal structure of nitrides. In Section 4 resonance studies of different kinds of defects in GaN, and in Section 5 in AIN and BN are presented and discussed. The short summary is given in Section 6.

2. The resonance technique

2.1. The spin Hamiltonian

Electron spin resonance involves the resonant absorption of electromagnetic radiation by unpaired electrons in magnetic field. Consider, for example, a single free electron of mass mo having spin S = 1/2 and a magnetic moment \\L\ = ms-g-P, where P = eh/4TtmoC is the Bohr magneton. In the absence of magnetic field, magnetic moment of this electron is randomly directed. Application of magnetic field Ho removes spin degeneracy, and electron magnetic moment \L fines up parallelly (ms = -1 /2) or anfiparallelly (ms = +1/2) to the magnetic field. The energy levels corresponding to these two magnetic moment orientations are Zeeman levels of energies Ei,2 = msgPHo, where g is a dimensionless constant that determines the magnetic moment (it is equal to 2.0023 for free electron). Irradiation of such a system with photons of energy hv equal to the difference E2 — Ei = gPHo excites electron from a lower level to an upper one

Magnetic resonance studies of defects in GaN and related compounds Ch, 4

(a) (b)

m., = +1/2

79

Fig. 1. Zeeman (a) and hyperfine (b) splitting of electron levels in magnetic field. Possible resonance absorption transitions and respective spectra are shown.

and resonant absorption of radiation is observed (see Fig. 1). For a g value of 2 and a magnetic field HQ = 330 mT, the resonance frequency is about 10 GHz. Then, resonance transitions may occur as a result of absorption of about 1 cm~^ energy.

Atoms or ions having unpaired number of valence electrons are of non-zero angular momentum and possess a permanent magnetic dipole moment. Unpaired electron systems can exist also in semiconducting crystals. Such electrons may be localized in a vicinity of point defects, such as impurity atoms or native defects, as well as they may exist as highly delocalized electrons in conduction or impurity bands. Their presence in semiconductors can be detected by means of ESR technique. On the basis of ESR data, such as a number of resonance lines, their positions and angular dependencies, there is possibility to determine chemical nature of magnetic defects, their charge state and local symmetry of lattice site they occupy.

Unpaired electrons in a crystal structure are subject to many different interactions. These interactions involve: coupling of orbital and spin motion, the Zeeman interaction with an external magnetic field, interaction with the electric field of neighboring ions (crystal field), interaction with magnetic moments of their own and nearby nuclei, etc. Generally, theoretical description of unpaired electrons interactions in a magnetic field is rather complex, therefore spin Hamiltonian method is commonly used [14-17]. In this approximation only transitions within a small group of the lowest energy levels, populated with electrons at room or lower temperature, are considered. The higher energy levels are typically so distant (often above some hundreds to thousands of wave number) that their interaction with the lower ground levels may be neglected. Therefore, it is possible to regard these ground states as an isolated set of levels and to describe their magnetic properties without reference to states laying higher in energy scale.

80 Ch. 4 M. Palczewska and M. Kaminska

The problem of finding the ground states for an ion with unpaired electrons (magnetic ion) in a crystal lattice is usually solved in two steps. Firstly, the ground energy level of free ion is determined and secondly, its modification by interaction with surrounding ions (called ligand ions) in a crystal structure is considered. The simplest description of such modification is known as the crystal field approximation. In this approximation it is assumed that neighboring ions interact with the central magnetic one entirely through electric field produced at the magnetic ion site. The ligand ions give rise to a crystal field potential that reflects the local symmetry of the magnetic ion environment. This results in a level splitting for the unpaired electrons corresponding to a Stark effect. The nature of this splitting, its magnitude and level multiplicity, depends mainly on a symmetry of magnetic ion's surroundings. Typically, this crystal field splitting is of an order of 10^ cm~^ In some cases, as for instance of the rare earth (RE) ions, the unpaired electrons in the 4f shell are screened by electrons of closed 5s and 5p shells. This weakens the crystal field influence on RE ions, and leads to crystal field splitting of about 10-100 cm~^

Ions in crystal structure are arranged in a regular manner, and specific magnetic ions may occupy strictly determined site or sites in a crystal lattice. Therefore, each magnetic ion occupying the same type of lattice site is surrounded by an identical group of neighboring ions, what means that each such magnetic ion is located at lattice site of the same local symmetry. However, in some cases the local site symmetries of magnetic ions are the same, but corresponding local systems of coordinates for these ions have different orientation in crystal lattice. Some elements of crystal symmetry are necessary to transform these local systems of coordinates into each other. In such a case the given external magnetic field can have different angles with coordinate axis pinned to specific magnetic ion sites, and it is a reason why such sites are named magnetically inequivalent. Though the symmetry of the ion surroundings is determined by all ions creating the crystal structure, in practice the crystal field at magnetic ion sites is determined largely by the nearest neighbor ions. Therefore, usually only these ions are considered when a site symmetry is described.

In many cases, magnetic ions as well as surrounding ligand ions have non-zero nuclear spins. Therefore, the interaction of nuclear and electron magnetic moments leads to additional splitting of energy levels of unpaired electron system. As a result, splitting of a single resonance line into few components can be also observed in ESR spectra. This additional resonance line structure is called a hyperfine structure when electron spin interacts with its own nucleus spin, and a superhyperfine structure when it interacts with surrounding ligand nucleus spins.

The general form of a spin Hamiltonian can be written as [14]:

/f = P H g . S + S . D . S + S . A . I - P N H g N l + I Q I , (1)

where the first term describes the interaction between the effective electron spin S and applied magnetic field H, the second one is related to the zero field splitting caused by crystal field or spin-spin interactions, the third one refers to magnetic hyperfine and superhyperfine interactions of electron spin S with nuclear spin I, the fourth and fifth terms describe the Zeeman interaction of nuclear spin I and the nuclear electric quadrupole interaction, respectively. The last two terms have been neglected up to

Magnetic resonance studies of defects in GaN and related compounds Ch. 4 81

now for all known paramagnetic defects of GaN, In general case g, D, A, gN and Q are the tensors which couple the indicated vectors. The independent elements of the coupling tensors are the coefficients of the independent terms in the spin Hamiltonian. In the majority of cases a suitable choice of coordinate axes (known as principal axes) eliminates the number of independent tensor elements to not more than three. The form of the spin Hamiltonian in any particular case depends on symmetry.

In cubic crystal field the first three terms of the spin Hamiltonian are isotropic in the case of S < 2.

For S = 5/2 and cubic crystal field the spin Hamiltonian takes the form [15,16]:

i^, = P . H • g • S + l/6a[S^ + S^ 4- S^ - 1/5S(S + IK3S^ + 3S - 1)] + S • A • I,

(2)

where parameter a characterize the cubic crystal field and ^, T) and ? refer to the cubic axes. For the case where axial (Csv) symmetry with distinguishing z-axis holds it is necessary to add two axial terms to Eq. 2, the terms with parameters D and F which characterize axial component of crystal field. The form of such complete spin Hamiltonian is eventually the following [15,16]:

/ / = H, + D [ S ^ - 1 / 3 S . ( S + 1)]

+1/180F [35S^ - 30S(S + 1)S^ + 25S^ - 6S(S + 1) + 38^(8 + 1)^], (3)

where the z-axis of the axial terms may not coincide with any of the cubic axes used to describe cubic component of crystal field in Eq. 2. For 8 = 1/2 both axial terms in Eq. 3 are equal to zero, whereas for 8 > 1 and for 8 > 2 the first and second axial terms in Eq. 3 differ from zero, respectively.

When the symmetry of the magnetic ion site is axial, the symmetry of g tensor should also be axial. For z-axis parallel to c-axis of crystal field the gz = g , gx = gy = g± and generally g 7 gj_. Therefore, the spin Hamiltonian describing the Zeeman interaction with magnetic field for axial symmetry may be written as [15,16]:

p . H . g . S = p • (g Hz8z + gxHx8, + g^Hy8y), (4)

Similarly, the spin Hamiltonian describing hyperfine interaction for axial symmetry may be written as [15,16]:

S • A • I = A 8zlz + Aj.8xlx + Aj.8yly. (5)

From the above it is evident that in case of axial crystal field and 8 = 1/2 the spin Hamiltonian may be written as a sum of Eqs. 4 and 5.

All elements forming group III nitrides have non-zero nuclear spins and quite large magnetic moments (see Table 1). Therefore, the hyperfine interactions in these compounds results in splitting or broadening of resonance lines (Fig. 1). So far, the superhyperfine interaction of unpaired electrons in GaN has not been visible in E8R spectra.

The crystal field approach to resonance problems, described above, may be successfully used for many impurity atoms or native defects, for which the unpaired electrons are localized in the inmiediate vicinity of the lattice site occupied by them. In contrast to


Table 1. Nuclear properties of elements creating group III nitrides

Nucleus

lOg

i iB 27 Al ^^Ga 7^Ga ''Hn ''Hn 14N

Natural abundance (%)

19.8 80.2 100 60.1 39.9 4.3

95.7 99.63

Nuclear spin

3 3/2 5/2 3/2 3/2 9/2 9/2

1

Magnetic moment PN

1.8006 2.6880 3.6385 2.0108 2.5549 5.4960 5.5072

0.40357

Electric quadrupole moment (|e|-10-24 cm^)

0.086 0.040 0.150 0.168 0.106 0.846 0.861

0.0193

these deep centers, there is another group of defects — so-called shallow impurities, for which electron density is strongly delocalized, and energy levels are very close to the band gap edges. Shallow impurities generally contribute to extra carriers, electrons or holes, in semiconducting crystals. The resonance properties of the unlocalized carriers are determined largely by the energy band structure of the host lattice [4].

Non-localized electrons may exist either in the conduction band or in an impurity band. The latter is formed by overlapping of donor wave functions at high defect concentration. The detailed calculation of the band structure in semiconductors is not simple, therefore semiempirical approximation, namely the k p perturbation theory, have been developed [18,19]. It allows to obtain the expressions for energies and wave functions of conduction electrons in the vicinity of a semiconductor band extremum.

According to theoretical predictions based on the k p calculation in frame of five-band model for a cubic direct-gap semiconductors, the g value of conduction band is given by the expression (3) in [20], which after some simple transformations may be written in the following form:

A _ 1 = _ ^ ( ^0 . A- \ go 3 VEîEo + Ao) (£ ; - Eo){E'^ - Eo - A'^) J ' ^

where go is the free electron g value equal to 2.0023. The meaning of the rest of the symbols used in Eq. 6 can be easily read from Fig. 2, in which the band structure at F point for a cubic direct-gap semiconductor, limited to energy bands involved in the five band k p calculations, is schematically shown. In agreement with notation in Fig. 2, Eo is the r^ - r^ gap, Ao is the valence-band spin-orbit splitting (AQ = F^ - Vj), AQ is the conduction-band spin-orbit splitting (AQ = F^ - F^), EQ is the F^ - F^ gap. The energies origin is taken at the top of F^ band. The energies P^ and ?'^ = X^P^ describe couplings of the conduction band with the valence band or the upper conduction bands, respectively.

For wide band-gap crystals, the spin-orbit splittings AQ and AQ are much smaller than the energy gap EQ. Therefore, they may be neglected in the denominators of Eq. 6, which becomes simplified to:


Fig. 2. Schematics of the energy bands structure near F point in a cubic direct-band semiconductor. Only energy bands involved in the five band k-p calculations of the conduction electrons g value are shown.

For wurtzite type crystals, like GaN, the procedure described above, leading to Eq. 7, allows to compare theoretically predicted g value of unpaired electrons only with average g value derived from ESR measurements. Moreover, merely few parameters (Eo, EQ and AQ) present in Eqs. 6 and 7 have been determined experimentally for GaN crystals. Values of the remaining parameters ( AQ, P^ and X) may be only estimated from comparison with the respective parameters of other semiconducting compounds.

In a case of shallow acceptors, their resonance properties are determined mainly by the valence band structure. In cubic A^B^ compounds the spin-orbit interaction leads to the splitting of the valence band into three bands. Two of them, the light-hole band Eg and heavy-hole band T\, are degenerated at k = 0, and marked as T\ in Fig. 2. The third one, Fy band lies AQ below the Fg bands (see Fig. 2). Therefore, a hole ground state at k = 0 is fourfold degenerated (including spin) and it may be described by total angular momentum J = 3/2. The degeneration of the valence band at k = 0 is related to the symmetry of the lattice structure, and it may be lifted (except for spin) by applying uniaxial stress. The resonance transitions between Zeeman splitted levels of two doublets are then possible. Real crystals are commonly strained, what leads to spontaneous lifting of the valence band degeneration. However, randomness of the intemal stress directions causes broadening of the ESR lines [4,5], and magnetic resonance signals are difficult to be detected.

An axial component of the wurtzite crystal structure splits the valence band, lifting its degeneracy at k = 0. This splitting, generally much higher than induced by random strain, makes the observation of a hole state resonance transitions possible. The uppermost valence band has F9 symmetry and two lower bands transform as F7 [21]. For a hole being lighdy bound to a shallow acceptor, the predicted values of g factor are highly anisotropic: g (F9) = 4.0 and gi. = 0 [22]. Reduction of g (F9) value.


experimentally observed in some cases [22], was assigned to partial hole localization. The gj. = 0 value is recognized as a fingerprint of an effective mass-like acceptor [22].

2.2. Experimental technique

In this part, only brief description of magnetic resonance techniques is given, especially with intention of helping readers not familiar with such experimental methods. For deeper understanding, and in order to get more details it is recommended to look into monographs on ESR [4,14-17,23] or ODMR [8,24] methods and results of studies on defects performed by use of them [2-8,25].

As mentioned above (Section 2.1), in ESR experiment the resonance absorption of electromagnetic radiation causes electron transitions between energy levels to split in magnetic field. From simple resonance condition (Section 2.1) it follows, that higher radiation frequency requires higher magnetic fields. Generally, it is possible to use any frequency in ESR experiment. However, at lower frequencies sensitivity of ESR method decreases, and also the corresponding resonance magnetic field may become comparable with the field at electron place caused by surrounding nuclei with nonzero magnetic moments. Therefore, typically used microwave frequencies are of about 10 GHz (X-band), 23 GHz (K-band), 35 GHz (Q-band) and recently also of about 100 GHz (D-band). Usually microwave sources can only be tuned within a very narrow range of frequencies, so the resonance conditions in ESR experiment are conmionly met by varying the magnetic field.

Investigated samples are placed in a microwave cavity, where standing microwaves may be created in order to enhance the magnetic field amplitude Hi of the microwave radiation. The magnification factor of the unloaded cavity is defined as [15]:

ITTVQX (mean stored energy)

power dissipated in cavity

Typical values of Qo-factor are of the order of about 5 x 10^. Introduction of any sample to a cavity causes increase of power loss, even out of resonance. This power loss clearly results in a loss of sensitivity due to a decrease of cavity Q-factor. Frequently, using small size samples (in comparison with the cavity dimensions) may minimize this problem. Sometimes the specific loss of the sample itself is large (e.g. metallic samples) and in such case the substantial loss of sensitivity is difficult to avoid.

During ESR experiment, microwave source is tuned to resonant frequency (VQ) of the applied cavity, and this frequency is kept constant while the magnetic field is varied. For the magnetic field meeting resonance condition, microwave power is absorbed by unpaired spins, which leads to a decrease of the cavity Q-factor. This can be described by the imaginary (absorptive) part x" of the sample magnetic susceptibility. On the other hand, the resonant frequency of the cavity changes when the magnetic field is tuned through the sample resonance condition, allowing an evaluation of the real (dispersive) part x' of the magnetic susceptibility. Both methods of resonance observation: changes in cavity Q-factor {x''W\) or changes in cavity frequency ix'î) may be used, depending on the way of the microwave circuit is adjusted. The first approach is usually preferred.


In most cases in ESR experiments, high sensitivity and good resolution are achieved by means of so-called phase-sensitive detection, associated with appropriate magnetic field modulation. In such a method, high frequency modulation is applied (typically 100 kHz) to magnetic field slowly changing across the absorption line, causing the magnetic field to oscillate around the mean instantaneous value. The receiver is only sensitive to signals of the same frequency and phase as the high frequency magnetic field modulation, and any signals that do not meet these requirements are suppressed, leading to improve sensitivity. Such detection method permits the recording of the derivative of the microwave power absorption with respect to the magnetic field, and thereby improves the resonance line resolution. It is especially useful when the separation between absorption lines is of the order of the line widths.

At resonance, transitions between the two electron levels occur in both directions: upwards caused by energy absorption and downwards accompanied by energy emission. Thus, under thermal equilibrium conditions, for much lower electron population at higher energy level, upward transitions prevail, and it results ii;i microwave energy absorption. However, when electrons remain sufficiiehtly long time at the excited level, such situation leads to saturation of microwave absorption and therefore magnetic spins can absorb no more power. /

It is obvious, that for ESR method it is useful when the resonance lines are narrow, because it helps to detect ESR active centers as well as increases sensitivity of the method. In ESR experiments a line broadening may be caused by many different processes such as: dipolar spin-spin and exchange interactions, unresolved hyperfine and superhyperfine structures, inhomogenity in the crystal structure and poor uniformity of the applied magnetic field. Only the last contribution to the line broadening is controllable, and may be decreased through high uniformity of the magnet gap field. The remaining contributions are caused by nature of crystal and defects under examination themselves and cannot be avoided.

In real crystals, electron spins may also interact with lattice vibrations (phonons) what allows them to lose energy by non-radiative processes, characterized by spin-lattice relaxation time Ti. From Heisenberg's uncertainty principle it follows that shorter lifetime leads to larger energy uncertainty and as a consequence wider resonance lines. Therefore, many ESR experiments, especially for semiconductors, are performed at low temperatures in order to diminish interactions with lattice as well as to reduce the undesired electrical conductivity of some semiconductors. This results in longer relaxation time Ti and narrower resonance lines. On the other hand, however, electrons remaining longer at excited level may cause saturation, which leads to reductions of the observable signal and distorts the absorption shape. In some cases decrease of microwave power level allows to avoid problems with the signal saturation.

In ODMR experiment, resonance transitions are observed through their influence on luminescence processes in crystals. Similarly to a conventional ESR technique, in ODMR experiment sample is placed in a cavity resonator, in uniform magnetic field. The resonator walls must provide possibility to excite the sample with a laser beam, and to get the emission light back with minimal degradation of the microwave performance. The incident microwave power is switched on and off with audio frequency (100 Hz to 5 kHz), and a lock-in amplifier is used to detect any changes in the emission properties


that are induced when the magnetic field is adjusted for resonance during its slow sweep through the appropriate range. Similarly as in ESR experiment, ODMR measurements are usually performed at low temperatures.

3. Nitride crystals

The group III nitride crystals can exist in two basic structures: wurtzite and zincblende. The nearest neighbors of each atom, group III metal as well as nitrogen, create exactly the same surroundings in both structures. Each metal atom is enclosed in tetrahedron of four N atoms, and each N atom is enclosed in tetrahedron of four metal atoms. The difference between wurtzite and zincblende structures consists only in different stacking sequence of tetrahedral bounded group III metal-nitrogen bilayers. As a result, the local atomic environments are nearly identical, while the overall synunetry of the hole crystal is determined by the stacking periodicity.

This difference can best be visible when one looks at the nitride crystal along a chemical bond direction: [111] in the case of zincblende structure or equivalently [0001] (c-axis) in the case of wurtzite one. As it is shown in Fig. 3, for wurtzite structure (Fig. 3b) the three nearest neighbors of metal atom, located at one end of this bond, are aligned with the three nearest neighbors of nitrogen atom placed at the opposite end of the bond. Differently, in the zincblende structure (Fig. 3a) the three nearest neighbors of metal atom are rotated by 60° in relation to the three nearest neighbors of nitrogen atom.

Let us now compare two possible adjacent positions of an impurity atom substituting for one of components of nitride compound (in Fig. 4 one can trace it for an impurity atom substituting for Ga atom). In the zincblende structure, such two lattice positions are equivalent. In the wurtzite structure, rotation by 60° around [0001] direction for an impurity atom, placed at one of the sites together with its four nearest neighbors, is necessary in order to make it crystalographically equivalent to an impurity atom placed at the second site. These two sites are magnetically distinguishable for ions with electron spin above 3/2. In the mathematical formalism of spin Hamiltonian, distinction between

{111}

{0001}

Fig. 3. Bonding between metal III and nitrogen atoms in adjacent planes for zincblende (a) and wurtzite (b) structures. The three tetrahedral bonds are 60° rotated in zincblende structure and they are aligned with each other in wurtzite structure.


O Ga • N

(a) (b) Fig. 4. The zincblende (a) and wurtzite (b) structures.

these two types of sites in the wurtzite structure is described by connection of each site with its own set of cubic axes (see Section 2.1, Eqs. 2 and 3).

So far, all existing experimental results indicate that transition metal impurities substitute for the Ga ion in GaN structure and the angular dependencies of their resonance lines display the synmietry of the substitutional site.

Gallium nitride and aluminum nitride crystals, grown by different techniques, are mostly of the wurtzite structure, although zincblende crystals can be obtained by epitaxial growth on silicon or gallium arsenic substrates under special conditions. For boron nitride a stable phase has the zincblende structure.

4. Resonance studies

4.1. Shallow donors

As-grown undoped GaN epitaxial thin films, as well as single bulk crystals, are conmionly n-type conductive with the concentration of electrons ranging typically from 10^ to a few times 10 ^ cm~^ The residual donor has not been positively identified up to now, and defects of either intrinsic or extrinsic origin have been proposed as the source of high free carrier concentrations. For many years, the n-type conductivity of GaN has been commonly associated with presence of nitrogen vacancy [26,27], because of typical gallium-rich growth conditions of GaN. However, residual oxygen [28] and silicon [29] have also been proposed as prime candidates. Both silicon and oxygen contamination are difficult to avoid. Moreover, silicon has been commonly used as the intentional donor dopant and free electron concentration up to the 10^ cm~^ range has been achieved [30].

One of technique, which could shine some light at the origin of dominant shallow donor defect in GaN, is ESR. First results of GaN studies by means of ESR measurement were published in 1993 for wurtzite [31] and zincblende [32] type structures.


In [31] authors measured unintentionally doped thin GaN films of wurtzite structure, with carrier concentrations <2 x 10 ^ cm"^, grown on sapphire substrates by low-pressure metal-organic chemical-vapor deposition (LP MOCVD) method. The only resonance signal which was clearly attributable to the GaN film, and not to sapphire substrate, was a sharp Lorentzian anisotropic resonance line (AB ^ 5 G at 4.2 K) observed at g = 1.9510 and g±_ — 1.9483. The orientation dependence of its g value was fitted by (g^cos^0 4- g^sin^©)*/-^, where 0 was an angle between the magnetic field and the c-axis. The degree of anisotropy (g —gj_) and the average g value obtained in [31] were similar to those observed for donors in ZnO, a semiconductor which also crystallizes in the wurtzite structure.

In [31], the authors gave a number of arguments supporting the association of the sharp resonance line with donors creating an impurity band. The average g value was near 2, as expected for electrons in a shallow donor level or in a conduction band of a wide band-gap semiconductors such as GaN. The slight anisotropy of g value was consistent with the hexagonal symmetry of the crystal. The resonance line was quite narrow, and its linewidth was lower than that for isolated defects in any of III-V semiconductors (in which the resonance lines are broadened by electron spin hyperfine interaction with the ligand nuclear spins). In all of the samples measured in [31] the ESR lines had quite sharp Lorentzian shape due to motional averaging of residual hyperfine interactions with the ligand nuclei (primarily Ga) at low temperature. A conduction-band ESR would not show this line narrowing but this is consistent with a resonance due to an impurity donor band for which the averaging interaction (and narrowing) increases with temperature increase. Finally, the ESR line was not easily saturated by microwave power, consistent with a delocalized center rather than a localized one.

As mentioned above (Section 2.1), resonance properties of nonlocalized electrons in shallow donor band in semiconductors are determined mainly by the energy band structure of the host lattice. In [31], using a five-band k p approximation, the average g value equal to 1.95 was obtained. The following parameters were applied: known from experiments were values of EQ = 3.5 eV, EQ = 8.5 eV, AQ = U meV and the values of A;, = 0.2 eV, p2 ^ 22 eV, X^P^ = 10 eV (see Eq. 7, Section 2.1) were estimated. The obtained average g value was in a good agreement with the measured one, strongly supporting the identification of the resonance signal with the shallow donor band.

Undoped n-type zincblende GaN thin films were studied in [32]. The GaN films, with carrier concentration of the order of 10^^-10^^ cm~^ at room temperature, were grown by electron-cyclotron resonance microwave plasma-assisted molecular beam epitaxy (MBE) on silicon substrate. The dependence of their conductivity on temperature was consistent with electron transport in the conduction band for temperatures higher than about 50 K, and in a shallow donor band at lower temperatures. The observed ESR signal had an isotropic g value equal to 1.9533 ± 0.0008 and independent on temperature, a Lorentzian line shape, and a linewidth (18 G at 10 K) which changed with temperature [32]. The measured changes of the ESR signal intensity and its linewidth with increasing temperature allowed the authors of [32] to attribute this isotropic resonance signal to electrons predominantly in a band of autodoping centers (presumably N vacancies) at low temperatures, and in the conduction band at higher temperatures. Using a five-band model k p (Eq. 6, Section 2.1) and appropriate parameters for GaN (EQ = 3.2 eV, EQ =


8.7 eV, Ao = 0.009-0.016 eV, A'Q = 0.06-0.1 eV, P^ = 28 eV, \^ = 0.4) a g value equal to 1.95 ± 0.01 was obtained, in a good agreement with the experimental value [32].

The same effective-mass (EM) donors were found in ODMR spectra obtained on the broad emission band peak at about 2.2 eV (so-called yellow luminescence) in undoped wurtzite GaN layers. The values and anisotropy of g factor, corresponding to the observed sharp ODMR resonance were the same as for ESR line. The broadening of the ODMR line (linewidth of about 2 mT) in comparison to the ESR linewidth (about 0.5 mT) was due to donor-acceptor exchange interaction, inherent to ODMR processes [33-38]. Moreover, the same anisotropic ODMR signal was measured on a donor-acceptor pair band with zero phonon line at 3.27 eV [36] as well as on luminescence bands coming from Mg [35-40] or Zn [38,39] doped films.

Ligand hyperfine interactions of an inhomogeneously broadened ESR lines can be resolved by electron-nuclear double resonance (ENDOR) technique [41]. In this method simultaneous electron and nuclear spin transitions are monitored. The optically detected ENDOR experiment (ODENDOR) was also used to study EM donor defects in n-type unintentionally doped wurtzite GaN layers [42,43]. Both studies of ODENDOR were done for the 2.2 eV yellow luminescence band and revealed Ga hyperfine structure in the EM donor resonance. Whether the Ga ion is in the core of the donor defect or in its close neighborhood could not be unambiguously established [42,43].

More systematic ESR studies of GaN wurtzite layers, both undoped and Si-doped at different concentrations, were performed in [33,44,45]. The anisotropy of ESR signal and the values of g parameter were the same for undoped and Si-doped layers, and equal to the values obtained in [31] as discussed above. The intensity of the line increased with the increase of Si dopant up to 10 ^ cm~^ (see Fig. 5). For higher concentration the line broadened and was undetectable for n = 6 x 10 ^ cm~^ [44,45] which is above Mott transition for GaN. Therefore, this line was assigned to shallow donor center in Si-doped crystals as well. However, there was no certainty that the line originated from Si donor itself, because no characteristic satellites from hyperfine interaction of Si isotope 29 could be seen [44,45].

The ESR signal of similar parameters was also observed for AMMONO GaN microcrystals grown in the presence of erbium [46]. However, the resonance line showed no anisotropy in this case, because the measurement was performed on powdered material. The line was identified as an average signal of an anisotropic shallow donor signal, seen by Carlos et al. [31].

An ESR resonance signal, with a little bit different values of g factors, and lower anisotropy than the line discussed above, was observed in bulk wurtzite GaN crystals [47] grown by high nitrogen pressure (HNP) method [11]. ESR studies were performed on lightly Mg doped GaN samples (about 0.3 at% of Mg in Ga solution). The crystals showed n-type conductivity with free electron concentration in the order of 10^ cm~^ at room temperature. The ESR measurements revealed an anisotropic line at g = 1.9543 ± 0.0005 and gj_ = 1.9527 ifc 0.0005, assigned to shallow donor in neutral charge state [47]. The observed value of g-factor was very close, but easily distinctive from the one already ascribed to shallow donor in GaN and discussed above [31] (see Figs. 6 and 7). The possible reason for different values of g-factor and lower anisotropy of shallow donor in bulk GaN crystals could be difference in chemical origin of that donor center.


1

i

n = 2.8*10''cm"' , A

MOCVD GaN : Si layers

n = 1.3*10''cm''

17 -3 n = 5*10 cm

I . lift iiiAtAAjJfr^ ly ti

n=1.23*10' 'cm"'

n = 5.6* 10'"cm"'

H II c, X-band, T = 6 K J — I — L - j — I I I I I i_«i. - L JL

332 334 336 338 340 342 344 346 348 350

magnetic field [mT]

Fig. 5. The ESR spectra of GaN: Si layers observed for different Si concentrations. Free electron concentration n measured at T = 300 K is indicated for each spectrum.

Oxygen nature should be strongly considered as possible candidate, since bulk GaN crystals suffer from oxygen contamination [48,49].

4.2. Deep donors

Other defects attributed to donor-type centers, mainly much deeper than defects described above Section 4.1), have been found by the ODMR technique (they have not been observed using classical ESR). In ODMR technique magnetic resonance is detected by monitoring spin dependent optical processes, most often a photoluminescence (PL). It allows one to observe defects, which are not necessarily paramagnetic in thermal equilibrium, and to conclude about their role in a particular PL process. This is in contrast to pure ESR experiment, which allows observing shallow donors only in n-type and shallow acceptors only in p-type samples.

The ODMR observations of any defects in crystal structure must naturally start with PL investigations. Typically in n-type undoped GaN films two PL bands have been observed at low temperature. The first one, consisting of several sharp lines around 3.5 eV has been assigned to free and bound excitons [21]. The second one is


338 339 340 341 342 343 344 345 346 347 348

3

E CO

r"' T - •» r • • ' 1 • » — \ — ' — r - •

H||c J

u^j^yîtfaiftiffi^yr^ttyV^^

wurtzite bulk GaN wurtzite leyer GaN/Al Oj

H 1 c

— ' — « — ' — I ' 1 . 1 . 1

• ' — r ' .V,

;./|

.. .'• r

' 1 r"~~| 1 n , ^ , „ . , ,

X-band, T = 6K

• f

1 I 1 1 I 1 1

338 339 340 341 342 343 344 345 346 347 348

magnetic field [tiiT]

Fig. 6. The ESR spectra of shallow donors in wurtzite GaN layers and wurtzite bulk GaN crystals obtained at 9.4 GHz, with magnetic field oriented parallel and perpendicular to the crystalline c-axis.

1.955 1 1 1 1 — 1 — . — p -

h ' A A A

t ^^'^'^ ' ^ -V L ^ A

f

\ %..— -^.^

r •**• \ • L • layer GaN / Alp3 *\ 1 \ \ *• A C L caicuiateu tor L gj= 1.9514

\ gL= 1.9486

H||c r 1 . 1 . 1 . 1

- 1 , 1 1 1 y 1 n

^ wurtzite bulk GaN J 1 1 * J A' "1

"• ~" calculatca tor J g,= 1.9543 1

V A g,= 1.9527 ] \ . A J

j

J • ]

* • H

*• 1 *.• H

1 . 1 -. 1 ^

1.954 h

1.953 V-

% 1.952 1-

00

1.951 h

1.950

1.949

-20 0 20 40 60 80 100 120

0[degrees)

Fig. 7. The angular dependencies of g values observed in wurtzite GaN layers and wurtzite bulk GaN crystals.


a broad band with a maximum at about 2.2 eV (the so-called yellow luminescence) [37,38,50]. In addition to these two, shallow donor-shallow acceptor recombination band characterized by a zero-phonon line (ZPL) at 3.27 eV with a series of LO-phonon replicas at lower energies has been also found in many n-type GaN films [51]. This band was easily observed for highly resistive samples, but could be also detected for undoped GaN layers with higher electron concentrations at low light excitation power densities [50]. In some cases of undoped highly resistive GaN layers, the PL spectra revealed an additional broad band, centered at 3.0 eV [35,38,50]. However, such samples had no PL band with ZPL line at 3.27 Ev (shallow donor-shallow acceptor recombination) what suggested the reduced numbers of both residual shallow donors and acceptors in studied GaN films [50].

The first ODMR observation of defects in undoped wurtzite GaN layers grown by LP MOCVD on sapphire substrate was described in [34]. Two luminescence-increasing resonances with very different g factors were found on the 2.2 eV emission band for 24 GHz microwave frequency. The first anisotropic resonance line had average g = 1.95, the identical value as the centers observed in the ESR measurements (Section 4.1) and was assigned to delocalized electrons in shallow donor band [31]. The second ODMR signal (labeled DD [36,37,40] and later DD2 [50]), also found on 2.2 eV emission band, was anisotropic as well with g = 1.989 ± 0.001 and g_L = 1.992 ± 0.001 and relatively broad with the full width at half-maximum (FWHM) equal to about 13 mT [34,36,37,40]. Its g factor anisotropy with g_L > g was opposite to that found for the delocalized shallow donors. The obtained g values were also quite different from those predicted for a shallow hole state associated with the Jz = ± 3/2 ground state valence band of wurtzite structure [34]. However, the negative g shift (difference between the broad ODMR line average g value and the free electron g value of 2.0023) was in an agreement with expectation for donor defects. The large linewidth of that broad resonance, very similar for K- and Q-band ODMR experiments, indicated the existence of unresolved hyperfine interactions of unpaired electron spin with either a central nuclear spin of defect atom, or with surrounding ligands [37]. Both kinds of hyperfine interactions are significant for deep electronic levels, for which the electronic density is localized in the immediate vicinity of the impurity center. Therefore, the observed new ODMR resonance signal was associated with a deep donor state [34].

Deeper donor defects DD were also observed in p-type GaN layers. Their ODMR resonance signals obtained on strong emission bands peaked at about 3.0 or 2.8 eV were found in Mg-doped [37,39,40] and Zn-doped [39] GaN films, respectively.

The other ODMR resonance signal, also assigned to deep donor center, was observed in n-type undoped, highly resistive wurtzite GaN thin layers, having broad emission band centered at about 3.0 eV [33,50]. ODMR spectra measured on this broad band revealed two luminescence-increasing resonances. The first, narrow one, with anisotropic g value [31,34] was again assigned to residual shallow donor defects. The second, broad (FWHM ^^18 mT), isotropic signal (labeled DDi in [50]) had g value equal to 1.977 ± 0.002 reported in [50], and a slightly different g value of 1.978 reported in [33]. The negative difference between the g value and the free electron g value (equal to 2.0023) suggested an assignment of this resonance line to donor-type state [50]. On the other hand, the larger difference between g value of DDi resonance (in comparison


with average g values of DD2 ODMR signal) indicated that the later donor defect was a deeper one, with wavefunction more localized in crystal lattice [50]. Moreover, the same conclusion could be drawn from resonance line shape studies. The lineshape of DDi could be fitted with a Lorentzian curve [50], in contrast to the Gaussian lineshape typically observed for the anisotropic ODMR line labeled as DD [36,37,40] or DD2 [50], detected on the 2.2 eV emission band. Therefore, the new resonance DDi was tentatively assigned in [50] to an intermediate donor state located below the conduction band edge, between the shallow donor states with average g value equal to 1.95 and the deeper donor defects DD2 (or DD) with average g value equal to about 1.99.

It is worth to mention that the broad (peak — peak distance AHpp = 9.5 mT) resonance line at g = 1.997 was also observed in undoped MOCVD GaN layers in photo-ESR experiment, only for excitation energies of the light above 2.6 eV [52]. Therefore, authors of [52] attributed this isotropic light induced ESR signal to deep donor defect having an energetic position of Ec —2.65 i : 0.05 eV.

ODMR spectra could not be measured on the sharp strong excitonic emission at 3.472 eV (exciton bound to neutral donor) as a consequence of short lifetime of this band (much shorter than 1 |xs) [33,37]. In contrast to excitonic emission, the ODMR spectra were obtained on the shallow donor-shallow acceptor recombination band characterized by a ZPL at 3.27 eV and revealed a single luminescence-increasing resonance [36]. Its g value was identical to that found in ESR [31] and ODMR [34,36] measurements, and was assigned to delocalized electrons at shallow donor level. No additional resonances were detected on this emission band [36].

43, Acceptors

So far magnesium is the only acceptor dopant in GaN crystals that can be successfully used to obtain p-type conductivity in a reproducible way. Taking into consideration GaN-based devices, it is important to achieve a high p-type doping level. Unfortunately, the energy level of Mg acceptor in GaN is relatively deep, about 200 meV above the valence band [53], thus limiting the electrically active acceptors at room temperature to less than 1% of substitutional Mg centers. On the other hand, another problem limiting p-type conductivity of GaN crystals has appeared for higher Mg doping level, namely self-compensation [54], the effect known also for wide band-gap II-VI semiconductors [55].

Doping of GaN crystals with Mg during MOCVD growth results in highly resistive layers. The reason of this is a passivation process of Mg acceptors by hydrogen, which leads to creation of neutral magnesium-hydrogen complexes [56]. Therefore, a post-growth treatment is required to activate the Mg acceptors [57]. Mg-doped GaN epitaxial layers obtained by molecular beam epitaxy (MBE) method are p-type without any post-growth treatment [58], because this technique does not involve hydrogen during the growth process.

Other than Mg impurities have also been investigated for the purpose of finding an acceptor of GaN with smaller ionization energy, which could contribute to enhancing the p-type conductivity. Up to now, Zn, C, Ca and Be have been tested, but Mg is still recognized as the best p-type dopant of GaN crystals [59].


The first ODMR results on acceptor doped wurtzite GaN layers grown by MOCVD on sapphire substrate were presented in [35] and then in [36-40]. The resonance signal of both acceptor dopants, Mg [35-40] and Zn [38,39], were detected as microwave induced changes in luminescence intensity. Most often, K-band (microwave frequency about 21 or 24 GHz) was used in ODMR experiments. The dominant emission observed in PL spectra from p-type GaN layers was a broad band, peaked at about 3.0 or 2.8 eV for Mg [35,36] and Zn [38,39] acceptors, respectively.

The ODMR spectra of Mg-doped wurtzite GaN layers obtained on a broad PL band at about 3.0 eV revealed three different resonance lines [35-38]. Two of them were observed with the same g values as found for the two lines detected on 2.2 eV emission band for undoped GaN films (see Section 4.2). Therefore, these two resonance fines observed in Mg-doped GaN samples were assigned to delocalized electrons of EM shallow donor and to deep donor DD (or also DD2 in [50]) states [35-40]. The third broad anisotropic resonance signal was observed exclusively in Mg-doped GaN layers. Its anisotropic (axial) g factor observed for hole concentration equal to about 1 x 10 ^ cm"^ at room temperature was equal to g = 2.080 ± 0.01 and gj_ = 2.000 ± 0.01 [36,37,40]. The FWHM of the signal was equal to about 25 mT. Recently it was shown [39] that its axial g values changed and depended on Mg concentration. The largest g factor anisotropy was observed in the least heavily doped layer, for which g = 2.084 ± 0.002 and gj. = 1.990 ± 0.005. For the most heavily Mg doped GaN films the degree of anisotropy (g — gj_) was reduced by more than a factor of two and obtained values of g factor were equal to g = 2.067 ± 0.001 and g i = 2.022 ± 0.002 [39]. The authors of [35-40] related this line to Mg related defect, most probably in the form of a complex.

Similar results were obtained on wurtzite GaN layers doped with Zn impurity. In ODMR spectra, measured on the broad blue emission band centered at about 2.8 eV, two resonance signals were detected [38,39]. The sharper one was assigned to delocafized electrons of EM shallow donor level. The second resonance, of a weakly anisotropic g factor (g ^ 1.997 ± 0.002, gj_ = 1.992 ± 0.002) and FWHM equal to about 7 mT, was connected with presence of Zn acceptor dopant in wurtzite GaN layers [38,39].

It should be stressed that for both acceptor dopants, the observed broad resonance lines with g factor about 2 were Mg or Zn specific, and for that reason both ODMR signals were tentatively assigned to the Mg [35] or Zn [38,39] acceptors, respectively. However, the problem arose how the experimentally obtained values of g factors could be reconciled with theoretically expected g values for shallow acceptors in wurtzite structure. As mentioned above (Section 2.1), the resonance properties of shallow states are determined largely by the energy band structure, and approximation of effective mass (EM) is conmionly used for g value calculations. In wurtzite GaN structure the valence band is split by crystal field and spin-orbit interactions into Fg, Fv and F7 states with the highest F9 state [21]. In this case the predicted g value is highly anisotropic with g = 4.0 and gj. = 0 [22], what distinctly differs from g factor of Mg or Zn centers obtained in ODMR experiments. On the other hand, the authors of paper [38] checked also another alternative, namely F7 as the upper valence band state, what could be caused by strain induced axial field in thin GaN layers that reverses the sign of intrinsic wurtzite axial field splitting. In such a hypothetical case, the expected EM acceptor g value (for axial field splittings large compared with the spin-orbit one) would be


equal to near 2 and of small anisotropy with g < g± [38]. It is however opposite to the g factor anisotropy measured for Mg resonance, for which experimental g > g±. Therefore, the authors of paper [38] concluded that the Mg acceptor resonance in GaN by no means showed EM behavior.

The anisotropy of g factor for hole bound to negatively charged core of an acceptor center in semiconducting compounds having similar ionic character and lattice structure as GaN is known from experiments (see literature presented in [38,39]). By comparison of the discussed g factor anisotropy for Mg (g > gj.) the authors of [38,39] indicated that the paramagnetic hole was mainly localized at the four nearest-neighbor N ligands.

Recently, a resonance line assigned to Mg acceptor in wurtzite MOCVD GaN layers intentionally doped with Mg has been also observed using ESR method [44]. As-grown Mg-doped epilayers were of high resistivity because of a well-known effect of acceptor passivation by hydrogen [56,57]. Prior to annealing, the samples did not show any paramagnetic signal as well. Rapid thermal annealing (RTA) at temperature 750°C for 10 min in N2 atmosphere of Mg-doped crystals led to hydrogen outdiffusion, and as a result to p-type conductivity of the layers (with hole concentration of about 8 x 10^ cm~^). Also, a new anisotropic ESR signal was found. Its g factor value was similar to the one of Mg-related ODMR signal described above [35-40], but ESR experiment allowed for determination of g value with higher precision. The ESR spectra related to Mg acceptor in wurtzite GaN crystals for directions of magnetic field parallel and perpendicular to c-axis are shown in Fig. 8. The angular dependency of the measured

310 315 320 325 330 335 340 345 350 355

325 330 335 340

magnetic field [niT]

Fig. 8. The ESR spectra of Mg acceptor in neutral charge state in wurtzite GaN layers measured for parallel and perpendicular directions of magnetic field H to c crystal axis. The narrow resonance line at magnetic field about 336 mT is due to the quartz sample holder.


2.08

30 60

angle [degrees]

Fig. 9. The angular dependence of g factor for Mg related acceptor in wurtzite GaN layer.

resonance line is shown in Fig. 9. The solid line in Fig. 9 was calculated for the best fitted values of g factor: g = 2.0728 ± 0.0015 and g_L = 1.9886 ± 0.0015. Further introduction of hydrogen into GaN: Mg crystals, by thermal annealing in ammonia atmosphere, caused a decrease of the ESR anisotropic line and led to its complete disappearance after 30 minutes of annealing at temperature 600°C. Another RTA annealing in an N2 atmosphere restored the ESR anisotropic line again. Therefore, the measured ESR line in p-type wurtzite GaN layers was assigned to Mg-acceptor in the neutral charge state [44]. The observed changes in the magnesium related ESR signal for annealed GaN: Mg layers are shown in Fig. 10.

4.4. Transition group ions

Transition metals are often trace impurities in many semiconducting compounds, difficult to avoid during semiconductor growth and processing. They typically substitute for metallic component in III-V and II-VI compounds, giving two or three electrons to bonds, respectively. The remaining electrons stay as well localized ones, within a close vicinity to maternal atom. Especially interesting are electrons coming from not fully filled d or f shells, since they influence optical properties of semiconductors. Also, these electrons constitute systems of non-zero spin and therefore can be detected by means of ESR technique.

Most of transition metal impurities may exist in different ionization states. They donate or accept one or in some cases several electrons, as the position of Fermi level is varied within the forbidden band. The d or f shell electrons of transition ion impurities are localized, and therefore can not be described in the approximation of effective mass


0)

3

E OS

a: CO UJ

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

MOCVD GaN : Mg

as-grown

SlA#*^ (b) NH3

RTA

(d)

H II c, X-band, T = 6 K * - * ' • ' • ' ' • « ' ' ' • • ' ' • • ' ' '

310 315 320 325 330 335 340 345

magnetic field [mT] Fig. 10. The ESR spectra of Mg acceptor in as-grown GaN layer (a) and after three thermal annealing procedures: RTA at 750°C in N2 atmosphere (b), annealing at 600°C in NH3 atmosphere (c) and again RTA at 750°C in N2 atmosphere (d). The narrow resonance line at magnetic field about 336 mT is due to the quartz sample holder.

theory. To characterize the resonance properties of these electrons in microwave range, a method of spin Hamiltonian together with crystal field theory is used (see Section 2.1).

The first transition metal impurity of GaN, for which the ESR data were reported, was iron [60]. Few years later, the ESR spectra for manganese, iron and nickel were published [61,62]. All these metals were elements of iron transition group, for which electrons gradually filled 3d shell as the atomic number increased. So far all investigated transition metal impurities of GaN have substituted for Ga ion in GaN structure, and angular dependencies of their resonance lines displayed symmetry of the substitutional site.

Both iron and manganese showed five fine structure transitions in ESR spectra, what indicated total electron spin S = 5/2. It meant that charge states were 3+ and 2+ for iron and manganese impurities, respectively. Their 3d shell was half-filled, with a ground state consisting of five electrons having spins coupled in parallel. The total orbital momentum of these states was equal to zero, and therefore a free-ion ground state configuration was ^85/2. These ions, together with other half-filled d or f shells (Cr+, 3d^ and Eu "*", Gd^+ and Tb'^^, 4f^), are often called S-state ions, and form a special class from the point of view of crystal field theory. Up to the first order of perturbation


theory, they do not interact with a crystal field because they have no orbital momentum. Therefore the spin sextet (2S + 1, S = 5/2) has no other splitting than the Zeeman one, and as a result single hne should be observed with free electron g value equal to 2.0023. However, the six-fold spin degeneracy is usually partially lifted by a cubic crystal field, giving for magnetic field B = 0 three, close to each other, doublets. A crystal field of lower symmetry changes magnitude of level splitting, as well as the symmetry of the resulting anisotropy, but it can never reduce the total degeneracy of energy level below two (in agreement with Kramers theory). Magnetic field is necessary to remove the spin degeneracy of doublets [14,15]. Therefore, the spectrum is usually rather complex with both fine and hyperfine structures present in it.

The ESR spectrum of both Fe^+ [60] and Mn " [61,62], having 3d^ electron configuration and a ground state ^85/2 can be analyzed for wurtzite GaN structure with a spin Hamiltonian of the form written in Eq. 3 with axial form of Zeeman interaction term shown in Eq. 4 (see Section 2.1). Additionally, only for Mn-ions, the hyperfine interaction with a 100% abundant magnetic nucleus ^^Mn with nuclear spin I = 5/2 was observed, and each line of fine structure was split into six hyperfine components. Therefore, the spin Hamiltonian for Mn " ions includes also term equal to S • A • I describing an interaction between the electron spin S = 5/2 and the nuclear spin of ^^Mn I = 5/2 (see Eq. 5, Section 2.1). For Fe ions, the only isotope of non-zero nuclear spin, ^^Fe of I = 1/2, has 2.15% abundance and no hyperfine interaction was observed for iron d impurity in GaN.

The presence of the second term in the spin Hamiltonian (Eq. 2, Section 2.1) leads for electron spin S = 5/2 to doubling of the five-line spectrum for general orientation of the magnetic field H with respect to the crystal lattice. This doubling was distinctively observed for both ions, for Fe^^ as well as for Mn " [60-62], and it resulted from two types of sites which were crystallographically equivalent in wurtzite structure, but which could be distinguished magnetically (see Section 3). The parameters of the spin Hamiltonian, obtained from the best fit to experimentally measured angular dependencies of resonance lines of Fe " [60,62] and Mn "*" [61,62] ions, are listed in Table 2. The ODMR lines of Fe " ions were also observed, and spin Hamiltonian parameters obtained from a fit to them were in a good agreement with the ESR ones within the limits of experiment accuracy [60].

Assignment of an intense anisotropic ESR line, observed for some wurtzite GaN

Table 2. The parameters of the spin Hamiltonian for transition metal ions in GaN crystals

Ion g gj. D a - F a A Ref. (10-4 cm-') (10-4 cm-') (iQ-^cm-') (10"^ cm"')

Fe3+ 1.990 ±0.005 1.997 ±0.005 -713 ± 5 +52 ± 6 +48 ± 5 [60] [62]

~4 - 5 70 [61] [62]

A = 110±5 [63] Ai = 290 ± 5

Mn2+ Ni3+

Er3+

1.995 1.999 2.10 2.10

2.861 ±0.003

1.995 1.999

%4.2, S' = 1/2 %2.1,S = 3/2 7.861 ± 0.003

715 240

> 1.5*10^

Magnetic resonance studies of defects in GaN and related compounds Ch, 4 99

layers and reported in [62], was not as direct as in the case of Fe " and Mn^+ ions described above. A very characteristic anisotropy of this line, observed for angular dependence of ESR signal, together with its calculated positive g shift (i.e. (g —2.0023) > 0) indicated electron configuration d [62]. Therefore, this ESR spectrum was attributed to the trace impurity of nickel in the charge state 3+, substituting for Ga ion in GaN structure [62]. In an electric field of cubic symmetry, the ground state of a free Ni^+ ion C F) splits into two orbital triplets, ^^2 and " Ti, and a ground-state orbital singlet, Âi [14]. Trigonal component of the crystalline field, present in GaN structure, together with the spin-orbit interaction caused splitting of the ' A2 ground state into two Kramers doublets. In such case the ESR spectrum can be described by the spin Hamiltonian shown in Eq. 3 and Eq. 4 (see Section 2.1), which for S = 3/2 will take a shorter form [62]:

H = g pHzS, + gxP(HxSx + HySy) + D [S, - 1/3S(S + 1)] (8)

The z denotes c-axis of the crystal. The parameter D characterizes the axial crystal field (wurtzite structure). For strong zero-field case, it means that the magnitude of zero field splitting 2D is much larger than the microwave energy at X-band frequency, and only transitions within the lowest Kramers doublet can be observed in ESR experiment. Therefore, the spin Hamiltonian described in Eq. 8 can be transformed as [62]:

// = g'pH,s; + gip(Hxs; + Hys;) where g' is the effective g value, and S' is an effective spin S' = 1/2. The spin Hamiltonian above has no hyperfine term, because nickel has only one stable isotope ^^Ni of natural abundance 1.13% having non zero nuclear spin, I = 3/2. The angular dependencies of Ni " ESR lines, calculated using spin Hamiltonian described in Eq. 8 with parameters S = 3/2, g = gx = 2.10 and D = 2 cm~^ are in good agreement with experimental data [62]. An analogy was revealed between the spin Hamiltonian parameters of Ni^+ ions in GaN and ZnO crystals [62]. Similarly, such analogy was pointed out for Fe " and Mn "*", also in GaN and ZnO. Such comparison is plausible, because both crystals have the same hexagonal (wurtzite) structure and close physical parameters [60-62].

Authors of [62] could not completely exclude that the anisotropic ESR line, described above and attributed to Ni- " ions in GaN layers, might in fact be connected with the presence of another impurity, isoelectronic to Ni "*", e.g. Fe^ or other ions of 4d^ or 5d^ configuration. These doubts were justifiable since no hyperfine interaction was observed in the ESR spectrum [62]. Also, Ni in the measured samples was not an intentional impurity.

Very recently, the ESR spectra of Er "*" ions in bulk wurtzite GaN crystals were obtained [63]. Erbium is a metal of rare earth (RE) group with unfilled 4f shell. These unpaired 4f electrons of Er "*" are screened by closed outer shells of 5s and 5p electrons, what reduces the crystal field interaction on 4f electrons. In such case, so-called weak crystal field approximation can be used, since the interaction of 4f electrons with surrounding ligand ions is weaker than the spin-orbit coupling, and the ground state can be described in terms of the total angular momentum quantum number J. In general, crystal field can partially remove the degeneracy of (2J -f- 1) states. For ions with an


odd number of electrons, the crystal field lifts such degeneracy completely, except for the twofold degeneracy imposed by Kramers theorem, so that the levels consist of (J -f 1/2) doublets. However, magnetic field raises Kramers degeneracy completely and ESR may be observed. This is not always the case for ions with an even number of electrons, for which the ground state may be an orbital singlet with energy distance to first excited level too large for ESR [14,15].

The ESR method can be very useful to determine the local-site symmetry of RE impurity in a crystal structure. The main reason of it arises from large spin-orbit coupling of the RE ion, compared to the crystal field effect. It leads to large difference between the g factor of free electron (equal to 2.0023) and the g values obtained for unpaired electrons of RE ion incorporated into crystal lattice [64]. These values are characteristic of the nature of the crystal field and differentiate between various possible sites of RE impurity in crystal structure. For RE ions with 4f electrons shielded by 5s and 5p shells, splitting of the free electron ground state by the crystal field is determined approximately by the electrostatic crystal field point charge model, and depends on its strength and symmetry [65]. Therefore, a comparison of g value obtained in experiment with the g values expected for different possible sites in crystal structure allows determining the way of RE incorporation. In some cases, a small correction in g value of RE ion due to covalency effects should be taken into consideration [66].

The electronic configuration of Er^^ ion is 4f ^ with a ground state " 115/2. In a cubic field, the sixteenfold degeneracy splits into three Eg quartets and two doublets r6 and r7 from which either r6 or FT state corresponds to the lowest level of Er " in tetrahedral coordination [65]. Theoretically predicted g value for F^ state is 6.8, while it is 6.0 for F7 doublet state. A ground state of substitutional Er " ion on a metallic site surrounded by four anions is of F7 nature [67].

A hexagonal structure can be treated as a cubic one, modified by an extra axial electric field. If this field is small in comparison with the cubic interactions, an average g factor gav = l/3(g 4- 2gj_), obtained from experiment, can be compared with theoretical predictions made for the cubic type of local symmetry [68].

The ESR spectrum of wurtzite bulk GaN crystals revealed a single anisotropic line, with visible much smaller eight lines of hyperfine structure (see Fig. 11). Therefore, the observed resonance signals were assigned to Er " ions, which consisted of ^ Êr isotope of nuclear spin I = 7/2 and natural abundance of 22.9%. The observed lines were the only ESR fines seen in the whole range of applied magnetic field (up to IT). The ESR spectrum could be described by an effective axial spin Hamiltonian (see Eqs. 4 and 5 in Section 2.1), which contained terms due to electron Zeeman splitting and hyperfine interaction of effective spin S = 1/2 with ^ ' Er of I = 7/2:

H = pH(g Sz cos © + g^Sx sin 0 ) + A Szlz + Aj.(SxIx + Syly)

where z is parallel to the c-axis of the crystal. The obtained angular dependence of g value is shown in Fig. 12, where solid line was calculated for the best fitted parameters, listed in Table 2. For Er- " ions in GaN crystals, the ratio (A_L g /A gx) is equal to 0.99, what indicated that the first excited state of Er^+ was sufficiently distant from the ground level, and first order theory approximation including only matrix elements within a J = 15/2 manifold gave quite good agreement with the ESR experiment.


I I t I I I I I I ; I I I I I I I I t I I I I I I I » I I I I I

-3* I (a) wurtzite bulk GaN : Er

* • ' * ' * • • • • * ' • • • ' '

200 210 220 230 240 250 260

magnetic field [mT]

I •! I I I I ' I [ I ' ' ' ' I ' ' • ' I ' • ' ' I

wurtzite bulk GaN : Er

H I c, X-band. T = 6 K

60 70 80 90 100 110 120

magnetic field [mT]

Fig. 11. The ESR spectra of Er^+ ions in GaN bulk crystals measured at 6 K for magnetic field parallel (a) and perpendicular (b) to c-axis.

Knowing values of the g factor for Er^+ ions, gav value was determined for GaN crystals, assuming that the crystal field is mainly of cubic type with a small hexagonal contribution. The gav value was equal to 6.05, and it was close to the predicted value for a ground state of T-j symmetry, what indicated Er substituting for Ga in GaN


60 70 80 90

e [degrees]

Fig. 12. Angular dependence of Er " g factor in GaN bulk crystals. The solid line was calculated using the relation g^ = g^cos^0 + g^^sin^© with g = 2.861 and gx = 7.645, where 0 is the angle between the magnetic field and the c-axis.

Structure. Therefore, ESR experiment determined that Er impurity in bulk GaN crystals was mostly isolated one, and it occupied the Ga site. It seemed puzzling, however, that no traces of ESR lines coming from Er~0 complexes were observed, although there was a strong evidence of oxygen presence in the investigated crystals. Such complexes have been observed with ESR technique in other semiconductors like Si and GaAs [63].

4.5. Electron-irradiated GaN

As it clearly comes out from the previous parts of this chapter, our knowledge about defects in GaN is still insufficient, despite of great efforts undertaken for defect studies in the last years. The hope is that electron irradiation of GaN crystals may help to understand the role and properties of intrinsic defects present in this material. Recently, ODMR studies of as-grown and electron-irradiated MOVPE wurtzite undoped GaN layers on sapphire substrates have been performed [69,70]. Before irradiation, three distinct PL bands at 3.47, 3.27 and 2.2 eV energy and two ODMR signals originating from EM shallow and DD deep donor defects in 2.2 eV PL band were observed, what is typical of high quality n-type GaN layers (see Sections 4.1 and 4.2). After irradiation with 2.5 MeV electrons, the two higher energy PL bands vanished completely, and the 2.2 eV band decreased about 15 times. Nevertheless, the same two ODMR lines could still be weakly detected via the 2.2 eV PL band [69]. Simultaneously, at least two overlapping PL bands appeared with maxima at about 0.85 and 0.93 eV. ODMR studies in the higher energy range (above 0.88 eV) revealed three new anisotropic spectra labeled LEI (g = 2.004 ± 0.001, gx = 2.008 d= 0.001), LE2 (g = 1.960 ± 0.002,


g_L --2.03) and LE3 (gj. = 2.002 ± 0.005, ^Â_L = (1580 ± 50) MHz). For lower light energy (below 0.83 eV), apart from LEI and LE2, an additional new ODMR signal LE4 (g = 2.050 ± 0.002, gx -1.97) was observed [69]. All four ODMR signals had electron spin S = 1/2. An additional structure of ODMR signal was observed only for LE3 defect. Its angular dependence has been successfully simulated in [69] as arising from hyperfine interaction of electron spin S = 1/2 with the two naturally abundant Ga isotope atoms of nuclear spin I = 5/2 (see Table 1). Therefore, LE3 defect was at first tentatively assigned to a displaced Ga atom, either in interstitial or antisite position, isolated or complexed with another defect [69].

Unfortunately, subsequent annealing studies of electron irradiated GaN layers performed in [70] have not confirmed such defect model and authors of [70] are not certain about origin of the LE3 defect at present.

5. Resonance studies of AIN and BN

Much less of magnetic resonance studies have been undertaken for other nitrides than GaN. Therefore, the knowledge of ESR or ODMR active defects in these compounds is rather poor up to now. The results of performed investigations of different nitride compounds are presented in short below. The data obtained for mixed AlGaN crystals are followed by discussion of results for AIN, and in the end-magnetic resonance studies of BN are sunmiarized.

A similar single anisotropic resonance line to the one originating from EM donors in GaN was observed in a series of mixed wurtzite AlxGa(i_x)N crystals grown on 6H-SiC substrates by MOCVD method, where the Al mole fraction x changed from 0 to 0.26 [33]. The ESR linewidth did not vary appreciably with x, indicating good homogeneity of thin films studied. For all AlxGa(i_x)N samples, the same degree of anisotropy (g — gjL4) ~0.002-0.003 was found. The measured average g values changed linearly from 1.95 to about 1.963 for Al mole fraction x varying from 0 to 0.26 [33]. Calculations of the donor average g value for mixed AlxGa(i_x)N crystals were also done, on the base of a simple five-band k p approximation [33] (Eq. 7, Section 2.1). For such crystals, the value of energy gap EQ was taken from respective spectra of optical absorption measurements. The difference (EQ—EQ), which according to theoretical calculations weakly depends on x, was assumed equal to 5.5 eV, the value for GaN [33]. On the other hand, (since Ga spin-orbit splitting is much larger than Al) the spin-orbit splitting of the r^ conduction band, AQ, primarily due to cations, was taken to be equal to 0.25 (1 — x) eV, where 0.25 eV is AQ value for GaN [33]. For the spin-orbit splitting of the valence band, AQ, most of all due to anions, a constant value was used, equal to 11 meV as determined from optical studies for GaN [21]. The parameters P^ and \^ were assumed equal to 17 eV and 0.4, respectively, consistently with their values obtained for other III-V and II-VI semiconductors. The authors of [33] assumed that both of these parameters were constant for the whole range of measured Al composition in mixed AlxGa(i_x)N crystals. The calculated average g factors for different values of Al mole fraction in the thin films under study were in a good agreement with the experimental data discussed above [33].

Polycrystalline wurtzite AIN ceramics containing 10 ppm of Cr impurities were


studied using ESR and photoluminescence methods in [71]. Their ESR spectra revealed a sharp isotropic signal of g = 1.9970, associated with a distinctive resolved hyperfine structure containing 4 much weaker lines with a hyperfine coupling constant A = 1.907 mT. The number of hyperfine components and their intensity in relation to the central line (equal to about 10%) were consistent with the isotope ^^Cr (I = 3/2, 9.5%). The authors of [71] assigned the chromium impurity of d electron configuration, i.e. Cr " , as most likely explanation for the observed ESR signal. The isotropy of the central resonance signal (g = 1.9970) ascribed to Ê (D) ground state of Cr " ion indicated that the Ê trigonal field splitting due to AIN wurtzite axial field was small and comparable to the splittings induced by random strains in crystal. After fast neutron irradiation the Cr " ESR signal nearly vanished, what was explained as a result of creation of nitrogen vacancies in AIN structure [72] leading to a change of Fermi level, and as a consequence to a change of Cr charge state (from Cr^+ (3d^) to Cr' ^ (3d^)) [71].

ESR signal assigned to electron trapped at N^~ vacancy was observed for neutron-irradiated polycrystalline AIN samples [73]. A broad line of g value equal to 2.007 ± 0.001 and a width of about 7.7 mT was observed already at room temperature. Its shape was similar to the Gaussian one with an exception of the tails, as usually seen for F-type centers [73]. The line shape and its broadening were explained in [73] by the unresolved hyperfine interaction of electron trapped in the nitrogen vacancy (S = 1/2) and nuclear spin of its closest neighbors, i.e. four nearest aluminum nuclei (I = 5/2, see Table 1). A hyperfine constant, equal to A = (10.9 ± 0.5) x 10"" cm~\ was determined [73].

Very recently, single AIN crystals coming from different suppliers were studied using ODMR method [70,74]. The crystals were not intentionally doped, but most of them contained oxygen and carbon as unintentional impurity, and a few samples might also have been contaminated with bismuth, titanium, vanadium or chromium at different concentrations in particular crystals. The authors of [74] observed many strong, well-resolved anisotropic ODMR signals in visible luminescence for this set of as-grown AIN crystals, and could distinguish twelve different defect centers. For all observed ODMR lines the spin Hamiltonian parameters were determined [74]. Unfortunately, the absence of any resolved hyperfine structure for most centers except one, (named D5) did not allow for chemical identification of the impurity involved. The ODMR line of D5 center with electron spin S = 1/2 displayed an anisotropic flat-topped shape that was simulated quite well by including an anisotropic hyperfine interaction with impurity atom of 100% abundance and nuclear spin I of 7/2 > I > 3/2. This D5 center was tentatively assigned to a displaced aluminum ^Âl host atom of some kind [74]. However, the D5 spectrum indicated some similarity to ESR signal observed for neutron-irradiated polycrystalline AIN samples and attributed to a nitrogen vacancy [70,73].

BN films studied by ESR in [75,76] were grown by RF diode sputtering from a hexagonal BN-target in nitrogen atmosphere and it was found that layers produced by lower N2 partial pressure had a zincblende structure. The ESR spectra consisted of a single line with unresolved hyperfine structure and Gaussian shape. Its isotropic g-value changed a little, depending on N2 partial pressure, between 2.0024 and 2.0029 and was equal to 2.0025 ± 0.0004 for cubic BN films. The linewidth also changed with N2


partial pressure and was equal from 3.1 to 1.7 mT. The concentration of paramagnetic defects were found to depend on partial pressure of N2 and therefore ESR signal was assigned to nitrogen vacancy, expected in such films in a variable concentration [76].

Similar isotropic single ESR line was also observed in undoped zincblende BN crystals by other authors [77]. Its peak-to-peak width was 2.7 mT and the g value was 2.00248, very close to the parameters of ESR Hne reported in [75,76].

Interesting studies of highly defective metastable wurtzite phase of BN were performed in [78]. Heat treatment of such BN led to phase stabilization process: wurtzite BN-zincblende BN. By means of ESR it was found that this thermal treatment is accompanied by at least one order of magnitude decrease in concentration of paramagnetic defects. Unfortunately, the authors of [78] did not give any parameters of the observed ESR signal.

6. Summary

In this chapter an attempt was made to present the main achievements of magnetic resonance studies on defects in nitride compounds.

In spite of huge amount of work performed on nitrides, especially in the last 5 years, not too much has been clarified in the area of defect identification. One of the main reasons is difficulty to obtain bulk nitride crystals, the best materials for ESR studies, because of technological problems in growing them.

The best knowledge has been achieved for GaN. The ESR signal due to shallow donor characteristic for MOCVD grown GaN is well established. Its parameters are the same for undoped n-type as well as Si-doped layers. However, it has not been definitively proved that Si is the main shallow donor defect in MOCVD-grown GaN. Signal coming from shallow donor in bulk GaN of slightly different parameters has also been identified. In this case oxygen nature should be strongly considered as possible origin, since bulk GaN suffers from oxygen contamination. Two different deep donors have been found by ODMR in GaN layers but no suggestion about their nature has come yet. On the other hand, quite clear situation is in the area of two main acceptors of GaN, namely Mg and Zn. Their magnetic resonance spectra have been positively identified and found to follow the well known process of hydrogen passivation and its diffusion out of acceptor centers. Transition metal impurities, common trace impurities of many semiconductors, are far from being known in GaN when it comes to their magnetic resonance properties. Up to now ESR spectra of only manganese Mn " (3d^), iron Fe " (3d^), nickel Ni " (3d^) and recently erbium Er " (4f^^) have been published. The studies of electron-irradiated GaN have not come up to expectations and have not led to positive identification of any of hoped-for simple native defects.

Even much less is known about magnetic resonance-active defects in AIN and BN. For mixed AlxGai_xN (0 < x < 0.26) layers ESR signal of shallow donor has been found, but the origin of this donor remains still unknown. Also, ESR spectrum observed for polycrystalline AIN ceramics, containing intentional Cr impurities, has been attributed to Cr^+ (3d^). Finally, in some studies nitrogen vacancy related ESR defects have been suggested in AIN and BN materials.

Since it seems that intentional doping of nitrides and studies of such materials have


just started, one can expect much more yet to come in the area of defect identification in nitride compounds in the coming years.

Acknowledgements

The authors would like to acknowledge special assistance of the Institute of Electronic Materials Technology for MP during preparation of this work. The paper was also partially supported by the Committee for Scientific Research (Poland) under Grant 7T 08A 031 15 and ITME project No 02-1-1018-9.

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III-V Nitride Semiconductors: Defects and Structural Properties M.O. Manasreh (Ed.) © 2000 Elsevier Science B. V. All rights reserved

CHAPTER 5

Characterization of native point defects in GaN by positron annihilation spectroscopy

K. Saarinen

1. Introduction

Gallium nitride exhibits electronic, optical, and thermal properties, which make it a promising material for optoelectronic and high-power devices. Especially, its large direct band gap (3.4 eV) and strong interatomic bonds enable the construction of very efficient blue light-emitting diodes and promise the development of long-lifetime blue lasers. Unfortunately, GaN and related materials are difficult to fabricate. Since lattice-matched substrates for GaN epitaxy are generally not available, dislocation densities as high as 10^^ cm~^ are conmion in overlayers grown by metal-organic chemical vapor deposition (MOCVD) on sapphire. These and other extended defects have been studied extensively (for example, see [1-7] and citations therein). Much less is known about simple point defects such as vacancies and interstitial atoms, although it is likely that they are formed at high concentrations in the crystal growth of GaN.

Point defects induce localized electron levels into the band gap of the semiconductor. These states can trap charge carriers, thus inducing compensation, scattering of free carriers, and subsequent change of electrical properties. Moreover, the states interact with light, inducing increase in the absorption or emission photons in radiative recombination processes. For example, the parasitic optical transition leading to yellow luminescence is observed in both GaN bulk crystals and epitaxial layers. The atomic structure of the defect responsible for the yellow emission has been much debated, although even the positions of the electronic levels participating in this optical process have been under discussion [8-11].

The understanding and control of these effects requires both the identification of the defects as well as the characterization of their physical properties. Traditionally the experimental information on point defects has been obtained by electrical and optical characterization techniques, such as Hall measurements and infrared absorption. Although the defects can be detected in these experiments, their atomic structures remain very often unresolved. The methods based on electron paramagnetic resonance (EPR) are more sensitive to the structure of defects, but so far these techniques have given only limited information in GaN materials. An experimental technique is thus needed for the unambiguous defect identification. This goal is reached for vacancy-type defects by utilizing the positron annihilation spectroscopy.

Thermalized positrons in solids get trapped by the vacant lattice sites. The reduced electron density at the vacancies increases positron lifetime and narrows the positron-

110 Ch. 5 K. Saarinen

electron momentum distribution. The detection of these quantities yields direct information on the vacancy defects in solids. Positron lifetime measurements can be used to probe homogeneous defect distributions in semiconductor substrates. This technique is relatively simple to implement, but yet very powerful in identifying the atomic structure of the defect, its charge state and concentration. Defects in the near-surface region 0-3 xm can be studied by a monoenergetic positron beam. This technique is well suited for

the defect studies of epitaxial semiconductor materials. The information provided by positron experiments is especially useful when combined with those of other spectroscopies. The correlation of positron measurements with electrical and optical methods enables quantitative studies of technologically important phenomena such as electrical compensation, light absorption and photoluminescence.

In this chapter we present a brief overview of positron annihilation spectroscopy in Section 2. The goal is to introduce the reader with this technique at the level which is needed for understanding the results in GaN materials. More extensive reviews of the experimental methods can be found in the literature (see [12-16]). The positron results concerning the native defects in GaN bulk crystals are presented in Section 3. The vacancies in GaN layers on sapphire are discussed in Section 4 by summarizing the existing data in samples doped n-type with O or Si or p-type with Mg. The formation of point defects at various growth conditions of GaN layers are reviewed in Section 5. These include studies of stoichiometry, dislocation density and substrate material. Section 6 is a brief sununary.

2. Positron annihilation spectroscopy

In this section we review the principles of positron annihilation spectroscopy and describe the experimental techniques. The thermalized positrons in lattices behave like free electrons and holes. Analogously, positrons have shallow hydrogenic states at negative ions such as acceptor impurities. Furthermore, vacancies and other centers with open-volume act as deep traps for positrons. These defects can be experimentally detected by measuring either the positron lifetime or the momentum density of the annihilating positron-electron pairs.

2.1. Positron implantation and diffusion in solids

The basic positron experiment is schematically shown in Fig. 1. Positrons are obtained from P+ active isotopes like ^^Na, ^^Co, ^Cu and ^^Ge. The most commonly used isotope is ^^Na, where the positron emission is accompanied by a 1.28 MeV photon. This photon is used as the time signal of the positron birth in positron lifetime experiments. The stopping profile of positrons from p+ emission is exponential. For the ^^Na source (Emax = 0.54 MeV), the positron mean stopping depth is 110 |xm in Si and 40 |xm in GaN. The positrons emitted directly from a radioactive source thus probe the bulk ofa solid [12-16].

Low-energy positrons are needed for studies of thin layers and near-surface regions. Positrons from P^ emission are first slowed down and thermalized in a moderator. This is usually a thin film placed in front of the positron source and made of a material (e.g.

Characterization of native point defects in GaN Ch. 5 111

1.28 MeV 511±AEkeV

^^Na source

Lifetime t

/y\ Angular ^ correlation

180° ±0

Sample

Doppler broadening 511keV±AE

Fig. I. Schematic figure of positron experiment, where positron is implanted into a sample from ^ Na source. The positron lifetime is determined as a time difference between 511 keV annihilation photons and a 1.28 MeV photon emitted together with a positron from ^^Na. The Doppler shift AE and the angular deviation 0 result from the momentum of the annihilating electron-positron pairs.

Cu or W) which has a negative affinity for positrons. Thermalized positrons close to the moderator surface are emitted into vacuum with an energy of the order of 1 eV and a beam is formed using electric and magnetic fields. The positron beam is accelerated to a variable energy of 0-40 keV and in this way the positron stopping depth in the sample is controlled. The typical positron beam intensity is lO'^-lO^ e"*" s~ [12-17].

For monoenergetic positrons, the stopping profile can be described by a derivative of a Gaussian function with the mean stopping depth [16,18]

x = AE"[kcWl (1)

where E is the positron energy, A = (4/p) jxg/cm^; n ^ 1.6, and p is the density of the material. The mean stopping depth varies with energy from 1 nm up to a few |xm. A 20 keV energy corresponds to 2 |xm in Si and 0.8 |xm in GaN. The width of the stopping profile is rather broad and the positron energy must be carefully chosen so that e.g. the signal from an overlayer is not contaminated by that from the substrate or surface.

In a solid, the fast positron rapidly looses its energy via ionization and core electron excitations. Finally, the positron momentum distribution relaxes to a Maxwell-Boltzmann one via electron-hole excitations and phonon emissions. The thermalization time at 300 K is 1-3 ps, i.e. much less than a typical positron lifetime of 200 ps [19,20]. Positron behaves thus as a fully thermalized particle in semiconductors.

The transport of thermalized positrons in solids is described by diffusion theory. The positron diffusion coefficient has been measured in several semiconductors by implanting low-energy positrons at various depths and observing the fraction which diffuses back to the entrance surface [21-23]. The diffusion coefficient at 300 K is in the range of 1.5-3 cm^ s~K The total diffusion length during the finite positron lifetime


T is

L+ = (6D+T)^/^ ^ 5000 A. (2)

If defects are present, the positron may get trapped before annihilation and this naturally reduces the effective diffusion length.

2.2. Experimental techniques

2.2.1. Positron lifetime spectroscopy Lifetime spectroscopy is a powerful technique in defect studies, because the various positron states appear as different exponential decay components. The number of positron states, their annihilation rates and relative intensities can be determined. In a positron lifetime measurement, one needs to detect the start and stop signals corresponding to the positron entrance and annihilation times in the sample, respectively (Fig. 1). A suitable start signal is the 1.28 MeV photon accompanying the positron emission from the ^ ^Na isotope. The 511 keV annihilation photon serves as the stop signal. The positron source is prepared by sealing about 10 ixCi of radioactive isotope between two thin foils. The source is then sandwiched between two identical pieces (e.g. 5 X 5 X 0.5 mm^) of the sample material. This technique is standard for bulk crystal studies. Pulsed positron beams have been constructed for lifetime spectroscopy of thin layers [24,25], but so far they have not been used much in defect studies.

The standard lifetime spectrometer consists of start and stop detectors, each of them made by coupling a fast scintillator to a photomultiplier. The timing pulses are obtained by differential constant-fraction discrimination. The time delays between the start and stop signals are converted into amplitude pulses, the heights of which are stored in a multichannel analyzer. About 10^ lifetime events are recorded in 1 h. The experimental spectrum represents the probability of positron annihilation at time t and it consists of exponential decay components

^ = X^/A,exp[-A,r], (3)

where n{t) is the probability of positron to be alive at time t. The decay constants Xi — \/Xi are called annihilation rates and they are the inverses on the positron lifetimes x/. Each positron lifetime has the intensity of /,. In practise the ideal spectrum of Eq. 3 is convoluted by a Gaussian resolution function which has a width of 200-250 ps (full width at half maximum, FWHM). About 5-10% of positrons annihilate in the source material and proper 'source corrections' must be made. Due to the finite time resolution, annihilations in the source materials, and random background, typically only 1-3 lifetime components can be resolved in the analysis of the experimental spectra. The separation of two lifetimes is successful only, if the ratio A1/A.2 is > 1.5.

Fig. 2 shows positron lifetime spectra recorded in undoped and Mg-doped GaN bulk crystals [26]. Positrons enter the sample and thermalize at the time t = 0. The vertical axis of Fig. 2 gives the number of annihilations at a time interval of 25 ps. In the heavily Mg-doped sample the positron lifetime spectrum has a single component of 165 ± 1 ps at 300 K corresponding to positron annihilations in the defect-free lattice. The


GaN • Undoped n-type O Highly Mg-doped

Fig. 2. Examples of positron lifetime spectra in undoped and highly Mg-doped GaN bulk crystals. A constant background and annihilations in the source materials have been subtracted from the spectra, which consist of 2 X 10^ recorded annihilation events. The solid lines are fits to the sum of exponential decay components convoluted with the resolution function of the spectrometer. The data in the highly Mg-doped sample was recorded at 300 K and it has only a single component of 165 di 1 ps. The spectrum in the undoped crystal was recorded at 490 K and it can be decomposed into two components of xi = 150 ± 10 ps, 12 = 235 ± 5 ps, and h = 48 db 6% [26].

undoped sample has two lifetime components, the longer of which (t2 = 235 ps) is due to positrons annihilating as trapped at native Ga vacancies. For more discussion see Section 3.

The experimental results are often presented in terms of the average positron lifetime lav defined as

f '(-57)=r *"«=!:'"'• (4)

The average lifetime is a statistically accurate parameter, because it is equal to the center-of-mass of the experimental lifetime spectrum. Hence it can be correctly calculated from the intensity and lifetime values even if the decomposition represented only a good fit to the experimental data without any physical meaning. For example, the positron average lifetimes in the two spectra of Fig. 2 are 191 ps (undoped GaN) and 165 ps (Mg-doped GaN). The difference is very significant because changes below 1 ps can be reliably observed in the experiments.

2.2.2. Doppler broadening spectroscopy The Doppler broadening spectroscopy is often applied especially in the low-energy positron beam experiments, where the lifetime spectroscopy is usually very difficult due to the missing start signal. The motion of the annihilating electron-positron pair causes


o O

5 10

10'

-

r

--

_

•

o

! \

Positron annihilation in GaN lattice

Energy resolution (Sr-85 source)

1 \

T"

/ /° / o •

• o

• • o • • • o • •

• o i • • o

r O

o

^

L _

\ \ °\ o \

• o • • o •

• o •

• • o • •

° : • • o • \

° \ o \ o \

< ^ ^ \ ^

1

— f - a ~j

J J

j ~H

H

J

-\ H

] J

---

L ^ 500 505 510 515 520

Gamma ray energy (keV)

Fig. 3. Example of a Doppler broadening spectrum recorded in GaN bulk material. The energy resolution function (full-width-at-half-maximum FWHM = 1.3 keV) has been measured using the 514 keV photons of ^^Sr source. The resolution function has been shifted to 511 keV and both curves have been normalized to the same peak-to-background ratio.

a Doppler shift in the annihilation radiation (Fig. 1)

AE = \cpL. (5)

where pi is the longitudinal momentum component of the pair in the direction of the annihilation photon emission. This causes the broadening of the 511 keV annihilation line (Fig. 3). The shape of the 511 keV peak gives thus the one-dimensional momentum distribution pipi) of the annihilating electron-positron pairs. A Doppler shift of 1 keV corresponds to a momentum value of p^ = 3.91 x 10"^ rriQC.

The Doppler broadening can be experimentally measured using a Ge gamma detector with a good energy resolution (Fig. 3). For measurements of bulk samples, the same source-sample sandwich is used as in the lifetime experiments. For layer studies, the positron beam hits the sample and the Doppler broadening is often monitored as a function of the beam energy. The typical resolution of a detector is around 1 keV at 500 keV (Fig. 3). This is considerable compared to the total width of 2-3 keV of the annihilation peak meaning that the experimental lineshape is strongly influenced by the detector resolution. Therefore, various shape parameters are used to characterize the 511 keV line. Their definitions are shown in Fig. 4, where the raw data such as in Fig. 3 has been (i) shown after background reduction, (ii) folded about the energy of 511 keV corresponding to AE = /7L = 0, (iii) plotted as a function of the electron momentum PL using Eq. 5, and (iv) normalized to a unit area.

The low electron-momentum parameter S is defined as the ratio of the counts in the central region of the annihilation line to the total number of the counts in the line (Fig. 4). In the same way, the high electron-momentum parameter W is the fraction of


10-

s OQ

2 H 5 10"

H

^ 2 2 ^ . .

CaN

( i ; iN laUicc

0 10 20 30 ELECTRON MOMENTUM (10'^ mQc)

Fig. 4. Positron electron momentum distributions in the GaN lattice and at the Ga vacancy. The lineshape parameters S and W are defined as integrals of the shaded areas in the figure.

the counts in the wing regions of the line (Fig. 4). Due to their low momenta, mainly valence electrons contribute to the region of the S parameter. On the other hand, only core electrons have momentum values high enough to contribute to the W parameter. Therefore, S and W are called the valence and core annihilation parameters, respectively.

The high-momentum part of the Doppler broadening spectrum arises from annihilations with core electrons which contain information on the chemical identity of the atoms. Thus the detailed investigation of core electron annihilation can reveal the nature of the atoms in the regions where positrons annihilate. In order to study the high-momentum part, the experimental background needs to be reduced. A second gamma detector is placed opposite to the Ge detector and the only events that are accepted are those for which both 511 keV photons are detected [27,28]. This coincidence technique is utilized in the experimental data of Fig. 4. The coincidence detection of the Doppler broadening spectrum enables the measurement of electron momenta even up to /? % 60 X 10~^ moc ^ 8 a.u.

2.3. Positron states and annihilation characteristics

2.3.1. Positron wave function, lifetime and momentum distribution After implantation and thermalization the positrons in semiconductors behave like free carriers. The various positron states yield specific annihilation characteristics, which can be experimentally observed in the positron lifetime and Doppler broadening experiments. The positron wave function can be calculated from the one-particle


Schrodinger equation [15]

_^V^«/ /^( r ) + V(v)^îv) = £^^+(r) , (6) 2m

where the positron potential consists of two parts

V(r)=: Vcoui(r) + VeorT(r). (7)

The first term is the electrostatic Coulomb potential and the second term takes into account the electron-positron correlation effects in the local density approximation. Many practical schemes exist for solving the positron state ^+ from the Schrodinger equation [15].

A positron state can be experimentally characterized by measuring the positron lifetime and the momentum distribution of the annihilation radiation. These quantities can be easily calculated once the corresponding electronic structure is known. The positron annihilation rate X., the inverse of the positron lifetime T, is proportional to the overlap of the electron and positron densities

= A- = TTTQC I ( l/x = X = nr^cj dr\ip^(r)\'n(r)y[n{r)l (8)

where ro is the classical radius of the electron, c the velocity of light, n(r) the electron density, and y[n] the enhancement factor of the electron density at the positron [15]. The momentum distribution p(p) of the annihilation radiation is a non-local quantity and requires knowledge of all the electron wave functions ^, overlapping with the positron. It can be written in the form

|2

(9) P(P) = ^ E / clr^"''"^+(r)^/(r)Vy(iO

where V is the normalization volume. The Doppler broadening experiment measures the longitudinal momentum distribution along the direction of the emitted 511 keV photons, defined here as the z-axis

P(PL) = / / dpAPyPip)^ (10) J—oo J—oo

The momentum distribution /o(p) of the annihilation radiation is that of the annihilated electrons, because the momentum of the thermalized positron is negligible.

The calculated positron density in a perfect GaN wurtzite lattice in shown in Fig. 5 [29]. The positron is delocalized in a Bloch state with k+ = 0. Due to the Coulomb repulsion from positive ion cores, the positron wave function has its maximum at the interstitial space between the atoms. The positron energy band E^{k) is parabolic and free particle-like with an effective mass of m* ^ 1.5 mo [15,30]. The calculated positron lifetime is 156 ps [29].

2.3.2. Deep positron states at vacancy defects In analogy to free carriers, the positron also has localized states at lattice imperfections. At vacancy-type defects where ions are missing, the repulsion sensed by the positron is lowered and the positron sees these kinds of defects as potential wells. As a result.


Fig. 5. The delocalized positron density in perfect GaN lattice according to theoretical calculations. The c-axis of the wurtzite structure is vertical in the figure. The positions of the Ga and N atoms are marked with open circles and diamonds, respectively. The contour spacing is 1/6 of the maximum value [29].

Fig. 6. The localized positron densities in ideal Ga and N vacancies in GaN according to theoretical calculations. The c-axis of the wurtzite structure is vertical in the figure. The positions of the Ga and N atoms are marked with open circles and diamonds, respectively. The contour spacing is 1/6 of the maximum value [29].

localized positron states at open-volume defects are formed. The positron ground state at a vacancy-type defect is generally deep, the binding energy is about 1 eV or more [15]. Fig. 6 shows the calculated density of the localized positron at unrelaxed Ga and N vacancies in GaN [29]. The positron wave function is confined in the open volume formed at the vacancy. The localization is clearly stronger in the case of Ga vacancy because the open volume of Voa is much larger than that of VN-

In a vacancy defect the electron density is locally reduced. This is reflected in the positron lifetimes, which are longer than in the defect-free lattice. For example, the calculated lifetimes in the unrelaxed Ga and N vacancies are 209 and 160 ps, whereas the lifetime in the GaN lattice is 156 ps [29]. The longer positron hfetime at Vca is due to the larger open volume compared with that of VN. The positron lifetime measurement is thus a probe of vacancy defects in materials. Direct experimental information on vacancies is obtained when (i) the lifetime spectrum has long components associated


with annihilations at vacancies, as seen in Fig. 2, and (ii) the average lifetime Xav (Eq. 4) increases above that in defect-free lattice, i.e. tav > "CB, which is also evident in Fig. 2.

Positron annihilation at a vacancy-type defect leads to changes in the momentum distribution p(p) probed by the Doppler broadening experiment. The momentum distribution arising from valence electron annihilation becomes narrower due to a lower electron density. In addition, the localized positron at a vacancy has a reduced overlap with ion cores leading to a considerable decrease in annihilation with high momentum core electrons. Experimentally, the increase of S parameter and decrease of W parameter are thus clear signs of vacancy defects in the samples. As an example, the experimental momentum distribution in the Ga vacancy is indeed much narrower than that recorded in the defect-free GaN lattice (Fig. 4).

2.3.3. Shallow positron states at negative ions A negatively charged impurity atom or an intrinsic point defect can bind positrons at shallow states even if these defects do not contain open volume [31,32]. Being a positive particle, the positron can be localized at the hydrogenic (Rydberg) state of the Coulomb field around a negatively charged center. The situation is analogous to the binding of an electron to a shallow donor atom. The positron binding energy at the negative ion can be estimated from the simple effective-mass theory

13.6eV / m * \ Z^ Eion,n = r— — - T ^ 10 - lOOmeV, (11)

where s is the dielectric constant, m* is the effective mass of the positron, Z is the charge of the negative ion, and n is the quantum number. With Z = 1-3 and n = 1-4, Eq. 11 yields typically ion = 10-100 meV, indicating that positrons are thermally emitted from the Rydberg states at 100-200 K.

The hydrogenic positron state around negative ions has a typical extension of 10 A and thus positrons probe the same electron density as in the defect-free lattice. Consequently, the annihilation characteristics (positron lifetime, positron-electron momentum distribution) are not different from those in the lattice. In the experiments we thus get Tion = "CB, 5'ion = SB and Wion = WB for the lifetime, 5 and W parameters at the negative ions. Although the negative ions cannot be identified with these parameters, information on their concentration can be obtained in the positron lifetime and Doppler broadening experiments [31,32].

2.4. Positron trapping at point defects

2.4.1. Positron trapping rate and trapping coefficient The positron transition from a free Bloch state to a localized state at a defect is called positron trapping. The trapping is analogous to carrier capture. However, it must be fast enough to compete with annihilation. The positron trapping rate K onto defect D is proportional to its concentration co

KD = I^DCD' (12)

The trapping coefficient fio depends on the defect and the host lattice. Since the


positron binding energy at vacancies is >1 eV, the thermal emission (detrapping) of positrons from the vacancies can be usually neglected. Due to the Coulombic repulsion, the trapping coefficient at positively charged vacancies is so small that the trapping does not occur during the short positron lifetime [33]. Therefore, the positron technique does not detect vacancies in their positive charge states. The trapping coefficient at neutral vacancies is typically fjio ^ lO ' -lO^^ at. s~ independently of temperature [33-35]. This value means that neutral vacancies are observed at the concentrations > 10^^ cm~^.

The positron trapping coefficient at negative vacancies is typically /JLD ^ 10^^-10^^ at. s~ at 300 K temperature [33-35]. The sensitivity to detect negative vacancies is thus >10^^ cm~- . The experimental fingerprint of a negative vacancy is the increase of /XD with decreasing temperature [34,35]. The T"^/^ dependence of /JLO is simply due to the increase of the amplitude of the free positron Coulombic wave as the thermal velocity of the positron decreases [33]. The temperature dependence of fio allows to distinguish experimentally negative vacancy defects from neutral ones.

The positron trapping coefficient /Xion at the hydrogenic states around negative ions is of the same order of magnitude as that at negative vacancies [32,36]. Furthermore, the trapping coefficient exhibits a similar T"^/^ temperature dependence. Unlike in the case of vacancy defects, the thermal emission of positrons from the negative ions plays a crucial role at usual experimental temperatures. The principle of detailed balance yields the following equation for the detrapping rate <5ion from the hydrogenic state [15]

Typically ion concentrations above 10^ cm~^ influence positron annihilation at low temperatures (T < 100 K), but the ions are not observed at high temperatures (T > 300 K), where the detrapping rate (Eq. 13) is large.

2.4.2. Kinetic trapping model In practise the positron annihilation data is analyzed in terms of kinetic rate equations describing the positron transitions between the free Bloch states and localized states at defects [12,13]. Very often the experimental data show the presence of two defects, one of which is a vacancy and the other is a negative ion. The probability of positron to be in the free state is «fi(0» trapped at vacancies ny{t) and ions wionCO- We can write the rate equations as

driB - T - = - ( ^ f i -^KV + KiordriB + îonîon, (14) At

Any

"dT

dnw

= KyriB — V^y, (15)

= KmnnB " (îon + 5ion)«ion, (1^)

at

where A., K and 8 refer to the corresponding annihilation, trapping and detrapping rates.

120 ^^- ^ K. Saarinen

Assuming that the positron at r = 0 in the free Bloch state, Eqs. 14-16 can be solved and the probability of positron to be alive at time t is obtained as

3

n{t) = Wfi(0 H-«v(0 + «ion(0 = X ] î exp[-X,r], (17)

indicating that the lifetime spectrum -dn{t)/dt has three components. The fractions of positron annihilations at various states are

/•OO

r]B = dtXsnBit) = 1 - Y}ion - rjv, (18) Jo

r)v= f dtkynvit) = "^^^^ , (19) Jo )^B-\-K:V -^

1 + îon/îc

poo ^.^^

rjion = / dr, Xionnionit) = 7 '^ ^ . (20) Jo (1 + îon/-îon) ( Afi + /Cy + . ' ' ' " )

These equations are useful because they can be related with the experimental average lifetime Xav, positron-electron momentum distribution P(PL) and Doppler lineshape parameters S and W as

tav = ^ B T B + ??ion'Cion + rjvTy, (21)

piPl) = r)BpB{PL) + rjionPioniPl) + TlvPviPl), (22)

S = TJBSB + y?ion*5ion + rjvSy, (23)

W = r?B W5 + r ionWion + y/vWv. (24)

Eqs. 18-24 allow the experimental determination of the trapping rates Ky and fCjon and consequently the defect concentrations can be obtained from Eq. 12. Furthermore, these equations enable the combination of positron lifetime and Doppler broadening results and various correlations between Xav, P(PL)^ S and W can be studied.

At high temperatures, all positrons escape from the hydrogenic state of the negative ions and no annihilations take place at them. In this case the lifetime spectrum has two components

h' =^~B'-^f^v. (25)

^2 = '^v, (26)

h = l-h= "' , . (27) Ky -\- AB — AD

The first lifetime xi represents the effective lifetime in the lattice in the presence of positron trapping at vacancies. Since Ky > 0 and /2 > 0, xi is less than x^. The second lifetime component xi characterizes positrons trapped at vacancies, and it can


be directly used to identify the open volume of the vacancy defect. When y/jon = 0 and ion/ ion > 1 the determination of the positron trapping rate and vacancy concentration

is straightforward using Eqs. 18-24

Kv = IXyCy = A5 = Afi = A^ — - - . (28) " V — "tflu Ov ~ O Wy — W

Notice that in this case tav, S and W depend linearly on each others. The linearity of experimental points in the (Xav, S), (Xav, W) and (5, W) plots provides thus evidence that only a single type of vacancy defect is trapping positrons in the samples.

3. Native vacancies and negative ions in GaN bulk crystals

Bulk GaN crystals are ideal substrates for the epitaxy of GaN overlayers for optoelectronic components at the blue wavelength. Such material can be synthesized of liquid Ga in high N overpressure at elevated temperatures [37,38]. Nominally undoped GaN crystals show usually high n-type conductivity with the concentration of electrons exceeding 10^^ cm~^. This is most likely due to the residual oxygen atoms acting as shallow donors [39,40]. When GaN is doped with Mg the electron concentration decreases and for sufficiently high amount of Mg dopants the samples become semi-insulating. It is interesting to study how the movement of the Fermi level toward the midgap changes the formation of charged native defects such as the Ga vacancy. Another basic question concerns the mechanism of the electrical deactivation. One can consider either (i) the gettering role of Mg leading to the formation of MgO molecules [41] or (ii) electrical compensation of O j donors by Mg^^ acceptors.

In this section we review our recent works [26,29,42,43] and show that Ga vacancy acts as a native defect in GaN crystals. We pay special attention to the identification of Voa by correlating the results of positron experiments with those of theoretical calculations. Our data indicate that the formation of Ga vacancies is suppressed by Mg doping. We show further that most of Mg is in a negative charge state, suggesting that the loss of n-type conductivity is due to compensation of OjJ donors by MgQ^ acceptors.

3.1. Samples and their impurity concentrations

The bulk GaN crystals were grown at the nitrogen pressure of 1.5 GPa and temperature of 1500°C [38]. We studied three samples, where the Mg doping level was intentionally varied during the crystal growth (Table 1). The Mg and O concentrations of the samples were determined experimentally by secondary ion-mass spectrometry (SIMS). The absolute concentrations were calibrated by implanting known amounts of O and Mg to undoped epitaxial GaN layers, where the residual Mg and O concentrations were well below 10 ^ cm~^

The secondary ion-mass spectrometry indicates that the oxygen concentration is about 4 X 10^^ cm"^ in undoped GaN (Table 1). The concentration of conduction electrons (n = 5 x 10 ^ cm~^ at 300 K) in this sample is thus almost the same as oxygen concentration. This is in good agreement with the previous evidence [39,40] that the n-type conductivity of GaN is due to unintentional oxygen doping. In the lightly Mg

122 Ch, 5 K. Saarinen

Table L

Sample

The concentrations of impurities

Undoped Lightly Mg doped Heavily Mg-doped

Oxygen concentration

(cm-3)

4 X 10^^ 12 X 10^9 9 X 10'^

and defects in the studied GaN bulk crystals

Magnesium concentration

(cm-3)

1 X 10'^ 6 X 10'9 10 X 10'^

Ga vacancy concentration

(cm-3)

2 x 10*^ 7 X 10^^

<10^6

Negative ion concentration

(cm-3)

3 X 10^^ 6 X 10^9

The magnesium and oxygen concentrations were determined by secondary ion mass spectrometry. The concentrations of Ga vacancies and negative ions are obtained from the positron annihilation data.

doped GaN the concentration of oxygen is 12 x 10 ^ cm~^, which is slightly larger than the Mg concentration of 6 x 10 ^ cm~^. The electrical experiments indicate that the sample has n-type conductivity, but the carrier concentration is less than in the undoped sample. The heavily Mg-doped sample has the O concentration of 9 x 10 ^ cm"^ and the Mg concentration of 1 x 10^^ cm~^ According to the electrical experiments the sample is semi-insulating. This is reasonable since the impurity concentrations determined by SIMS show that [Mg] % [O].

3.2. Positron lifetime results

The positron lifetime spectra in undoped and heavily Mg-doped GaN have been presented in Fig. 2 in Section 2. The temperature dependence of the average positron lifetime in various GaN crystals is shown in Fig. 7. Positrons annihilating in the heavily Mg-doped sample have only a single component of 165 ± 1 ps at 300 K (Fig. 2). The lifetime is almost constant as a function of temperature (Fig. 7).

These observations indicate that the heavily Mg-doped GaN is free of vacancy defects trapping positrons. In perfect GaN lattice the positron state is very delocalized and the positron density has its maximum in the interstitial region (see Fig. 5 in Section 2). The calculated lifetime in defect-free GaN lattice is 154 ps, which is in reasonable agreement with the experimental resuh XB = 165 ps. The lifetime XB = 165 ps can be estimated also on the basis of the lifetime decomposition at low temperature [42]. In heavily Mg-doped GaN all positrons thus annihilate in the delocalized state in the GaN lattice with the bulk lifetime XB = 165 ps. The slight increase of the bulk lifetime as a function of temperature (Fig. 7) can be attributed to the lattice expansion.

The positron lifetime spectrum recorded in undoped GaN is clearly different from that in highly Mg-doped sample (Fig. 2). The annihilation probability at t > 0.5 ns is much larger in the undoped GaN, indicating that the average positron lifetime Xav is longer than XB = 165 ps. In fact, lav = 167 ps at T = 10-150 K, and it increases up to Tav = 190 ps at 500 K (Fig. 7). In lightly Mg-doped GaN the positron lifetime is equal to XB = 165 ps at low temperatures of 10-200 K (Fig. 7). At 200-500 K, however, Xav is clearly larger than XB and reaches a value of 180 ps at 500 K. Since Xav > XB in both undoped and lightly Mg-doped samples, we can conclude that these GaN crystals contain vacancy defects.

The lifetime spectra recorded at 300-500 K in the undoped and lightly Mg-doped


290 h

250

210

S 190

o

180

170

160 L

^

GaN • Undoped n-type O Lightfy Mg-doped A Highly Mg-doped

300

Temperature (K) 500

Fig. 7. The average positron lifetime and the second lifetime component T2 VS. measurement temperature in GaN bulk crystals. The solid lines correspond to the analyses with the temperature dependent positron trapping model, where concentrations of Ga vacancies and negative ions (Table 1) are determined as fitting parameters [29,42].

GaN can be decomposed into two exponential components (Figs. 2 and 7). The positrons trapped at vacancies annihilate with the longer lifetime ly = ^2 = 235 ± 5 ps. Roughly the same lifetime has been observed also in thick epitaxial films on sapphire [44]. Within experimental accuracy the lifetime Xy = 235 ± 5 ps is the same in the n-type undoped crystal and in the lightly Mg-doped sample (Fig. 7), indicating that the same vacancy is present.

3.3, Identification of the native vacancy

Positron trapping and annihilation with the lifetime xy = 2 3 5 ps is observed at native vacancies in n-type GaN crystals. This value is typical for a monovacancy in materials which have the same atomic density as GaN, such as Al. It is also highly improbable that the N vacancy could induce such a long lifetime of Xy = 235 ps because the open volume at VN is very small. It is thus rather straightforward to associate the observed lifetime xy = 235 ps with Ga vacancy or a complex involving Vca-

The identification of the Ga vacancy can be put on a firm theoretical basis by


calculating the positron lifetimes theoretically from Eqs. 6-8. The electron densities were constructed using the atomic superposition method. The positron states (Eq. 6) were solved in a supercell of 256 atomic sites in a periodic superlattice using the generalized gradient approximation for electron-positron correlation [27,45].

The calculated positron densities at ideal Ga and N vacancies have been shown in Fig. 6 in Section 2. Both vacancies are able to localize the positron. However, the localization is clearly stronger in the case of Ga vacancy, because the open volume of Vca is much larger than that of VN. This fact is reflected in the calculated positron lifetimes, which are ty = 209 ps and xy = 160 ps for unrelaxed Ga and N vacancies, respectively. The experimental value of 235 ps can thus be associated with the Ga vacancy but not with the N vacancy.

The positron lifetime experiments show thus unambiguously that the native vacancies in GaN crystals belong to the Ga sublattice and have an open volume of a monovacancy. According to theoretical calculations [9,10,46], the Ga vacancy is negatively charged in n-type and semi-insulating GaN and thus acts as an efficient positron trap. On the other hand, the N vacancy is expected to be positive and repulsive to positrons [9,10,46,47]. In fact, the experimental and calculated positron lifetimes at Voa are in very good agreement if the lattice relaxation around Voa is taken into account. Fig. 8 shows the calculated positron density at the Ga vacancy, where the neighboring N atoms are relaxed 5% outwards. The relaxation lowers the electron density and increases positron lifetime. For the structure shown in Fig. 8 the calculated difference Xv — x^ is equal to the experimental value xy - x^ = 70 ps, thus yielding evidence that the N atoms surrounding Vca are indeed relaxed about 5% outwards. In fact, such a relaxation is expected for the Ga vacancy on the basis of theoretical calculations [9,10]. Unfortunately, the present positron experiments do not tell whether Voa is an isolated defect or part of a larger complex.

Fig. 8. The localized positron densities in a Ga vacancy in GaN according to theoretical calculations. The structure of the Ga vacancy has been relaxed 5% outwards. The c-axis of the wurtzite structure is vertical in the figure. The positions of the Ga and N atoms are marked with open circles and diamonds, respectively. The contour spacing is 1/6 of the maximum value [29].


3.4. Positron trapping at negative ions

At low temperatures the average positron lifetime decreases and the lifetime at the Ga vacancy xy remains constant (Fig. 7). This behavior indicates that the fraction r]y = (Xa — TB)/(TV — XB) of positrons annihilating at vacancies decreases. Since the positron trapping at negative Ga vacancies should be enhanced at low temperatures (Section 2), the decrease oir]y\^ due to other defects which compete with Ga vacancies as positron traps. Negative ions are able to bind positrons at shallow (<0.1 eV) hydrogenic states in their attractive Coulomb field (Section 2). Since they possess no open volume, the lifetime of positrons trapped at them is the same as in the defect-free lattice, tion = Xfi = 164 db 1 ps. The average lifetime increases above 150 K, when positrons start to escape from the ions and a larger fraction of them annihilates at vacancies.

The temperature dependence of the average lifetime can be modeled with kinetic trapping equations introduced in Section 2. Positron trapping coefficients at negative Ga vacancies /xv and negative ions /Xion vary as T'^^^ as a function of temperature [12,15]. The positron detrapping rate from the ions can be expressed as h{T) a

Eiofi is the positron binding energy at the Rydberg state of the ions (Eq. 13). The fractions of annihilations at Ga vacancies r]v and at negative ions r]ion are given in Eqs. 19-20 and they depend on the concentrations cy = Ky/fjiy and Qon = ' ion/z ion of Ga vacaucics and negative ions (Eq. 12), respectively, as well as on the detrapping rate S[on(T) (Eq. 13). We take the conventional value /xv = 2 X 10 ^ s"^ for the positron trapping coefficient at 300 K [12,13]. Inserting the annihilation fractions YJB, ??ion» and rjy from Eqs. 18-20 into the equation for the average lifetime tav = ÎB'^B + ion'Cion + Îv^v (Eq. 21) the resulting formula can be fitted to the experimental data of Fig. 7 with cy, cion, Ation and Eion as adjustable parameters. As indicated by the solid lines in Fig. 7, the fits reproduce well the experimental data with the positron binding energy of £"100 = 60 db 10 meV and trapping coefficient /Xjon = (7 ± 4) x 10^^ (T/K)~^-^. These values are close to those obtained previously in GaAs [36,48].

3.5. Defect concentrations and electrical compensation

The analysis explained above yields estimates for the concentrations of Voa and negative ions (Table 1). The Ga vacancy concentration is cy = 2 x 10 ^ cm~^ in the undoped GaN and Cy = 7 X 10^ cm~^ in the lightly Mg-doped crystal. In the heavily Mg-doped GaN no Ga vacancies are observed indicating that their concentration is below the detection limit of 10* cm~^. The concentration of Vca thus decreases with increasing Mg doping and the Ga vacancies disappear completely when the material gets semi-insulating, i.e. [O] ^ [Mg]. The same observation has been done also in Mg-doped GaN layers on sapphire [49,50]. This behavior is in good agreement with the results of theoretical calculations, which predict a low formation energy for the Ga vacancy and Voa-ON complex only in n-type material [9,10,46]. The creation of Ga vacancies in the growth of GaN crystals seems to follow thus the trends expected for acceptor defects in thermal equilibrium.

126 ^h. 5 K. Saarinen

The concentration of negative ions is 3 x 10 ^ cm~^ in undoped GaN and about 6 X 10^ cm~^ in lightly Mg-doped crystal. The ion concentration cannot be determined in heavily Mg-doped sample because no competitive positron trapping at Ga vacancies is observed and the positron annihilations at the ions cannot be distinguished from those in the GaN lattice. Due to the uncertainties in the values of positron trapping coefficients /xy and / ion the experimental errors of the absolute concentrations of negative ions are large, of the order of 50%. In the lightly Mg doped sample Cion represents the lower limit concentration only, because at temperatures of T < 200 K the average lifetime saturates at the value XB corresponding to annihilations in the GaN lattice.

In spite of the experimental inaccuracies the data indicates clearly that the concentration of negative ions increases by at least an order of magnitude with the Mg doping. Furthermore, the estimated concentrations of negative ions are close to those of Mg impurities as determined by the SIMS measurements (Table 1). Hence, it is natural to attribute the negative ions to MgQ . The positron results thus show that a substantial part of the Mg impurities is in the negative charge state in Mg-doped GaN bulk crystals. This suggests that the conversion of n-type GaN to semi-insulating with Mg doping is mainly due to an electrical compensation of oxygen donors with negatively charged Mg acceptors. The electrons originating from O donors are transferred to Mg acceptors charging them negatively. Since positron trapping at MgQ^ requires long-range Coulomb attraction, we can infer that MgQ^ ions are not spatially correlated with positive O^ donors. However, we cannot exclude the formation of MgO molecules [41], which may also contribute to some extent in the electrical deactivation of Mg-doped GaN crystals.

3.6. Conclusions

The positron experiments show the presence of Ga vacancies and negative ions in GaN crystals. The concentration of Ga vacancies decreases with increasing Mg doping, in good agreement with the trends expected for the Vca formation energy as a function of the Fermi level. The concentration of negative ions increases with Mg doping and correlates with the Mg concentration determined by SIMS. We thus associate the negative ions with Mg^^. The negative charge of Mg suggests that the loss of n-type conductivity in the Mg doping of GaN crystals is mainly due to compensation of Ojlj donors by Mg^^ acceptors.

4. Defects and doping in GaN layers grown on sapphire

The growth of thin epitaxial overlayers form the basis of electronic and optoelectronic device structures made of GaN and related alloys. The defects in such materials are thus technologically very important. From scientific point of view it is interesting to compare the structure and properties of defects in GaN layers with those in the GaN crystals. The influence of doping on the formation of vacancy-type defects in GaN layers is the topic of this section. We review systematic positron experiments [42,49,50] in variously doped 1-3 |jLm thick GaN layers grown by metal-organic chemical vapor deposition (MOCVD) on sapphire substrates.


Mean implantation depth (|im)

4s (U

S

0 0

0.47

0.46

0.45

0.44

0.43

0.42

0 0.26 0.79 1.5 2.4

_ p - ^ 1 ^ _

* • GaN(Mg) bulk crystal ° O GaN(Mg) unannealed

- *• • GaN(Mg) ann. at 750 °C -A

• • •

_ • _J • AO • ••

.9.?.$. 4Ad<l fi.2.aAa02.AfeQ- GaN ° ^ AA OQ lattice

A o°0 J

AA O A A O O

A A ^ -

U 1 \ 1 Li 10 20 30 40

Positron energy (keV)

Fig. 9. The low electron momentum parameter S as a function of the positron implantation energy in three Mg-doped GaN samples. The dashed line indicates the reference level of the S parameter in defect-free GaN lattice. The top axis shows the mean stopping depth corresponding to the positron implantation energy [50].

4.1. Mg doped GaN layers

Positron studies of thin 1-3 |xm epitaxial layers are performed by implanting typically E = 0-50 keV positrons into the sample utilizing a monoenergetic positron beam. The positron lifetime spectroscopy requires a pulsed positron beam, which are not yet in routine use. Hence, most of positron studies in thin overlayers are done with the Doppler broadening technique [42,49,50]. This is the case also in GaN layers, where no positron lifetime results are published yet.

In Doppler broadening spectroscopy the 511 keV annihilation line is described using the conventional low-momentum parameter S (see Section 2). Fig. 9 shows the S parameter as a function of the incident positron energy in three Mg-doped GaN samples. One of them is a heavily Mg-doped GaN bulk crystal, which is free of vacancies as explained in Section 3. The two other samples are Mg-doped GaN layers on sapphire. The as-grown layer is semi-insulating, but the sample annealed at 750°C exhibits p-type conductivity.

The incident positron energy can be converted into the mean positron implantation depth (top axis of Fig. 9) using Eq. 1. For a given positron implantation energy £", the S{E) parameter is a linear superposition of the values characterizing different positron

128 Ch, 5 K. Saarinen

annihilation states, weighted with the annihilation fraction r){E) for the corresponding state (see Eqs. 21-24)

S{E) = r]s{E)Ss + r)i{E)SL + ??subs(^)5subs. (29) In Eq. 29 5s, 5L, and 5subs represent the values of S parameter at the surface, in the

GaN layer, and in the substrate, respectively. When the layer contains defects we can write

r)L{E)Si = r)B{E)SB + J^ r)oi(E)Soi, (30)

where SB and Sot are the S parameters in the GaN lattice and in the defect i, respectively. In the GaN(Mg) bulk crystals no positrons annihilate at defects (rjoi = 0) and thus the surface annihilation fraction r]s(E) depends only on the positron diffusion length and implantation depth. As seen in Fig. 9 at E = 0 positrons annihilate with the S parameter Ss = 0.475 on the surface of the sample. When positron incident energy increases S parameter decreases and finally saturates at SL = SB = 0.435. Since the heavily Mg-doped GaN crystals are free of vacancies (Section 3), the S parameter 5^ = 0.435 characterizes positron annihilations at the defect-free GaN lattice.

In the Mg-doped GaN layers the S parameter (Fig. 9) decreases rapidly with increasing energy from the surface value Ss, whereafter it reaches a plateau. This plateau is the same as the value SB = 0.435 in the defect-free GaN(Mg) crystal, indicating that no positron annihilations take place in the open volume defects. At £" > 25 keV the S parameter decreases rapidly in Fig. 9. At these incident energies, positrons penetrate and annihilate in the sapphire substrate with a very low 5 parameter 5subs = 0.41.

No vacancy-type defects are thus observed in GaN(Mg) layers in the experiment of Fig. 9. The absence of positron trapping at vacancies has been further confirmed by temperature-dependent experiments [50]. The S parameter in GaN(Mg) layers is almost constant as a function of temperature in the range T = 10-600 K, which is typical for positron annihilations in the defect-free lattice. Although no vacancies are detected in p-type and semi-insulating GaN(Mg) layers, these samples may contain open-volume defects in positive charge states. For example, the nitrogen vacancy is expected to be positive both in semi-insulating and p-type GaN according to theoretical calculations [9,10,46] and experiments [47]. Furthermore, its formation energy should be low in p-type doping conditions [9,10,46]. Unfortunately, positron experiments give no information of VN, because its repulsive positive charge prevents positron trapping.

4.2, Nominally undoped n-type GaN layers

Nominally undoped GaN layers grown by MOCVD on sapphire show n-type conductivity typically in the n = 10^^-10^^ cm"^ range. This conductivity has been attributed to nitrogen vacancies [8,51], but more recent evidence shows that it is rather induced by the residual oxygen acting as shallow donors in GaN [9,10,52]. Secondary ion-mass spectrometry indicates that the oxygen concentrations are >10^^ cm~^ in the undoped samples studied by positron spectroscopy. In fact, the 'undoped' GaN layers are thus heavily doped with oxygen.


Mean implantation depth (p,m)

0.09 0.26 0.50 0.79 1.13

0.47

0.46

a 0.45

0.44

T T

• GaN(Mg) reference O Und.n=3.7xl0''cm^450K • Und.n=3.7xl0'^cm'\300K

A A A ,

» A A A A ^ 4 A A

••^•^ ^ ° o

J I L J L 5 10 15 20


25

Fig. 10. The low electron momentum parameter S as a function of the positron implantation energy in three nominally undoped GaN layers, which show n-type conductivity. The Mg-doped GaN reference sample indicates the level corresponding to positron annihilations in defect-free GaN. The top axis shows the mean stopping depth corresponding to the positron implantation energy [50].

4.2.7. Observation of native vacancies Fig. 10 shows the 5 parameter as a function of the incident positron energy E in the defect-free Mg-doped GaN reference sample and in two undoped GaN layers. The surface induces a large S parameter of Ss = 0.47 at £" = 0. When E increases S parameter decreases until it levels off at E = 5-15 keV to a plateau value S^, which characterizes the GaN layer. At larger incident energies S parameter decreases as annihilations start to take place at the sapphire substrate.

The difference between the undoped and Mg-doped layers is clear. In the undoped n-type samples S parameter at the GaN layer SL is clearly larger than in the Mg-doped reference sample, i.e. SL > SB- AS explained in Section 2, the reduced electron density at open-volume defects narrows the positron-electron momentum distribution and increases the S parameter. Hence, the experiment of Fig. 10 shows that nominally undoped n-type GaN layers contain vacancy defects.

The vacancies in the undoped layers were further studied by recording the low-momentum parameter 5 as a function of temperature (Fig. 11). This experiment was performed at a fixed positron energy of 10 keV, because at this energy the contributions of the annihilation events at the surface and in the substrate are negligible and all annihilations take place at the GaN layer (rji = 1). The low-momentum annihilation


0.450 Y- GaN

0.445

0.435 o o n=2.0xl0»8 cm-3

J-100 300

TEMPERATURE (K)

500

Fig. 11. The low electron momentum parameter S vs. measurement temperature in various undoped GaN samples. The carrier concentrations of the GaN layers are indicated in the figure [42]. The solid lines are fits to the temperature dependent positron trapping model [32,36].

parameter S in the GaN(n = 2.0 x 10 ^ cm~^) layer increases only slightly as a function of temperature (Fig. 11). This increase is similar as observed in defect-free GaN(Mg) sample, and it can be attributed to the thermal expansion of the lattice. The S parameter in all other GaN layers is clearly larger (Fig. 11), indicating again that vacancies are present. The temperature dependence of the S parameter in GaN(n = 3.7 x 10 ^ cm"^) and GaN(n = 1.2 x 10 ^ cm~^) samples is similar to that of the average positron lifetime or S parameter in the GaN bulk crystal. The low-momentum parameter S decreases at low temperatures because less positrons annihilate at vacancies. As explained in Section 3, this behavior can be attributed to shallow positron traps such as negative ions.

4.2.2. Identification of vacancies The positron lifetime spectrum in bulk samples can be analyzed with two components thus enabling the distinction between free and trapped positron annihilation events. However, the Doppler broadened annihilation line cannot be decomposed directly into momentum density spectra originating from the lattice and the vacancies. The identification of the vacancies is thus less direct. On the other hand, the combined lifetime and Doppler experiments in GaN bulk crystals allow the detailed analysis of the data recorded also in the GaN layers.

The number of different vacancy-type positron traps in the material can be studied by investigating the linearity between the annihilation parameters Xav, S and W. If only


0.070 F

0.068

13

< O H

0.066

0.064

0.062

0.060

n Bulk crystal

O Layer n=2.0x]0'«cm-3

O Layer n= 1.2x10' cm-^

• Layer n=7.()xlO'''cm-3

• Layer n=3.7xl0''cni-3

I . I

0.435 J =j

0.440 0.445

S PARAMETER

0.450

Fig. 12. The electron-momentum parameters S and W in the GaN samples at various temperatures. The straight line indicates that the same defect (Ga vacancy) is found in all samples.

a single type of a vacancy is present, these parameters depend linearly on each other (Section 2), when the fraction riy of positron annihilations at vacancies varies: A — {\ — riy)AB + r]yAy, where A is lav, 5 or W. The data in all GaN samples at various temperatures form a straight line in the (5, W) plane (Fig. 12). The same type of vacancy is thus present in the bulk crystal as well as in all GaN layers.

In the GaN bulk crystal the positron lifetime experiments show that the native vacancies are in the Ga sublattice (Section 3). On the other hand, the results of Fig. 12 indicate that the vacancy in the layers is the same as that in the bulk crystals. We can thus assign the native vacancies in the nominally undoped GaN layers with the Ga vacancy. The (5, Xav) and {W, tav) plots can be used to determine the S and W parameters corresponding to the lifetimes XB = 165 ps in the lattice and xy = 235 ps at the vacancy. The relative changes of S and W due to positron trapping at the vacancy with Tv = 235 ps are 5^/5^ = 1.038(2) and WV/WB = 0.86(2).

To confirm the identification of the Ga vacancy the high-momentum part of the Doppler broadening spectrum can be recorded using the coincidence of two y ray detectors for background reduction [29,42,49]. This experiment yields the superimposed electron momentum distribution p(p) = (1 — r]v) PB(P) + IvPv(p)^ where Psip) and Pv(p) are the momentum distributions in the lattice and at the vacancy, respectively. For a sample with the measured (5, W) values rjy,

S/SB-1 W/WB-1 (31) SV/SB-I WV/WB-I'

can be determined using the positron trapping model and the parameters SV/SB = 1.038(2) and WV/WB = 0.86(2) deduced above (see Eqs. 18-24). Since the momentum distribution in the lattice psip) can be measured in the defect-free reference sample


Theoretical Lattice

V N vac. Ga vac.

Electron momentum (10 mQc)

Fig. 13. The lower panel presents experimental core electron momentum densities at the perfect GaN lattice and at the Ga vacancy. The upper panel shows the result of the theoretical calculation at perfect GaN and at N and Ga vacancies. The momentum distributions are normalized to unity [29,42].

such as heavily Mg-doped GaN crystal, the distributions pvip) at vacancies can be decomposed from the measured spectrum p{p).

Fig. 13 shows the core electron momentum distributions psip) and pv{p) in the perfect GaN lattice and at the vacancy defect present in the undoped GaN layers, respectively. The intensity of the core electron momentum distribution is clearly smaller in the vacancy than in the GaN lattice. However, the momentum distributions at vacancies and in the bulk have clearly similar shapes over a wide momentum range.

The core electron momentum distributions (Eq. 9) can be theoretically calculated in a straightforward way, since the wave functions of free atoms can be applied (Section 2). The curves in Fig. 13 were calculated using the atomic superposition method [27], the generalized gradient approximation and the state-dependent enhancement scheme [45,53]. The theoretical results show that the annihilations with Ga 3d electrons give the clearly dominant contribution to the measured core electron momentum distribution at


GaN lattice as well as at Ga and N vacancies. The shape of the momentum distributions is thus similar in all these three systems. The calculated momentum distribution at the Ga vacancy has a cleariy lower intensity than that in the GaN lattice (Fig. 13), because the contribution of Ga 3d is reduced due to the surrounding N atoms. At the N vacancy the neighboring Ga atoms yield a core annihilation component, which is as strong as in the bulk lattice (Fig. 13). The experimental curve is compatible with the Ga vacancy, but not with the N vacancy. The Doppler broadening experiments thus support the identification of the Ga vacancy in nominally undoped n-type GaN bulk crystals. However, the present results cannot be used to specify further if the Ga vacancy is isolated or part of a larger complex.

4.3. Si'doped n-type GaN layers and correlation with oxygen

Ga vacancies are experimentally observed in n-type GaN layers and bulk crystals, when the n-type conductivity is due to residual oxygen. It is interesting to study whether the formation of Ga vacancies is promoted by other impurities acting as shallow donors, such as Si. For this purpose a set of 3-5 ixm GaN(Si) layers grown by MOCVD on sapphire was studied. These samples contain an order of magnitude less oxygen than Si as determined by magneto-optical measurements [54].

The S parameter in GaN(Si) samples is shown in Fig. 14 as a function of the positron implantation energy E. A high Ss parameter is recorded at the surface of the sample at £• = 0, but with increasing energy S(E) curve decreases and saturates to a value Si characterizing the layer at £" > 15 keV. It is remarkable that the layer-characteristic value SL is equal to the bulk value SB recorded in the Mg-doped reference sample. No vacancies are thus observed in GaN(Si) samples, indicating that their concentration is <10^^ cm~^. The S parameter in the GaN(Si) varies with temperature in a similar way as in the GaN(Mg) reference sample, further confirming that positrons detect no Ga vacancies in the Si-doped GaN layers.

4.4. Summary and comparison with theoretical calculations

Positron experiments detect Ga vacancies in various GaN layers grown by MOCVD on sapphire. The following trends can be summarized for the formation of Voa as a function of doping: (i) No Ga vacancies are found in p-type or semi-insulating Mg-doped layers, (ii) Ga vacancies are found at concentrations >10^^ cm~^ in nominally undoped GaN layers, which show n-type conductivity due to residual oxygen, (iii) Much lower Ga vacancy concentrations are observed in samples, where the n-type doping is done with Si impurities and the amount of residual oxygen is reduced.

According to the positron experiments the presence of Ga vacancies in GaN layers depends both on the Fermi level and impurity atoms in the samples. The same general trend is found in the epitaxial layers as in the bulk crystals: Ga vacancies are formed only in n-type doping concentrations when oxygen is present. However, if a similar doping is done with Si donors, no Ga vacancies are formed. A natural way to explain this behavior is to associate the observed Ga vacancies with complexes involving oxygen, such as Vca-ON. Although the direct observation of oxygen surrounding Voa has not


Mean implantation depth (|j,m)

s CO

CO

CO

0.48

0.47

0.46

0.45

0.44

0 0.26

"1 \ — •

• •

T ^°V O

• - . AO

A O %

- . " ^ ^

J 1

0.79 1.5 2.4

f" ^ n

GaN(Mg) reference Si-doped, n= 1.3x10 cm' _J Si-doped, n = 5.3 x 10 cm" Si-doped,n=1.2xl0^^cm"^

• w 1

i»?fi»^8ll^... 1 1 L

10 20 30 40


Fig. 14. The low electron-momentum parameter S as a function of the positron implantation energy in three Si-doped GaN layers. The Mg-doped GaN reference sample and the dashed line indicate the level corresponding to positron annihilations in defect-free GaN. The top axis shows the mean stopping depth corresponding to the positron implantation energy [50].

been conclusive in the positron experiments so far, this is in principle possible using the Doppler broadening technique to probe the electron momentum density (Section 2).

Theoretically the formation energies of charged defects in thermal equilibrium depend on the position of the Fermi level in the energy gap, as shown in the calculated results of Fig. 15 [9,10,46]. The negatively charged defects such as the Ga vacancy have their lowest formation energy when the Fermi level is close to the conduction band, i.e. in n-type material (Fig. 15). On the other hand, the formation energy of Vca is high in semi-insulating and p-type material. These trends correlate well with the experimental observations with the positron spectroscopy, where Ga vacancies are observed only in n-type material. In fact, the theoretical results of Fig. 15 predict that the formation energy of Voa-ON pair is even lower than that of isolated Voa- This is consistent with the experimental arguments to associate the observed Ga vacancies with the Voa-ON complex. In general, the creation of Ga vacancies (or Vca complexes) in the growth of both GaN crystals (Section 3) and epitaxial layers seems to follow the trends expected for acceptor defects in thermal equilibrium.

The Voa-ON complexes may form at the growth temperature, when mobile Ga vacancies are trapped by oxygen impurities. Similarly, one could expect the formation of Vca-Sica complexes in Si-doped GaN, as suggested by Kaufmann et al. [55]. In the


1.0 2.0

Fig. 15. The formation energies of various defects in GaN as a function of the Fermi level |Xe according to theoretical calculations [10].

positron experiments of Fig. 14, however, these complexes are not observed. According to theory [9], the binding energy of Vca-ON pair (about 1.8 eV) is much larger than that of Voa-Sioa complexes (0.23 eV). The difference in stability is due to the electrostatic attraction: Voa and ON are nearest neighbors whereas Vca and Sica are only second nearest neighbors. The Voa-ON pairs are thus more likely to survive the cooldown from the growth temperature than Voa-SiGa- Hence, Ga vacancy complexes are detected by positrons only in materials containing substantial concentrations of oxygen, but their concentration in Si-doped material is much lower. However, the Vca-Sioa may be present in other type of GaN samples [55], particularly since the formation of Ga vacancies depends also on the stoichiometry of growth conditions as shown in Section 5.1.

4.5. Yellow luminescence

The parasitic yellow luminescence band at about 2.2-2.3 eV is commonly observed in n-type GaN. There is an increasing amount of evidence that this transition takes place between a shallow donor and a deep acceptor [8-10,56], and the Ga vacancy has been suggested as the defect responsible for the acceptor level [9,10,57]. Since Ga vacancies can be both identified and quantified by positron annihilation spectroscopy, it is interesting to compare their concentration with the intensity of the yellow luminescence.

The Ga vacancies were studied by positron measurements in a set of undoped n-type GaN epilayers grown on sapphire by MOCVD. The results of the Doppler broadening experiments have been given in Figs. 10 and 11 in Section 4.2. The concentration of the Ga vacancies can be estimated using the simple formula (Eq. 28)

[Voa] = ^ ^ ^ | ^ (32) /XyXfi {Sy - S)

at the high temperature plateau of Fig. 11, where the influence of negative ions and


Ga VACANCY CONCENTRATION (10 ^ cm' )

Fig. 16. The intensity of the yellow luminescence vs. the Ga vacancy concentration in GaN epitaxial layers. The inset shows the luminescence spectrum in the four studied layers, indexed according to the increasing Ga vacancy concentration [42].

Other type of shallow positron traps can be neglected (A at is the atomic density). Taking the positron trapping coefficient iiy ^ 10 ^ s~ and Sy/Ss = 1.038 we obtain the concentrations in the 10^* -10^^ cm~^ range. They are shown by the horizontal axis of Fig. 16.

The luminescence experiments were performed by exciting with the 325 nm line of a He-Cd laser. In order to probe approximately the same region below the surface of the epilayer as in the positron experiments, the luminescence was excited from the substrate side of the sample. The emitted radiation was analyzed by a 0.5-m monochromator equipped with a photomultiplier. In order to compare the yellow luminescence of different samples its intensity was averaged over the surface of a particular sample and the same optical alignment was used to collect the light emitted by each sample. No special normalization to the band-edge luminescence was done, but it was rather assumed that the dominant recombination channels are non-radiative in each sample. In such a case the intensity of the yellow luminescence can be expected to be proportional to the concentration of defects participating in this optical transition.

Fig. 16 shows the intensity of the yellow luminescence in MOCVD layers as a function of the Voa concentration obtained from positron experiments. In this set of samples the yellow luminescence correlates perfectly with the concentration of the Ga vacancies. This correlation provides evidence that native Ga vacancies participate the luminescense transition by acting as the deep acceptors.

The experimental results in GaN bulk crystals support further that Ga vacancies are responsible for the yellow luminescence. The Ga vacancies are present at concentrations 10^^-10^^ cm~^ in undoped heavily n-type material (Section 3), which always shows


strong emission of yellow light [40]. Furthermore, no signs of Vca nor yellow luminescence is observed in semi-insulating Mg-doped crystals (Section 3). Very interestingly, recent results provide evidence that yellow luminescence is due to defects acting as compensating acceptors in n-type GaN [58]. Together with the present positron data this suggests that the Ga vacancy is the dominating intrinsic acceptor (see also Section 5.1) as well as responsible for the yellow luminescence. However, correlations such as that in Fig. 16 are inherently complicated, mainly because the quantification of photolumines-cence data is difficult. For example, the yellow luminescence has been observed to disappear after electron irradiation [59-61], most likely because other photoelectron recombination channels become possible due to the introduction of irradiation-induced defects.

5. Point defects and growth conditions of epitaxial GaN

Epitaxial GaN layers can be grown using several methods, the most common of which are the metal-organic chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE). The lattice mismatch at the layer/substrate interface induces dislocations in the layers at concentrations up to 10 ^ cm"-^. The quality and the properties of the layers depend further on various parameters such as the stoichiometry of the growth conditions, growth temperature and the intermixing of the atoms between the layer and the substrate. In this section we review the positron results concerning the point defects formed in GaN layers under various Idnds of growth conditions.

5.1. Stoichiometry of the MOCVD growth

The formation of Ga vacancies was studied in samples where the stoichiometry of growth conditions was varied in the MOCDV reactor [62]. The undoped GaN layers of thicknesses 1-5 jxm were grown on sapphire substrates by MOCVD technique at 950-1100°C, as described earlier [63]. The precursors employed were triethylgallium (TEGa) and ammonia (NH3). The same TEGa flow was used for all samples and the NH3 flow was adjusted to change the stoichiometry of the growth conditions. The V/III molar ratio varied from 1000 to 10,000. As reported earlier [63], the growth rate as well as the electrical and optical properties of the samples change strongly with the V/III molar ratio. At lower ratios the photoluminescence shows broadened band edge structures and enhanced donor-acceptor pair recombination. The carrier concentrations at room temperature decrease from 10^^ to 10^ cm~^ when the V/III molar ratio increases from 1000 to 10,000 [63].

All samples were investigated at room temperature as a function of the positron beam energy E (Fig. 17). When positrons are implanted close to the sample surface with £• = 0-1 keV, the same S parameter of 5 = 0.49 is recorded in all samples. This value characterizes the defects and chemical nature of the near-surface region of the sample at the depth 0-5 nm. At 5-15 keV the S parameter is constant indicating that all positrons annihilate in the GaN layer. The data recorded at these energies can thus be taken as characteristic of the layer. The lowest S parameter is obtained in the Mg-doped reference layer, where we get S = 0.434 at £ = 5-15 keV. This value corresponds to positrons annihilating as delocalized particles in the defect-free GaN lattice.


Mean implantation depth (jim)

0.47

0.46

0.45

0.44

0.43

0 0.09 0.26 0.50 0.79 1.13

- 1 ^ • 1 ' \ ' \ ' 1 ' r=|

\ GaN j • Mg-dopedref. J

" o O V/m ratio 5000 1 A V/m ratio 8000 "

o J

\ 1

" cP \ -

cP

=J ^ 1 1 \ ^ 1 1 1 1 L= 10 15 20 25


Fig. 17. The low electron-momentum parameter S as a function of the positron implantation energy in three GaN samples. The top axis shows the mean stopping depth corresponding to the positron implantation energy [62].

The 5 parameter in all n-type layers is larger than in the Mg-doped reference sample (Fig. 17). The increased S parameter indicates that the positron-electron momentum distribution is narrower than in the defect-free reference sample. The narrowing is due to positrons annihilating as trapped at vacancy defects, where the electron density is lower and the probability of annihilation with high-momentum core electrons is reduced compared to that of delocalized positrons in the lattice (Section 2). The increased S parameter is thus a clear sign of vacancy defects present in the n-type GaN layers.

The number of different vacancy defects trapping positrons can be investigated through the linearity between the low and high electron-momentum parameters S and W. If only a single type of vacancy is present, the W parameter depends linearly on the 5* parameter when the fraction of positron annihilations at vacancies rjy varies. The plot of the W parameter vs. S parameter thus forms a line between the endpoints (5^, WB) and (5v, Wy) corresponding to the defect-free lattice and the total positron trapping at vacancies, respectively. The S and W parameters of all samples are plotted in Fig. 18. All data points fall on the same line, which goes through the endpoint (5^, WB) = (0.434, 0.069) obtained in the Mg-doped reference sample. The same type of vacancy is thus found in all samples. The positron trapping fraction r)y and the S parameter vary from one sample to another due to the different vacancy concentrations.

The slope of the line in Fig. 18 characterizes the vacancy defect present in all layers. The value A5'/AW = 2 is the same as determined for the native Ga vacancy in


0.070

0.068 h

T ^

8000-i

0.435 0.440 0.445 0.450 0.455

S parameter

Fig. 18. The low and high electron-momentum parameters S and W in various samples. The V/III molar ratio of each sample is indicated in the figure. The straight line indicates that the same vacancy defect (Ga vacancy) is observed in all samples [62].

Section 4. To confirm the identification, we recorded the positron-electron momentum distribution in the Mg-doped sample and the layer with V/III ratio of 8000 using the two-detector coincidence technique [27]. The high-momentum part of the momentum distribution was similar as observed for the Ga vacancy (Fig. 13 in Section 4). We can thus identify the native vacancy in the GaN layers as the Ga vacancy. As explained in Section 4, the presence of Ga vacancies can be expected in n-type undoped GaN due to their low formation energy. The different levels of the S parameter in Fig. 17 indicate that the concentration of the Ga vacancies seems to depend on the stoichiometry of growth.

In the samples with the V/III molar ratios 8000 and 5000 the Doppler broadening experiments were performed as a function of temperature at 20-500 K. The curves were qualitatively similar as shown in Fig. 11 in Section 4. At low temperatures T < 150 K the S parameter decreases indicating that positrons are trapped at shallow traps such as the Rydberg states of negative ions in addition to Ga vacancies. At high temperatures T > 250 K positrons are able to escape from these traps. This effect increases the S parameter as a function of temperature, because more positrons are able to get trapped at vacancy defects. At 300-500 K the S parameter is constant indicating that the detrapping from the negative ions is complete. At these temperatures only Ga vacancies act as positron traps.

In order to quantify the concentration of Voa the S parameter data at 300 K was analyzed with the positron trapping model (Section 2.4.2). When Ga vacancies are the


10

10"

a

10'

10 ^ L i . 3000 6000 9000

V/III Molar ratio

Fig. 19. The concentration of Ga vacancies vs. the V/III molar ratio in undoped GaN samples. The straight line is drawn to emphasize the correlation [62].

only defects trapping positrons, their concentration can be determined with the simple formula (Eq. 28)

[Vca] fJiXB Sv - S'

(33)

where XB = 165 ps is the positron lifetime at the GaN lattice,[42] /x = 10 ^ s~ is the positron trapping coefficient [12] and Aat = 8.775 x 10^ cm~^ is the atomic density of GaN. For the S parameter at the Ga vacancy we take SV/SB = 1.046. This value is slightly larger than presented eariier in Section 4, because the energy resolution of the ganmia spectroscopy system used in this study (1.2 at 511 keV) is better than in our earlier study [42] (1.5 at 511 keV).

The results in Fig. 19 indicate that the concentration of Ga vacancies is proportional to the stoichiometry of the growth conditions. Rather low [Vca] ^ 10 ^ cm~^ is observed for the sample with the V/III molar ratio of 1000. When the V/III molar ratio becomes 10,000, the Voa concentration increases by almost three orders of magnitude to [Voa] ^ 10 ^ cm~^. This behavior shows that empty Ga lattice sites are likely formed in strongly N rich environment.

It has been shown in previous works that the V/III molar ratio has an influence on the growth rate as well as on the electrical and optical properties of the GaN layers [63]. The present results indicate that the formation of intrinsic point defects such as the Ga vacancy depend also heavily on the stoichiometry of the growth conditions. The Ga vacancy is negatively charged and thus acts as a compensating center in n-type material.


Table 2. The concentrations of free electrons, oxygen and Ga vacancies in the GaN layers grown with different V/III molar ratios

V/III molar ratio Carrier concentration Oxygen concentration Ga vacancy concentration (cm~^) (cm~^) (cm~^)

1000 10^0 >1020 3x10^^ 5000 4 X 10^^ 4 X 10'^ 8000 10^6 1 X 10*9 1 X 10*9

The oxygen concentrations were determined by secondary ion mass spectrometry and the concentrations of Ga vacancies were obtained from the positron annihilation data.

Indeed, the Hall experiments show that the free electron concentration decreases from 10^^ to 10^ cm"^ when the V/III molar ratio increases from 1000 to 10,000 [63]. Simultaneously, [Vca] increases from 10* to 10 ^ cm"^ (Fig. 19). The charge state of Vca in n-type material is 3— [9,10]. The compensation via the formation of Ga vacancies explains thus most of the decrease of the carrier concentration, when the V/III molar ratio increases from 1000 to 10,000.

In order to obtain a more quantitative picture of the electrical compensation of GaN the oxygen concentrations were determined in some of the samples using secondary ion-mass spectrometry. As seen in Table 2, the oxygen concentrations vary non-monotonously in the 10^^-10^^ cm~^ range when the V/III ratio increases from 1000 to 8000. Interestingly, the carrier concentration seems to follow approximately the relation n ^ [0]-[VGa] in the data of Table 2. The SIMS, positron and electrical data are thus consistent with the simple picture that free electrons are supplied by shallow O^ donors, which are partially compensated by negative Ga vacancies (or Voa complexes) acting as dominant deep acceptors.

To summarize, we have applied positron annihilation spectroscopy to study the vacancy defects in undoped GaN layers, where the stoichiometry was changed by adjusting the V/III molar ratio. Gallium vacancies are observed in all samples. Their concentration increases from 10^^ to 10^^ cm~^ when the V/III ratio changes from 1000 to 10,000. Hence, the Ga vacancies are formed very abundantly when the growth conditions become more nitrogen rich. The decrease of free electron concentration with increasing V/III molar ratio correlates with the creation of Ga vacancies. This effect can be attributed to the compensation of impurities induced by the negatively charged Ga vacancies.

5.2. Dislocations and the formation ofGa vacancies in GaN layers

The results of Sections 3 and 4 indicate that Ga vacancies (or complexes involving Voa) exist in GaN when the material is n-type and contains oxygen. The same trend is observed for both GaN bulk crystals and GaN grown by MOCVD on sapphire. However, the dislocation densities in these materials are very different. The lattice mismatch between GaN layer and sapphire substrate generates a highly dislocated region within a few hundred nanometers from the interface. The threading dislocations pass through the whole layer and have typically a high concentration of 10^° cm"^ [1].


Mean implantation depth (^m)

0.26 0.79 1.5 2.4

0.46 h

0.45

§ 0.44

0.43

O GaN(Mg) sample #1 • GaN(Mg) sample #2

''' "Se*o55^88S^®c

-• •• H

'oOo

c^

0 10 20 30 40


Fig. 20. The low electron-momentum parameter S as a function of the positron implantation energy in two Mg-doped GaN layers grown on sapphire. The top axis shows the mean stopping depth corresponding to the positron implantation energy. The maximum of the S(E) curve at E = 30 keV indicate the presence of open-volume defects at the highly dislocated GaN/AhOs interface [50].

On the other hand, the dislocation density in GaN bulk crystals is only <10^ cm~^. A relevant question is whether the formation of Ga vacancies in the GaN layers is related with the high concentration of dislocations.

Fig. 20 shows the S parameter in two semi-insulating Mg-doped GaN layers on sapphire, grown by two different groups in different MOCVD reactors. The S vs. E curve decreases rapidly from the surface value Ss and saturates at £" = 5-20 keV to the value SL characterizing the Mg-doped layer. The layer-characteristic value SL is equal to that in defect-free GaN lattice, indicating that both layers are free of Ga vacancies trapping positrons (see Section 4.1). However, the S{E) curves in the two samples are very different at £" = 20-40 keV, which corresponds to a depth of the GaN/sapphire interface. In sample #1 S parameter decreases at £" > 30 keV since annihilations start to occur at the sapphire substrate. The S{E) data in sample #2 forms a maximum around £• = 30 keV and decreases towards the sapphire value Ssubs only at larger incident positron energies.

The increased S parameter seen at £ = 30 keV is the fingerprint of open-volume defects, which are clearly present in the highly dislocated region at the GaN/sapphire interface in sample #2. According to the data of Fig. 20 these vacancies extend 100-300 nm from the interface into the GaN layer, but most of the Mg-doped layer is free of these defects. As concluded in Section 4.4 the absence of Ga vacancies in Mg-doped GaN can be explained by the high formation energy of these defects. The data of Fig. 20


Mean implantation depth (|Lim)

0.09 0.26 0.50 0.79 1.13

0.46

0.45

e 2

OH

0.44 h

0.43 h

"~l \

o •

o

•• o

h °°

\ 1 i n

GaN • Homoepitaxial layer o Mg-doped ref. layer

-

»•• •^— ••^•u ^y^ «_^

—

1 ^ ^ o

U 1

o

1 \ 1 L _

10 15 20 25


Fig. 21. The low electron-momentum parameter S as a function of the positron implantation energy in nominally undoped homoepitaxial GaN layer, which shows n-type conductivity. The Mg-doped GaN reference sample indicates the level corresponding to positron annihilations in defect-free GaN. The top axis shows the mean stopping depth corresponding to the positron implantation energy [50].

suggests that the dislocations have influence on the vacancy formation only at depths close to the interface between GaN and sapphire.

The lattice mismatch and the high dislocation density can be avoided by growing GaN layers homoepitaxially on the GaN bulk crystals. Such a sample has been studied in Fig. 21, which shows the S{E) results in n-type homoepitaxial layer and in the Mg-doped reference GaN. The homoepitaxial layer is not intentionally doped and its n-type conductivity is most likely due to oxygen impurities. As seen in Fig. 21, the 5 parameter in the n-type homoepitaxial sample is clearly larger than in the Mg-doped reference layer. This indicates that vacancies are present in the homoepitaxial GaN. The defects can be identified as Ga vacancies using the W vs. 5 analysis similarly as in Sections 4.2 and 5.1.

The presence of Ga vacancies in homoepitaxial n-type GaN and their absence in semi-insulating Mg-doped layers on sapphire are both indications that the formation of Ga vacancies depends much more on the doping than on the substrate material and dislocation density. Furthermore, the Ga vacancies are observed in n-type bulk crystals, where the dislocation density is <10^ cm'^. We conclude that the n-type doping (Section 4.2), presence of oxygen (Section 4.4) and the N rich growth conditions (Section 5.1) promote the formation of Ga vacancies, but the lattice mismatch, substrate


material and dislocation density seem to have influence on the vacancy concentration only close to the layer/substrate interface.

53. Interdijfusion of atoms at GaN layers grown by MBE on Si

Positron spectroscopy has been applied to study vacancy defects in GaN layers grown by molecular-beam epitaxy (MBE) on Si [64]. The SIMS experiments show that a strong intermixing of atoms takes place at the GaN/Si interface. The interdiffusion is accompanied by changes in the optical and electrical properties of the layers. New peaks appear in the photoluminescence and a highly p-type layer is formed at the GaN/Si interface [64].

The Doppler broadening of the 511 keV annihilation radiation was recorded as a function of the positron beam energy in nominally 0.78 |xm thick undoped GaN layers grown at 660, 720, 760, and 780°C directly on the Si( l l l ) substrates without buffer layers. The S parameter vs. the positron beam energy E is shown in Fig. 22 for all measured samples. The S(E) curve is a superposition of the specific parameter values for different positrons states. The fraction of positrons in each states varies with the beam energy, i.e. the positron stopping depth. At £" = 0 keV positrons annihilate at the GaN surface. Between 2 and 8 keV positrons stop and annihilate in the GaN overlayer. Above 10 keV an increasing fraction of positrons penentrate to the Si substrate and the S parameter shoots up towards the Si-specific value Ssi = 0.520(1).

Mean implantation depth (|j,m)

6

0.50

0.48

0.46

0.44

0 0.09 0.26 0.50 0.79 1.13

1 1 i 1 1 n

-' ^ ' T=780''C * V ••• J

\ A^V^-* 0°

T = 760»C V A , * * O°° \ * ' • o \ 4 A • o

\ ^ A • O 1 \ ATA • o

-: T = 720»C > V / -] \ A A^ / \ O* \ A* ^ • \

1' Xt''.- ° \ °°s»4i>»64»««;J...« J" T = 660*C J

o 1

0=° V o .

^ O 0

o 1

°°Oooo,OoooOoOoO° Lattice

J 1 1 1 1 l_ 10 15 20 25


Fig. 22. The low electron-momentum parameter S vs. positron implantation energy in undoped GaN/Si(lll) grown by MBE at various temperatures. The dashed lines indicate the specific S values for free positrons in the GaN lattice and trapped positrons in Ga vacancies [64].


0.07 h

0.06 h

g 0.05 2

0.04 h

0.03 h

r <5

h

h-

" T 1 " " -GaN Lattice

VGH X K

O T = 660»C • T = 720»C A T = 760"C A T = 780"C

1 i

"1 1 r

Vacancy cluster

0 1 ^

1 i 1

A

A

A

0.44 0.46 0.48 0.50 0.52

S parameter

Fig. 23. The (S, W) plot for the GaN/Si(l 11) layers. The surface effects have been dropped out. For the sake of clarity, the layer characteristic values have been marked by bigger symbols. The open circles with a central cross denote the positron-annihilation states [64].

The level of the plateau from 2 keV to 8 keV characterizes the corresponding GaN layer. In the layer grown at 660°C, the level is very close to that found for free positrons in the GaN lattice, SB = 0.434(1) (Section 4.1). In the other three layers the plateau levels are much higher, even above the specific values of the Ga vacancy determined earlier in Section 4. This is a clear indication of vacancy-type defects in the layers.

We use the (5, W) plot to illustrate the positron states and to estimate the specific (SD, ^D) values for the defect which trap positrons in the layers. The iS(E), W(E)) points have been marked on the plot in Fig. 23. The surface effects have been dropped out by skipping the points with E < 5 keV. The positions of the positron states in the defect-free GaN lattice and in the Si substrate have been indicated, too. For the sake of clarity, the plateau values averaged from 5 to 8 keV have been marked by bigger symbols. One can see that all the plateau points fall on one line which goes through the 'GaN Lattice' point. This means that the annihilations in the plateau regions arise as superpositions of two states: the free positrons in the lattice and the trapped positrons in defects. The defect is same in all layers and the specific defect state (So, WD) must lie on this line, too. If we extrapolate the (5, W) points of high E through the Si substrate state, we get a second line. The crossing point ('Vacancy cluster') is the positron state in the common defect present in all layers. All the experimental points fall inside the triangle 'GaN Lattice-Vacancy cluster-Si' meaning that the experimental data in Fig. 23 can be explained as superpositions of annihilations in these three positron states.

The defect which trap positrons in the GaN layers has the normalized specific values

146 ^h. 5 K. Saarinen

SO/SB = 1.10(2) and WD/WB = 0.75(3). These values are clearly different from those of the Ga vacancy {SVGJSB = 1.038, WWGJWB = 0.86), which are also marked in Fig. 23. We conclude that the defect is far from being a monovacancy. The decoration of a Ga vacancy by a Si impurity cannot change much the specific (S,W) values, as the Si atom occupies a substitutional site in the second nearest shell. Therefore the defect cannot be a Vca-Si pair. The high So and low WD values of the defect suggest an open volume at least twice that of a monovacancy, i.e. the defect is a vacancy cluster. Using the positron trapping coefficient of 10 ^ s~ we can estimate that the vacancy-cluster concentrations are <10^^ cm~^, 5 x 10 ^ cm~^, 8 x 10^ cm~^, and 1 x 10^ cm~^ in the layers grown at 660, 720, 760, and 780°C, respectively.

The SIMS results clearly demonstrate the strong Si diffusion across the GaN/Si interface when no buffer layer exists. The Si profile penetrates 100-300 nm to the GaN side. Looking carefully the positron results, we see that the S{E) values at the interface regions (E = 10-14 keV) increase rapidly above the plateau levels in Fig. 22, but the corresponding points in the S-W plot of Fig. 23 still continue to follow the 'GaN lattice-Vacancy cluster' line. This means that at the interface regions the positrons encounter vacancy-cluster concentrations which are 5-10 times higher than in the plateau regions.

Vacancies are known to be vehicles for substitutional atoms. In GaN samples grown by MBE on Si positrons do not detect Ga vacancies nor Vca-Si pairs. Instead, vacancy clusters are observed which are evidently stable traces left by diffusion processes during the layer growth. We can conclude that positron measurements detect vacancy clusters as a result of the strong interdiffusion across the GaN/Si interface without a buffer layer.

The Ga vacancy has been identified in MOCVD layers grown on sapphire and their concentration has been seen to correlate with the yellow luminescence intensity (Section 4.5). The PL results in the GaN layers on Si show no traces of the yellow band. This is consistent with the absence of the Ga vacancy signal in positron measurements.

6. Summary

Positron annihilation spectroscopy can be used to identify vacancy defects in bulk semiconductor crystals and epitaxial layers. It yields quantitative information on vacancy concentrations in the range 10 ^ - 10^^ cm~^. Positron localization into the hydrogenic states around negative centers can be applied to study also ionic acceptors that have no open volume.

Positron experiments detect Ga vacancies as native defects in GaN bulk crystals. The concentration of Voa decreases with increasing Mg doping, as expected from the behavior of their formation energy as a function of the Fermi level. The trapping of positrons at the hydrogenic state around negative ions gives evidence that most of the Mg atoms are negatively charged. This suggests that Mg doping converts n-type GaN to semi-insulating mainly due to the electrical compensation of O^ donors by Mg^^ acceptors.

Ga vacancies are observed as native defects in various n-type GaN overlayers grown by MOCVD on sapphire. Their concentration is >10^^ cm~^ in nominally undoped material, which show n-type conductivity due to residual oxygen. When similar doping


is done with Si impurities and less oxygen is present, the concentration of Ga vacancies is lower by at least an order of magnitude. No Ga vacancies are observed in p-type or semi-insulating layers doped with Mg. These trends agree well with the theoretical calculations, which predict that the formation energy of Ga vacancy is high in p-type and semi-insulating material, but greatly reduced in n-type GaN, and even further reduced due to the formation of Voa-ON complexes.

In addition to doping, the presence of open-volume defects in GaN layers depends on the growth conditions. The concentrations of Ga vacancies increases strongly when more N rich stoichiometry is applied in the MOCVD growth. On the other hand, the lattice mismatch and associated dislocation density seem to have less influence on the formation of point defects than doping and stoichiometry - at least at distances >0.5 |xm from the layer/substrate interface. This suggests that the formation of point defect in both epitaxial layers and bulk crystals follows mainly the trends expected for defects in thermal equilibrium.

Acknowledgements

I would like to acknowledge the essential contributions of my collaborators P. Hauto-jarvi, T. Laine, J. Nissila and J. Oila in the positron spectroscopy group of Laboratory of Physics at Helsinki University of Technology, Finland. I am grateful for the theoretical support and discussions with M.J. Puska, M. Hakala, T. Mattila and R.M. Nieminen. I would like to thank T. Suski, I. Grzegory and S. Porowski (UNIPRESS, Warsaw, Poland) for providing bulk GaN crystals for positron experiments and for many discussions. GaN epitaxial layers for positron studies have been supplied by J.M. Baranowski's group (University of Warsaw, Poland), O. Briot's group (Universite Montpellier II, France) and E. Calleja's group (Universidad Politecnica, Madrid, Spain). I would like to acknowledge their effort, collaboration and comments.

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CHAPTER 6

Persistent photoconductivity in Ill-nitrides

H.X. Jiang and J. Y. Lin

1. Introduction

Ill-nitride based devices offer great potential for applications such as high power and high temperature electronics, UV-blue light emitting diodes (LEDs) and lasers, and solar-blind UV detectors. Researchers in this field have made extremely rapid progress toward materials growth as well as device fabrication [1,2]. Despite the many efforts on these materials, understanding and control of impurity properties and p-type doping in these materials remain one of the most important aspects to be further improved. Needless to say, the future development of GaN devices depends critically on improving n- and p-type doping, which would rely heavily on the full understanding of physical properties of doped impurities, native defects, as well as impurity-defect complexes in these materials.

Due to their wide band gaps, effects of deep level centers on the Ill-nitride materials and devices are expected to be more pronounced than in narrower band gap materials. In deed, deep level centers and the associated persistent photoconductivity (PPC) effect, have been observed in a wide variety of Ill-nitride materials and structures. Their presence indicates possible charge trapping (or charge freeze out) effects in Ill-nitride devices, which could cause instabilities in such devices and hence have significant influences on the device performance. For example, there is evidence that the presence of deep level impurities are responsible for the current-voltage characteristic collapse seen in Ill-nitride field effect transistors (FETs) [3-5]. The prolonged carrier capture time in the PPC state was also shown to affect the photocurrent transient behaviors in AlGaN/GaN heterojunction UV detectors [6]. The research to determine the origin of PPC in Ill-nitrides has been driven not only by its peculiar and interesting physical properties, but more importantly by its relevance for device applications, i.e., an understanding of the physics as well as the control of PPC and the associated deep level centers is necessary in order to further optimize Ill-nitride devices.

PPC is the light-enhanced conductivity that persists for a long period of time after the removal of photoexcitation and has been observed in many semiconductor materials and structures configurations. At low temperatures the PPC decay times become extremely long (of the order of minutes to years) and incompatible with normal lifetime-limiting recombination processes in semiconductor materials. Earlier work on conventional III-V and II-VI semiconductors has shown that understanding of the PPC phenomena can provide mechanisms for carrier generation and relaxation. It is also known that

152 Ch. 6 H.X. Jiang and J. Y. Lin

the PPC has a profound effect on device operations, e.g., it is detrimental to the operation of AlGaAs/GaAs modulation doped heterojunction field effect transistors (MOD-FETs) [7-12]. On the other hand, PPC is useful for adjusting the density of the two-dimensional electron gas (2DEG) at a semiconductor interface [13] and for possible device applications such as memory device and optical gratings [14,15]. It can also be utilized to probe the profile of the impurities [16], properties of metal-insulator transition [17], and transport properties of the tail states in the density of states in semiconductor alloys [18,19].

PPC in many cases is related with deep level centers associated with defects such as vacancies, antisites, self-interstitials, and impurity-defect complexes. These deep level centers are considerably more localized compared with shallow impurities and often have energy levels located deep inside the bandgap. Moreover, in the vicinity of these deep centers, lattice relaxation is quite conmion [20]. For example, it is now known in AlGaAs alloys and other III-V semiconductors that the PPC effect is natural properties of what has been termed as the DX centers that under go a large lattice relaxation (LLR) [21] with a negative U character [22]. According to this model, which is illustrated schematically in Fig. 1, at low temperatures, PPC decay is prevented by a large carrier capture barrier. The large difference between the optical and thermal ionization energies (the Stokes shift) can be explained by LLR. Extensive work in this area has led to the conviction that the effect of PPC is strongly correlated with deep level centers that exhibit the property of metastability, which may occur when the lowest total energy of a particular atomic configuration varies with the charge states of the defects. This implies that there is a physical property that inhibits the relaxation of the center to its

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Persistent photoconductivity in ni-nitrides Ch. 6 153

ground state. In such a context, the PPC relaxation is related to a change in energy and configuration of the center that is associated with a return to its electronic ground state. Examples of such deep centers include EL2 centers in GaAs and DX centers in AlGaAs. The present knowledge on these types of deep level centers is based on nearly forty years of research efforts, which has been summarized very well in several review articles and books [11,23-25]. As for other III-V and II~VI semiconductors, the DX center in AlGaAs alloys can serve as a model that can be invoked in the study of deep level defects or impurities (or DX-like centers) in Ill-nitrides. For Ill-nitrides, however, the epitaxial films are grown on foreign substrates and contain high density of extended defects, such as dislocations, grain boundaries, and stacking faults. These make the understanding of PPC and the nature of deep level centers in Ill-nitrides more difficult.

Other mechanisms have also been proposed to account for PPC effect in a variety of semiconductors. In doped layered structures, the macroscopic barrier due to band offset at the interface between epitaxial layers or between epitaxial layer and substrate could also cause a spatial separation between photoexcited electrons and holes and hence PPC [26,27]. In undoped semiconductor alloys, the alloy-induced compositional fluctuations can also be a cause of the PPC effect, especially in tumary alloys with a large energy bandgap difference between the two compound semiconductors [28,29]. In such systems, photoexcited electrons and hole are localized at the low-potential sites in the conduction and valence bands at low temperatures. Since the low-potential sites in the conduction and valence bands are spatially separated, recombination rate of photoexcited carriers is reduced and PPC may result.

The aim of this chapter is to review PPC in Ill-nitrides and to provide an overview on such an effect in these materials. It is our intention to cover articles written prior to January 2000, but we are sure that there were related articles left out unintentionally. The PPC characteristics including its buildup and decay behaviors, evidence of DX-like centers as well as the nature of defects, and implications on PPC mechanisms are presented and discussed in Section 2. Effects of PPC on Ill-nitride devices including FETs and photodetectors are discussed in Section 3. In Section 4, possible uses of PPC are discussed. Concluding remarks are made in Section 5.

2. Characteristics and possible mechanisms of PPC in Ill-nitrides

The techniques which have been employed most often to characterize the PPC effect as well as to determine important parameters associated with deep level centers are temperature-dependent photoconductivity transient measurements which probe the capture and emission kinetics of carriers to and from the deep level centers (or localized states) as well as the carrier capture barrier. Spectral-dependent photoconductivity measurements are often employed to provide the optical ionization energy and optical cross section of the deep level center involved. Other techniques such as temperature-dependent Hall-effect, deep level transient spectroscopy (DLTS), photoluminescence (PL), and optical detection of magnetic resonance (ODMR) measurements can provide information on the energetic levels of deep level centers as well as carrier-defect scattering mechanisms.

PPC in Ill-nitride epitaxial layers was first observed in p-type (Mg doped) epilay-ers grown both by metalorganic chemical vapor deposition (MOCVD) and reactive


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T (K) Fig. 2. (a) A typical behavior of persistent photoconductivity (PPC) in a Mg-doped p-GaN epilayer grown by reactive MBE. (b) The dark conductivity as a function of temperature. The bottom curve (solid dots) represents data taken with the sample cooling down in the dark, while the top curve (open triangles) is for data taken with the sample illuminated at 10 K for about 10 minutes and then warming up in the dark (after [31]).

molecular beam epitaxy (MBE) [30,31]. PPC was also reported for Siidoped [32] and unintentionally doped n-type epilayers [33-36], and for AlGaN/GaN heterostructures [37-39]. A typical low temperature PPC behavior of a MBE grown p-type epilayer is shown in Fig. 2a, which shows that the conductivity increases by one order of magnitude after exposure to light and that the light enhanced conductivity persists for a long period of time [31]. As a consequence, sample's conductivity as a function of temperature depicts an hysteresis behavior such as the one shown in Fig. 2b, where the bottom curve represents data taken with the sample cooling down in the dark, while the top curve is for data taken with sample being illuminated at 10 K and then warming up in the dark. A similar hysteresis behavior of the dark conductivity was observed in the PPC state in AlGaAs alloys by Nelson in 1977 [40] and is now being regarded as the hallmark of DX like centers (or AX like centers) in semiconductors.

Several different mechanisms have been proposed as the origin of PPC observed in

Persistent photoconductivity in Ill-nitrides Ch. 6 155

GaN, which include deep level centers with bistable character [30,31], random potential fluctuations due to nonstoichiometry [32], GaN/sapphire heterointerfaces [35], and the unintentionally incorporated cubic crystallites in hexagonal GaN [41]. For AlGaN/GaN heterostructures, PPG was believed to be caused by the deep level centers in the AlGaN layers [37,38]. By studying the correlation between PPC and yellow luminescence bands near 2.2 eV in GaN, it was also suggested that an intrinsic defect such as a nitrogen antisite that may undergo a large lattice relaxation gives rise to PPC [35,36]. In this section, PPC characteristics in Ill-nitrides are presented, from which possible mechanisms of PPC are discussed.

2.1. PPC buildup and decay kinetics

One of the most common methods for identifying the PPC mechanism is to formulate its buildup and decay kinetics. It was observed that the PPC buildup kinetics in GaN epilayer such as those shown in Fig. 2a can be described by

Ippc(t) = ld + ( lmax- ld) ( l~e-"^) , (1)

where a~^ is a decay time constant during the buildup process. Id is the initial dark level and I ax is the saturation level. Such a PPC buildup behavior has been observed experimentally and formulated theoretically for DX centers in AlGaAs [42,43].

The decay kinetics of PPC seen in GaN epilayers are also similar to those of DX centers in AlGaAs and follow stretched-exponential functions [43,44],

Ippc(t) = Id + do - Id) exp [-(t/i)P], (p < 1), (2)

where IQ is the PPC level at the moment of light excitation being removed, x is the PPC decay time constant, and P is the decay exponent. The decay exponent P is typically weakly dependent on temperature and is around 0.2-0.3.

Fig. 3a presents PPC buildup transient of the MBE grown p-type GaN epilayer recorded for the first 100 seconds at 30 K. The solid curve is the least squares fit of data by Eq. 1. Fig. 3b shows the PPC decay obtained at three representative temperatures for relatively low buildup levels for the same sample. Each decay curve is normalized to a unity at t = 0, the moment at which the light excitation is terminated, and the dark level has been subtracted. The solid curves are the least squares fit of data by stretched-exponential functions of Eq. 2. As shown in Fig. 3b, the decay time constant x decreases with an increase of temperature and is typically around 10^ s even at room temperature. Several words regarding PPC data taking must be stated here. To ensure that each set of data obtained under different temperatures have the same initial conditions, the sample should always be heated up to a fixed temperature above 300 K and then cool down in darkness to the desired measurement temperatures. A 30 min waiting time is generally required before data acquisition. PPC has also been observed in an AlGaN/GaN heterostructure and its kinetics recorded at two representative temperatures (40 and 300 K) are shown in Fig. 4, in which similar PPC buildup and decay kinetics as those in GaN epilayers have been observed [37]. The PPC decay time constants, x, in this AlGaN/GaN heterostructure are very long, especially at low temperatures (e.g., x ? 10 s at 200 K). At temperatures T > 200 K, x is


o

1.0

0.8

0.6

0.4

0.2

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- 30 K o 200 K o 250 K

f i t t ing 1000 2000 3000 4000 5000

t(s) Fig. 3. (a) PPC buildup transient recorded for the first 100 seconds at 30 K for a Mg-doped p-GaN epilayer grown by reactive MBE. The solid curve is the least squares fit of data by Eq. 1. (b) PPC decay obtained at three representative temperatures for relatively low buildup levels. Each decay curve is normalized to a unity at t = 0, the moment at which the light excitation is terminated, and dark level has been subtracted. The solid curves are the least squares fit of data by stretched-exponential functions of Eq. 2 (after [31]).

thermally activated. The PPC decay exponents, P, are around 0.3 for all temperatures [37]. The PPC buildup and decay kinetics as well as their temperature dependence seen in Ill-nitrides bear a strong resemblance to those induced by DX centers in AlGaAs alloys. Thus it is quite nature to attribute the DC-like or AX-like centers to be the cause ofPPCinlll-nitrides.

2.2. Carrier capture barriers

Extensive work in a wide range of semiconductor materials has shown that the metastability effect such as PPC generally implies the existence of an energy barrier between the ground and the excited electronic states of a defect center, which must be overcome in order for the relaxation to occur. Since the energy gap of the host

Persistent photoconductivity in Ill-nitrides Ch, 6 157

15H

10H

"V T = 300 K

light off V data •

fitting

light on

2000 4000 6000 8000 10000

t(s) Fig. 4. PPC behavior in an AlGaN/GaN heterostructure sample measured at two different temperatures, where solid curves are the least-squares fit of the data using Eq. 1 for the buildup and Eq. 2 for the decay (after [37,38]).

materials limits the size of this energy barrier, Si devices operating at room temperature are not much affected, GaAs devices are affected generally at low temperatures, and Ill-nitrides with larger energy band gap should have the greatest effects, in particular for the minority carrier devices. In the context of the LLR model, DX centers (or AX centers) are characterized by four basic energies as schematically illustrated in Fig. 1. Ecap is the carrier capture barrier, Eth is the thermal activation energy for the emission of carrier from the DX (AX) level to the conduction (valence) band, Eop is the optical ionization energy that is the energy needed to optically excite a carrier from the DX (AX) level to the conduction (valence) band, and E^, is the impurity binding energy, which is usually the value obtained by Hall effect measurements.

From Fig. 1, one sees that the capture barrier must be overcome by carriers in the conduction (or valence) band in order to be captured by DX (AX) centers. Thus PPC decay is the process of thermal activation of carriers over the capture barrier Ecap' At very low temperatures, however, PPC decay is due to electron tunneling via multi-phonon emission in the configurational space [11,44], which gives rise to a weakly temperature dependent carrier capture [11]. As a consequence, the temperature dependence of T in these two different capture regimes can be described by [31],

T = Toexp(Ec/kT), (non- degenerate) (3a)

T = To exp [(Ec - EF)/kT], (degenerate) (3b)

158 Ch. 6 H.X. Jiang and J.Y. Lin

14

12

10

8

- (a)

/

/ 1

/ -y 1 1

/ • • •

/ A

P-GaN

E =129meV -C

1 1

0.000 0.005 0.010 0.015 0.020

l / T (K"')

lO 2 O

"T I \ I r

T=30 K • d a t a

fitt ing -I

25 50 75 100 125 150 175

tK(s) Fig. 5. (a) The Arrhenius plot of the PPC decay time constant x (In i vs. l/T) obtained for a Mg-doped p-GaN epilayer grown by Reactive MBE. The capture barrier (Ec) obtained from data taken above 150 K is about 129 meV. (b) PPC decay time constant x as a function of PPC buildup time tb. The solid curve is the least squares fit of data with Eqs. 7 and 8 (after [30]).

where Ec denotes the carrier capture barrier of the deep center measured from the band edge, Ep is the quasi-Fermi level, and hence (Ec—Ep) is the effective carrier capture barrier in the degenerate case. Fig. 5a presents an Arrhenius plot of x (In t vs. l/T) for a MBE grown p-type GaN epilayer, which clearly exhibits two different capture regions. The thermally activated capture region gives a value of 129 meV for the capture barrier (Ec) at low PPC buildup levels [corresponding to non-degenerate case of Eq. 3a]. Values ranging from 55 meV to 230 meV for Ec have been reported for n-type, p-type epilayers and AlGaN/GaN heterostructures [30-38]. These results thus suggest that there exist capture barriers that prevent photoexcited carriers capture by deep level centers in GaN.

In the degenerate state, it is expected from Eq. 3b that, at a fixed temperature, the PPC decay time constant x would decrease with an increase of free carrier quasi-Fermi level Ep. Usually the free carrier concentration and hence the quasi-Fermi level are


varied with the dopant level. With PPC the free carrier concentration at a fixed temperature can be conveniently varied in a single sample with excitation photon dose (product of excitation intensity and light exposure time). By utilizing this unique feature of PPC, a systematic dependence of the PPC decay time constant (t) on the relative free carrier concentration (or the PPC buildup time (tb) at a fixed excitation intensity) can be obtained. The experimental result for the same MBE grown p-type GaN is shown in Fig. 5b for 30 K (solid dots) [31].

The dependence of x on tb can be derived theoretically from Eq. 3b. If we choose the energy (E) to be positive in the valence band and zero at the valence band edge, then the free hole concentration (p) is related to the Fermi distribution function, f(T, Ep) = {1 + exp[(E — EF)/kT]}"^ and the density of states in the valance bands, g(E) = (2m*)^/V27t^h^ = CE^/^ by

= / f(T, EF)g(E)dE = C / p ^ dE Jo Jo l + e x p r ( E - E F ) / k T l 1 + exp [(E - EF)/kT]

(4) POO 1/2

= C(kT)^/2 / - ^ ;-dy, Jo (ey-^ + i) ^

where v = Ep/kT. Eq. 4 can be written as,

p = C(kT)^/2r(3/2)J(v), (5)

where 1 f^ yl/2 1 /•CX) 1/2

r(3/2) = n^/V2 and J(v) = / —^- dy. ^ ^ r(3/2) Jo (ey-- + 1 ) ^

Eq. 5 gives p in terms of Ep. However, what we need is Ep in terms of p. Such a mapping task has been accomplished previously [45], where a very accurate expression has been obtained for v [= v(J)] from J [= J(v)], which is,

V = log J + Ki log(K2J + K3) + K4J -f K5. (6)

In Eq. 6, Ki = 4.897, K2 = 3.311, K3 = 73.626, K4 = 0.133, and K5 = -21.051. From Eqs. 3b and 6, we obtain

^ toexp(Ec/kT)

^ ~ J(K2J 4- K3)î exp(K4J + K5)

Eqs. 5 and 1 also give

^ ^ C(kT)3/2r(3/2) " c(kT)V2r(3/2) ^^ - ^^P(-°^^b^] • (^)

The PPC decay time constant x as a function of the PPC buildup time (tb) is described by Eqs. 7 and 8 together, which have been used to fit experimental data of a MBE grown p-GaN epilayer. An example is shown in Fig. 5b for 30 K data, where the solid curve is the least squares fit of Eqs. 7 and 8 to the experimental data and a perfect agreement has been obtained. Note that by using the experimental value of a, e.g. a~^ = 23.5 s at 30 K as obtained from Fig. 3a, there are only two fitting parameters in Eqs. 7 and 8. These results gave further evidence that there exists an energy barrier which prevents the capture of photoexcited holes by deep level centers in MBE grown p-type GaN.

160 Ch. 6 KX. Jiang and J. Y, Lin

T^

fn _i6 L

—o

10'

12

14

16

18

9n

T Ul

K 4

'• ' ' n •

• •••

•

• • • 1 •

^ 100 200 300 400

\ T (K)

\ E =131meV

•

• 1

- GaN p - t y p e • !

1 1 1 1 \ • L - J

1.5 3.0 4.5 6.0 7.5 9.0 10.5

1000/T (1/K) Fig. 6. An Arrhenius plot of the equilibrium dark current for a Mg doped p-GaN epilayer grown by MOCVD. The inset shows the hole mobility as a function of temperature. The acceptor binding energy is estimated to be about 131 meV (after [30]).

2.3. Correlation ofPPC with metastable defects

2.3.1. Electrical data Extensive work has led to the conviction that the effect of PPC is strongly correlated with the property of metastability of defects. An anomaly slow thermal equilibrium process for the dark carrier concentration has been observed at low temperatures in a Mg-doped p-type GaN epilayer grown by MOCVD [30]. Fig. 6 presents an Arrhenius plot of the equilibrium dark current (at a constant applied bias of 1.5 V) of this MOCVD grown Mg-doped p-type GaN epilayer measured from 100 to 600 K. The inset shows the hole mobility, .h, as a function of temperature in the range between 150 and 350 K. In the investigated sample, |Xh has a maximum value of about 6 cm^/Vs and a minimum of about 2 cm^/Vs. The small variation in |jih indicates that the change in the conductivity with temperature is predominantly caused by the change in the hole concentration. A direct measure from the slope of the In(Id) vs. 1/T plot of Fig. 6 gives a value of 131 meV for the binding energy of the activated Mg acceptor, which is in agreement with Hall measurement results [46,47]. In p-type GaN samples, the hole conduction at room temperature is contributed by the activated Mg impurities, while inactivated Mg centers do not contribute to the hole conduction.


O

11.3 11.2 11.1 11.0 10.9

lo.a 6.Q 5.7 5.4 5.1

4.8

2.7

2.4

2.1

1.8

1.5

1.56

1.30

1.04

0.78

0.52 L * — • • • • • • •

(d) T=240 K]

(c) T=160 K-

k_ (b)

T=140 K-

• Data — Fitting (a)

T=120 K]

0.00 0.05 0.10 0.15 0.20 0.25

(10 s) Fig. 7. The dark current as a function of time for four representative temperatures, where t = 0 is defined as the time when the measuring temperature was attained by the sample. The solid curves are the least squares fits of data (soHd dots) by Eq. 9 (after [30]).

An intriguing observation is the complicated thermal equilibrium process of the dark current seen at low temperatures in this MOCVD grown p-GaN epilayer, as illustrated in Fig. 7. It was observed that it is necessary to wait for a very long period of time (typically a few hours) in order for the dark current to reach the equilibrium value. Fig. 7 presents the dark current as a function of time for four representative temperatures. The starting time (t = 0) in Fig. 7 was defined at the moment at which the measurement temperature was attained by the sample, a process typically takes 10 to 15 minutes and is short compared with the measuring time. We see that the dark currents are far from their equilibrium values immediately after the sample has reached the desired measurement temperatures. As shown in Fig. 7a, at temperatures T < 120 K, the dark current decreases initially and freezes into a lower value through out the investigated period of time, implying the process of holes capture by ionized defects takes about 500 seconds. As illustrated in Fig. 7b and c, two relaxation processes occur at higher temperatures (e.g. 140 and 160 K), i.e., an initial decrease in dark current is followed by a slow increase with a typical time constant of several hours. Notice that the true dark equilibrium level at 160 K is even higher than the initial dark level. On the contrary, an initial increase in dark current is followed by a slow decrease at temperatures above 240 K, which is shown in Fig. 7d. These results give a clear evidence for the existence of deep level defects with a bistable nature.


13

12

11

10

^ 9

a 8

GaN p - t y p e

T ppc

— Fitting

4 5 6 7 8 9 10

1000/T (1/K) Fig. 8. An Arrhenius plot of the PPC decay time constant, xppc (open dots) and T2 (solid dots). The solid lines are the least squares fits of data with a thermally activated behavior of Eq. 10 (after [30]).

The dark current Id(t) as a function of time in this MOCVD grown p-GaN epilayer can be described by

Id(t) = li - Ii [1 - exp(-t/Ti)] + l2[l - exp(-t/x2)], (9)

where Ii is the initial dark current at t = 0, n is the time constant for the free hole capture by an ionized defect centers, and T2 is the relaxation time constant of a neutral center from its metastable to stable state. Eq. 9 fits dark current data of this p-GaN epilayer very well for all temperatures as shown as solid curves in Fig. 7. From the fit one can also get I^ = Ij - I +12, the true equilibrium dark current at different temperatures. Although the starting time (t = 0) is somewhat arbitrarily chosen, the values of xi and 12 are unaffected by this arbitrary choice because the relaxation processes are exponential. Fig. 8 presents the Arrhenius plot of T2 (solid dots), which is thermally activated, a behavior that is similar to that of the PPC decay time constant (xppc) obtained from the same sample as indicated by the straight line. Both xppc and X2 can be described by

Xi = xoexp(Ei/kT), (Xi = X2 and xppc, Ei = Ec and Et) (10)

where Ec is the capture barrier for the photoexcited holes and Et is the potential barrier between the metastable and the stable states of the neutral defects. For the Mg-doped p-type GaN sample grown by MOCVD investigated, one obtained Ec = 55 meV and


Et = 68 meV, respectively. In Eq. 9, TI describes the capture of free holes in the dark state and is not thermally activated.

2.3.2. Optical data When metastable defect centers are directly or indirecdy involved in optical processes, the associated optical transitions can also exhibit similar characteristics as PPC, including degradation of transition intensity, long recovering time, optical metastability, and optical data and image storage behavior. Optical metastability was reported in bulk GaN single crystal grown from cold pressed GaN powder by sublimation in flowing ammonia [48]. Fig. 9 shows room temperature PL spectra of this GaN sample for different illumination times. The band-edge emission Une at 365 nm was the dominant line in the initial illumination time (t = 0 spectrum). As illumination time increases, a new emission line at 378 nm emerged. Its relative intensity to the band-edge emission line at 365 nm increases and its peak position shifts toward the longer wavelength with an increase of illumination time, as illustrated in spectra b-d in Fig. 9. After 36 min of exposure time, the emission intensity of the photo-induced emission line at 378 nm was even higher than the band-edge transition at 365 nm. The ratio of output intensities of the photo-induced band (378 nm) to the band-edge (365 nm) transitions increased by a factor of 4 during 36 min of exposure time. However, no physical damage was introduced to the surface of the sample as examined under the optical microscope. The observed phenomenon is metastable as demonstrated by the restoring of the original spectrum after leave samples aside for a while. It was argued that the gradual increasing in the emission intensity of the photo-induced line with longer exposure time indicates the creation and/or filling of trap levels. These traps are metastable centers, which can capture the carriers and keep them from participating in the radiative recombination process for a significantly long time. Such a long recovery time indicates that the

480 460 440 420 400 380 360 340 320 Wavelength (nm)

Fig. 9. Exposure time dependent room temperature PL spectra from a bulk GaN single crystal (after

[48]).


photo-induced levels have a large thermal activation energy. Obviously, these optical metastable behaviors are analogous to those of PPC.

New metastable defects emit blue light (BL) around 3.0 eV in addition to the yellow luminescence Une (YL) around 2.2 eV were also observed in n-type undoped GaN epilayers [49,50]. This metastable defect exhibited PL fatigue behavior under constant illumination at low temperatures. The slow decay of the BL intensity can be observed by eye. The color of the emitting light from the laser illuminated area changes from 'blue' to 'yellow' gradually. Fig. 10 shows the PL spectra from a GaN epilayer measured at r = 10 K. It clearly shows that the emission intensity of the BL line decreases with

10

0.5

0.0

1.0

I

0 ^

0.0

t-10 min.

t=5 mIn.

taOmin.

1.5 2.0 2.5 3.0 3.5

Photon eneigy (eV)

Fig. 10. Exposure time dependent PL spectra of a GaN epilayer (after [49]).


t

8lue lumtndscence at 430 nm (2.884 eV)

t TÎOK

i i 1 t,. ,„,l , i

A04A1«3(p(4/t,)

i..........^, il- ,1 n M , t 1 I

0 200 400 600 800 1000 1200 1400 imO Time (second)

3 10

a:

A0*A1e)cp(*i/t,)

M«6;e^;Ai«4ê^: t,«48di

Yellow lumlne^jem^ at 560 nm (2.214 eV) TMOK

J 0 200 400 mo 800 1000 1200 1400 I^K)

Time {second)

Fig. 11. Evolution of the emission intensities of the (a) blue (BL) and (b) yellow (YL) emission lines with exposure time. The solid lines are fittings to (a) an exponential decay and (b) an exponential growth characteristic (after [49]).

the exposure time while the output intensity of the YL line increases. Fig. 11 shows the evolution of the emission intensity of the BL and YL with time. Both increases of YL and decreases of BL emission line at low temperatures can be described by single exponential functions as shown as solid lines in Fig. IL The characteristic times for BL decreases and YL increases at 10 K are 359 s and 480 s, respectively. Both BL and YL emission intensities can be recovered to their initial intensities if the sample temperature is raised to room temperature. These metastable deep centers were suggested to be hole traps and native Ga vacancies in GaN.

Fig. 12 shows the emission spectra of an undoped GaN epilayer grown by MOCVD measured at 9 K under different illumination times [50]. Three band-edge exciton


0.12

0.10 h

0.06

<• 0.06

t g 0.04

0.02

0.00

-i L 3.470 3.475 3.480 3.485 3.490 3.495

Energy (eV)

Fig. 12. GaN excitonic emission at selected times during irradiation at 9 K (after [50]).

recombination peaks at 3.476, 3.482, and 3.488 eV were observed. The intensities of the two exciton peaks at 3.476 and 3.482 eV increased during light illumination with no change in peak energies, while that of the exciton peak at 3.488 eV did not change with illumination time at all.

Optical memory effects in GaN and AIN epilayers grown by atmospheric pressure MOCVD were also reported [51]. The room temperature (RT) band-edge PL intensity of GaN epilayer is significantly decreased at areas that have been exposed to a sufficient dose of UV light illumination, and that this effect can be reversed or 'erased' by illuminating these areas with longer wavelength laser light. Curve a of Fig. 13 shows PL intensity from band-edge emission line around 3.4 eV measured at different illumination times, which shows the variation of the band-edge (^^3.4 eV) PL emission intensity with He-Cd laser excitation time. Curve b of Fig. 13 illustrates the timing and duration of the sample excitation. During the 5 minutes of UV illumination, the PL emission intensity decreased continuously and reached an intensity level below 50% of the initial measured intensity. After turning off the UV illumination, the PL intensity started to recover to the initial intensity level. This memory effect could last for several days.

It was proposed that the long lifetime of the PL intensity recovery in these films constitutes a memory effect that can be used for optical recording [51]. By exposing selected points to various doses of UV illumination, their subsequent emission to optical excitation can be modulated. Fig. 14 illustrates the RT band-edge PL emission intensities (~ 3.4 eV) vs distance along the sample at different status of samples including (a) prior to UV writing exposure, (b) immediately after writing at points A-H with He laser light


100 T

a a

1 S3

140 I

100 ^ §-9

60 I t 20

10 I iiiiMi iitmn I HIM ttimn miiw itmnj .20

0.1 10 1000 100000 Time (min)

Fig. 13. (a) Time dependence of the band edge PL emission intensity of a GaN epilayer. (b) Timing and duration of He-Cd laser excitation (after [51]).

n 250 iT '**'''''*"'*''*"'^

(a)

B C D,E F . G , H (b)

M ' ' ' I -«- M ' ' ' ' i ' ' ' ' I 4 5 6 7 8 9 10

Distance along the sample (mm)

Fig. 14. Band-edge PL emission intensity ( ^3.4 eV) of a GaN epilayer versus distance along the sample measured (a) prior to UV writing exposure, (b) immediately after, (c) two days after, and (d) three day after writing at points A-H with He-Cd laser light for various duration (after [51]).

for various durations, (c) two days after writing at points A-H, and (d) three days after writing A-H. These results demonstrated the persistence of this memory effect at RT. Subsequent illumination of written points with red light (632.8 nm) can erase the optical memory effect after a sufficient delay. The same phenomenon has also been observed in a thin AIN film grown by atomic layer epitaxy. The combination of 'writing' by UV illumination, 'reading' by band-edge emission intensity, and 'erasing' by red light illumination may be used for erasable optical data or image storage.

Optical metastability has also been observed in InGaN/GaN multiple quantum wells [52]. In InGaN/GaN quantum wells, a short time exposure to a high intensity UV light results in long term, but reversible change of the optical properties. The retention time at room temperature ranges from days to weeks depending on the InGaN/GaN quantum


well structures. It was suggested that the optical memory effects observed in these materials can also be used for optical data storage, which has the advantage of longer memory times compared with other semiconductors.

2.4. Nature ofDX-like centers and their optical ionization energies

2.4.1. Earlier work Deep centers, in fact, have been observed in GaN polycrystalline GaN more than 20 years ago [53]. Photoconductivity spectra were measured for undoped high-resistive (p S 10^ ^ c m ) and heavily zinc doped polycrystalline GaN films. Impurity centers with short-range potentials were identified, which are now known as deep level centers. The ratio of the photo-current to the dark current in the high-resistivity samples was very large and around 100-200, indicating the photoconductivity in these materials was contributed by the photo-excited carriers from deep level centers. Fig. 15 shows the photoconductivity spectrum (solid dots in curve 1) and the absorption spectrum (curve 2) of the heavily doped GaN samples, which reveal several plateaus near 1.2 and 1.8 eV. The low energy part of the photoconductivity spectrum (below 2.2 eV) cannot be attributed to photoexcitation of carriers from effective-mass type shallow impurities. However, these results can be described very well by the model in which impurity centers are ascribed by short-range potentials (deep centers) [54]. The three different plateaus shown in the photoconductivity spectrum were attributed to the photo-excitation of carriers from three different deep centers with different optical ionization energies. Within the context of the deep level centers, the relative photon-capture cross section, Gopt, depends on the photon energy, hv, and can be described by

aoptaEi(hv-Eopt)^/Vhv, (11)

where Eopt is the optical ionization energy of the deep centers. Photoconductivity spectrum is proportional to a(hv) and showed similar dependence on photon energy as a(hv) does. An analysis of the photoconductivity spectrum data in Fig. 15 showed that there were three different kinds of deep centers with optical ionization energies around

9

fl

»- '

10-'

ttl-i

T

f ' if *

1 1 1

y^z

1 Z J £,eV Fig. 15. Photoconductivity spectrum (solid dots in curve 1) and the absorption spectrum (curve 2) of a heavily doped polycrystalline GaN sample (after [53]).


0.9, 1.2, and 1.7 eV, respectively. The calculated results from Eq. 11 with three different optical ionization energies 0.9, 1.2, and 1.7 eV are shown as dashed curves in Fig. 15. These values matched well with a typical optical ionization energy of about 1 eV observed in AlGaAs materials, considering a wider bandgap energy for GaN. It was also found that the photo-response kinetics was non-exponential and it was characterized by long photoconductivity rise and decay times, which both are known today as the main features of PPC.

2.4,2. Recent studies on GaN epilayers Several investigations have been carried out recently aiming at the identification of the physical origins of DX- and AX-like centers in GaN. Photocurrent spectra of a p-type GaN epilayer has been measure [33]. From the onset of photoconductivity spectra, it was suggested that metastable centers at 1.1, 1.4, and 2.04 eV above the valence band edge were responsible for the PPC in Mg-doped GaN. On the other hand, it was also suggested that Ga vacancies may be responsible for PPC in n-type GaN [34]. The spectral dependence of PPC in a MOCVD grown unintentionally doped n-type GaN epilayer has been measured [34]. Fig. 16 shows the variation of the relative optical absorption cross section as a function of excitation photon energy, obtained for this MOCVD n-GaN epilayer. The data were fit using Oopt a Ei(hv - Eopt)^/V(hv)^ The best fit to the data yielded an optical ionization energy Eopt = 2.69 eV. The observed temperature dependence of the PPC decay and its non-exponential shape were explained by a distribution of capture barrier around 0.2 eV with a width of around 26 meV.

PPC in undoped and Se doped MOCVD grown GaN epilayers under different

2.7 3.3 2.8 2.9 3.0 3.1 3.2

Photon Energy hv [eV]

Fig. 16. The relative optical absorption cross section as a function of photon energy, hv. The solid curve corresponds to the fitting result with Gopt (x (hv - Eopt)^'^/{hv)^, from which one obtains the optical ionization energy, Eopt = 2.69 eV (after [34]).


conditions including doping levels, excitation photon energies, and temperatures have been investigated [33,35,36]. It was found that PPC could be observed for the excitation photon energy down to the yellow band (2.2 eV). The results revealed that the origin of the PPC and YL might arise from the same intrinsic defects. This intrinsic defect is a deep level of about 2.2 eV below the conduction band. It was also suggested that the most probable candidate of the intrinsic defect is a nitrogen antisite Nca [33,35,36], which could have a metastable behavior similar to the arsenic antisite Asca ^^ GaAs [55,56]. The Noa defect can undergo a large lattice relaxation which creates an energy barrier to prevent the capture of photoexcited carriers by deep centers.

The correlation between of PPC and YL has also been investigated in more detail for radio-frequency plasma assisted MBE grown hexagonal GaN (h-GaN) epilayers on sapphire and cubic GaN (c-GaN) epilayers on GaAs and 3-C SiC substrates [57]. The PPC and PL measurements taken on h-GaN/sapphire, c-GaN/GaAs, and c-GaN/3C-SiC samples at room temperatures are shown in Fig. 17. A strong PPC, lasting for several days was observed in h-GaN/sapphire samples. PL measurements taken on the same sample showed broad YL spreading from 1.7 to 2.7 eV with a peak energy at 2.25 eV. However, in the c-GaN/GaAs and c-GaN/3C-SiC samples, neither PPC nor YL were observed. It was thus concluded that PPC was observed only in those samples which exhibit YL and that PPC and YL are related to each other. The PPC buildup transients were also measured at different excitation photon energies for h-GaN/sapphire as plotted in Fig. 18. It was found that the threshold (the minimum photon energy required) for observing PPC was around 1.6 eV, which is almost at the same energy at which the YL band starts raising. The excitation photon energy dependence of the photocurrent was also found to increase monotonically from 1.8 to 2.2 eV, which is consistent with the broad nature of YL band. These results suggested that the centers responsible for the PPC are also the centers which give rise to the YL band. The authors pointed out that neither the Ga interstitial nor the Ga or N vacancies are the likely candidates for the centers that give rise to PPC and YL band, because these defects should also be present in the cubic GaN in which no PPC and YL band were observed. However, a defect complex such as Nca-Gai, nitrogen antisite interacting with the neighboring Ga interstitial, could be a possible candidate for the deep center as well as the origin of PPC in GaN. The authors [57] further speculated that the formation of such antisites in h-GaN/sapphire is probably more likely than that in c-GaN/GaAs and c-GaN/3C-SiC due to the larger strain in the epilayers as a result of larger difference in the thermal expansion coefficient between the substrate and the epilayer.

2.4.3. Recent studies on AlGaN alloys and AlGaN/GaN heterostructures PPC as well as Si and O donors in AlxGai_xN alloys have also been investigated [58-61]. It was found that both O and Si in AlxGai_xN have two different energy states. One of them has an effective mass character and the other represents the localized state strongly coupled to the lattice. It was concluded that O (Si) donors have DX center characters and are metastable in AlxGai_xN for x > 0.27 (0.5). A configurational coordinate diagram including optical ionization energy, electron thermal emission and capture barriers was obtained for the deep centers in AlxGai_xN alloys [58]. It was also suggested that the low concentration of free electrons in Al-rich AlxGai_xN alloys was


PPC at 297K

0ffHiiiiiii|nnmM|(miHH| Ml

<

o

0.(

0.4

OJ

0

0.4

OJ

0.2

0.1

0

Q«N/OaAt

intiiniiiiiiiniiihumifhf

r GaN/3C-SiC

111111II111 •• III 11111 III 111111

PL at 297K j^l I I • I • I • • p ••! H H • • j 1 1 ^

JGaN/MpphlrcH

M l i | M H | n i t i n M h l H J

GftN/3C-SiC

r 1 1 1 1 1 1 1 1 1 1 1

s •

C9

10 c p.

i c 4 iL

i I I I 11 I I I I I I I I

2000 4000 fOOOl.5 I J 2.1 2.4 2.7 3

Time (sec) Photon energy (eV) Fig. 77. PPC and yellow PL band measurements taken on h-GaN/sapphire, c-GaN/GaAs, and c-GaN/ 3C-SiC samples at room temperature, showing the correlation between PPC and yellow emission (after [57]).

due to the formation of oxygen DX centers. These conclusions are consistent with those from the first-principle calculations [62-64].

In unintentionally oxygen-doped AlxGai_xN alloys, the free electrons freeze out with decreasing temperature [58,59]. The electron activation energy increases with increasing AIN concentration. PPC was observed in oxygen-doped AlGaN alloys with x < 0.39 at temperatures below 150 K. It was thus concluded that the localized state of O exhibits a metastable character resembling the behavior of DX centers in AlGaAs. Fig. 19 plots the dependence of the DX energy level on AIN concentration in oxygen-doped AlxGai_x.


I

2.4

1.«

1.2

0.6

0

0.4

Room Toinp>r«turo (207K)

i ^ - M - f a I I I t I M t 1 I ' < ' I ' ' ' » I I I I I"]

0

0.1

0.05

J^ PW-HHf-H I I I I I > I I I I I I I I I I I I I I I t^

^ ' • l'77eVi 1

• I •

0

0.04 I.

0.02

0

jPIN-«-*+» I I I I t i 111111 t'l i M M 1 1 1 M 1 1 M n 0 1000 2000 3000 4000 5000 6000

Time (sec) Fig. 18. PPC buildup transients measured at different excitation photon energies for a h-GaN/sapphire epilayer, showing the photon energy threshold (the minimum photon energy required) for observing PPC to be around 1.6 d= 0.2 eV, which is almost at the same energy at which the YL band starts raising (after [51]).

0.0 0.1 0.2 0.3 0.4 0.5 0.6

AIN concentration {yij

Fig. 19. Dependence of the DX energy level on Al content in AlxGai_x N:0. The DX level is extrapolated to intersect the conduction band (CB) minimum at an Al concentration of JC = 0.27 (after [58]).


1.6

1.2

0.8

0.4

0.0

J y

1 V^ ^^^ V

r—» 1 « 1 1 r—• r—

/o» 1

-• 1 ' 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Displacement (A)

Fig. 20. Configurational coordinate diagram for oxygen displacement along [0001] in AlGaN, based on first-principles calculations for GaN: O (after [58]).

It shows that the DX level intersects the conduction band minimum at x = 0.27. The optical ionization energy was also obtained by measuring the excitation photon energy dependence of the optical cross section of oxygen DX centers in Alo.39Gao.6iN alloy. The optical threshold energy Eopt of the oxygen DX center in Alo.39Gao.6iN is approximately 1.3 eV. The calculated parameters of oxygen DX centers in AlxGai_xN alloys are summarized in the configuration coordinate diagram in Fig. 20, which includes the oxygen displacement along [0001] direction, the emission and capture barriers, and the optical ionization energy [58].

For Si doped AlxGai_xN alloys with x between 0.5 and 0.6, PPC as well as a pressure induced electron freezeout was also observed for the localized states of Si donors. A PPC effect was observed and a majority of the photo-excited electrons remains in the conduction band up to 90 K. For 7 > 90 K, a gradual decreases of PPC was observed and PPC disappeared at 7 > 250 K.

Fig. 21 shows the hydrostatic pressure (HP) dependence of the free electron con-

2.2x10'

2.1x10'

«C 2.0x1 o"|-o

Alo.52Gao.48N-Si

1=300 K

0.5 1.0 1.5

Pressure (GPa)

Fig. 21. Electron concentration, ne, vs applied pressure for Alo.52Gao.48N:Si at T = 300 K. The mset shows pressure induced changes of electron conductivity for two different Al contents (circles, x = 0.52; squares, x = 0.58) (after [59]).


0.3

0.2

^ 0.1

^ 0.0

tif -0.1

^ -0.2

-0.3

F-. 1 ^

\ \ 1 • ••••.. --..f • ' • • . . •••••

r xs0.58l{ VjEox-fiOiMV 1

>ê|Ms- 8 meV j SampteC"*"-^]

J *,o<^^)" 1

: E „ \ •"••••.. 1

• ^ ^ S " ^ / • • • % 0.0 0.2 0.4 0.6 0.8 1.0

Alloy composition, x

Fig. 22. Energy positions of the localized (Si and O related) states vs Al content for AUGa i-xN:Si. Dots are experimental data for AlGaN:Si from [59]. Open and full squares are experimental data for AlGaN:Si from [60,61]. Open diamonds are experimental data for AlGaN.O from [58] (after [59]).

centration measured at T = 300 K for Si doped Alo.52Gao.48N alloys [59]. The inset plots the HP dependence of normalized conductivity for two Si doped AlxGai_xN alloys with X = 0.52 and 0.58. As seen from the inset of Fig. 21, a more drastic decrease of electron concentration was observed under HP for higher x. The results in Fig. 21 can be understood in terms of localized states of Si donors with its energy level moving deeper into the bandgap with increasing of HP The energy levels also move deeper into the bandgap with an increase of Al composition x. The lack of saturation of the free electron concentration below 90 K for dark condition implies the coexistence of the Si related effective mass type states and the DX like localized states. By analyzing thermal activation of electrons, two different activation energies were obtained, 8 ± 2 meV in the low temperature limit, giving the position of shallow state and 60 ± 5 meV in the high temperature limit, representing the energy position of the localized state.

The Al composition x dependence of the energy level of the localized states of Si and O relative to the conduction band edge, E-Ec, is plotted in Fig. 22 for Si (dots and squares) and O (diamonds). The inset of Fig. 22 shows the Arrhenius plot of the electron concentration for Si doped Alo.58Gao.42N alloys. It shows clearly that both localized states of Si and O get deeper into the bandgap as x increases. The localized state forms the corresponding level in the band gap in AlxGai_xN alloys with x > 0.5 for Si and X > 0.3 for O. These results also imply that one can obtain highly conductive Si doped AlxGai_xN alloys up to x = 0.5, contrary to O doping, in which case highly resistive samples are obtained for x > 0.3.

To clarify the origin of the PPC in Si doped AlxGai_xN alloys, electron concentration, Ue, under different conditions were measured, which are plotted in Fig. 23 [59]. In Fig. 23, a comparison is made between the temperature dependencies of n^ at an ambient pressure in the dark (squares) and after HP freeze out at 1.4 Gpa (circles) with the conditions after blue LED exposure at 77 K (diamonds). A persistent decrease in Ue was observed in the Si doped AlxGai_xN alloys resulting from HP freeze out, which indicates that the localized state of Si is strongly coupled to the lattice.

PPC and deep levels in n-type Alo.15Gao.85N/GaN heterostructures have been investigated by DC and AC photocurrent spectra performed using various illumination geometries [39]. It was suggested that PPC was correlated with the broad distribu-


2.2x10

2.0x10'

•O

1.8x10

1.6x10'

Aio.52Gao.48N-Si

After HPFO at 1.4 GPa

100 150 200 250

Temperature (K) Fig. 23. Electron concentration, ne, vs temperature at an ambient pressure in the dark (squares) and after high pressure freeze out at 1.4 GPa (circles) in comparison with the condition after blue LED exposure at 77 K (diamonds). The arrows show direction of temperature change (after [59]).

tion of defect levels with excitation energies lower than the bandgap energies in both Alo.15Gao.85N and GaN. A defect level with excitation energy of 3.36 eV was also obtained from the DC photocurrent spectra. A detailed analysis yielded that its concentration was low in GaN and that excitation of carriers from this level contributed primarily to PPC.

Fig. 24 shows photocurrent spectra for excitation energy ranging from 2.2 to 4 eV with illumination provided from (a) top (Alo.15Gao.85N side) and (b) bottom (sapphire side) of the sample [39]. In the spectra obtained with illumination from the top, peaks at 3.7, 3.42, and 3.36 eV can be seen, together with a broad tail extending from the GaN band edge to about 2.2 eV. The 3.7 and 3.42 eV peaks correspond to the band edges of Alo.15Gao.85N and GaN. The 3.36 eV peak was enhanced significantly while 3.7 and 3.42 eV peaks disappeared when illuminated from the bottom, as shown in Fig. 24b. The results in Fig. 24a and b thus suggested that the concentration of the defect centers associated with the 3.36 eV peak is low in the underneath thick GaN layer.

AC photocurrent spectra were also measured using a lock-in amplifier with excitation light chopped at a frequency f = 338 Hz [39]. In such a measurement, PPC with time constants much longer than 1/f was discriminated by the lock-in amplifier. A single peak observed at 3.42 eV was corresponding to the GaN interband transition. The signal between 3.7 and 3.4 eV was much smaller than that in the DC photocurrent spectrum shown in Fig. 24a and suggested that photocurrent induced by radiation in this energy range is caused by excitation of defect levels in the Alo.15Gao.85N layer.

2.4.4, Recent studies on GalnNAs quaternary alloys A Ill-nitride related material system, GaxIni_xNyAsi_y, quaternary alloys have also attracted a great deal of attention recently due to its potential applications in the next generation ultrahigh-efficiency multijunction solar cells as well as in optoelectronic devices for optical communications [65-71]. It has been demonstrated that this quaternary alloy system can be grown lattice-matched to GaAs substrates and its band gap energy can be tailored to around 1.0 eV by incorporating only a few percent of N concen-


(a) 1»

1.7

<

I 1.5 O 14 2 O ^ 1.3

1.2

2.0 2.5 3.0 3.5

photon energy (eV) 4.0

(b) - 1.7

< 1-6 U

3 1.4 o I 1.3

1.2

1.1

' i

[ 2.0V fofward bias

L

[-

' ' *

' 1 1 1

Ktumination

« * / 1 «i 1

« / 1 # f 1

* M 1 ' / 1

^^ W 1 >^' 1

y* 1 /' /I mumination x ^

from bottom 1 1 1 1

• • • • 1

% 1

« "J * 1 • 1 % J % 1 * 1 t * \ 1 % 1 % H % 1

H

• ii . ^^ J

\

2.0 2.5 3.0 3.5 4.0

photon energy (eV) Fig. 24. (a) Photocurrent spectra measured at various bias voltages for a 500 A Alo.15Gao.85N/GaN Schottky diode for illumination provided from the top of the sample, (b) Photocurrent spectra from the same structure, obtained at 2.0 V bias with illumination from the top (dashed line) and bottom (solid line) of the sample (after [39]).

tration under non-equilibrium growth conditions [65-71]. The 1.0 eV GaxIni_xNyAsi_y alloy system appears to be an ideal candidate material for the third junction in the multijunction solar cells. Very recently, a GaxIni_xNyAsi_y solar cell with an internal quantum efficiency (IQE) greater than 70% has been achieved [65]. However, the device performance is still rigidly limited partly due to the presence of defects in GalnNAs, which may result in low IQE and small minority carrier diffusion lengths.

PPC effect has been observed in unintentionally doped p-type GalnNAs epilayers [72]. The PPC decay behavior in the temperature region (50 ^ 320 K) is very well described by a stretched-exponential function of Eq. 2 and the PPC relaxation time


becomes very long below 175 K. The PPC level is still about 75% of its initial value after 1000 s of decay at 175 K. However, as the sample temperature was increased to above 320 K, no PPC effect was observed.

The Arrhenius plot of the PPC decay time constant {In x versus 1 /T) showed two distinct temperature regions, similar to the feature seen in p-GaN epilayers shown in Fig. 5a. At temperatures T > 220 K, i decreased rapidly with temperature following an activated behavior, from which the capture barrier Ec was obtained to be around 0.57 eV. However, t was only weakly dependent on temperature at T < 220 K. The decay exponent p increased linearly with T at T > 200 K and was also nearly temperature independent at T < 200 K. Detailed studies showed that the PPC decay kinetics observed in InGaNAs quaternary alloys were very similar to those of DX centers in AlxGai_xAs alloys and GaN.

The relative optical cross-section, aopt, as a function of excitation photon energy hv was also measured, from which an optical ionization energy of 0.70 eV was obtained. The free hole concentration /? as a function of reciprocal temperature was measured in darkness in the temperature range from 10 to 450 K. From the appearance of the Hall data, different slopes were present in the ln(p) versus 1/T plot, which indicates that more than one acceptor state may be involved in the conduction process. Furthermore, alloy scattering is probably very important in this quaternary material, which can lead to a hopping conduction in the low temperature region. However, the average impurity binding energy (Eb) estimated from the slope of the ln(p) versus 1/T plot in the high temperature region was about 67 meV. This gave a Stokes shift of about 0.64 eV (Estokes = Eopt — Eo). Such a large Stokes shift, which is one of the common features of lattice relaxation associated with impurities, provided an additional evidence that AX-like centers were the primary cause of PPC in GalnNAs. However, these results could not provide insight regarding the origin of the AX-centers in this material system.

3. PPC effects on heterojunction devices

As a consequence of PPC in AlGaN/GaN HFET structures, the device characteristics are sensitive to light and the sensitivity is associated with persistent photoinduced increase in the 2DEG carrier mobility and density. As for the AlGaAs/GaAs modulation doped field-effect transistors, PPC by itself is not a problem for device operation, but its presence indicates the possibility of other device instabilities associated with cases such as charge trapping. Effects of PPC are expected to be strong, in particular for the minority carrier devices based on Ill-nitrides. In majority-carrier devices or semiconductor LEDs and lasers, these effects are less prominent. However, to be shown in Section 4, the effects of PPC in AlGaN/GaN HFET structures can be minimized by varying the structural parameters.

3.1. Effects on heterojunction field effect transistors

The deep level centers located in the regions outside of the conducting channel could trap carriers and result a current collapse (CC) in the transistors, which have been observed in AlxGai_xN/GaN HFETs [3] and GaN metal-semiconductor field effect transistors


normal l-V illuminated 470nm fully collapsed

(dark)

10 20 DRAIN VOLTAGE (V)

Fig. 25. I-V characteristics of a GaN MESFETs measured under different conditions (after [5]).

(MESFETs) [4,5]. The effect of current collapse observed in GaN MESFETs, like PPC, can be reversed by liberating trapped carriers by thermal emission or light excitation.

The effect of light on the current collapse of GaN FETs has been studied by measuring the transistor characteristics under light excitation. An increase in the drain current was observed in an AlGaN/GaN HFET under light excitation with photon wavelengths near 360 nm, corresponding to the AlGaN band edge, and near 650 nm, which was associated with an unidentified trap located in the AlGaN barrier layers in the AlGaN/GaN HFETs [3]. An optically induced restoration of the drain current was also observed in GaN MESFETs [4]. Fig. 25 shows the I-V characteristics of a GaN MESFET obtained under different conditions including I-V curves under normal, illuminated under light with photon wavelength 470 nm, and fully collapsed (dark) conditions. The increase of drain current AI between the dark and under the illumination after the application of a high source-drain bias reflects the numbers of carriers that have been optically excited from the traps. The results suggested that traps responsible for the CC effect were located in the high resistive GaN insulting layer in the GaN MESFETs [4]. Photoionization spectra of GaN MESFETs revealed two electron traps, which are strongly coupled to the lattice [5]. Photoionization thresholds for these two traps were determined at 1.8 and 2.85 eV and both appeared to be the same traps associated with PPC in GaN epilayers.

The drain current under a high source-drain voltage in the dark and light excitation with different wavelength X was measured, from which the current collapse function S(>v.) was obtained [5],

where (t)(X) is the incident photon flux, t is the duration of light illumination time, AI(X) and Idark are the light-induced drain current increase and the fully collapsed (dark) drain current, respectively. The measured S(hv) as a function of incident photon energy hv is plotted as the open circles in Fig. 27, showing clearly two broad absorption associated with photoionization from two deep traps with optical ionization energies of 1.8 and 2.85 eV, respectively. The results of PPC spectral studies in GaN epilayers by Reddy

Persistent photoconductivity in lU-nitrides Ch. 6 179

W 10-17

10-18

10-18

r r - r

E 1 1 ;; t r

~, i E 1 -r

1 I /

' I ' M

§bo

/ & <• 1 1 1 . .

1 1 1 1 1 1 • 1

Trapl ly*^

r / ' |l.8eV

/ lo(hv)

1 1 1 1 t 1 1 »

' • 1 1 1 1 ' 1 1 1 1 1 1 1 1 1 1 1

1 o —

Trap2^<fw

0 / |2.8SeV

/ / • • • Bneddyetal.

/ • • • • Hirach et al. / OOOOTHISWORK

' ' ' ' ' ' • • ' • • • ' ' ' • • ' *

~ r |

q 1

1

j

3

1 \ \ \ 1

1.0 1.5 2.0 2.5 3.0 Photon Energy (eV)

3.5 4.0

Fig. 26. The measured current collapse function, S(hv), versus incident photon energy, hv, (open circles), showing clearly two broad absorption associated with photoionization from two deep traps with optical ionization energies of 1.8 and 2.85 eV, respectively. The results of PPC spectral studies in GaN epilayers by Reddy et al. [57] and by Hirsch et al. [34] are also included for comparison. When scaled in magnitude, the spectral dependence of PPC exhibits very similar spectral dependence of those traps observed in GaN MESFETs (after [5]).

et al. [57] and by Hirsch et al. [34] are shown (scaled in magnitude) in Fig. 26 to exhibit very similar spectral dependence as those traps observed in GaN MESFETs. This suggests that the traps responsible for the PPC observed in GaN epilayers are of the same origin as those responsible for the current collapse in the GaN IVIESFETs. The solid line in Fig. 26 is the plot of a fit of data with a convolution of the photoionization cross section with a Gaussian broadening function due to the strong coupling of deep centers with lattice. Since DX centers have been determined in AlGaAs to be responsible both for PPC and CC in AlGaAs/GaAs FETs [7-12], it is thus natural to attribute the type of deep centers being responsible for the observed CC in GaN and AlGaN/GaN FETs also to DX-like centers.

On the other hand, when the PPC effect is minimized in AlGaN/GaN HFET structures, the slow transient behavior in the switching characteristics of AlGaN/GaN HFETs was absent [73]. The turn-on and turn-off switching characteristics were measured for a IVIOCVD grown AlxGai_xN/GaN (x -^ 0.25) HFET (with a 0.6 jxm gate length and 37 (xm gate width) in response to picosecond electrical pulses applied to the gate. It was found that (a) both the on and off transient kinetics were well described by single exponential functions, (b) the switching speed (r^„ and T^^) was in the order of tens of ps, (c) the switching speed depended strongly on the gate-source bias VGS and drain-source bias VDS, and (d) the dependencies of ton on VGS and Vps were quite different from those of toff. More interestingly, the slow transient behaviors such as those observed in AlGaAs/GaAs HFETs [74,75] associated with DX centers were not observed in AlGaN/GaN HFETs and a switching speed of about 50 GHz was achieved in this device. These results showed that for a given device structure, the switching speed was directly correlated with the intrinsic material quality, namely the sheet density dependent drift mobility.

180 Ch, 6 H.X. Jiang and J. Y. Lin

260-

>

bo

> o

240 H

220-

200

180 H

160

140

120

-y^ 250ArvAI,,Ga,,N

250 A GaN 2nm l-GaN

Sapphire

14 21 28

T=300 K f=1 Hz

70 77 84

time (s) Fig. 27. Typical photo-responses of an AlGaN/GaN heterostructure photoconductor measured under a successive pulsed laser excitation (Xexc = 337 nm). The inset shows a schematically diagram of the AlGaN/GaN heterostructure used here (after [6]).

3.2. Effects on AlGaN/GaN heterostructure UVphotoconductors

PPC effect can influence the photocurrent (PC) transient characteristics of GaN photoconductors [6]. PC transient characteristics of an AlGaN/GaN heterostructure photo-conductor have been measured at different conditions. The PC transient characteristics of the AlGaN/GaN heterostructure was found to depend strongly on its history (or initial conditions). Fig. 27 illustrates the typical room temperature photoresponses of an AlGaN/GaN heterostructure to a successive N2 pulsed laser excitation at 338 nm starting from a dark equilibrium condition, measured at an excitation laser frequency of 1 Hz. As we can see from Fig. 27, the PC transient characteristics are different for the initial and the later pulses. The changes are progressive and can be summarized below: (i) the PC responsivity of the earlier pulses are smaller than those of the later pulses; (ii) the quasi-dark level of the previous transient is always lower than that of the subsequent transients; and (iii) the eariier PC transients decay faster than the later transients. The results shown in Fig. 29 imply that the detectivity (or sensitivity), dark level, and response speed of UV detectors fabricated from AlGaN/GaN heterostructures will all depend on the device history.

The PC decay transients can be described very well by an exponential function and


^

P

I o

S

100

90

80

70

60

140

JH 120

O 8.6

2. ®°

7.6

7.2

_ -p , ,

1 ^-^-^ 1 > ^ 1 * X

J ^

] • (a) 1 1 ' I "

I ^/

1 (b) 1 1 ' 1

1 y^^

- 1 — , , ,

-, , , ,

T=300K ^=1Hz

1 • 1

1 • 1

•

-, , , ,

— 1 1 1 1 1 j

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• data ] Au«>««« H Tilling 1

a"' = 33.1 S \

1 • 1 •

a = 33.0 S ]

1 ' I •

V . \ M _ • ]

• • .

a' = 33.2 S 1 • 1 1 1 1 1

50 100 150 200 250 300

time (s) Fig. 28. Characteristic parameters of photoconductivity transients versus pulsed illumination time obtained for an AlGaN/GaN heterojunction photoconductor. (a) The photo-responsivity, (b) the dark conductivity level, and (c) the PC decay time constant, x. The solid curves are the least squares fit of experimental data with Eq. 13 by replacing y(t) with the photo-voltage, dark level, or decay time constant T. The fitted values of a~^ for these three parameters are all identical, a~' = 3.1 ± 0.1 (after [6]).

the decay time constant, x, increases gradually with the number of successive excitation pulses. Fig. 28 plots (a) the photovoltage (or the photo-responsivity), (b) the quasi-dark level, and (c) the PC decay time constant t as functions of the pulsed laser illumination time. An interesting feature exhibited in Fig. 30 is that all of these three physical parameters, y(t), have a systematic dependence on the pulsed laser illumination time and the exact dependence is identical to the PPC buildup kinetics of Eq. 1 by replacing Ippc with y(t),

y(t) = yd + (ymax - yd)(i - e""^). (13) Here y(t) describes the time dependence of the three physical quantities (photo-responsivity, dark level, and PC decay time constant), yd (ymax) denotes their values near the initial dark (saturation) state, and a~^ is a characteristic time that is required for the device to reach the saturation (or steady) state. The solid curves in Fig. 30 are the least

182 Ch, 6 H.X. Jiang and J. Y. Lin

squares fit of data with Eq. 13. The fitted values of a"^ obtained from Fig. 30a-c are all identical, i.e., a"^ = 33.1 ±0.1 s. This clearly demonstrates that the observed characteristics are directly correlated with the effect of PPC in the AlGaN/GaN heterostructure and can have a significant effect on the characteristics of the UV photodetectors based on AlGaN/GaN heterostructures, including sensitivity, noise property, dark level, and response speed.

4. The uses of PPC

The principal feature of PPC, namely the prolonged carrier capture and recombination times, has been utilized to probe the transport properties of II-VI semiconductor alloys [17-19]. In the PPC state, the electron concentration in the conduction band can be conveniently varied in a single sample with excitation photon dose, so direct comparisons between different electron concentrations can be made more easily. The distribution of the tail states in the density of states (DOS) caused by alloy disorder, for example in AlGaN alloys, can be determined through the use of PPC. Contrary to the AlGaAs alloys, the effect of alloy disorder in AlGaN system is very strong due to the large energy gap difference between AIN and GaN. Important parameters such as the total DOS below the mobility edge in the conduction band of AlGaN alloys can be determine through the use of PPC, regardless what is the origin of PPC itself. Moreover, the magnitude of PPC can also be used to monitor the electronic qualities of AlGaN alloys and AlGaN/GaN heterostructures.

4,1. Effects of alloy fluctuation in Al^Gai^x^ alloys probed by PPC

PPC has been used to study the effects of alloy fluctuations on the electron transport properties of AlxGai_xN alloys [76]. By utilizing the unique features of PPC, namely the very long lifetimes of the photoexcited carriers and the continues variation of the electron concentration in the conduction band, the electron mobility (/x^) as a function of electron concentration in) in a single sample can be measured. Fig. 29 shows a typical PPC behavior for one of the MOCVD grown and undoped Alo.35Gao.65N epilayers. The time-dependent PPC decay Ippc(t) can be very well described by a stretched-exponential function of Eq. 2. The fitted values of x and f> for the data shown in Fig. 31 are 1350 s and 0.35, respectively. However, as illustrated in Fig. 31, the PPC buildup kinetics in Alo.35Gao.65N epilayers can no longer be described by Eq. 1 and in fact the use of Eq. 1 results in a poor fit, particularly near the PPC saturation region (bold part).

If the PPC buildup can be described by Eq. 1, then a linear time-dependent behavior at the initial PPC buildup stage, /ppc(0 oc {at < 1), is expected. Initial PPC buildup kinetics in Alo.35Gao.65N epilayers has been monitored by systematically varying excitation intensity, lexc- Fig- 30 shows the time-dependent PPC buildup behaviors during the first 50 seconds measured for varying Iexc» which clearly illustrates that for the samples studied here, a linear time-dependent PPC buildup at the initial stage was absent.

On the other hand, previous work has shown that the electron transport properties in II-VI semiconductor alloys are strongly influenced by the tail states caused by the alloy


4 H

40

1 ^ 39

I 37 H

Light off J

PPC decay fitted by: IpVtH+a„-Vexp(-(t/T/)(

PPC buildup fitted by:

-Dark Level

Light on

Al Ga N 0.35 0.65

T=300 K I =L

0 1000 2000 3000 4000

Time (s) Fig. 29. PPC measured at 300 K for an Alo.35Gao.65N alloy grown by MOCVD. The least squares fit for the PPC buildup (open circles) with Eq. 1 and for the PPC decay (open squares) with Eq. 2 are plotted as solid lines. The bold line near the saturation level indicates the disagreement between the experimental data and Eq. 1 (after [76]).

disorder [17-19]. In semiconductors (n-type) with alloy fluctuations, the conductivity results mainly from the electron hopping between localized states when the electron quasi-Fermi-level, Ef, is below the mobility edge, Em [77]. Assuming that the Fermi distribution is a step function (at low temperatures) and that the alloy disorder induced an exponential tail states in the conduction band edge, a quadratic time-dependent initial PPC buildup was derived from the Kubo-Greenwood formula [17-19],

/," PPC {t) — Id + const. [1 - exp(-QfO]

oc t^{at < 1), (14)

which agreed well with experimental observations in ZnxCdi_xSe alloys. The quadratic time-dependent initial PPC buildup behavior implies that the electron mobility (/x ) in the tail states of ZnxCdi_xSe alloys is proportional to the electron concentration (n), {jie) a {n), since the conductivity cr(t) is effectively proportional to the product of (/>6en), where () stands for an assemble average and {n) is proportional to [1 — exp(—Of/)]-

However, for Alo.35Gao.65N epilayers, the initial PPC buildup behavior is neither linear nor quadratic with time. Instead, the observed PPC buildup behavior follows


0 10 20 30 40 50

Time (s) Fig. 30. The kinetics of the initial PPC buildup for an Alo.35Gao.65N alloy measured at four different excitation light intensities, i.e., lexc = lo, 0.4Io, 0.16I0, 0.064Io. The dark currents have been subtracted out. The solid curves are the least squares fit of data with Eq. 15, with the fitted value of y being approximately 2.9 ± 0.2 for different lexc (after [76]).

/ppc(r) = Id + const, [l - exp(-QfO]''

oct^(at < 1), (15)

where a and y are constants. The least squares fits of the initial PPC buildup data with Eq. 15 are plotted in Fig. 30 as solid lines with the fitted value of y being approximately 2.9 ± 0.2 for different lexc- The initial PPC buildup behavior in Alo.35Gao.65N epilayers is also caused by the tail states in the conduction band due to alloy fluctuations, similar to the case in ZnCdSe alloys. The novel feature exhibited by the initial PPC buildup kinetics observed in Al xGai_xN alloys, (/ppc(0 c< r^^"^^^), can be attributed to a unique functional dependence of (/x > on {n) to be described below.

The experimentally measured functional form of (/z ) vs (n) in Al xGai_xN alloys is shown in Fig. 31, which shows that /x is a constant when n is below a critical value He and it increases with « at « > AZ . This behavior is caused by the electron filling effects in the localized tail states in AlGaN alloys. When n < ric, electrons are localized in the tail states and contribute to the Hall-mobility only through hopping or tunneling. As « increases and reaches a certain critical value itc, the electron quasi-Fermi-level, Ef, reaches above the mobility edge E^, at which a transition from localized electron transport to a free electron transport takes place. Thus the electron mobility is expected to increase with n above ric. The experimentally measured dependence of (/x ) on {n) in

Persistent photoconductivity in IlJ-nitrides Ch. 6

92-

185

C/3

91

90

89

88

87

86

85

84

Alo.35G\.sN T =300 K

1.40 1.45 1.50 1.55 1.60

n(lO'W) Fig. 31. The measured electron mobility as a function of electron concentration (open squares) for a Alo.35Gao.65N alloy and the least squares fit (solid line) of the data with Eq. 16 (after [76]).

Al xGai_xN alloys can be well described by

M = Ao + A{n - ncYO{n - ric). (16)

where |Xo is the electron mobility 3i n < ric and 9(n — ric) is a step function, with A, He, and p being fitting parameters. The second term in Eq. 16 describes the conduction contributed by electrons with energies above E^. The least squares fit of data with Eq. 16 is plotted as the solid line in Fig. 31 and the fitted values are /XQ = 86.4 cm^/Vs, He = 1.46 X 10 ^ cm~^, and p = 1.6, respectively.

Since the measured electron concentration in darkness is about 1.43 x 10 ^ cm~^ ^ He, SO (n — He) corresponds approximately to the photoexcited electron concentration, HQ. From the fitted value of HQ (^ 1.46 x 10 ^ cm~^), we can also conclude that the total density of the band tail states below the mobility edge in AlxGai_xN alloys is about 1.46 X 10^^ cm"^, which is direcdy correlated with the degree of alloy fluctuations in these materials. From Eq. 16 and Fig. 33, one obtains /z^ a [n^(0]^'^ (for n > ric). One therefore obtains /ppc(0 oc a(t) a (/Xen ) a [rieit)]^^ oc r - , since rieit) ex t at Q?/ < 1 from Eq. 1. On the other hand, when one fits the initial PPC buildup kinetics shown in Fig. 30 directly to Eq. 15, /^pc(0 a r^, y = 2.9 ± 0.2 (at < 1), which is very close to the value obtained from the mobility measurements. Thus one can conclude that the initial PPC buildup kinetics in AlGaN alloys shown in Fig. 30 is a nature consequence of the unique relationship between /Xg and n described by Eq. 16. These results have demonstrated that alloy fluctuation strongly influences the transport properties of AlGaN alloys and that the PPC effects can be utilized to probe


the properties induced by alloy fluctuations, such as the density of the tail states and the mobility behavior near the mobility edge. Moreover, these results also indicate that for Ill-nitride device applications using AlxGai_xN, effects of alloy fluctuations are important even at room temperature due to the large band gap difference between GaN and AIN.

Different relationships between jie and n as well as the initial PPC buildup kinetics observed in AlxGai_xN and ZnxCdi_xSe alloys may be due to the fact that the band gap difference between AIN and GaN (AEg = 2.8 eV) is much larger than the difference between ZnSe and CdSe (AEg = 1.1 eV), which may result in a stronger effect of alloy fluctuations as well as a different distribution of the tail states in AlxGai_xN alloys.

4,2, Electronic quality ofAlGaN/GaN HFET structures probed by PPC

The correlation between the PPC effect and the electronic quality of MOCVD grown AlGaN/GaN HFET structures was investigated [78]. The generic structure of samples used in for this particular study consisted of a 1.3 |Jim highly insulating GaN epilayer followed by a Alo.iGao.gN spacer layer (between 4 and 25 nm) and finally a Si-doped Alo.2Gao.8N epilayer of 25 nm. A total of seven samples with varying growth or structural parameters were studied, all of which exhibited PPC effect. Fig. 32 presents the PPC results obtained for three representative samples measured at two different

"~^ 0.2-^

Sample No. T=20K A 1

onsmiaii'^xri X'

nvnymnmwM

200 400 600

t(s) 800 1000

Fig. 32, Buildup and decay kinetics of PPC in three Alo.zGao.gN/GaN HFET structures measured at two representative temperatures, (a) T — 300 K and (b) T = 20K. Here /ppc denotes the persistent photocurrent measured at time t and /d the initial dark current levels (after [78]).

Persistent photoconductivity in lll-nitrides Ch. 6 187

Table 1. Hall-effect and PPC results measured at 20 and 300 K of the seven Alo.2Gao.8N/GaN HFET structures, together with the structural parameters (spacer and Si-doped AlGaN layer thicknesses), the relative Si-doping levels (SiJij flow rate), and the growth pressure

Sample no.

1 2 3 4 5 6 7

Mobility (cmVVs)

20 K/300 K

4950/1230 3760/870 2920/884 2150/573 1620/703 600/280 2800/485

Sheet density (lO^Vcm^) 20 K/300 K

0.93/1.15 0.76/1.37 0.78/1.13 0.84/0.92 0.69/0.74 0.99/1.16 0.11/0.10

HsM (lO^VVs)

20 K/300 K

4.95/1.42 2.86/1.19 2.28/1.00 1.81/0.53 1.13/0.52 0.59/0.33 0.31/0.05

PPC ratio [(Ippc - Id)/Id] X 100%

20 K/300 K

3.31/3.42 5.84/5.32 7.10/6.75 8.34/11.2 37.4/14.3 39.2/18.3 200/300

i-AIFaN/ n-AlGaN thickness

(nm)

6/25 8/25 4/25 6/25 6/25 6/25 25/25

SiH4 (seem)

3 1 1 1 1 0 0

Pressure (torr)

100 150 150 150 100 100 77

All structures were grown at 1050°C in a variable pressure MOCVD. Here Ippc denotes the buildup levels of the persistent currents for a fixed excitation intensity and buildup time span and U the initial dark current levels.

temperatures. We can see that the decay time constants of the low temperature PPC are very long. Interestingly, the magnitude of PPC in AlGaN/GaN HFET structures and hence the device instabilities can be minimized by varying the growth conditions as well as structural parameters. Table 1 summarizes the Hall and PPC measurement results for all seven structures with different structural and growth parameters. As shown in Table 1, the magnitude of PPC or the photoinduced conductivity enhancement ( ppc — h) over its dark level {Id) is about 200% in sample #7, but is negligibly small (only about 3%) in sample #1.

The general trends shown in Table 1 are that samples possess higher mobilities as well as higher sheet carrier densities exhibit reduced PPC. By carefully inspecting the results summarized in Table 1, we can clearly see that the magnitude of PPC, or the photoinduced conductivity enhancement, has a systematic dependence only on the product of the 2DEG sheet carrier density and mobility, i.e., n^/x, the most important intrinsic material parameter for the HFET device design. In Fig. 33, the magnitude of PPC versus n /x measured at 20 K (a) and 300 K (b) are replotted. At both temperatures, the magnitude of PPC decreases monotonously with an increase of n^/x, follows the relationship of

Rppc = A(/2,/x)-^ (17)

Here the magnitude of PPC (Rppc) is defined as [(/ppc — Id)/ld\ and A and a are two constants. As illustrated in Table 1, the better structures (i.e., larger values of W5/X) were achieved by varying the AlGaN space layer thickness, the Si-doped AlGaN layer thickness, the doping levels in the Si-doped AlGaN layer, and the growth pressure. The electronic qualities (or n /x values) of these HFET structures can be further improved by adjusting the four parameters described above until the magnitude of PPC further reduces to zero.

In desired structures with minimal PPC effects, enhanced mobilities can be accomplished by barrier or channel doping. However, at much greater sheet carrier densities.


10^1

o £L CL Q:

|0 J 1tf

wU

10"

23 , , -1 .47

Kc= 10" (nn)-

10'

ioS

10" 10"

nu(1/Vs)

o 10" 8:

a: lON

10-

. 1 , . , . . . , , , , 1 , 1 I I I I 11

(b) T=300K

1 Rppc=io M

I I I I I I n I I I I i"i I n I I

10" 10"

n ^ (Ws)

Fig. 33. The magnitude of PPC, Rppc = [/ppc(0 — IdMh^ or the photoinduced conductivity enhancement for a fixed excitation intensity and build time span (/ppc — Id) over its dark level (7 ) as a function of the product of the sheet carrier density and mobility, n /Lt obtained from seven different \\FEV structures. The solid lines are the least squares fits to experimental data with Rppc = A(wj/x)~". The fitted values of a A are 1.47 (lO^^) and 1.26 (10^^) at 20 and 300 K, respectively (after [78]).

the population of the higher-lying subbands could limit the overall mobility of the structure due to intersubband scattering as well as the loss of the true two-dimensional character due to a virtual continuum of bands being populated [79,80]. Thus a trade-off between these effects must be considered in the design and optimization of AlGaN/GaN HFETs.

5. Concluding remarks

Our understandings of the properties of PPC and associated deep level centers in Ill-nitrides have built on the early studies on AlGaAs alloys. Studies of PPC in Ill-nitrides, just as any other topics in this field, are driven primarily by technological developments and needs. This trend will be continued. Current devices in the Ill-nitrides all take advantages of heterostructures and quantum wells. In this sense, understanding and control of PPC as well as the associated deep level centers and their effects


on devices based heterostructures and quantum wells will become more and more important. As the nitride materials quality further improves, the nature of deep level center as well as their characteristics can be identified. With the insights from theoretical calculations, the detailed information regarding the energy levels as well as their atomic configurations in IE-nitride lattices will be understood.

Acknowledgements

We are indebted to many of the pioneers as well as our respected friends in the field. Professor H.J. Queisser, Dr. J.D. Chadi, Professor J. Furdyna, Professor D. Redfield, Professor G. Neumark, and Professor D.C. Look, whose earlier work on PPC and DX like centers in conventional III-V and II-VI semiconductors have inspired us greatly. We are grateful to Professor Hadis Morkoc and Professor M. Asif Khan for their long term collaboration and support. We would like to acknowledge assistance from the following members in our group, J.Z. Li, J. Li„ K.C. Zeng, C. Johnson, M. Smith, R. Mair, C. Ellis, and S.X. Jin. We would like to take this opportunity to thank Dr. John Zavada, Dr. Kepi Wu, Dr. Yoon Soo Park, Dr. Vem Hess, and Dr. Jerry Smith, for their insights and constant support.

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CHAPTER 7

Ion implantation, isolation and thermal processing of GaN and related materials

Bemd Rauschenbach

1. Introduction

GaN has attracted a widespread attention for the fabrication of blue light-emitting diodes, blue laser diodes and high-power or high-temperature devices (see e.g. [1,2]). These applications are related to very distinct properties of GaN such as the large direct bandgap or the high thermal conductivity.

Ion implantation has become a highly developed tool for modifying the structure and properties of semiconductors. The energetic implants are applied in the doping of semiconductor material, the formation of insulator regions to isolate the active regions of circuits, in the fabrication of optical active regions and also in the device application. The advantages of the ion implantation are: • An accurate dose control is possible by measurement of the ion current. • The depth distribution of the injected dopants and the introduced lattice disorder are

directly related to the ion energy and the masses of the target material and ion. By variation of the ion energy and dose the concentration profile of the impurities and also the structural changes can be tailored.

• In contrast to high temperature processing the ion implantation is an intrinsic low temperature process, although subsequent annealing is generally necessary. In this respect it differs greatly from the diffusion approach, where high temperatures during doping may lead to decomposition of the near surface region.

• Ion implantation is insensitive to the lattice structure, lattice defects and the presence of impurities.

• The implantation process is not constrained by thermodynamic considerations. This means, that any species of ion may be implanted into any host. A wide concentration range can be achieved with the upper limit generally set by the sputtering yield rather than by equilibrium solubility.

• Ion implantation can be included in the semiconductor process technology and implantation machines can be designed for specific applications. To understand and to control the electrical and optical properties of group Ill-nitride

is one of the great challenges associated with the development of semiconductors. It is well-known that wide band gap semiconductors are difficult to dope by ion implantation due to the native defects and the high resistance against the damage recovery. As the quality of epitaxial GaN layers continues to improve, ion implantation is considered to be a promising doping technology. Recent progress has been made in this field

194 Ch. 7 B. Rauschenbach

such as the controlled p-type doping, damage annealing, implant isolation, implantation induced optical activation as well as device fabrication. The main disadvantage of the ion implantation in semiconductors is related to the lattice disorder caused by implanted ions. Because of the high background electron concentration of the as-growth GaN, ion implantation with high concentrations of acceptors is generally needed to compensate the native electron background and to realize the transition to p-type. However, the crystalline structure is diminished by implantation induced damage after implantation with high dopant concentrations. Consequently, a precise control of implantation conditions such as ion energy, temperature during implantation, ion dose, etc., and an optimal annealing process are essential to successful doping by ion implantation.

The purpose of this review is to present an introduction into and a review of the state of ion implantation in GaN and related III-V materials. Although significant progress has been reported for doping and isolation of wide band gap semiconductors, there are still many problems to be solved before an extensive application of ion implantation in device fabrication can be realized. In recent years several excellent review papers have appeared addressing various aspects of the implantation technology of group Ill-nitrides [3-5]. This review is devoted to the implantation induced damage and the defect annealing. The realization of the controlled n-type and p-type doping by ion implantation is discussed with the main emphasis on the results of GaN. Then, the impurity luminescence and isolation by ion implantation are discussed.

2. Ion implantation process

2.1. Range and range distribution

When an energetic ion strikes a solid surface the ion will in general lose energy through scattering events involving the Coulomb interaction with the target atoms. This collision process is a complicated many-body event described by an extremely difficult Hamiltonian. The problem can be simplified when it is recognized that the interaction range is very short (forces between the ion and target atom decrease rapidly with the distance). This circumstance allows to consider the interaction of the incident ion or the recoiling target atom with the target atom individually and to ignore the contributions due to more remote lattice atoms. In this so-called binary collision approximation the slowing down process of an incoming ion in a solid can be roughly divided into two energy loss mechanisms: the elastic or nuclear energy loss (Coulomb interaction between two screened positive charges) and the inelastic or electronic energy loss (direct electron-electron energy transfer, excitation of band and conduction electrons, excitation or ionization of strongly bounded target and projectile electrons). Energy loss of an ion through an amorphous material is given by

dE , _ _ / d E \ / d E \

- = -NS(E) = ( - )_ + (_)^ ,„ where N is the atomic density, dE is the energy loss by an ion traversing a distance dx and S(E) the stopping cross-section. The so-called stopping power dE/dx, depending on the mass and velocity of the ion and the target, can be separated into the nuclear

Ion implantation^ isolation and thermal processing ofGaN Ch. 7 195

105

'r^ o k—

o E

X H HI "D

10^

103

102

10^

1 ' ' E3 E,

(dE/dx), ~ E'^

1 • """^x^"^""^^

\

X

1

(dE/dx),-E'

(dE/dxG (dE/dx)„|

^ ; 10 102 103 lO'^ 105 106

Ion energy (keV)

Fig. 1. Dependence of the nuclear (dE/dx)n and the electronic (dE/dx)e stopping power in GaN on the energy of incident Ca" ions. Also indicated are the characteristic energies Ea, Eb and Ec (after [6]).

and the electronic stopping cross-sections, Sn(E) and Se(E), corresponding to the two energy loss processes. The nuclear stopping dominates at low energies and the electronic stopping at high energies. This behavior is illustrated in Fig. 1 for the implantation of Ca"^-ions into GaN. Three characteristic energies are given: Ea ^ 30 keV, is the energy where the nuclear stopping power reaches its maximum, Eb ^ 270 keV is the energy where the electronic and nuclear stopping power are equal and Ec ^ 50 MeV is the energy where the electronic stopping power has its maximum [6]. It is important to notice that host atoms are severely displaced only in the energy regime in which nuclear stopping power dominates, while electronic stopping usually does not create extensive damages. Inverting the expression (Eq. 1), the total path length R(E) travelling by a particle of initial energy before coming to rest is

'^ dE R(E)

Jo (2)

NS(E) Clearly, for individual projectiles the number of collisions, the energy transferred

and thus the total path length will vary. The ion range normal to the surface, termed the mean projected range Rp(E) is smaller than R(E). The range traveled along the axis perpendicular to that of incidence is called the lateral range Rx. The stochastic fluctuations in the energy loss mechanisms lead to a spreading ion range described by the projected range straggling ARp. The spreading (standard deviation) is a function of mass ratio (mass of the target material to the mass of the incident ions, M2/M1) and will increase with increasing depth into the target. The straggling effect results in an ion depth distribution C(x) which is approximately Gaussian in shape

C(x) O

/TTT ARt exp

(X - Rp)^

2AR2 (3)

where 4> is the ion dose in [ions/cm^]. The maximum or peak concentration is Cmax = 0.4<l>/ARp. Furthermore, as a result of multiple collisions the ions will be deviated from

196 ^h. 7 B. Rauschenbach

their original direction and there will be lateral spreading (lateral straggling ARj.) of the incident ions. ARx = ARp for M2/M1 ^ 10, ARj. = 0.5 ARp for M2 = Mi, and AR_L ^ ARp for M2/M1 = 0.1. In practice, the lateral spreading is only of relevance when the implanted region is defined by a mask window.

Two general methods for the calculation of the range and range distribution have been developed. Firstly, an analytical approach based on the Boltzmann transport equation was pioneered by Lindhard et al. [7], and is often referred to as LSS theory. A more exact calculation is available using the PRAL (Project Range ALgorithm) code [8]. Second, Monte Carlo binary collision computer simulations are carried out for range and damage analysis, where both a random target (e.g. TRIM, TRansport of Ions in Matter, or TRIDYN, dynamical TRIM) or a single-crystalline targets (e.g. MARLOWE) are used (details see [9]). As an example, the mean projected range Rp(E) and the projected range straggling ARp of several ion species for implantation with energies up to 500 keV into GaN calculated using TRIM are shown in Fig. 2a. On this basis, the concentration versus depth distribution can be calculated with Eq. 3. Fig. 2b shows the calculated calcium concentration distribution in GaN for implantation with a dose of 1 x 10 " Ca'^-ions/cm^ and three different energies. With increasing ion energy and depth of ion penetration the maximum concentration decreases because of the larger standard deviations.

By comparison with experimental results, the Gaussian distribution is often not a satisfactory fit. The experimentally determined doping profiles tend to be asymmetrical, that means the concentration distributions are shifted or spread out. Often the Pearson distribution is used which based is on the first four moments (Rp, ARp, skewness, kurtosis).

Additional physical effects can influence the concentration distribution. Mainly three effects have to be discussed in this context:

2.1.1. Influence of sputtering The sputtering yield Y is the number of ejected target atoms per incident ion and depends on E, Mi, M2, angle of incidence and temperature. For the implantation in GaN and related compounds the sputtering effect plays an important role for low energy implantation with heavy ions, because the nuclear stopping is large under these conditions (see Fig. 1). Eq. 3 can easily be extended to include the sputtering effect. Now, the concentration profile is described by

.(X) = ^ ^x — Rp + z X — Rp

erf—-=r^ erf— - (4) V5ARp V2ARp

where Y is the sputtering coefficient and z = O Y / N is the thickness of the sputtered layer [10]. Sputtering yields between about 0.25 and 2.0 have been measured after Ar^-ion bombardment of GaN with energies between 150 and 600 eV [11]. Unfortunately, more detailed information about the sputtering yield of GaN cannot be found in the literature.

2.1.2. Influence of radiation enhanced diffusion In presence of ion irradiation, the thermally activated migration of implantation-induced vacancy and interstitial defects is known as radiation enhanced diffusion (RED). The

Ion implantation, isolation and thermal processing ofGaN Ch. 7 197

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Fig. 2. (a) Calculated values of the mean projected range Rp(E) and the projected range straggling ARp for several ion species after implantation with energies up to 500 keV into GaN. (b) Calculated calcium concentration distribution in GaN for implantation with a dose of 1 x 10*" Ca"*"-ions/cm^ and three different energies.

diffusion can be significantly enhanced under irradiation by both increasing the concentration of implantation-induced defects and by creating other diffusion mechanisms via usually not active defect species [12]. The descriptions based on a set of coupled chemical rate equations. The radiation-enhanced diffusion coefficient DR is given by the sum DR = CyDv + QDi, where Cv,i are the concentrations of the interstitials or vacancies and Dv,i are the diffusivities of vacancies or interstitials induced by implantation. The diffusivity is calculated from the equation Dyj = Doexp(-AHv,i/kBT), where AHv,i is the migration enthalpy of the vacancy or interstitial atoms and ICB is the Boltzmann constant. The influence of the RED on the concentration distribution of the implanted atom species can be approximately calculated under the assumption that the diffusion of

198 Ch, 7 B. Rauschenbach

implantation induced vacancies determines the diffusion process (the migration enthalpy of interstitials is very small, AHi < 0.3 eV) [10]. The concentration profiles become increasingly asymmetrical and larger depths are reached in presence of the RED.

2.13. Influence of channeling In the preceding discussion the target is assumed to be amorphous and isotropic. However, the interactions between the incoming ions and the lattice atoms will be minimized if the ions are directed down a crystallographic axis or plane. A careful alignment between the ion beam direction and a planar or axial channel is to give an enhanced penetration into the solid which can be as much as 10 Rp. The key parameter is the critical acceptance angle which depends on the ion energy, the ion species and the lattice parameters. The implantation at angles between the main crystal axes and the ion beam smaller than the critical angle gives rise to tails of in the concentration profiles. Consequently, the shape of the concentration distribution is difficult to predict.

Two standard approaches to overcome channeling are (i) the implantation into a tilted target (tilt angle e.g. T off main crystal axes) or (ii) low-energy self-ion implantation to amorphize the near surface region.

Especially for doses higher than 10 ^ ions/cm^ the precise reproducibility of the concentration profiles is difficult to realize because the radiation damage generation reinforces the dechanneling.

2.2. Damage and damage distribution

An energetic ion which penetrates into a solid loses its energy via both electronic excitation/ionization and elastic collisions with the target atoms before coming to rest in the host lattice. The latter process, dominant at low ion velocities, leads to atomic displacements (radiation damage).

The energy required to displace an atom from a lattice site and form a Frenkel pair is larger than the so-called displacement energy Ed. For example, the threshold displacement energy for GaN is 24.3 eV [13]. The primary knock-on target atom (PKA) will collide with other lattice atoms which in turn will displace further lattice atoms. Thus an avalanche-like process of moving atoms which distribute the energy in successive collisions until the energy is below Ed is obtained. Assuming that only those recoiled atoms become displaced which received an energy E > Ed, the total number of displaced atoms Nd is obtained from the modified Kinchin-Pease relationship [14] to

Nd(x) = 0 . 8 ^ ^ (6) zbd

where FD(X) is the deposited energy depth distribution function, i.e. the total energy deposited in elastic collision processes or nuclear recoil loss. The damage energy is smaller than the nuclear stopping power of the primary ion because the recoils partially lose their kinetic energy by electronic processes in subsequent collisions. A rough approximation is FD(X) = 0.7 . . . 0.8 Sn(E(x)). Commonly, the number of


150 200 250 Depth [nm]

Fig. 3. Defect concentration distribution in GaN measured by RBS/C (solid points) and calculated by TRIDYN (line) after implantation with 5 x 10 ^ Ca^/cm^ and an energy of 180 keV (after [15]).

displacements per atom, dpa, is used to describe the damage and is given by the equation

.FD(X)C|> dpa(x) = 0.8- (7)

2Ed N

The damage distribution is in a similar form as the distribution of the implanted ions,

FD(x)dx = NSn(E(x))dx (8)

however, the peak is closer to the surface. The Gaussian form of the damage distribution reflects the statistical nature of the scattering events. Conmionly used algorithms for defect formation are based on the previously mentioned TRIM or TRIDYN codes. As an example, in Fig. 3 the measured depth distribution of defects after Ca^-ion implantation in GaN is compared with results of a Monte-Carlo simulation. The agreement between the measured and simulated curves is good. A comparison of the mean projected range of 180 keV Ca-ions after implantation in GaN (see Fig. 2a) with the mean projected damage range (peak in Fig. 3) demonstrates that the damage profile is closer to the surface. The shape of the damage profile tends to be non-Gaussian. It is obvious that the calculation only refers to the initial damage situation during the passage of the ion. A complete or partial lattice recovery can occur after the implantation process. This results in an overestimation of the defect concentration by simulation especially for implantation at higher temperatures. Consequently, the temperature at which the target is bombarded is an important parameter since it governs the mobility of defects.

As long as the collision density is sufficiently small, so that each collision can be described by a binary event, the energy deposition is given by the linear Boltzmann transport equation. For such a linear cascade, the number of defects varies linearly with the total deposited elastic energy. The concept of successive binary collisions with a fixed threshold energy does no longer hold if in a cascade volume each atom receives more than 1 eV/atom. A collective motion of all cascade atoms (thermal spike concept)


is a better picture to describe this state (displacement cascade). Such highly disordered region is not in thermal equilibrium. The energy deposition within a cascade survives for times between 10"^^ and 10"^ s. The final state of such a cascade is critically dependent on relaxation process and it can vary from an amorphous region to a region in which there is perfect epitaxial regrowth.

2,3, Defect evolution

In semiconductors, the implanted ions are incorporated interstitially, which causes small lattice deformations and generate defects. Especially, the latter accumulate during the implantation process. In the linear cascade regime, the damage build-up would result from the defect accumulation up to a critical defect density and in the displacement cascade regime, a disordered region including amorphization would arise due to direct ion impact mechanism. In semiconductor targets it can be observed that an amorphous region is built-up around the whole ion track, whereas in the case of metals only a small amorphized volume around an implanted ion can be kept. Consequently, a substantial difference in order of magnitude of amorphization doses has been measured in semiconductors (10^-^-10*^ ions/cm^) and metals (10^^-10 ' ions/cm^).

The evolution of the damage formation in dependence on the ion dose and temperature depends mainly on both the energy density deposited by the implanted ions and the impurities acting as disorder stabilizers. A large number of semiconductor implantation experiments exhibit that the crystalline-to-disorder (amorphization) transition results from the combination of these two effects (disorder production and chemical stabilization). For the process of damage generation and accumulation until amorphization a sigmoidally shaped curve of damage as a function of doses on a double-log scale has been found. This behavior has been observed for one-component semiconductors, such as Si, Ge and also III-V compound semiconductors. It is obviously that this transition occurs locally, since the fraction of disorder or amorphous volume changes continuously with the ion dose.

Several models describe the dose dependence of the disorder or amorphized fraction. In general, the time (dose) evolution of phase transformation under isothermal conditions has been described by the Johnson-Mehl-Avrami equation [16]. This equation has become widely used to analyse transformations, in spite of the fact that the interpretation of its parameters is far from straightforward. Morehead and Crowder [17] proposed a model which hypothesized that each ion impinging on the target produces a cylindrical amorphous core. Amorphization occurs when such damage cores completely fill the area of the target. According to this semi-quantitative model, the critical dose for amorphization decreases with increasing ion mass and is constant at sufficiently low temperature. Gibbons [18] has modified this model by assuming that an amorphous layer can also be produced by the overlap of damaged, nonamorphous regions associated with individual damage clusters. In this model amorphization (most extreme possible disorder) is supposed to occur either by a direct ion impact mechanism (n = 1) i.e. immediate amorphization caused by the first ion penetrating an undamaged region, or by overlapping of damaged regions around the ion collision cascades (n > 2), as during amorphization by accumulation of defects. The transformed volume fraction Vtr/Vo can


be expressed as

Vtr(O) . ; ^ ( V i o n ^ , , , ^, —TT— = 1 - 2 ^ jl e x p ( - V i o n O ) (9)

^^ /=o • where Vion is the damage volume around the track of the implanted ion and Vo the total volume being implanted. The integer n is the number of ions required in the same region to cause amorphization. Therefore, simultaneous thermal defect relaxation during ion implantation at high temperatures has been taken into account [17].

2.4. Post-implantation annealing

The aim of the post-annealing process is both to activate electrically the dopants and to eliminate the implantation induced defects. In general the situation after implantation is characterized by the presence of several kinds of damage: heavily disordered crystalline regions, locally amorphous zones and an amorphous layer. The residual damage after annealing results in stacking faults, twins, dislocation lines, dislocation loops and point defects. Especially, the residual disorder in III-V semiconductors will compensate the electrical activity of dopants.

The diving force for the transition from the damage state (non-equilibrium state) to a nearly damage-free state (equilibrium state) is the minimization of the appropriate thermodynamic energy function. It is often the configuration for which the lowest strain is attained. The following mechanisms contribute to the recovery: • migration of defects to fixed sinks (e.g. surfaces, dislocations, grain boundaries), • annihilation of defects by recombination (e.g. vacancies with interstitials), • agglomeration into more complex defects (e.g. formation of dislocation loops or

vacancy-impurity complexes), • trapping at impurities.

These processes are thermally activated by annealing and require high temperatures for long times. In general, the annealing of extended defects requires very high temperatures (> 1000°C). The temporal change of the concentration Cj of defect type j during annealing is given through a rate equation to

? = -kc; (10) dt ^

where, a is the rank of reaction (e.g. a = 1 for vacancy-interstitial annihilation), k is the rate constant and can be obtained from thermodynamic consideration to

k = k o e x p ( - ^ ) (11)

where ko is a temperature-independent constant which contains an entropy term and the jump rate and AE is the activation energy of the defect reaction. The type of defects can be determined by measuring of the activation energy using isothermal or isochronal annealing experiments. For example, the isochronal annealing experiment is characterized by annealing at a defined temperature for the duration At and a subsequent measurement of the defect concentration at room temperature (RT). This procedure is repeated many times for higher annealing temperatures.

In


Together with Eq. 11, the integration of Eq. 10 leads for a first-rank reaction (a =

""[IS]—(-a where Ci and Ce are the measured defect concentrations before and after the annealing step at the temperature T. By fitting the measured concentration with Eq. 12 the activation energy and also the rate constant ko can be determined.

The recovery by the mentioned defect reactions has been extensively studied. But, no broadly accepted model exists for semiconductors. Nevertheless, through a large number of systematic electrical resistivity, channeling and electron paramagnetic resonance (EPR) measurements it was possible to develop a qualitative model of recovery at isochronal annealing. There different recovery stages with increase of temperature are distinguished: • recombination of close interstitial-vacancy pairs at the lowest temperature, • free migration of interstitials, • growth of interstitial clusters followed eventually by dislocation loop formation, • free migration of vacancies, • growth of vacancy clusters, • dissociation of defect clusters at the highest temperature.

Usually, the total recovery of compound semiconductors will not be obtained. Especially, irradiated III-V semiconductor materials show a poor recovery characteristic and exhibit a high degree of residual disorder in form of point defects, twins and stacking faults. These residual defects dramatically influence the electrical and optical properties.

In praxis, furnace annealing and rapid thermal annealing (RTA) are used to remove the implantation induced damages and to activate the dopants. The furnace annealing of GaN and related materials is restricted both regarding relatively low temperatures, because these materials begin to decompose when the temperature is above 750-800°C and long annealing times are used (several hours). Prolonged annealing at these temperatures broaden the implanted dopant profiles. The post annealing distribution is given by

C(x,t) y27i(AR2 + 2Dt)

exp "2(AR2+2Dt) diexp

(x + Rp)^ "2(AR2+2Dt)

(13)

where D is the diffusion coefficient and t is the annealing time. The sign before the last term in Eq. 13 reflecting all out diffusing atoms from the surface (+) or through the surface (—).

The disadvantages of the furnace annealing can be overcame using RTA by lamps with processing times of few seconds (1-30 s). The sample is typically heated to higher temperatures (< 1200°C) through transparent windows coupled with highly reflective mirrors. The emissivity and absorption are strongly influenced by the bulk and surface properties of the implanted samples. Consequently, these optical properties can change drastically by the implantation conditions (impurity content, damages, etc.) and surface coatings.


3. Implantation induced defects

As the quality of epitaxial GaN films continues to improve, ion implantation is considered to be a promising doping technology in fabricating planar devices of GaN and related group Ill-nitrides, because it can introduce a well-defined impurity concentration in a designed region and, therefore, allows isolation of devices from each other.

3.1. As-grown defect state

GaN and related nitride layers are grown in their wurtzite structure on hexagonal sapphire (a-Al203) and 6H-SiC substrates. Because of the large lattice mismatch (approximately 15% between sapphire and GaN and 3% between SiC and GaN) and the differences in thermal expansion between deposited layer and the substrate material, point defects (native and extrinsic) and as well as one- and two-dimensional structural defects (dislocations, planar faults, etc.) are generated. These defects can profoundly influence the electrical, optical and mechanical properties.

The native defects with the lowest formation energy and very low transition levels are the nitrogen vacancies, V f, and the gallium vacancies, Voa, [19]. In the thermodynamic equilibrium, the nitrogen vacancies can be excluded as the source for the n-type doping of as grown GaN, i.e. the nitrogen vacancy acts as a single donor. Donor impurities such as carbon, silicon and oxygen which are unintentionally incorporated during the growth may be also responsible for the n-type doping of the as-grown GaN. These elements occupy Ga and N substitutional lattice sites as well as interstitial sites. For example, silicon on a Ga site, Sioa, is a shallow donor, oxygen and also carbon sit on nitrogen sites, CN, or form a defect cluster with Ga vacancies, CN-Voa [20].

Epitaxial GaN layers usually contain a high density of dislocations, microtwins and stacking faults. In general, dislocations start at the interface between substrate and the GaN layer and extend through the entire layer thickness. The main slip system in hexagonal GaN is 1/3<11 20> {0001} with a Burgers vector b = l / 3 < l l 20> equal to the shortest lattice vector along a close-packed direction. Dislocation densities in the range of 10^-10^^ cm"" have been measured.

3.2. Damage buildup and amorphization

The technique of ion implantation is extremely attractive for the fabrication of GaN and related III-V compound devices because it can introduce a well defined impurity concentration in a designed zone. However, this technique is still far away from application in processing GaN based semiconductor devices, primarily owing to ion beam induced lattice disorder, which deteriorates the electrical and optical properties. Although the research on GaN is in the ascendant, there remains almost a blank of understanding about the implant damage buildup, removal and their effects on the transport properties of GaN devices. So far there are only a few papers, which demonstrate damage generation due to ion implantation. Therefore, more work in both theory and experiment is necessary to get a reasonable picture of this important area. The


damage of GaN films before and after implantation can be characterized by Rutherford backscattering/channeling spectrometry (RBS/C), cross-sectional transmission electron microscopy (XTEM), high resolution X-ray diffraction (XRD) and Raman spectroscopy (RS). In Table 1 studies are summarized which investigate the damage in GaN by ion implantation.

Tan et al. [21-23] have studied the amorphization of GaN by Si"^-ion implantation at liquid nitrogen temperature (LNT). For a dose smaller than 1 x 10* Si'^-ions/cm^ the residual disorder consists of a dense network of small loops, clusters and dislocations whereas for a dose greater than 2.4 x 10^^ Si'^-ions/cm^ an amorphous structure is formed. These results indicate that the amorphous threshold for GaN is very high in comparison to other compound semiconductors (e.g. AlxGai_x As). Consequently, GaN is extremely resistant to amorphization during LNT implantation.

Recently, systematic investigation of damage generation and accumulation until amorphization induced by Ca" -, Mg"^- and Ar"^-ion implantation in GaN films at different temperatures have been published [6,24-27]. Fig. 4 shows [0001]-aligned and random backscattering spectra of the GaN films implanted with different Ca"*"-ion doses at LNT. It demonstrates the whole process of damage generation and accumulation until amorphization as a function of the ion dose. With the increase of Ca"^-ion fiuence, a damage peak arises in the channeling spectra. When the dose exceeds 1 x 10 ^ ions/cm^, this peak grows up more quicldy, accompanied by a broadening towards the surface and greater depth, and reaches the random level at the dose of 6 x 10 ^ ions/cm^. This means that a closed amorphized layer is formed. Jiang et al. [28] have shown that the damage evolution after implantation of the lighter element oxygen into GaN at low temperature (210 K) ranges from dilute defects up to the formation of a disorder saturation state that was not fully amorphous. It was found that the defects are

100 200 300 400 500 600 700 800

Channel

Fig. 4. [0001]-oriented RBS/C spectra (2.5 MeV, ' He2+) illustrating the damage buildup in GaN films for 180 keV Ca+ implantation with different doses at LNT (after [25]).

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immobile at this low temperature. This indicates again that GaN is extremely resistant to implantation-induced damage. From the distribution of the nuclear energy deposition a critical energy deposition per unit volume can be determined to 90 eV/atom and 8 x 10 ^ keV/cm^, respectively, above which amorphization at low temperatures dominates. This is one order of magnitude higher than that of Si [29]. Therefore, GaN is extremely resistant to amorphization compared to other semiconductors.

Another feature in Fig. 4 is the change of the surface peak in the channeling spectra. It decreases gradually with increasing fluence and disappears almost at the dose of 3 X 10 ^ ions/cm^, as the buried damage layer expands towards the surface. This is an indication for the collapse of the surface crystal structure.

A detailed analysis of such RBS/C spectra show the damage generation in the low dose range [25,30]. The channehng spectrum for the dose of 1 x 10 ^ ions/cm^ coincides almost with the virgin sample. Until this dose the channeling spectra of both implanted and unimplanted films do not differ significantly. Therefore, the dose of 5 X 10^ ions/cm^ should be regarded as the critical dose for the generation of stable damages that can be detected by RBS/C.

These studies are profitably supplemented by measurements using high resolution X-ray diffraction. Fig. 5 illustrates the XRD spectra of the GaN (0002) peak before and after Ca" implantation with different doses at LNT. The unimplanted film exhibits a very sharp (0002) peak with a full width at half maximum (FWHM) of less than 0.06°. After implantation, a new peak on the left side of the (0002) peak appears. It grows up and shifts towards smaller angles with increasing fluence. Expansion of GaN crystal

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lattice due to ion implantation accounts for this phenomenon and is confirmed by TEM results [30]. The extent of the lattice expansion depends on the defect concentration which increases synchronously with the ion dose. Hence, increasing intensity of the new peak is the consequence. However, it has been also found that an amorphous phase arises at the dose of 3 x 10 " ions/cm^. After that the new peak gradually shrinks with the rapid development of the amorphous component and finally collapses when the dose reaches the threshold of 6 x 10 ^ ions/cm^. Thus, XRD results testify once again that the dose of 6 x 10 ^ cm"- is the critical dose for the amorphization of GaN films at LNT. It should be noted, that the diffraction peaks are partially overlapped, i.e., a more detailed analysis should be performed by refinement of the spectra.

It can be summarized that the amorphous component arises at the dose of 3 x 10 " Ca"^-ions/cm^, dominates at 1 x 10 ^ Ca'^-ions/cm^ and develops into an stable amorphous layer at 6 x 10 ^ Ca'^-ions/cm^ after implantation at LNT. Obviously, the maximum damage concentration exists in a depth below the surface, which corresponds to the mean projected damage range (peak of the nuclear energy deposition), and broadens gradually towards the surface and greater depth with increasing ion dose. The shape of the distribution of the displaced atoms is very similar to that of the nuclear energy deposition.

X-ray pole figure measurements can be performed to measure the texture of doped GaN in the selected directions. It has been found that the new peak has the same texture as the (0002) peak [29]. Hence, it can be concluded that the new peak originates from the expanded (0002) lattice in the implanted layer. Impurity implantation in GaN leads to a lattice expansion rather than a formation of a new phase. According to the well-known models of amorphization (see Section 2.3), it can be assumed that an amorphous layer can also be produced by the overlap of damaged, non-amorphous regions associated with individual damage clusters. In the case of GaN, point defects dominate at low ion doses. They provide appropriate nucleation sites for the formation of localized amorphous clusters in which the free energy of the defective crystal exceeds that of the amorphous phase. As the dose increases, local amorphous nucleation can be produced by the overlap of individual defects, dislocations or damage clusters. This can be verified by the fact that the amorphous component was found at a critical dose (e.g. 3 X 10^^ Ca+-ions/cm^ [30,31] or 8.4 x 10^ Si^-ions/cm^ [22] after implantation at LNT). At this time, the GaN lattice can still maintain its basic integrity, containing only isolated amorphous nuclei. However, once the amorphous nuclei forms, it grows, through damage accumulation, into the underlying crystalline regions with further irradiation. On the other hand, the defects induced by implantation at LNT can be thought of in a 'frozen' state. Thus, the possibility of formation of secondary defects is greatly increased. The amorphous nuclei can grow up by overlapping with each other or with adjacent secondary defects such as clusters and loops. At the threshold dose the amorphous nuclei are closely connected all together, and the GaN crystalline collapses into an amorphous phase.

Ca has been supposed to be a potentially superior shallow acceptor in GaN considering d-electron core relaxation effects [32]. On the other side, Ar is an electrically inert element, and its atom mass is almost equal to that of Ca. The comparison of the structural characteristics between Ar"^- and Ca^-ion implanted GaN films helps to understand


100 200 300 600 700 800 400 500

Channel

Fig. 6. [0001]-oriented RBS/C spectra (2.5 MeV, " He " ions) illustrating the damage buildup in GaN films for 180 keV Ar" -ion implantation at LNT with different doses: unimplanted (•••), 5 x 10* ion/cm^ ( - • - ) , 5 X 10 4 ions/cm^ ( - • - ) , 1 x 10 ^ ions/cm^ (-A-), 3 x 10* ions/cm^ ( - • - ) , 6 x 10 ^ ions/cm^ (- • -) and random (—). The inset shows a part of the backscattering spectra, containing only the information about Ga atoms at lower doses: unimplanted (—), 1 x 10 ^ ions/cm^ ( ), 5 x 10 ^ ions/cm^ (• •.) and 1 X 10 3 ions/cm^ (---) (after [25]).

the influence of implantation-induced damage on the electrical properties of the doped GaN [4]. The damage buildup for Ar^-ion implantation in GaN at LNT is displayed in Fig. 6. A similar progress as for Ca'^-ion implantation is shown (see Fig. 4). One can notice again that the dose of 5 x 10 ^ Ar"*"-ions/cm^ is necessary to generate a damage detectable by RBS/C. Moreover, implantation with the dose of 6 x 10 ^ ions/cm^ leads to amorphization. Thus, the thresholds for amorphization of GaN films are proved to be 6 X 10 ^ ions/cm^ for both Ca^- and Ar^-ion implantation with the energy of 180 keV at LNT. The results indicate that the nuclear collision process determinates the lattice disorder at low-temperature implantation. The diffusion of defects, i.e. the dynamical annealing during implantation can be neglected at these temperatures.

The dependence of the normalized minimum yield Xmin of the [0001]-channeling on the implantation doses demonstrates the progress of amorphization induced impurity implantation. Liu et al. [25] have shown that the Xmin values of the virgin films increases slowly up to the dose of 3 x 10 " ions/cm^ after Ca" - or Ar"^-ion implantation at LNT. When the dose is in excess of 8 x 10 " ions/cm^, Xmin rises drastically and reaches the random level at 6 x 10 ^ ions/cm^. One can find that the damage induced by Ar"^-ion bombardment at the dose of 3 x 10 ^ ion/cm^ exceeds that of Ca"^-ions. This is consistent with the results of the implantation at room temperature [24]. A sigmoidally


shaped curve of damage versus implantation doses on a double-log scale has been also found for other III-V compounds, such InP, GaAs and InAs [33]. It can be sununarized that after low dose implantation in III-V semiconductors the backscattering yield increases until a saturation level of about 10 ... 15% is reached, which then remains constant over a broad dose region that is dependent on the substrates temperature during implantation. Then, for very high doses the implanted regions become amorphous.

The damage evolution in GaN and related compounds at implantation with temperatures greater LNT has also been studied [26,31,34-37]. Recently, Parikh et al. [34] found that ion implanted GaN at room temperature showed a higher damage (below amorphization) compared to GaN implanted at higher temperatures (e.g. at 550''C) with doses up to 1 X 10 ^ Mg+- and Si"^-ions/cm , respectively. This can be expected since at higher temperature the dynamical annealing during implantation is increased.

The damage buildup for Ca" -ion implantation at room temperature is displayed in Fig. 7. A similar progress as for Ca' -ion implantation at LNT is shown. Again, the process of damage generation and accumulation until amorphization as a function of the ion dose is illustrated. A damage peak arises in the channeling spectra with increase of the Ca" -ion fluence. This peak grows up slowly when the dose is lower than 1 X 10 ^ ions/cm^, but rather quickly over 1 x 10 ^ ions/cm^, accompanied by a broadening towards the surface and greater depth. In consequence, there is a striking contrast between the spectra implanted with the doses of 1 x 10 ^ ions/cm^ and 3 x 10 ^ ions/cm^. The buried damage layer centers around the mean projected range (about 100 nm below the surface) corresponding to the damage peak in the channeling spectra. At the dose of 7.3 x 10 ^ ions/cm^, the damage peak of the aligned channeling spectrum reaches the random level, i.e. a closed amorphized layer is formed. Thus, the dose of 7.3 X 10 ^ ions/cm^ is revealed as the threshold dose for amorphization of GaN by 180 keV Ca" -ion implantation at room temperature.

500 1000 1500 2000

Backscattering energy (keV)

Fig. 7. [0001]-oriented RBS/C spectra (2.5 MeV, "^He^+'ions) demonstrating the damage buildup in GaN films on sapphire for 180 keV Ca+-ions implantation with different doses at room temperature. Each elemental symbol shows the leading edge of the depth profile (after [26]).


CO c 0

c CO E CO

CC

:i: >ir1>J

K'Vv^^NrW*^^^

asgrownVW'**^ | A (LO)

6701

400

Raman shift (cm' )

800

Fig. 8. Raman spectra of GaN before and after 180 keV Ca+-ion implantation with different doses (unit: cm~^) at room temperature. The spectra were taken in z(xx)z backscattering configuration (after [26]).

The application of the Raman spectroscopy allows a more detailed analysis of the implantation-induced point defect formation before the amorphous phase can be detected. As example, Fig. 8 illustrates Raman spectra of the GaN before and after 180 keV Ca" implantation at room temperature in the dose range from 5 x 10 ^ to 5 X 10 ^ ion/cm^. The two longitudinal optical modes of E2 at about 571 cm"^ and Ai(LO) at 736 cm"^ are observed as expected from the Raman selection rules in semiconductors with wurtzite structure for the z(xx)z configuration. With increase of the ion fluence, four new peaks at 300, 360, 420 and 670 cm"^ appear. The modes at 360,420 and 670 cm"^ were assigned to vacancy related crystal defects as a result of ion implantation, while the broad structure at 300 cm"^ was explained by disorder-activated Raman scattering [38]. Besides the occurrence of new peaks the disappearance of the signal from the E2 and Ai(LO) modes after implantation with the dose of 3 x 10^^ ions/cm^ is the most striking feature. This decrease in intensity originates from the following two contributions: destruction of the crystal lattice in the implanted region and loss of transparency the suppressing signal from the underlying unimplanted GaN. Compared with the RBS/C analysis in Fig. 7, in which a great variance between the spectra implanted with a dose of 1 x 10 ^ and 3 x 10^ ions/cm^ is revealed, it can be concluded that the GaN structure has undergone a substantial transition through damage accumulation.

In order to understand the structural nature of the damaged layer, high resolution XRD has been performed to monitor the change of the GaN (0002) peak after


implantation at temperatures equal or greater room temperature. One remarkable characteristic is that a new peak (shoulder) also appears on the left side of the (0002) peak after implantation with a dose of 5 x 10 ^ ions/cm^. This phenomenon has been observed by studying Ca+- and Ar" -ion implantation at LNT [25,30] and after Mg" -ion implantation at room temperature in GaN [36,37]. Lattice expansion of GaN due to ion implantation accounts for this phenomenon and was confirmed by TEM results [25]. It should be pointed out that the process of damage accumulation until amorphization at RT (from 3 x 10 ^ to 7.3 x 10 ^ ions/cm^) takes much longer than the same process (from 3 X 10 ^ to 6 x 10* ions/cm^) for the implantation at LNT. This is attributed to the result of stronger dynamic annealing at room temperature, i.e. a part of the defects are in-situ annealed out by the beam heating during the process of implantation. Although the dynamic annealing exists also at LNT [22,30] it works more efficiently to restrain damage accumulation at room temperature. Roughly half of the defects produced by Ca" -ion implantation at room temperature are removed by dynamic annealing [24].

It is demonstrated in Fig. 9 that the lattice expansion increases synchronously with the ion dose. Generally, the lattice expansion takes places by incorporation of dopants into interstitial sites or by occupying of larger substituents at Ga- or N-vacancies. Larger lattice expansions have been found when the samples were implanted at LNT, compared with those implanted at room temperature or 200''C for the same dose. Thus, it is reasonable to assume that ion implantation at LNT produces more damage than at higher room temperatures. This, from another side, proves once again that the samples which were implanted at higher temperatures must have undergone stronger dynamic annealing during the implantation. It can be concluded that the lattice expansion relies mainly upon the ion dose, but the extent of the expansion is subjected to the substrate temperature. It is interesting that the expansion from Ar doping is some greater than that from Ca doping for the same doses, in spite of smaller volume of Ar atoms [29].

CO c CO o

5§ CM T".

to -6 M— Q> O C © " O C/) CO CO CL CD CO O

c

10 Liquid nitrogen temperature Room temperature

Ca"*" dose (cm' )

Fig. 9. The expansion of GaN (0002) planar spacing versus Ca+-ion doses for different implantation temperatures, d and do are the (0002) planar spacing as-implanted and unimplanted, respectively (after [31]).


For partly ionic III-V compounds, the influence of the charge of dopant atoms on the lattice expansion should be additionally taken into account. In contrast to Ar, Ca atoms can set up chemical bonds with N atoms and reduce their volume when they occupy Ga vacancies. Thus the lattice expansion was somewhat restricted. Consequently, Ar doping leads to greater lattice expansion than Ca doping.

The results suggest that ion implantation for p-type doping has to be carried out below this dose, in order to avoid unrecoverable structural damage and to achieve better transport properties. On the other hand, implantation with higher doses is generally needed to compensate the native electron background of GaN and to realize p-type reverse. This conflict uncovers the essential difficulty for p-type doping of GaN by ion implantation.

3.3. Damage recovery

The main drawback of ion implantation in wide-bandgap semiconductors is related to the lattice disorder caused by energetic ions. Although GaN is extremely resistive against amorphization, it is not easily removed by thermal annealing even in the high temperature range of 1100°C [24,39] at which the electrical activation of dopants can be achieved. Additionally, GaN is known to degrade during post-annealing at temperatures over 800°C [40,41].

It is well laiown that the density of ion damage is a critical parameter for the subsequent defects removal and for the electrical activation of the implanted dopants [42]. The residual damage makes the electrical and optical properties of the doped GaN films undesirable and limits the application of ion implantation doping in GaN. Therefore, it is imperative to determine the relationship between damage buildup, recovery and the implanted dose. So far only a few contributions (see Table 1) concern with this important topic [26-28,31,38,43-49], but detailed information, such as the quantitative dependence of the implant damage on the dose, the critical dose, below which implantation-induced damage can be well removed by rapid thermal annealing (RTA), the impact of the residual damage on impurity activation and on electrical transport properties, has not been reported.

Two different procedures are known for annealing after ion implantation. On the one hand, conventional tube furnace (CTF) and on the other hand the so-called rapid thermal annealing (RTA) are used. For the choice of the annealing approach, the best possible optimization of the thermal process is crucial with regard to anneal defects, to limit diffusion, to activate the dopants and to suppress the decomposition of the near-surface region. The furnace annealing is used to realize temperatures up to 1000°C for some hours. To overcome the limited temperature range, RTA treatments by tungsten-halogen lamps as heat sources with processing times of a few seconds are suitable up to 1200°C. Recently, RTA equipment have been developed which are capable to achieve temperatures up to 1900°C [50]. These RTA systems possess a molybdenum intermetallic composite heater and allow heat fluxes up to 100 W/cm^ in the order of seconds. Annealing of implanted GaN at high temperatures is extraordinarily difficult, because GaN begins to degrade at temperatures higher than 800°C. Several ways are used to anneal implanted GaN [5,43,51-53] by furnace or RTA, namely by four


methods: (i) face-to-face arrangement so that the onset of the nitrogen loss can be suppressed, (ii) placing the implanted sample in a SiC-coated graphit susceptor in which powered AIN or InN are contained for production of a nitrogen vapor pressure over the sample, (iii) surface protection by Si3N4, SiC or AIN encupsulant layers, and (iv) annealing under a high nitrogen overpressure. The usual environment is NH3 or Ar for the furnace annealing and N2 or a mixture of N2 and NH3 for the RTA treatment.

Virtually all experiments have shown that an annealing process up to temperatures of about 1200°C is insufficient to completely remove the implantation damage. Significant implantation induced damage remains after RTA or conventional furnace treatment at high temperatures when GaN has been implanted with Si"^-ions doses below 10 " ions/cm^ [45] or 10 ^ ions/cm^ [43], with Si"^-ions and Mg"^-ions up to doses of 10 ^ ions/cm^, with Er"^-ions up to doses of 5 x 10^^ ions/cm^ [46], with 0^-ions up to doses of 5 X 10^ ions/cm^ [28] and with Ca"^-ions or Mg'*"-ions up to doses of 7.3 X 10^^ ions/cm^ [27,31]. An example is given in Fig. 10. RBS/C spectra of GaN after Ca"^-ion implantation with different doses at room temperature and after RTA treatment in flowing N2 are shown [25]. For doses below 1 x 10 ^ ions/cm^, the channeling spectra exhibit the similar shape to that of the unimplanted sample. Especially, those implanted with doses lower than 8 x 10 " ions/cm^ coincide almost with the virgin's. This result indicates that the implant damage after room temperature implantation can be well removed by RTA, if the sample was implanted at low doses. Therefore, Ca'^-ion implantation for p-type doping should be carried out below the dose of 8 X 10 "* ions/cm^ at an ion energy of 180 keV, in order to avoid unrecoverable structural damage and to achieve better transport properties. For the Ca"^-ion dose of 3 X 10 ^ ions/cm^, the damage peak can still be observed in the channeling spectrum. This means that significant damage remains after the RTA process. It seems reasonable

500 1000 1500

Backscattering Energy (keV)

2000

Fig. 10. [0001]-oriented RBS/C spectra (2.5 MeV, ' He^+ôns) illustrating the damage residual after rapid thermal annealing at 1150°C for 15 s in flowing N2. GaN were implanted at room temperature. The data for two Ca+-ion implanted GaN samples are multiplied by a factor of 2 (after [26]).


to increase the annealing temperature and to prolong the annealing time. However, the fact that GaN begins to decompose at temperatures over 800°C [41] limits the possibility of long-time annealing at higher temperatures. Similar results could be obtained after RTA treatment of GaN implanted at LNT [24,27]. It has been found that the implant damage can be well removed after the process of RTA, if the implantation dose is lower than 3 x 10 " Ca"^-ions/cm^ the dose at which the amorphous component arises. The amorphization of GaN develops very slowly up to the dose of 8 x 10*" Ca+-ion/cm^ (see Fig. 5) because of dynamic beam annealing [30]. However, when the dose exceeds 1 X 10 ^ Ca"^-ions/cm^, the tendency of amorphization is increased more and more rapidly. Great residual damage remains in the doped GaN films and no significant reduction of damage can be observed even after 1150°C activation [31]. Therefore, Ca+-ion implantation at low temperature for p-type doping should be carried out at a dose below 3 x 10 " cm~^ in order to avoid unrecoverable structural damage and to achieve better transport properties. On the other hand, since unimplanted GaN films have generally a very high background electron concentration (about 1 x 10^^ cm~^ for a MBE as-grown GaN film), a high dose of acceptors (>1 x 10^^ ions/cm^) is needed to be implanted for the realization of p-type reversion. Unfortunately, this high dose implantation introduces unrecoverable damage, and the doped p-type carriers are easily trapped and compensated by the radiation defects, resulting in a less effective activation even after a high temperature annealing. Consequently, p-type doping in GaN is difficult to realize by ion implantation.

The role of RTA is assessed by quantitatively comparing the area density of displaced atoms of the as-implanted and annealed samples. Fig. 11 shows the dose dependence of the density of the displaced atoms in GaN implanted with 180 keV Ca+- and 90 keV

101'

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m io'6

as Ca' -implanted y

critical level

Ca"*" implanted &/annealed

^ n

Mg" implanted & annealed

10' 10'5

Implanted ion dose (cm' )

w

Fig. 11. Dose dependence of the displaced atomic density induced by 180 keV Ca+-ion and 90 keV Mg+-ion implantation in GaN at room temperature before (filled dots and triangles) and after (open dots and triangles) rapid thermal annealing at 1150°C for 15 s in flowing N2 (after [31]).

Ion implantation, isolation and thermal processing of GaN Ch. 7 215

Mg"^-ions at room temperature [31]. For Ca'*"-ion implantation, the density of the displaced atoms decreases after the process of RTA by an order of magnitude if the dose is lower than 8 x 10 "* ions/cm^. At this dose an initial amorphous component has been formed which is not easily removed by RTA [6]. Ronning et al. [54] found also that GaN after Be'^-ion implantation with a low dose up to 3 x 10 ^ ions/cm^ is almost recovered after annealing at 1100°C for 1 h. When the dose is higher than 8 x 10 "* Ca~^-ions/cm^, the residual damage increases, and only a portion of the implantation induced damage can be annealed out. Moreover, for doses in excess of 3 x 10 ^ ions/cm-^, great damage resides and no significant damage recovery can be achieved. This results indicates that the density of ion damage is a critical parameter for the subsequent defect removal and for the electrical activation of the implanted dopants. A similar relationship has been observed for Mg"^-ion implanted GaN (Fig. 11). Recovery of the implantation-induced damage can be achieved up to a dose of 2.5 x 10 " Mg"^-ions/cm^, a dose which is about three times higher than of Ca'^-ion implantation for the same amount of residual damage. In this sense, Mg"^-ion implantation has an advantage over Ca'^-ion implantation for p-type doping. For both Ca" - and Mg" - ion implantation, it can be concluded, quantitatively, that an integral defect density of 2 x 10^ ions/cm^ is a critical level. Below this the implantation-induced damage can be well reduced by RTA. However, significant damage resides still after RTA if the integral damage density is higher than this critical level.

This result reflects that the present annealing conditions are not suitable for highly doped GaN. Since the implanted p-type carriers are easily trapped and compensated by the radiation defects, it is necessary, especially for the highly doped GaN, to explore new annealing conditions and new methods to remove the damage and to activate the dopants.

Exploring new ways and means to effectively remove the radiation damage by high dose implantation should also be placed on the agenda. Recently, Zolper [47] compared the melting point and activation temperature of the common compound semiconductors and deduced that the optimum implant activation temperature for GaN may be close to 1700°C. However, at this temperature GaN will decompose and a protective layer on GaN must be deposited before annealing and removed after annealing. Cao et al. [51] observe a strong reduction in lattice disorder of GaN implanted with several donor and acceptor species after annealing at 1500°C compared to samples annealed at 1100°C.

Strite [48] and Suski [49] found that under considerable N2 overpressure GaN can be annealed at temperatures as high as 1550°C without significant N loss enabling efficient optical activation of implanted Zn in GaN. Annealing experiments of Si"^-ions implanted GaN up to 1500°C under high N-overpressure (up to 15.3 kbar) have also demonstrated that the RES channeling yield is equivalent to that of the unimplanted sample and no macroscopic surface decomposition could be observed [5,35]. Another way is to repress the damage buildup during the implantation. According to experiments by Liu et al. [26], it seems attractive to carry out ion implantation at high substrate temperature. Alternately, one can implant GaN in a smaller dose increment and anneal in between the implants to recover damage completely [34]. Anyway, the most important factor that affects p-type doping by ion implantation is the undoped background electron concentration which should be kept as low as possible.


4. Doping

The doping of semiconductors is very important for the control of its electrical properties. It is known that all intrinsic GaN layers are characterized by n-type conductivity. In general, the background electron concentration in unintentionally doped GaN is approximately between 10 ^ and 10^^ cm~^ using van der Pauw geometry Hall measurements (HM). Different species have been discussed to be responsible for this high carrier background concentration (nitrogen and gallium vacancies, impurities such as Si, O or C acting as shallow donors, antisite defects, for details see Section 3.1). Bulk mobilities between 50 and 300 cm^/Vs at room temperature are typical for undoped GaN material. The doping of wide band gap semiconductors by ion implantation is difficult due to this high background concentration. A high implantation dose of acceptors is generally needed to compensate the native electron background. However, this means the crystallinity is degraded by the implantation-induced damage.

Consequently, the doping by ion implantation is carried out in two steps: (i) implantation of the dopant species, and (ii) post-implantation annealing at higher temperatures at which the electrical activation of dopants can be achieved and the implantation induced damage can be removed. Studies to the lattice site location and redistribution after annealing are necessary to explain the electrical and optical results after doping by implantation.

4.1. Lattice site location

Only few results have been published on the examination of lattice sites after ion implantation into GaN although the knowledge of the lattice occupation is an important prerequisite for the explanation of the optical and electronic qualities of doped materials. So, only a few works are known about the study of the location of potential dopants [56,57]. In [58] or rare earth doping in GaN [59,60]. The location of implanted foreign atoms relative to the GaN lattice were determined by Rutherford backscattering in combination with ion channeling (RBS/C), nuclear reaction analysis (NRA) and also emission channeling technique (EC).

GaN is frequently doped with the acceptor Mg. Fig. 12 shows examples of the lattice site analysis by RBS/channeling measurements. The angular scans through the <0001> axis before implantation show a nearly complete Ga sublattice. Angular scans though the <10 11> direction are also shown in Fig. 12 after Mg'^-ion implantation and subsequent annealing. The random fraction demonstrates that the GaN lattice is still partially damaged because the minimum yield for Ga is increased from about 5% up to about 20%. The incomplete overlap of the Ga scan and the Mg scan indicates that the Mg atoms have partially occupied the sites of the Ga sublattice. It can be assumed that only about 75% of the Mg atoms are in regular Ga sites of the lattice.

Ca has been also suggested as a shallow acceptor in GaN [32]. Kobayashi and Gibson [57] have studied the Ca dopant site in the GaN lattice after Ca-ion implantation at LNT and subsequent annealing at 1100°C. More than 80% of the Ca-atoms are slightly displaced from the Ga site after implantation and move to the exact Ga site after annealing. It is assumed that the displaced Ca-atoms in the as-implanted state form


Tilt angle from <0001> -1 0 1

1.0 1

• D

N 1 0.5-E o Z

0.0-

V\H Mg^

l \ ^^/j^

1 , , 1

31 32 Tilt angle from <10i1>

Fig. 12. Angular scans through the <0001> and the <10 11> axis for GaN before and after implantation with 1 X lO'^ Mg"*"-ions/cm^ and annealing at 1150°C for 15 s.

donor-like point defects and that Caca becomes electrically active when these defects are broken by subsequent annealing.

The lattice location of the donor Si after implantation in GaN was examined by the same authors [56]. The results indicate that all Si atoms occupy substitutional sites in GaN after annealing at 1100°C. The electrical activation of this donor seems to be connected with the annealing process at this temperature. Dalmer et al. [60] expects that Li acts as a donor atom if located on interstitial sites and as an acceptor atom if located on substitutional sites. Interstitial sites in the center of the c-axis hexagons of GaN have been found after Li-ion implantation at temperatures up to 700 K. Above this temperature, Li atoms are able to diffuse, interact with vacancies and occupy substitutional Ga-sites. An oxygen co-implantation leads to a strongly changed intensity of the luminescence [59]. The local lattice environments after In"^-ion implantation and subsequent annealing up to 900°C have been studied by emission channeling technique (a-EC) and perturbed y-y-angular correlation [58]. The majority of the In atoms were substitutional as-implanted in a heavily defective lattice. Recovery of the damage between 600 and 900°C leads a to defect free surrounding with half of the In atoms occupying substitutional lattice sites.

Finally, very few information is available about the location of dopants after implantation. Further studies are necessary in order to clarify the physical processes of GaN doping by ion implantation.

4.2. Impurity redistribution

The production of group-III-nitride semiconductor devices places a challenge to the performance of ultra-microanalysis, including thin film, and the three-dimensional distribution analysis of the low-level dopant concentration required in semiconductor material for semiconductor device production. Identifying the major elements is most


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Fig. 13. SIMS depth distributions of oxygen (70 keV, 5 x 10'" ions/cm^) implanted in GaN before and after annealing at 1125°C for 15 s (after [4,62]).

Straightforward. Analyzing the minor or trace elements is dependant on the sensitivity of the used method. The concentration distribution in GaN after ion implantation and also subsequent annealing is preferentially studied using secondary ion mass spectrometry (SIMS). SIMS is a sensitive technique which can detect all elements in many cases with detection limits smaller than 10 ^ cm"^. Measurements of the concentration profiles after implantation in GaN with doses greater than 10^ ions/cm^ have been reported in literature. In general, Cs primary ion bombardment is used to measure negative secondary ions and a O ion primary ion beam is used to measure positive secondary ions. In some cases, other techniques, such as Rutherford backscattering spectrometry (RBS) [61] and elastic recoil detection analysis (ERDA) [15] are used to analyze the implantation depth profiles. Figs. 13 and 14 show typical oxygen [62] and calcium [15] concentration distributions after implantation in GaN and also after RTA annealing at high temperatures The profiles are characterized by the expected Gaussian-like shape of the distribution. The important feature in both figures is that no measurable redistribution is seen after annealing. Consequently, an upper limit can be determined for the diffusion of the implanted species in GaN at this annealing temperatures (2.7 x 10"^^ cmVs for O in GaN at 1125°C and 1 x 10"^^ cmVs for Ca in GaN at 1150°C). The lack of significant redistribution has been observed for potential acceptor species, donor species and also species for optical applications. A redistribution could not been detected after implantation with F+-, Be"^- and Zn^-ions [63], Mg+-and Si+-ions [64], Ca+- and 0+-ions [39,62], Si+-, Be+- and Zn-^-ions [47], C+- and Ca'^-ions [15], Si+-ions [53] and Mg^-ions [65] in GaN and subsequent annealing at higher temperatures. This effect is also known for the implantation of AIN with Be"^-or Ge"^-ions [63] and InN with Be+-ions [64] and annealing up to temperatures of 8(X) and 600°C, respectively. These experiments demonstrate the high thermal stability of the

Ion implantation, isolation and thermal processing ofGaN Ck 7 219

60

50 i O

after implantation after annealing simulation

660 640 620 600 Channel

Fig. 14. ERDA depth distributions of Ca (180 keV, 5 x 10^^ ions/cm^) implanted in GaN before and after annealing at 1150°C for 15 s. For comparison, the calculated concentration distribution using TRIM is also given (after [15]).

implanted materials and indicate that the occupied lattice sites by the implanted species are very stable. In contrast, the thermally stimulated redistribution could be measured in GaN after implantation with Se" - and S+-ions and annealing at 700 and 600°C [63,64], respectively, and also after implantation of Mg"^-, Se"^- and Zn"^-ions and annealing at temperatures greater than 1000°C [47,54,66]. There a slight diffusion of the implanted species towards the surface is detectable.

43. N-type doping

Typical experimental conditions for the implantation of n-type dopants are summarized in Table 2. N-type doping of GaN by ion implantation is predominately done with Si"^-ions at room temperature and the temperature of liquid nitrogen (LNT). While the element Si is the most common, other elements such as O, Te, S, Se and also N may be used (see Table 2). Oxygen was also proposed as donor [41] because its 6 valence electrons on a N site would be a single donor (N has 5 valence electrons). The donor behavior of N-vacancies follows from a missing N atom surrounded by four Ga atoms that provide three valence electrons. Two of these electrons can be donated to the conduction band [67]. Se is of particular interest being a nitrogen site donor and shows an interesting compensation behavior at high doping levels. Oxygen is of interest as a possible alternative n-type dopant. The first experiments to the n-type doping by ion implantation have been carried out by Chung and Gershenzon [68].

The n-type doping of GaN by Si^-ion implantation has been studied by Zolper and coworkers (overview about their results see [4,69]) and as well by other groups [70-73]. Fig. 15 shows the sheet resistance of GaN after Si"^-ion implantation with a dose of 5 X 10 " ions/cm^ and subsequent annealing at temperatures between 700 and llOO^C for 20 s [4,74]. Fig. 15 demonstrates that for temperatures greater than 1050°C

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Fig. 15. Sheet resistance of GaN after Si^-ion implantation (200 keV, 5 x 10*" ions/cm^) at room temperature and subsequent annealing at different annealing temperature for 10 s (after [4,74]).

the n-type conductivity is significantly increased. It can be assumed that the implanted Si occupy Ga sites at lower temperatures, where the Si dopants are compensated by the implantation induced defects which are annealed above 1050°C. The sheet electron concentration has been determined to 4.25 x 10 ^ cm^, corresponding to 93% of the implanted Si atoms forming active donors on the Ga sublattice assuming a Si donor ionization energy of 62 meV (see Table 3). The ionization level is given

Table 3. Summary of the experimentally determined ionization energies (position of the energy levels below the conduction and above the valence band, respectively) after ion implantation in GaN

Ion species Ionization energy level (meV)

Ref.

Nv 0 0 Si S Te

Acceptors Be Be Mg Mg + P Zn Ca Ca

53 lb 8 78

28.7 62 and 29^

48 ± 1 0 50 ± 2 0

1290 150 ± 1 0

240 171 and 116^

580 1000

169 ± 12

[77] [68] [62] [69] [53] [51]

[78] [79] [78] [69] [78] [78] [62]

^ Two different methods were used to determine the ionization energy.


by a least-squares fit to the data in Fig. 15. The Arrhenius plot of the resistance versus the inverse temperature can also be used to estimate the ionization energy. Then this energy level is slightly lower (^29 meV [69]) than those determined from the sheet carrier concentration. The Arrhenius plot of the sheet electron concentration in dependence on the annealing temperature leads to the carrier activation energy, which gives information about the diffusion mechanisms during annealing. The high activation energy of 6.7 eV for the Si donor activation in GaN have been explained in terms of a substitutional diffusion process [69]. Likely, the interdiffusion of N and Ga to appropriate lattice sites designates the electrical activation after Si+-ion implantation. Chan et al. [70] have determined activation energies in GaN after Si+-ion implantation and annealing between 600 and 1000°C in the range from 1.4 to 3.6 eV. These energies correspond to the formation energy of annealing induced defects (vacancies or depassivated impurities). It is presumed that the defect formation dominates the optical and electrical properties of GaN stronger than the implantation itself.

The room temperature sheet electron concentration in GaN after Si" - or Ar"^-ion implantation and subsequent annealing at 1100°C for 15 s is given in Fig. 16 [43]. A significant donor activation could be observed for doses > 5 x 10* Si"^-ions/cm^. For doses lower than this critical dose it is supposed that the background carbon concentration of the as-grown GaN (~5 x 10 ^ cm"^) compensates the implanted Si species [5]. For the highest dose, 1 x 10 ^ cm~^, 50% of the implanted Si"^-ions generate ionized donors at room temperature. Additionally, the sheet electron concentration in GaN as a function of the in dose after Ar"^-ion implantation and subsequent annealing is presented in Fig. 16. For all doses the concentration of free electrons in Si"^-ion implanted GaN is over a factor of 100 times higher, although the chemical inert element Ar with a heavier mass than Si produces a higher defect density. Consequently,

i o c o o c

0)

x:

10*' 10'^ 10 dose (cm" )

Fig. 16. Sheet electron concentration in GaN versus implantation dose after Si+- and Ar"^-ion implantation (100 and 140 keV, respectively) and annealing at 1100°C for 15 s. The top line represents 100% activation of the implanted dose assuming full ionization (after [43]).


the possibility that the implantation induced damage alone was generating the free electrons can be ruled out [4]. A detailed analysis by Kobayashi and Gibson [56] has demonstrated that Si in GaN after implantation and subsequent annealing at 1100°C for 30 min occupies substitutional lattice sites (see also Section 4.1). Therefore the electrical activation of this donor species is directly due to the formation of the substitutional Si.

The influence of higher annealing temperatures on the sheet resistance, carrier concentration and mobility of Si"^-ion implanted GaN have been studied [79]. The highest electron concentrations have been achieved after annealing in N2 ambient at 1150°C to about 8 x 10 ^ ions/cm^ [72], at 1400°C to about 6 x 10 ^ ions/cm^ [55] and at 1400°C to about 5 x 10 ^ ions/cm^ [53], where an encapsulation of the GaN samples with AIN films provides protection against the surface degradation. The room temperature carrier mobility also increases with the increasing annealing temperature up to 35 cm^/Vs [72] and 55 cm^/Vs [55], respectively. The application of annealing temperatures higher than 1400°C leads in general to a decrease in the sheet resistance and the mobility, which is consistent with Si self-compensation.

Besides the Si'^-ion implantation, the implantation of 0"^-ions [62,68,75], S" -, Se" -and Te^-ions [51] into GaN have been used for n-type doping (see Table 2). The experimentally measured ionization energies of the donors are summarized in Table 3. These energy levels are rather shallow so that the majority of the donors are ionized at room temperature. The achieved sheet electron concentration after implantation with group VI ion species (S, Se, Te) are below the values reported for Si"*"-ion doping. Therefore, the group VI elements are not advantageous for the formation of n-type layers in GaN. A relatively shallow energy level of about 78 meV below the conduction band edge at 4.2 K has been measured after 0"^-ion implantation in GaN and subsequent annealing at 1000°C (see Table 3). A donor state with a ionization energy of about 29 meV could be indicated after O'^-ion implantation into GaN and annealing at 1100°C [62]. It is supposed that the poor activation efficiency of only 3.6% results from the insufficient vacancy generation by this light element or/and from the existence of a second, deeper O energy level.

4,4. P-type doping

In principle, GaN can be made p-type by implantation of group II elements such as Be, Mg, Ca, Zn and Cd substitutionally for Ga. But these elements form deep acceptors with an activation energies larger than 150 meV. The high ionization energy of the acceptor species significantly limits the number of ionized free holes at room temperature. Therefore, the search for an alternative acceptor species that has a lower ionization energy is of particular interest.

The high n-type background concentration more or less universally measured makes it unlikely that p-type doping would be easily obtained. Because of the high background electron concentration (>10^^ cm~^) in undoped GaN, the ion implantation with high concentrations of acceptors is generally needed to compensate the native electron background and to realize the reverse to p-type. In the case of high dopant concentrations (high ion doses), however, the crystalline structure is degraded by implantation induced damage. Beside the search of acceptors with a low ionization energy, for a successful


p-type doping by ion implantation two conditions must be fulfilled: (i) a high ion dose is necessary for the effective compensation of the native carrier concentration and (ii) the ion dose should be small in order to avoid unrecoverable structural damage and to achieve better transport properties by subsequent thermal annealing. Unfortunately, these two conditions cannot be simultaneously carried out.

It is generally accepted that the upper limit of implantation dose for doping of semiconductors is determined by the onset of amorphization and the impurity solubility level. For single element semiconductors, such as Si, it is possible to realize epitaxial recrystallization and to completely activate the implanted dopants by means of thermal annealing in the relatively low temperature range of 550-600°C, if the sample has been rendered amorphous during ion implantation [17]. However, for III-V compound semiconductors, amorphization must be avoided if electrical activity of implanted dopants is desired [80].

Once the amorphous clusters have formed, they are quite difficult to remove by thermal annealing (for details see Section 3.3). It can be argued that the upper Hmit of the implanted dose for p-type doping should be below a critical dose (dose which corresponds to the formation of amorphous clusters) in order to avoid unrecoverable damage and to achieve better transport properties. On the other hand, implantation with higher doses is generally needed to compensate the native electron background of GaN and to realize p-type reverse. Unfortunately, such a high dose results in local amorphization. This conflict uncovers the essential difficulty in p-type doping of GaN by ion implantation.

In Table 4 the experimental conditions for doping of potential acceptors by ion implantation and subsequent annealing are summarized. To date, the cpnunonly used relatively shallow acceptor in GaN is Mg with an ionization energy between 150 and 170 meV [81]. This energy level is still deep compared to acceptor levels in other III-V semiconductors such as GaAs or InP [82]. The annealing of Mg'^'-ion implanted GaN were carried out under pure N2-gas ambient, because using NH3 leads to incorporation of hydrogen which forms a complex with Mg, which neutralizes its doping action. Additionally, the Mg doping efficiency can be reduced because of its tendency to interact strongly with oxygen. The Mg-oxide complexes produced by this interaction are electrically inactive. Ca has been also proposed as a potentially superior shallow acceptor in GaN considering d-electron core relaxation effects [32].

The first successful experiments to the p-type doping by ion implantation have been reported by Rubin and coworkers [84], but details have not been published. GaN layers have been implanted with Mg+-ions at energies between 40 and 100 keV and annealed at 800°C for 30 min. Zolper and colleagues [23,51,65,74,76] have studied the p-type doping by Mg+-ion implantation into GaN in detail (see also Table 4). In general, the Mg"^-ion implantation into GaN alone does not produce a noticeable p-type doping effect after post-implantation annealing [74]. Room temperature Hall measurements have shown that only 1% of the implanted Mg generates holes [51]. It can be assumed that the compensation of the intrinsic background electron concentration is incomplete after Mg+-ion implantation. Additionally, the n-type carrier background is enhanced by the residual implantation induced damage.

It is known, that the co-implantation of phosphorus seems to be necessary to achieve

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Fig. 17. Sheet electron concentration versus annealing temperature (for 15 s) in unimplanted GaN and after Mg+- and P+-ion co-implantation (180 and 250 keV, respectively) in GaN (after [4]).

p-type conductivity in III-V semiconductor materials (e.g. see [85]). Likely, P occupies the N sites in GaN (reduction of the N-vacancies), and then the probability of Mg to occupy a Ga site is increased. Consequently, co-implantation has been studied in GaN to achieve the p-type doping. Pearton et al. [74] have measured a sharp n-to-p conversion in the conductivity after implantation of 180 keV Mg~^-ions and 250 keV P'^-ion both with 5 X 10 " ions/cm^ and annealing at 1050T for 15 s (see Fig. 17). In contrast, the n-type conductivity of GaN after implantation of IVlg' -ions alone remains up to 1100°C. An activation of about 62% could be estimated. The ionization energy level (see Table 3) of Mg in GaN is about 171 and 116 meV, respectively [69].

The high ionization energy of Mg acceptors limits the application of Mg as p-type dopant species. Less than 1% of the implanted Mg atoms are electrically active as acceptor in GaN at room temperature [62]. According to theoretical studies by Strite [32], Ca should be a shallower acceptor than Mg. The p-type doping of GaN has been realized by Ca+-ion implantation alone [24,62] or co-implantation of Ca+- and P'^-ion [62] followed by thermal annealing at higher temperatures (Table 4). The role of the co-implanted phosphorus species can be discussed in a manner analogous to Mg. Fig. 18 shows the n-to-p transition for Ca+-ion implantation and Ca+-ion and P'^-ion co-implantation with doses of 5 x 10'"* ions/cm^ [62]. The behavior of the sheet resistance as function of the annealing temperature is very similar to Mg. The transition to the p-type condition is achieved at 1100°C. The ionization level is 169 meV (see Table 3) and therefore very close to the 171 meV reported for Mg" - and P+-ion co-implantation. From this, only 0.14% of the Ca acceptors will be ionized at room temperature. PL studies by Mensching et al. [24] indicate an increase in the intensity of donor-acceptor-pairs (DAP) compared to the donor bound exciton (DQX) which indicate the presence of p-type carriers for doses greater than 1 x 10 ^ Ca"^-ions/cm^ and after annealing at 1150°C for 15 s.


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M^Ca:p-type 1 -A^Ca+P:p-type

1 . . . .

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1 . . . . 1 . . . .

1000 1050 1100 1150 1200

annealing temperature (°C)

Fig. 18. Sheet electron concentration versus annealing temperature for GaN either unimplanted or implanted with Ca'^-ions or Ca+- and P+-ions (180 and 130 keV, respectively) in GaN (after [4]).

Besides Mg and Ca doping by ion implantation, Be"^-ions were implanted in the hope that it would lead to shallow acceptor levels and subsequently conducting p-type GaN layers. Ronning et al. [86] have demonstrated that isolated Be is an acceptor in GaN with an ionization energy of about 150 meV. Unfortunately, Be displays damage-enhanced diffusion at temperatures greater than 900°C and is immobile once the point defects concentration is removed [51].

Carbon is expected to be an acceptor if it substitutes for N in GaN [83]. Up to now, p-type conductivity in GaN after C"^-ion implantation and subsequent annealing at temperatures smaller than 1150°C [27] and smaller than 1300°C [51] could not be achieved.

5. Impurity luminescence

The group-Ill nitrides GaN, AIN and InN are interesting due to their potential application for optoelectronic devices at short wavelengths. Optical spectra of III-V semiconductors provide a rich source of information on their electronic properties because the photons can interact with lattice vibrations and with electrons localized on defects (for details see e.g. [82]). Possible methods to excite the sample are the pho-toluminescence (PL), the cathodoluminescence (CL) and the electroluminescence (EL). Photoluminescence is the process, in which photons of energy higher than that of the bandgap are used to excite the sample to emit photons. The production of radiation by an external current is known as electroluminescence, while the light emission by electron bombardment is called cathodoluminescence. The PL spectrometry is preferentially used for the characterization of the electronic properties of GaN. With the availability of continuously tunable laser, a new emission spectroscopy has become possible, the photoluminescence excitation spectroscopy (PLE). It has become important for studying thin layers on opaque substrates.

228 ^^- 7 B. Rauschenbach

Optical emission spectra are characterized by different peaks which can be attributed to several excited states in the semiconductor material. High-quality semiconductors, such as GaN, are strong emitters of band gap radiation, if they have a direct-band gap and electronic dipole transitions are allowed. Then the electron-hole pairs will thermalize and accumulate at the conduction and valance band extrema, where they tend to recombine. These band-to-band transitions dominate at higher temperatures where all the shallow impurities are ionized. The emitted photon energy is given by Ec ~ Ey, where Ec is the energy of the conduction band edge and Ey is the energy of the valence band edge.

At sufficiently low temperatures, the carrier are frozen on impurities. The photoex-citation process in a p-type semiconductor with NA acceptors per unit volume creates free electrons with a density of Ue in the conduction band, where Ue < NA- These free electrons can recombine radiatively with the holes trapped on the acceptors. Such a transition, known as free-to-bound transition is characterized by the emission of photons with an energy of Eg — EA, where EA is the shallow acceptor binding energy (this process is inverse for n-type semiconductors). Consequently, PL spectra of such transitions contain information about the impurity binding energies.

A compensated semiconductor contains both ionized donors and acceptors. By optical excitation, electrons are created in the conduction band and holes in the valence band. Then, these carriers can be trapped at the ionized donor or acceptor sites and produce neutral donor and acceptor centers. A donor-acceptor pair transition (DAP transition) is given when electrons on the neutral donors recombine radiatively with holes on the neutral acceptors. In a first approximation, the photons emitted in a DAP process have the energy EA — ED, where EA and ED are the acceptor and donor binding energies, respectively.

At low temperatures, the photoexcited holes and electrons can be attracted to each other by Coulomb interaction and generate excitons. As a result of the hole-electron annihilation the free-exciton emission peak can be detected in the PL spectra. Excitons can be also attracted to neutral donors or acceptors sites via van der Waals interaction. Such neutral impurities are very efficient at trapping excitons, known as bound excitons, because the attraction lowers the exciton energy. In PL spectra measured at low temperatures a sharp peak can be identified with the recombination of an exciton bound to a neutral donor atom, usually denoted by D^X or I2, or with an exciton bound to a neutral acceptor (A^X or Ii). The binding energy of an exciton is close to the band gap energy, where the ratio of the binding energy of a bound exciton to that of a free exciton will depend on the ratio of the hole effective mass to the electron effective mass.

High-temperature free exciton luminescence can also be expected when the thermal lattice energy kT is of the order of the binding energy. In GaN typical values of the exciton energy are near 20 meV. As a consequence, free exciton peaks appear in the PL spectra at room temperature (kT % 25 meV).

5.7. Implantation-induced optical activation

The purpose of the studies of the photoluminescence after non-rare earth ion implantation into GaN or related group Ill-nitrides are: (i) investigation of the implantation


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Fig. 19. Low-temperature PL spectra of GaN before and after Ar'*'-ion implantation (180 keV, 5 x 10 ^ ions/cm^) and post-implantation annealing (15 s at 1150°C in N2 ambient).

induced damages, (ii) increase of the PL efficiency of these materials at room or higher temperatures and (iii) fabrication of optoelectronic devices by selective area implantation. First experiments have been carried out in the 1970s by Pankove and Hutchby [78,88] and by Metcalfe et al. [89]. The annealing after ion implantation has been recognized as crucial for the optical activation of the implanted species.

The efficiency of the photoluminescence in GaN has been investigated after noble gas ion implantation [78,90,91] and in dependence on the condition of the subsequent annealing [92]. Typical low temperature PL spectra of GaN before and after Ar'^-ion implantation and also post-implantation annealing are shown in Fig. 19. The intensity of the PL spectra is drastically decreased. The luminescence is dominated by a donor bound exciton (D^X) at 3.472 eV, known as I2 and the 3.41 eV band coinciding with the L2 line. In most of the implanted GaN samples the narrow peak at about 3.45 eV has been detected independent on the ion species [78]. The ion dose dependence of the L2 intensity indicates that the 3.41 eV luminescence is not related to a particular impurity but to structural defects. Joskin et al. [90] have studied the photoluminescence of GaN after low dose He'*"-ion implantation in detail. The fine structure of the near-band gap PL in dependence on the temperature and the ion dose is characterized by several sharp lines. The main feature is that oxygen can form a complex, which is characterized by a strong localization of free carriers and a large lattice distortion.

Broad luminescence bands with different energetic locations have been observed after ion implantation of 35 dopants in GaN and damage annealing [78,88]. Especially, the ion species Zn, Mg, Cd, As, Hg, Ca, P, and Ag are producing a characteristic spectral photoluminescence. For example, the characteristic blue photoluminescence at about 2.9 eV of Zn acceptors was even the basis of the first light emitting diode generation [93]. Consequently, the PL of Zn"^-ion implanted GaN has been studied by Strite et al. [52,66,94] and Suski et al. [49,95]. In these studies high pressure annealing procedures (up to 16 kbar) have been used which enable the application of increased annealing temperatures up to 1550°C. The Zn-acceptor related blue PL intensity after Zn+-ion

230 Ch. 7 B. Rauschenhach

implantation in GaN could be maximized by annealing at an N2'Overpressure above 1350°C after which the PL intensity exceeds that of epitaxially doped GaN material with( metal ion species, e.g and 1 X 10 ^ ions/cm^, gives rise to an intense near-infrared defect luminescence at 1.51 |xm[96].

/ith comparable Zn concentration by the factor 15. The implantation of other transition aetal ion species, e.g V+-ions with an energy of 250 keV and doses between 1 x 10 ^

5.2. Luminescence by rare earth ion implantation

Rare earth doped semiconductor materials have received attention because of possible application in the optoelectronics for low power, temperature insensitive, continuous wave sources of 1.54 |xm (0.806 eV) radiation. Especially, the rare earth element Er has shown luminescence at this wavelength corresponding to a transition between the energy levels " In/a and \si2 in triply charged erbium, Er^+, under the influence of the crystal field. The lanthanide rare earth elements possess partially filled 4f shells. These are screened by the outer closed 5s^ and 5p^ shells. Consequently, intrashell transitions of 4f electrons give rise to sharp emission spectra, where this spectra is approximately independent of the host lattice and relatively insensitive to temperature. Fig. 20 shows schematically the energy level diagram for the free Er"^-ion and also the splitting of the levels in a solid due to the Stark effect, labeled with the standard Russel-Saunders (LS coupling) notation.

The incorporation of the rare earth elements into GaN during growth by different methods is studied in detail. Room temperature infrared and visible emission by both photoluminescence and electroluminescence have been achieved by hydride vapor phase epitaxy (HVPE) and metalorganic molecular beam epitaxy (MOCVD). However, several problems still restrict the utilization of rare earth doped semiconductor materials

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including GaN in optoelectronic devices. First, the achieved quantum efficiencies are too low for practical applications (i.e. PL lifetime is too small), because presently the Er solubility in semiconductor materials is too low. Second, in Er-doped Si and GaAs it has been observed that the luminescence is quenched by several orders of magnitude when the temperature is increased from LNT to room temperature. Partially, thermal quenching effect on the luminescence efficiency can be reduced when a codoping with light elements such as O and F has been carried out [97]. Third, the understanding of both the incorporation in the host lattice and the excitation mechanism for the emission is not yet sufficient.

Ion implantation of rare earth ions has attracted attention as improvements in the growth process has made high quality GaN more readily available. Several groups have implanted Er"^-ions, but also Pr+-, Yb"^-, Tm+- and Nd^-ions (see Table 5). The Er"^-ion implantation is often combined with an 0"*"-ion coimplantation. The implantation is followed by a subsequent annealing process at temperatures between 650 and 1050°C (see Table 5).

A few studies on lattice site location of rare earth elements in GaN after implantation at room temperature have shown that these atoms immediately occupy relaxed substitutional sites [59]. RBS/C studies have shown that after subsequent annealing more than 70% of the implanted Er^-ions occupy Ga sites [46]. An annealing at temperatures greater than 800°C and the coimplantation of O'^-ions do not influence significantly the rare lattice sites.

A typical PL spectra of GaN after implantation with 2 x 10* Er"*"-ions/cm^ and 1 X 10 ^ O" - ions/cm^ at room temperature and subsequent annealing at 900°C for 30 min in flowing NH3 is shown in Fig. 21 [98]. The excitation source was an InGaAs laser diode with 100 mW at 983 nm. Erbium atom induced luminescence was only observed after annealing. Polman et al. [99] suppose that the annealing process can promote the implanted Er^^-ions to Er^^-ions as well as the formation of erbium oxide (Er203). On the other hand, the annealing increases the annihilation of the implantation induced defects. Since the laser excitation energy was below the GaN band gap, the observed luminescence appears due to direct optical excitation of Er"^-ions. The insert schematically shows the three energy levels in Er^^ involved in this PL process (see also Fig. 20). The PL spectra, characterized by the 1.54 |xm luminescence line, have been measured at LNT and at room temperature. It is suggested that the peak at 1.54 |xm corresponds to the radiative transition from the first excited state Îi3/2 to the Îi5/2 ground state. This 1.54 jxm luminescence line has been observed in the PL or PLE spectra after Er'^-ion implantation [100-103], after coimplantation of Er" - and 0"^-ions [61,98,104-108], after Pr+-ion implantation [109], Nd+-ion implantation [100] and also after coimplantation of Er" - and 0"^-ions in the cathodoluminescence spectra [110] and electroluminescence spectra [104].

The erbium ions can be also excited to the third excited ^ 19/2 state by pumping with 809 nm light [61]. Then, the erbium ions quickly relax nonradiatively to the excited " 113/2 state and radiatively to the ground state (see Fig. 20). Detailed studies with below band gap excitation have shown that well resolved crystal-field split intrashell emissions of rare earth ions implanted in GaN can be observed. For example, Silkowski et al. [100] have detected the three manifolds of the 4f lines ' F3/2 to " 19/2, ' F3/2 to " 111/2 and ' F3/2 to


Table 5. Optical activation of GaN and related compounds by ion implantation: experimental conditions of implantation, annealing, layer deposition and analysis

Condition of implantation

Target: ion

GaN 35 species P, As V Zn Zn Zn Zn Zn C O Si, Ar Be, Mg Be He Ar Er Er-hO^ Er + O^ Er + O Er + 0 ^ Er + O'' ErH-O^ Er + O" Er-hO" Er + O" Er, Er + O Er,Nd Tm,Yb O + Tm Pr

AIN Er + O Er + O

Energy (keV)

40,82 250 200 200 200 200 200 390 390

200, 300 100, 200

1800 180 280

300 + 40 400 + 80

300 350 + 80 350 + 80 350 + 80 350 + 80 300 + 40 300 + 40

160, 160 + 25 910, 1150

60 13 + 60

300

300 + 40 300

Dose (xlO*^ cm~2)

10-^ 10-2 0.08-50

0.1 0.1 0.1 0.1 0.1 0.5

0.05-0.82 0.01-0.25

7 0.05

410-3 0 .2+1

0.1, 1 + 10 0.3

1 + 10 0.02-1+0.1-10 0.01-5 + 0.1-10

2 + 1 0 0.2 + 2 0.2 + 2 0.5,5

0.01,0.05 0.02

0.4 + 0.02 0.47, 1

2 + 1 0 3

Material

sapphire sapphire sapphire sapphire sapphire sapphire sapphire sapphire

6H-SiC 6H-SIC 6H-SiC sapphire sapphire sapphire

GaAs, sapphire sapphire sapphire sapphire sapphire sapphire sapphire sapphire sapphire 6H-SiC

sapphire

GaAs GaAs

Substrate

Deposition technique

MOVPE MOVPE MOVPE MOVPE MOVPE MOVPE MOCVD

MOCVD, MBE

MOVPE MOCVD MOCVD MOCVD MOMBE

CVD MOMBE MOCVD

MOCVD MOCVD lA-MBE HVPE

MOCVD MOCVD MOVPE

HVPE, MBE, MOCVD

MOMBE MOMBE

%2>/2 after Nd"^-ion implantation at low temperature (see also Fig. 20). Fig. 22 shows a PLE spectra measured at room temperature after Er^- and 0"^-ion coimplantation [107]. The Er^+ PL was monitored at 1.54 |xm (inset). The PLE spectra is characterized by a broad band ranging from 425 to 680 nm and sharp bands. Thaik et al. [107] have found coincidences between the PLE peaks and the Er^"^-intra 4f transitions " 115/2 to "^^1/2, %y2 to 2Hn/2, " 115/2 to ^83/2, Îi5/2 to ^F9/2 and 115/2 to 111/2 after Er+- and 0+-ion implantation and subsequent annealing. The broad band is attributed to Er " excitation processes involving defects in GaN.

It is obvious, that the PL intensity is quenched by several orders of magnitude when going from the low temperature to the room temperature measurement (Fig. 21). The


Table 5. (continued)

Condition of

Target: ion

GaN 35 species P, As V Zn Zn Zn Zn Zn C O Si, Ar Be, Mg Be He Ar Er Er + O^ Er + 0 ^ Er + O Er + 0 ^ Er + O'' Er + O^ Er + O*' Er + 0 ^ Er + O^ Er, Er + 0 Er, Nd Tm,Yb O + Tm Pr

AIN Er + O Er + O

annealing

Temperature (°C)

1050 600-930

800-1100 1050-1250 950, 1000 1100-1500

<1550 600-1100

300, 600, 900

900 900 900

650-700 800

600-900 800, 900

800 650 800

600, 900, 1000 700-1000

800

1050

<900 650-700

Time

1 h 15 min-6 h

1 h 15 min, 1 h

1 h I h

90s

10 min

30 min

0.5-1 h

45 min 0.5-4 h

30, 45 min 45 min

1 h 0.5 h

30 min, 120 s 90 min 10 min

I h

Gas ambient

NH3

N2 ^2'

NH3,N2'^ N2^ N2^

NH3, N2

N2

NH3

NH3 N2, NH3

NH3 NH3

N2

NH3

Ar

Analysis

PL CL PL

TEM, SIMS, XRD, PL SIMS, XRD, PL

PL, XRD SIMS, PL

SIMS, XRD, PL, RBS PL

PL PL

PL, SEM PL, PLE SIMS, PL

CL PL EL PL PL

PLE PL PL

RBS/C PL

PL, EC

PL

PL PL

Ref.

[78] [89] [96] [66] [94] [52] [95] [49] [66]

[86] [90] [91]

[101-103] [106] [110] [112] [104] [105] [98] [61]

[107] [108] [46] [100] [59]

[109]

[106] [112]

lA-MBE, ion assisted molecular beam epitaxy; SEM, scanning electron microscopy. ^ Co-implantation (partial). ^ Co-implantation. ^ At pressure of 10 kbar. ^ At pressure of 190 atm. ^ At pressure up to 16 kbar.

temperature dependent PL and PEL intensities after Er+-ion implantation with and without 0"^-ion coimplantation have been studied in a wide temperature range. Very different results have been reported for the Er^+-related peak intensities at 1.54 |xm. It has also been observed that the integrated PL luminescence at room temperature is reduced to 50% [106] or approximately 38% [105] of its value at 77 or 6 K.


1.0

0.8 +

0.6 +

(A C Q)

3 0.4f a.

0.2 +

0.0

GaN:Er,0 Pump: 100mW at 983 nm

77K-

Room I Temp.

E c CO

00 O)

41 V. '1

£ c o> CO

7 dl •1

i1 /2

'13/2

1450 1500 1550 1600 Wavelength (nm)

1700

Fig. 21. Photoluminescence spectra taken at 77 K and room at temperature from a GaN sample implanted with 2 X 10^^ Er+-ions/cm^ and 1 x 10'^ O"^-ions/cm^. The sample was annealed at 900°C for 30 min in flowing NH3. The insert is a schematic illustrating the three energy levels involved in the PL process (after [98]).

Thaik et al. [107] have measured a weak PL temperature quenching for temperatures up to 550 K and Torvik et al. [98] illustrate that the PL intensity at 1.54 \im can be stronger at room temperature than at LNT after pumping around 998 nm. The intensity of the PL peaks is also dependent on the condition of annealing and ion the dose. Systematical investigations have shown that the annealing at temperatures higher than 800°C significantly effects the rare earth ion related PL intensity [100,105]. It is suggested that the annealing at higher temperatures produces the best recovery of implantation induced defects and reduces the non-radiative decay. The studies to the dependence of the luminescence efficiency on the ion dose demonstrates that on the one hand the efficiency was strongly dependent on the Er^-ion dose and much less on the O'^-ion dose [105] and on the other hand a high oxygen to erbium ratio pronounced the Er^"^-ion related PL intensity [98]. Likely, the optically active erbium forms a complex together with oxygen, where an Er atom substituting for Ga is coupled to two O atoms

[111]. Kim and coworkers have studied the excitation mechanisms for the intra-4f shell

emission using PL and PLE spectroscopies in Er'^-ion implanted GaN over the entire spectral range from above the 3.5 eV band gap to the near infrared [101-103]. Especially, the observation of multiple Er " sites in the implanted material by site-selective PLE spectroscopy have been studied at 6 K on the 1.54 |xm Îi3/2 to " 115/2 emission


ON

— I 1 r

ErrGaN

T 1 1 r

I 525 nm

' l 5 /2 ' * 'l1/2

980 nm I

920 940 960 980 1000 1020 Excitation Wavelength (nm)

440 480 520 560 600 640

Excitation Wavelength (tm)

680

Fig. 22. Photoluminescence excitation spectrum of Er"*"-ion implanted GaN. The Er " PL was monitored at 1.535 |xm (after [107]).

in detail. After Er^-ion implantation and thermal annealing at 900°C several broad, below gap absorption bands, which excite three distinct, site-selective Er^+ PL spectra. It was suggested that the excitation of two of this bands involves optical absorption by defects and the third PL band involves the optical absorption of an exciton bound to an Er " related trap within the band gap. In addition, single Er atoms at Ga sites can be assumed on the simple structure of the site-selective PL and PLE spectra. These investigations have shown that the excitation is dominated by trap-mediated mechanisms. Consequently, the moderate thermal quenching of the PL intensity in GaN at room temperature (e.g. in contrast to the strong quenching in GaAs after Er''"-ion implantation) can be explained by a thermal ionization of the excited traps before the energy is transferred to Er"^-centers [102].

In summary, neither the microstructure of the optically active rare earth element sites nor the excitation mechanism of the intra-4f shell emission at multiple rare earth element sites after ion implantation in group Ill-nitrides have been analyzed in detail. Gaining deeper insight into the incorporation and excitation mechanisms will be crucial in the advancement of rare earth doped Ga based III-V optoelectronic devices.

6. Isolation by implantation

Ion implantation can be utilized to form damaged regions selectively in the semiconductor material. These regions are of value for their high resistivity, high defect densities and short carrier lifetimes. They provide insulating device isolation for integrated


circuits. It is also of advantage that the used thickness in the semiconductor device technology is compatible with the ion implantation range.

The damage in implanted semiconductors leads to defects which are characterized by dangling bonds or, from the point of view of energy, by the formation of deep defect energy levels. With increase of the ion dose, an increasing density of these deep defects is formed. Consequently, the Fermi level moves within the band gap. The energy of the dangling-bond defects lies within a band of energies centered on the average bond energy. The defects include both acceptors and donors, which compensate each other and form high resistive material. For example, the position of the Fermi level stabilization energy (position in the band gap) in n-GaN is about 830 meV below the conduction band level and about 900 meV on top of the valence band level [5]. The position of these levels is sufficiently deep for compensation, although the levels are not at midgap (the band gap of GaN is about 3.39 eV). Ga-based semiconductor materials (e.g. GaAs, AlGaAs, GaP, etc.) create midgap electron or hole traps by ion implantation. These materials are characterized by a high resistivity after implantation. The compensation of the free carriers by damage-related levels is successful only up to a specific temperature at which the damage anneals out. Above this temperature, the sheet resistance is dramatically reduced to the unimplanted value (details see [113]).

Another method to produce thermally stable high-resistivity regions by ion implantation in III-V semiconductors is the implantation of species which form chemically induced deep levels in the midgap. A subsequent annealing procedure is required to promote the implanted species onto a substitutional lattice site and to create thermally stable compensating deep levels. This method is complementary to the damage-induced method because the chemically induced isolation is thermally stable only up to the temperature at which the damage is annealed out. This temperature is in the most III-V semiconductors also the temperature at which the implanted species occupy substitutional sites and form the high-resistivity region [113]. At higher temperatures a high sheet resistance remains in the material by chemically induced isolation.

The implantation of metal ions in combination with a subsequent annealing to form small metallic precipitates is an altemative procedure. The metal inclusions act as internal Schottky contacts that deplete charge of either sign in a spherical depletion region [114]. This compensation mechanism was not applied for GaN until now.

In general, the sheet resistivity is obtained from a van der Pauw geometry Hall measurement. It should be noted (i) that this measurement gives an average value of the resistivity over the whole region the current flows through (e.g. the average resistivity of the unimplanted material and the implanted top layer) and (ii) that the contribution of the unimplanted material to the resistivity increases with the temperature, i.e. the determination of the resistivity for the implanted layer becomes progressively inaccurate. This problem can be overcomes using the capacitance-voltage measurement (I-V characteristic) [115]. Especially, the implantation induced formation of p-n junctions are characterized by a asymmetric behavior of the forward- and reverse-bias currents in the I-V characteristics.

In Table 6 the experimental conditions of studies to the formation of insulating regions by ion implantation in GaN and related compounds are summarized. It is obvious, that the preferred ion species are hydrogen and also nitrogen and fluorine


Fig. 23. [5,74]).

300 400 500 600 700 800 900 1000

annealing temperature (**C)

Sheet resistance as function of annealing temperature for N'^-ion implanted n- and p-GaN (after

ions. In order to produce a uniform nuclear stopping damage distribution over a large thickness the implantation is carried out at multiple energies and a set of doses. The first experiments to the formation of insulating regions in GaN and related compounds by ion implantation have been carried out by Pearton and coworkers [74,80,116,117]. The majority of the studies concentrate on the determination of the resistivity as a function of the annealing temperature after ion implantation. Fig. 23 shows an example [5]. Undoped n-GaN with a background carrier concentration < 4 x 10 ^ cm~^ and n-type GaN doped with Si or Mg during the layer growth process were implanted with nitrogen ions. The sheet resistance increases with the annealing temperature between 400 and 750°C, where the resistivity is about three order of magnitude higher (>5 x 10^ Q/D in both conductivity types) than the sheet resistivity after annealing at 400°C (<10^ ^ /D in n-type GaN and <10^ ^ / n in p-type, respectively). Annealing at higher temperatures leads to a decrease of the resistivity to about of 10^ Q/\3 at an annealing temperature of about 950°C. As described above, for both n- and p-type GaN implanted with N"^-ions the typical behavior appears after annealing. The annealing up to the specific temperature (here 750°C) reduces the carrier hopping and increase the sheet resistivity. This means that the initial conductivity is compensated by introduction of implantation induced deep level traps. Above this specific temperature the conductivity increases again because the deep levels are removed by annealing [113]. Consequently, (i) the isolation is realized by implantation damage without chemical compensation and (ii) the implantation defects in GaN are thermally more stable than in other III-V semiconductors. A similar behavior of the resistance in dependence on the temperature has been also observed for the annealing of GaN after implantation with He+- or N"^-ion [118,119] and for the anneahng of lUxAlx-iN and lUxGax-iN, respectively, after implantation of N+-, 0+- or F+-ions [75,80,120,121]. The activation energy of the damage-induced traps can be obtained by examining the resistivity versus the inverse temperature curve. According to Kato et al. [122] the resistivity is proportional to the Arrhenius term exp(EA/kT), where EA is the activation energy for motion of the


Table 6. Formation of insulating regions in GaN and related compounds by ion implantation: experimental conditions of implantation, annealing, layer deposition and analysis

Condition of

Target: ion

GaN H H H

H H H D H, He H H He He He N, He N N N Be, N

InN F H

AIN H H

IrixGai-x^ F N, F, 0 N, F

IrixAlj-xN F N, F, 0 N, F, 0

AlxGai^xN Be + N

implantation

Energy (keV)

40 40

20-150 20-300 25-300 25-300

50 50

320 30

2000 5400 5400

5400^ 20-550 50-250

70 60, 180,400

40-300 40

40 50

40-300 40-270 40-270

40-300 100

40-270

60, 180, 400

Dose (xlO''* cm-2)

50 50 20

40

10, 100, 10^ 10, 10^

10-^-100

10-3

(4-25) X lO"'* (36-208) X lO-'*

(7-36) X 10-3 0.2-0.6

0.01-1 1-10

0.8-2 50

50 50

0.8-2 0.05, 0.5, 5 0.05, 0.5, 5

0.8-2 1-10

0.05, 0.5, 5

2-10

Material

GaAs GaAs

sapphire

sapphire sapphire

sapphire sapphire

sapphire

sapphire sapphire sapphire sapphire

sapphire sapphire

GaAs GaAs

GaAs GaAs

GaAs GaAs GaAs

GaAs

GaAs

sapphire

Substrate

Deposition technique

MOMBE MOMBE MOCVD PA-MBE MOCVD MOCVD MOCVD MOCVD MOVPE

MOVPE

MOVPE MBE

MOVPE MOCVD MOCVD

MBE MOCVD

MOMBE MOMBE

MOMBE MOMBE

MOMBE MOMBE MOMBE

MOMBE MOMBE MOMBE

MOCVD

trapped electrons by hopping from one damage site to another. Binari et al. [118] have determined the activation energy for N+- and He+-ion implanted GaN to about 760 meV and Pearton et al. [74] for N+-ion implanted p-GaN to 900 meV and for N+-ion implanted n-GaN to 830 meV. The compensation generated by these deep levels is responsible for the increased resistivity after implantation. Although these activation


Table 6. (continued)

Condition of

Target: ion

GaN H H H

H H H D H, He

H

He He N, He N N N Be, N

InN F H

AIN H H

InjcGa/_xN F N,F, O N,F

In,Alj.,N F N,F, O N,F, O

Al,Gaj_,N Be + N

annealing

Temperature (°C)

<900 <700 1200

300-675 300-700 100-980 511-709

1000

170 <850

400-950 300-1150

600 <900

<900 <700

600 150-900 400-900

600 <1100

150-900

1000

Duration

20min 20min

60s

1-30 h 1 h

30 s

2h 30 min

10 s

60s 20 min

20 min 20 min

60s 30 s 30 s

60s

30 s

1 h

Gas ambient

N2

N2

N2

N2

N2

N2

N2

N2

N2

N2

N2

N2

N2

NH3

Analysis

SIMS SIMS

HM, SIMS

IR IR, ODEPR, PL

IR, TEM, NRA, RBS NRA, RBS/C

PL, RES

DLTS

DLTS HM RES HM

HM, SIMS, RBS OAS

HM, CV

HM SIMS

SIMS SIMS

HM HM HM

RES RES HM

HM

Ref.

[126,127] [63] [16]

[130] [131]

[124][125] [132] [123]

[129]

[133] [134] [118] [74] [73] [77]

[137]

[80] [126,127]

[126,127] [63]

[80] [120] [121]

[80] [75] [120]

[138]

PA-MBE, plasma assisted molecular beam epitaxy; NRA, nuclear reaction analysis; RES, resistivity measurement; ODEPR, optically detected electron paramagnetic resonance; DLTS, deep level transient spectroscopy; OAS, optical admittance spectroscopy. ^ Implanted at 25 K.

energies, which represent the position of the Fermi level, do not correspond to the midgap energy of GaN (^1.75 eV) a significantly higher resistance can be obtained. The experimentally determined activation energies are summarized in Table 7.


Table 7. Comparison of the experimentally determined activation energy EA for motion of the trapped electrons by hopping conductivity (represents the position of the compensating defect level in the energy gap) after ion implantation into different III-V nitride semiconductors with the midgap energy (represents the half the band gap energy Eg)

Material

n-GaN

p-GaN InxAli_xN,x =

InxGai_xN,x = X = 0.37

X = 0.47 AlGaN/GaN InN

:0.75

= 0.33

1/2 Eg (meV)

1750

1750 1250

1400

1250

950

(meV)

-830 -290 -760 +900 -580 -540 -190 -400 -390

-650 -710 -350

Ion species

N+ H+

N+, He+ N+ N+ N+ 0+ N+ N+

N+ He+ + P+

N+

Ref.

[74] [118] [118] [74] [5]

[120] [120] [120] [121]

[121] [136] [121]

^ The negative sign of EA corresponds to the position below the conduction band and the positive sign to the position above the valence band.

In contrast to other III-V semiconductor materials (GaAs, InP, InGaAs, AlInAs, etc.) the dependence of the electrical isolation of GaN and other binary and ternary nitrides by ion implantation on the ion dose, annealing time, impurity distribution and composition have been studied only in few papers. It is not surprising that the compensation is dependent on the ion dose since the number of defects is also a function of the dose (see Section 2).

The evolution of the sheet resistance after multiple fluorine ion implantation in InN or ternary In-nitrides and the subsequent annealing up to 600°C for 60 s is characterized by a restoration of the initial conductivity. The sheet resistivity is only increased by an order of magnitude after annealing in dependence on the ion dose [80]. The dependence of the formation of deep compensating acceptors which trap free electrons on the implantation dose is well known for other III-V semiconductors [113]. Nevertheless, the annealing conditions for F+-ion implanted InN are not sufficient to realize a high sheet resistance. A more detailed study of the dependence of the resistance on the ion species and annealing temperature of implanted ternary In containing nitrides has been published by Vartuli et al. [120]. InÂli.^N and In^Gai.xN samples were implanted with N"^-, O" - and F'^-ions at three different doses and subsequent annealed at temperatures between 150 and 900T for 30 s (see Table 6). The results of this study indicates that none of these implanted atoms produces chemical-induced deep levels. All implantation induced changes of the electrical properties are due to the buildup of damage related deep levels. The sheet resistance has its maximum after annealing between 600 and 700*^0, where the resistance for InxAli_xN is one order of magnitude lower than for InxGai_xN. The annealing at higher temperatures restored almost the initial conductivity. It should be noted that the F" -ion implantation in lUxAli.xN produces only one order


of magnitude increase in sheet resistance while after N" - or 0"^-ion implantation an increase over three orders of magnitude could be measured [75]. Recently, the enhanced compensation after N" - or 0"^-ion implantation were interpreted by some chemical components to the compensation process [5].

Hydrogen implantation compensates through two effects. On the one hand the implantation induced dangling bonds are compensated by charges of either sign and on the other hand hydrogen (protons) passivates shallow dopants by forming neutral complexes with shallow donors or acceptors. The passivation of semiconductor material by hydrogen ion implantation is a very weak effect and characterized by the high ion range, which can be extended over several microns, and the noticeable out-diffusion at annealing [124,125]. The concentration distribution after hydrogen ion implantation in GaN [63,116,126] AIN [63] and InN [126] have been studied by SIMS. In principle, it can be established that the concentration distribution remains unchanged up to high annealing temperatures. No detectable diffusion of hydrogen in GaN until 8(WC [116,126,127] and 700°C [63] have been measured, respectively. The dose dependence of the resistance after H+- and He"^-ion implantation in the dose range between 10^^ and 10 ^ ions/cm^ has been demonstrated by Uzan-Saguy et al. [123]. The resistance increases by eleven orders of magnitude and the band-to-band photoluminescence emission is nearly completely quenched. The non-linear increase of the resistance has been observed for doses higher than about 5 x 10 ^ ions/cm^. Consequently, the presence of potential barriers for electronic transport across extended defects is assumed. The subsequent RTA annealing at 1000°C for 30 s has returned the resistance to almost its preimplantation value. The annealing of GaN up to 1150°C after implantation with a high N'^-ion dose (implanted concentration 5 x 10 ^ cm"^) leads to a damage which is thermally stable, i.e. the resistivity decreases only slightly with the annealing temperature [73].

The compensation of GaN by hydrogen ion implantation is differently discussed in literature. High resistivity GaN material could be formed after implantation with protons and deuterium. The ratio of the resistivity after implantation and annealing to that before implantation could be determined to about 3 . . . 4 [116] and to about 10 . . . 11 [118,122,128], respectively. With exception from hydrogen implanted p-GaN, the annealing at high temperatures results in the decrease of the resistance back to the initial value. The implanted p-GaN shows above 400**C an increasing of the hydrogen passivation of the acceptors. For the H^-ion implanted GaN an activation energy of only about 290 meV has been estimated [118]. Detailed studies of the defects created by proton implantation into GaN have been carried out [129-131]. Fig. 24 shows IR vibrational spectra of GaN implanted with deuterium (a) and hydrogen ions (b) after subsequent annealing at different temperatures [131]. Several new vibrational bands have been found after implantation and also annealing. For example, the two new vibrational bands at 2254.7 cm~* and 2329.7 cm~^ in the as-implanted state. The lines can preferentially be assigned to nitrogen-dangling bond defects which are decorated by hydrogen. The intensities of the selected absorption lines have been detected versus the annealing temperature. A partial dissolution of these Vca-Hn complexes due to annealing has been observed. Wampler et al. [132] have investigated the location of implanted deuterium in GaN by nuclear reaction analysis. This study has shown that the implanted deuterium occupies sites near the center of the c-crystal axis and excludes

242 Ch. 7 B, Rauschenbach

0.0020

(D 0.0015 a c (Q n o 0.0010

0.0005

nnnnn

.(a)

• . 1 450' ,

h J, , ,v-V-'»-V»—' V \AArt/V\/

300-

0' — 1 — . — 1 _ _ . 1

1 ' iV-»-»''V'Vt

>ÂA^^

vn*o*v-VA

2200 2250 2300 2350 3000 3050 3100 3150

Frequency (cm'^)

Fig. 24. Vibrational spectra measured near 4.2 K for (a) deuterium implanted GaN and (b) hydrogen implanted GaN samples which were subsequently annealed at the temperatures indicated (after [131]).

the occupation of nitrogen lattice sites. The deep level transition spectroscopy (DLTS) has been used to characterize the formed defects by high energy He irradiation in GaN [129,133,134]. Different electron traps with energy levels between 0.13 and 0.95 eV below the conductivity band could be identified. These energies can be assigned to specific defects, where the proton and He+-ion irradiation partially creates different defect types.

The ion implantation has been successful used for the isolation of AlGaN/GaN heterostructure field effect transistor structures [135,136].

7. Devices

In the semiconductor technology, the ion implantation allows to implant selected areas and to realize devices such as light emitting diodes (LEDs) or junction field effect transistors (JFET). Although only a few results are known for the ion implantation in GaN and related compounds, different experiments were undertaken to manufacture electronic devices. The studies were aimed at the fabrication of low-ohmic contacts, p-n junctions, light-emitting diodes and field effect transistors.

Ohmic contacts are limiting factors in the GaN devices. Therefore, the realization of good reliable metal contacts is an important condition in achieving high performance GaN based devices. Recently, Lester et al. [140] have studied the formation and quality of ohmic contacts formed by nonalloyed Ti/Al metallization on Si-ion implanted GaN. A specific contact resistance as low as 10~^ ^ cm^ could be formed. Also Burm and coworkers [141] have fabricated Si+-ion implanted ohmic contacts on GaN, where the overlay metal was Ti/Au. The measured maximum contact resistance was 0.097 Q mm and the specific contact resistance was 3.6 x 10"^ ^ cm^.


photoresist

T T T T

SI-GaN s p-type n-type

W gate contact

Fig. 25. Schematic of the implantation processing steps for a GaN JFET (after [144]).

As early as in the year 1969, Maruska and Tiefjen [142] have shown that GaN LEDs emit at 430 nm (violet) after implantation with Mg"^-ions and at 590 nm (yellow) after co-implantation with Mg+- and Zn^-ions. The implantation of Zn+-ions alone generates a green emission. Torvik et al. [104] have demonstrated the room temperature Er "*"-related electroluminescence at 1.54 and 1 |xm from a Er"^-ion and O'^-ion coimplanted GaN metal-insulator n-type LED. A insulating GaN layer has been implanted with both ion species and then annealed at 800^*0 for 45 min in flowing NH3. The co-implantation leads to a 20 times increase in the Er-related PL. The LED was dc reversed biased, where the integrated emission around 1.54 |xm showed a linear dependence on the applied current between 100 and 318 (jiA.

GaN p-n diodes have been formed by Mg'^-ion implantation in n-type GaN epitaxial layers and subsequent annealing. Kalinina et al. [65] have demonstrated that a rectification factor of not less than 10^ at a voltage of 3 V can be obtained for such p-n mesa structures. The first GaN junction field-effect transistor (JFET) has been realized with multiple ion implantation by Zolper and coworkers [39,143]. Fig. 25 shows schematically the implantation steps for a GaN JFET. The device processing contains the implantation steps besides the activation annealing at high temperatures: Si"^-ion implantation of the n-channel, Ca+-ion implantation of the p-gate and nonself-aligned Si'^-ion implantation of the source and drain regions. A gate turn-on voltage of 1.84 V at 1 mA/mm of the gate current was achieved.

The hydrogen ion implantation has been also used to isolate the mesa at the fabrication

244 Ch. 7 B. Rauschenhach

of an AlGaN/GaN modulation-doped FET [135]. A very effective isolation of such a FET has been achieved after co-implantation of P^-ions with two different doses (5 x 10* and 2 x 10^^ ions/cm^) followed by He+-ion implantation (6 x 10 ^ ions/cm^) [136]. The sheet resistance was about 10 ^ ^ /D and the activation energy 0.71 eV.

Notwithstanding the vast promise of the GaN material, there is still very limited work in the field of ion implantation in GaN electronics. As a consequence, a comparison of the state of ion implantation in GaN electronic and optoelectronic technology with those of silicon or gallium arsenide based technology is clearly not warranted. With increasing research and investments in technology, ion implantation is very likely to fulfill its enormous potential as the ultimate method in the GaN based technology.

Acknowledgements

The author would like to acknowledge Wolfgang Bruckner, Liu Chang, Jiirgen Gerlach, Stephan Mandl, Bemd Mensching, Wolfgang Reiber, Stephan Sienz, Axel Wenzel (Uni-versiat Augsburg), H. Riechert (Siemens AG), A. Kritschil (Universitat Magdeburg), S. Fischer (Universitat GieBen), W. Assmann (Universitat Munchen), H. Riechert and R. Averbeck (Siemens AG Munchen), A. Lell (Osram Opto Semiconductors Regensburg), R. Sauer, W. Limmer and A. Komitzer (Universitat Ulm) for their collaboration on this work. Portions of this work were supported by the Schwerpunktprogramm 'Gruppe Ill-Nitride und ihre Heterostrukturen' of the Deutschen Forschungsgesellschaft (DFG).

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CHAPTER 8

Radiation and processed induced defects inGaN

ED. Auret and S.A. Goodman

1. Introduction

During several semiconductor-processing steps, for example particle irradiation for lifetime tailoring [1,2], dry etching [3,4], metallization [5,6] and device isolation [7,8] the semiconductor is intentionally or unintentionally exposed to a variety of particles with energies ranging from a few eV to several MeV. When these particles impinge on the semiconductor, they enter into it, transfer energy to the semiconductor lattice and introduce defects. These defects can have a profound influence on the semiconductor properties and on the characteristics of devices fabricated on it [3-6], which may be either beneficial or deleterious, depending on the application.

In order to avoid the deleterious effects of some of these particle-induced defects and utilize the beneficial effects of others, depending on the application, it is imperative to understand the effect of radiation on electronic materials and devices fabricated on them. To achieve this, it is essential that the electronic properties and concentration of radiation induced defects should be known, allowing calculation of their effect on the properties of electronic materials and devices. In addition, the structure, introduction rate, introduction mechanism and thermal stability of the defects should be determined, so that they can be reproducibly introduced, avoided or eliminated, depending on the application. Regarding electrical techniques for defect characterization, deep level transient spectroscopy (DLTS) [9], which allows independent studies of different defect species in the same semiconductor, has played a key role in providing most of this information. Hall effect measurements [10] have also contributed a fair deal to our understanding of radiation-induced defects and its effect on carrier mobility and donor and acceptor concentration. As far as the electrical characterization of simple devices are concerned, current-voltage (I-V) and capacitance (C-V) measurements have traditionally been used to evaluate the effect of defects on diode performance and the free carrier density of semiconductors, respectively.

In order to successfully characterize process-induced defects by DLTS, it is ideally necessary to start with defect-free semiconductor materials. For most semiconductors this is, however, not possible. The closest to this ideal is high quality silicon that contains very low concentrations (usually below the DLTS detection limit) of hole and electron trap defects with deep levels in the band gap. Most compound semiconductors contain at least one deep electron or hole trap. For example, GaAs grown by all techniques except liquid phase epitaxy (LPE) contains significant concentrations of the infamous

252 Ch. 8 ED, Auret and S.A. Goodman

EL2 defect [11] (an electron trap) whereas molecular beam epitaxy (MBE) [12] and LPE [13] grown GaAs contain their own characteristic set of electron and hole traps, respectively. It has been proposed that the EL2 is also introduced during high-energy particle irradiation [14], which is exactly why the starting material should contain as low as possible concentrations of defects in order that such findings be uniquely established. GaN, too, is no exception. Several studies have shown that n-type material contains at least two to three prominent electron traps with energy levels in the upper half of the band gap, depending on the growth method. This will be elucidated in Section 2.

Since these growth-induced defects have an inhibiting effect on the detection of process induced defects, we shall devote a few paragraphs in Section 2 to describe which defects are present in GaN grown by different epitaxial techniques. This should not be seen as a complete review of growth induced defects, but rather as a guideline as to which defects can be expected in epitaxially grown GaN when attempting to characterize process induced defects in it.

2. Defects in epitaxially grown GaN

In this section we briefly discuss and summarize the defects detected by DLTS in as-grown GaN. The properties of the defects, the substrates, buffer layers, epitaxial layers and some growth parameters are summarized in Table 1. In Fig. 1 we compare the DLTS 'signatures' of the defects in the form of conventional DLTS Arrhenius plots, using data from the literature.

The first DLTS report of growth induced defects in GaN was by Hacke et al. [15] who used a SBD structure fabricated on n-GaN grown by hydride vapor-phase epitaxy (HVPE). The n-GaN was grown on two different types of buffer layers, either MOVPE grown GaN or sputtered ZnO. They detected three electron traps in both substrate types, labeled El, E2 and E3, with activation energies of 0.264, 0.580 and 0.665 eV,

2 3 4 5 6 7 8 9 10

iooon'(K-^) Fig. L DLTS Arrhenius plots of the electron defects detected in as-grown (unirradiated) n-GaN.

Radiation and processed induced defects in GaN Ch. 8 253

respectively. In addition, they demonstrated that the concentration of the deepest of these three levels depended on the type of buffer layer (GaN or ZnO) between the sapphire substrate and the HVPE epitaxial layer.

In Si-doped GaN grown by metalorganic vapor-phase epitaxy (MOVPE), Gotz et al. [16] detected two electron traps (E2 and Ei) with activation energies (not T^ corrected) of 0.18 and 0.49 eV, respectively. These appear to be the same as the E1 and E2 in HVPE grown GaN. Subsequentiy, Hacke et al. [17] found, what appears to be the same two levels located at Ec —0.26 eV and Ec —0.62 eV, respectively, in undoped MOVPE GaN. An interesting observation on the part of Hacke et al. [17] was that the concentration of the level at Ec —0.62 eV increased significantly in weakly doped n-type GaN. Lee et al. [18] grew MOVPE layers using trimethylgallium (TMGa) and triethylgallium (TEGa) as the alkyl sources. Using DLTS they detected three distinct deep levels in films grown by TMGa (El, E2 and E3) with activation energies of 0.14, 0.49 and 1.44 eV, respectively. The shallowest two of these defects are presumably the same as the El and E2 mentioned above for MOVPE grown GaN. Interestingly, only a level at 1.63 eV, speculated to be the same as that at 1.44 eV, was detected in the layer prepared using TEGa. It must be noted that due to the high peak temperature the 'signature' of defect E3 was determined from a 2-point Arrhenius plot, and may consequently not be accurate. Lee et al. [18] proposed that the two shallower levels are either related to the carbon and/or hydrogen atoms from the methyl radicals, or alternatively, that they are due to the slight difference in growth temperatures of the two layers.

Recently, Auret et al. [19] have also reported the presence of two prominent electron traps (E02 and EOS) with activation energies of 0.27 and 0.61 eV, respectively, in undoped MOVPE grown n-GaN. For these calculations the emission rate, Cn, was taken as 3.3 X lOl^^Gxpi—Et/kT). These traps seem to be the same as the El and E2 in HVPE and MOVPE grown GaN, and are seemingly characteristic of GaN grown by this method. By using special pulse conditions, Auret et al. [19] were also able to show the existence of two other less prominent traps (EOl and E03) in this material of which the DLTS peaks are obscured by the peaks of the major defects at normal pulse conditions.

For p-type GaN grown by MOVPE, Gotz et al. [20] used a p'^-n structure and detected three hole traps with activation energies of 0.21, 0.39 and 0.41 eV in the lower half of the band gap. However, using ODLTS, they found a dominant deep level with an optical threshold energy for photo-ionization at about 1.80 eV This level is positioned near midgap and is the dominant defect. Although several deep levels were detected, their concentrations are small compared to the total acceptor concentration and would hence not influence the acceptor concentration through compensation.

The properties of electron traps in reactive MBE (RMBE) grown GaN, with a free carrier concentration of 6 x 10 ^ cm~^, were reported in considerable detail by Wang et al. [21]. They characterized five electron traps and found their activation energies to be 0.234, 0.578, 0.657, 0.961 and 0.240 eV. The first of these (0.234 eV) is thought to be the same as the 0.264 eV level reported by Hacke et al. [17] and the 0.18 eV level reported by Gotz et al. [16] The second level (0.578 eV) has a very similar signature as the 0.58 eV level of Hacke et al. [18], the 0.49 eV level of Gotz et al. [16] and the 0.598 eV level reported by Haase et al. [22]. The third level (0.657 eV) appears to be the same as the 0.665 eV level measured by Hacke et al. [17] and the 0.67 eV level measured

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Hacke et al. [15] in HVPE grown GaN. The DLTS signatures of the last two levels (0.961 and 0.240 eV) were found to be considerably different from all the other defects in any other form of epitaxial GaN and were consequently ascribed to the RMBE growth method itself. Almost concurrently, Fang et al. [23] reported on the defects in reactive Si-doped GaN layers grown by RMBE under different conditions. The first layer was grown at 750°C, directly on the buffer layer while the second was grown at 800°C on a r^^ layer which was first grown on the buffer layer. The first layer contained two well resolved electron traps at 0.20 and 0.21 eV below the conduction band, but with quite different capture cross sections. Arrhenius plots showed that the 0.20 eV level is most Ukely the same as the level observed in MOVPE and HVPE layers. On the other hand, the 0.21 eV level is the same as that of a defect introduced in HVPE grown GaN by 1 MeV electron irradiation, speculated to be the nitrogen vacancy, VN [24]. In the second layer the 0.20 eV level was not observed, but instead a dominant level at 0.44 eV below the conduction band was observed. This level has not yet been detected in GaN layers grown by HVPE or MOVPE.

Finally in this section, we present some data of GaN grown by epitaxial lateral overgrowth (ELO) — a method that has been shown to significantly reduce dislocations is the epitaxial layer [25]. In Fig. 2 we compare DLTS spectra (recorded in our laboratories) of defects in GaN grown by HVPE (curve a), MOVPE (curve b), ELO-MOVPE (curve c) and RMBE (curve d). The spectra were all recorded using the same pulse

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conditions and the same lock-in-amplifier frequency. The carrier concentrations of the materials were, however, different and this should be borne in mind when attempting to compare the defect concentrations.

From these curves, it is clear that the defect E02 is present in all four types of GaN. E05 is definitely present in HVPE, MOVPE and ELO-MOVPE GaN. In RMBE GaN it seems that E05 is present, but the peak, indicated as *E05-h??', is very broad, perhaps due to the presence of another peak superimposed on it. Clearly, only RMBE contains the defect, E, in detectable concentrations. This figure also shows that E06 is only detected in significant concentrations in HVPE GaN.

Ideally, for studying process-induced defects, one would like to start off with defect free material. However, since this does not seem to be presently possible for GaN, one has to select the material with the least defects. From the data presented in this section it is clear that GaN grown by MOVPE or ELO-MOVPE is the preferred choice, simply because it contains only two prominent peaks below 400 K — the region usually scanned by DLTS.

3. Defects introduced by high energy irradiation

High energy irradiation of semiconductors has been the most frequently used method to introduce defects in them for the purpose of studying the properties of these defects. The performance of several device types, including fast switches [26] and detectors [27], has been improved by subjecting the devices to controlled doses of particle irradiation. High-energy particles also enter semiconductor devices inadvertently, for example in the form of cosmic irradiation in outer space [28]. For this, and any other form of defect engineering, it is essential that the electronic properties of the defects involved should be known so that their influence on materials properties and device behavior can be calculated. Further, the structure and composition of the defects should be known so that they can be reproducibly introduced. In the case of GaN, the investigation of particle induced defects is still in its infancy and only a few papers have appeared concerning the electrical characterization of radiation induced defects and their influence on materials properties and device performance.

3.1. Gamma and electron irradiation

Irradiation by high energy gamma rays or electrons has particularly been effective in introducing point defects — the simplest of all defects, it provides a convenient tool for producing native defects due to elastic displacement of host atoms. Knowledge of the properties of point defects is of extreme importance because these defects can play a cardinal role in altering the properties of semiconductors.

Regarding studies of defects induced in GaN by high energy (MeV) electrons, Linde et al. [29] have firstly reported that 2.5 MeV electrons introduced two broad photoluminescence bands in a 1 [xm thick GaN/AliOs layer and they also showed that the yellow luminescence was strongly quenched. In the new photoluminescence bands four new ODMR signals were observed. Emstev et al. [30] exposed n- and p-type GaN to electron and gamma irradiation at room temperature, they observed that the

258 Ch. 8 ED. Auret and S.A. Goodman

intensity of the yellow band strongly increased upon irradiation. They concluded that the yellow luminescence in GaN is associated with native point defects. A further paper by Buyanova et al. [31] concluded that high energy electron irradiation up to a dose of 4 X 10^ cm~^ quenches many of the PL emissions in the visible spectral range and stimulates the formation of defects responsible for the appearance of several PL bands in the near infra-red (NIR) spectral range. It would appear that there is some uncertainty regarding the role of particle irradiation and the yellow luminescence intensity. Factors such as material quality, growth technique and irradiation conditions play a role in the modification of the luminescence properties of GaN.

Look et al. [32] used Hall measurements to detect and identify the nitrogen vacancy (VN) at 0.07 eV below the conduction band in GaN, introduced during irradiation with 0.7-1.0 MeV electrons. Subsequently, Fang et al. [24] were the first to employ DLTS to show that electron irradiation introduced a defect, which they labeled E, with a level at 0.18 eV below the conduction band and introduction rate of 0.2 cm~^ These authors speculated that E is the same as the VN detected by Hall measurements although its introduction rate is considerably less than the 1.0 cm~^ for the N-vacancy. In order to account for the large difference in the measured activation energies, they proposed that the capture cross section of this defect is strongly temperature activated, leading to a large capture barrier (^0.11 eV in this case). Subsequently, Polenta et al. [33], illustrated that the DLTS spectrum for this trap consists of two components, EDI and ED2 with a thermal energy of 60 meV and 110 meV, respectively (not the 140-200 meV reported by other DLTS studies) and different capture cross-sections (Fig. 3 and Table 2). The microscopic nature of these two defects (EDI and ED2) has not been experimentally verified and further experiments are required to cast more light on the nature of this defect.

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Table 2. Electronic properties and introduction rates of electron defects introduced by high energy electrons, protons and He-ions

Defect label

ERl ER2 ER3^

ER4 ER5 E^ EDI ED2

Activation energy (eV)

0.13 d= 0.01 0.16 ±0.03 0.22 ± 0.02 0.20 ± 0.02 0.20 ± 0.02 0.78 ± 0.05 0.95 ± 0.03

0.18 0.06 ± 0.005'^ O.lliO.OlO'^

Apparent capture cross-section (cm2)

2 ± 1 X 10-'^ 4 ± 2 x 10-'^

1.9±1 X lO-''* 4 ± 1 X 10-'5

3 . 5 ± 1 X 10-15 1 ± 1 X 10-15 3 ± 1 X 10-1^ 2.5 X 10-15

1-3 X 10-20^ 5-8 X 10-19^

Introduction rate (cm-i)

30 ± 1 0 ^ 400 ± 150'

1±0.3^'^ 600 ±100^

3270 ± 200 y 1510±300y 3030 zb 500 y

0.2 0.3^-1'

Reference

Auretetal. [19] Auretetal. [19]

Auretetal. [19] Goodman et al. [53]

Auret et al. [36] Auret et al. [36] Fang et al. [24]

Polenta et al. [33] Polenta et al. [33]

^ Introduction rate by high energy electrons. ^ Combined introduction rate of at least two defects by high energy electrons (labeled EDI and ED2 by Polenta et al). ^ Thermal energy and temperature independent capture cross-section. ^ Introduction rate for 2.0 MeV proton irradiation. ^ Introduction rate for 5.4 MeV He-ion irradiation. ^ Believed to consist of at least two defects.

Goodman et al. [34] have used DLTS to study the defects introduced by high energy electrons in IVIOVPE grown GaN with a free carrier concentration of 2-3 x 10 ^ cm"^. This layer was 5 microns thick and grown on a buffer layer on sapphire. The radiation source was a 20 mCi Sr ^ radio-nuclide emitting electrons with energies in the 0.2-2.4 MeV range at a dose rate of 1.3 x 10^ cm~^ s~^ In Fig. 3 the spectrum after irradiation is shown. For completeness the results of Polenta et al. [33] are illustrated in the inset of this figure. From this figure and its inset it is clear that when interpreting DLTS data of radiation induced defects, even for electron irradiation (generally believed to introduce discrete, simple point defects) caution has to be exercised. Goodman et al. [34] have experimentally observed the defect ER3 to consist of contributions from at least two defects, this was initially proposed through modeling by Polenta et al. [33]. This modeling adopted an exact fitting procedure which takes into account the temperature dependence of the capture cross-section. As shall be shown in Sections 3.2 and 3.3, the ER3 defect is also observed after high energy proton and He-ion irradiation [35,36]. The electronic properties of defects observed after high energy (electron, proton and He-ion irradiation) particle irradiation of n-GaN are summarized in Table 2 and in the form of Arrhenius plots in Fig. 4.

3.2. Proton bombardment

In many semiconductors hydrogen is an impurity which exhibits very complex behavior because of its high diffusivity and chemical reactivity [37]. The presence of this element in a semiconductor can influence the mechanical and optoelectronic properties of several semiconductor materials. In this section we will not discuss the issue of the


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role of hydrogen and doping in GaN, but will concentrate on electrically active defect production in this material due to hydrogen irradiation.

Contrary to the case of electron irradiation, the damage created during MeV proton implantation is not uniform in semiconductors. For example, the range of 2 MeV protons in GaN is approximately 43 microns. Within this region the vacancy concentration as calculated using TRIM increases from 2.5 x 10"^ Vac/ion/A at the surface to a maximum of 3.6 x 10"" Vac/ion/A at 43 microns. Several types of defects are created in the damaged region. Firstly, near the surface where the energy loss is mainly due to electronic stopping, point defects are formed. Secondly, towards the end of the proton range, energy transfer occurs mostly by nuclear stopping and the high rate of energy transfer in this region gives rise to the formation of extended defects. Thirdly, the protons (hydrogen) can interact with the point defects and form complexes. This has been vividly illustrated for hydrogen implantation of Si where hydrogen related defects were positively identified. The different nature and concentrations of these defects result in a spatial variation of the semiconductor properties. Weinstein et al. [38] implanted GaN with hydrogen and deuterium to probe the possible interactions of H with lattice defects that are introduced during implantation. The vibrational bands that were observed near 3100 cm~* were assigned to nitrogen-dangling-bond defects created by implantation and decorated by hydrogen.

It is well known that proton implantation like other ion or particle irradiation reduces the free carrier density of the material under implantation. Pearton et al. [39] found that this free carrier reduction occurred through two mechanisms: first by creating electron and hole traps at around Ec -0 .8 eV and Ey +0.9 eV that lead to compensation in both types of material and second, by leading to the formation of (AH)° complexes, where A is any acceptor (Mg, Ca, Zn, Be, Cd). The formation of electron hole pairs is


useful for material isolation and the complex formation produces unintentional acceptor compensation.

The device performance of several device types, including fast switches [26] and detectors [27], has been improved by subjecting the devices to controlled doses of particle irradiation. Specifically, hydrogen implantation of Si has been successfully used to spatially tailor the carrier lifetime in switches in order to optimize their switching speed.

Hydrogen related defects in compound semiconductors are not as well understood as in Si. Particularly, for GaN very little experimental information is available. Neugebauer and Van de Walle [40] predict a large negative-U effect for interstitial hydrogen.

The first DLTS investigation of proton implantation in GaN was reported by Auret et al. [19]. For that investigation, they used GaN with a free carrier density of 2-3 x 10^^ cm~^, grown by metalorganic vapor phase epitaxy (MOVPE). Following the chemical cleaning and metal contact deposition the diodes were bombarded with 2 MeV protons to a dose of (3 ± 1) x 10 ^ cm"- at a dose rate of approximately 1 x 10 ^ cm~^ s~ in a Van de Graaff accelerator. This proton dose did not reduce the carrier concentration by more that 10%. The proton bombardment induced defects, as well as the defects in unirradiated GaN, were characterized by DLTS using a Stanford Research lock-in amplifier (model SR830), which facilitated transient analysis at pulse frequencies of as low as 1 mHz. The 'true' electron capture cross sections, a^ , were calculated using the variable pulse width method [41].

DLTS spectra were recorded using pulse widths, tp, from 50 ns up to 10 ms. From this they observed that the detection of defects in the as-grown as well as irradiated GaN depends rather critically on the pulse width. Fig. 5 depicts the DLTS spectra of

100 150 200

Temperature (K)

300

Fig. 5. DLTS spectra of as-grown and proton-irradiated n-GaN. Curve a: as-grown epitaxial n-GaN. Defects EOl, E02 and EOS were recorded at filling pulse widths of 50 ns, 50 |JLS and 2 ^,s, respectively. Curves b-d: DLTS spectra of proton bombarded epitaxial n-GaN, recorded using filling pulse widths of 400 ns, 2 ms and 20 ms, respectively. Curves a-c were recorded at 46 Hz and curve d at 10 Hz. All spectra were recorded at a quiescent reverse bias of 2 V and filling pulse amplitude of 0.5 V.

262 Ch. 8 ED. Auret and SA. Goodman

control (not bombarded) and proton bombarded SBDs. The control sample (curve a) contained three defect peaks below 300 K, labeled EOl, E02 and E03. Curves b-d in Fig. 5, recorded using different filling pulse conditions, show that proton bombardment introduces the defects ER1-ER3. Defect ERl could only be clearly detected when using pulse widths, tp, of less than 2 ^xs. Using a filling pulse width of tp = 400 ns, the activation energy of ERl was determined as 0.13 ± 0.01 eV below the conduction band. For pulse widths larger than 1 IJLS, the ER3 peak appears and seems to reach a maximum for a pulse width of about 1 ms at 121 K, indicating that the components of ER3 have small electron capture cross sections. As the ER3 amplitude grows with increasing pulse width, it obscures the detection of the much smaller ERl peak. When increasing the pulse width to above 1 ms, the ER3 peak showed a broadening. Scans recorded at low frequencies and wide filling pulses, e.g. curve d at 10 Hz and 20 ms, revealed that this broadening is due to another peak, ER2, on the low temperature side of ER3. The extraordinary large pulse widths required to detect ER2 indicate that its real electron capture cross section is even smaller that of ER3 (unlike their almost identical apparent capture cross-sections).

Remembering that defect ER3 consists of at least two defects, the signature which is determined using tp = 50 |xs is an 'average' value. This pulse width yields a strong ER3 signal but it is too narrow for ER2 to capture a significant amount of carriers and thus to contribute to the DLTS signal at the temperatures where we studied ER3. The energy level thus determined, Ec —0.20 di 0.01 eV, is similar to that of a defect, labeled E, with a level at Ec —0.18 eV, observed by Fang et al. [24] after electron irradiation of MOVPE (metal-organic vapor phase epitaxy) grown GaN. These authors pointed out that, should this defect have a temperature activated capture cross section, its actual position in the bandgap may be close to that of VN (EC —0.07) [32], but no firm identification has yet been made. ER3 has also been observed after irradiating epitaxial GaN with electrons from a ^°Sr source (Section 3.1) and 5.4 MeV He-ions from an " Am radionuchde (Section 3.3). To extract the electronic properties of ER2, spectra which were recorded at different frequencies, using pulses just sufficient to saturate ER3, were subtracted from spectra recorded with a wide enough pulse to clearly show the ER2 signal. This procedure yielded an activation energy of 0.16 ± 0.03 eV. For summary purposes the electronic properties of defects in n-GaN after high energy particle bombardment are listed in Table 2.

Whereas ERl could also be detected in He-ion irradiated GaN, we could not observe ER2 in the same GaN irradiated with electrons and He-ions. There are two possible explanations for this. Firstly, the proton irradiation dose rate in this study was much higher than the dose rates during electron and He-ion irradiation. In the case of the introduction of mobile point defects, this implies that their concentration may be large enough so that they can interact with each other to form complexes, before being able to diffuse away. Secondly, TRIM calculations showed that the concentration of substitutional hydrogen is of the same order of magnitude as the number of vacancies introduced. ER2 may therefore be related to substitutional hydrogen or complexes of hydrogen with irradiation induced defects.

By using the pulse-width method [41], an attempt was made to measure the 'true' capture cross section, Qn, of ER3. It was, however, not possible to measure its saturation


peak height accurately because, at pulse widths where ER3 appears to saturate (tp > 1 ms), the ER2 peak, which is superimposed on ER3 (Fig. 5, curve d), starts to grow with increasing tp, thereby adding to the ER3 peak height. By assuming that increases in the ER3 peak at r > 1 ms are due to the growth of the ER2 peak and that the ER3 peak is saturated for these pulse widths, the capture cross section of ER3 was calculated as an = (8 ± 4) x 10"^^ cm^ at 121 K. This value On is significantly smaller than that extracted from the Arrhenius plot (ana = 4 ± 1 x 10"^^ cm^), indicating that an may be thermally activated. However, attempts to confirm this by measuring an at different temperatures were unsuccessful, most likely because of the influence of the overlapping ER2 peak. The small value an suggests that ER3 is in a neutral or negative state when capturing electrons. This deduction is substantiated by recent evidence from He-ion irradiated GaN (Section 3.3), which indicates that ER3 does not exhibit typical Poole-Frenkel [42] electric field enhanced emission for a Coulombic well.

Finally, the defect concentrations, Nt, were determined using the fixed bias variable pulse method in conjunction with the formalism of Zohta and Watanabe [43]. Following this, the introduction rates, rj = A^^/(proton dose), of ERl, ER2 and ER3 were calculated as 30 it 10 c m - \ 400 ± 150 cm"^ and 600 ± 100 c m - \ respectively. The introduction rate of ER3 for 2 MeV protons is about 5 times smaller than for 5.4 MeV He-ions and 3000 times larger than for 1-2 MeV electrons. The ratios of these introduction rates scale roughly with the mass ratios of the particles.

In summary, using DLTS, three electron traps, ERl, ER2 and ER3, introduced by 2 MeV proton bombardment in epitaxial GaN, were characterized. The most prominent of these, ER3 which we believe to consist of at least two defects, is introduced at a rate of 600 =t 100 cm"^ and has a level at Ec -0.20 ± 0.01 eV. ER3 has also been observed in GaN which was bombarded with high-energy electrons and He-ions. The small capture cross-section of ER3 [(8 ± 4) x 10"^^ cm^] implies that it is in a neutral or negative state when above the Fermi level. ER2, with an energy level at Ec —0.16 ± 0.03 eV, is introduced at a rate of 400 ±150 cm~^ This defect was not observed in identical GaN irradiated with electrons and He-ions and it may therefore be a hydrogen-related defect. A less prominent defect, ERl, with a level at 0.13 ± 0.01 eV, is introduced at a rate of 3 0 ± 1 0 c m - ^

3.3. He-ion bombardment

In the world of microelectronics, one of the critical processing steps is the definition of the device active area. One method of active area definition is by implant isolation, this procedure simplifies device processing by maintaining a planar wafer surface. One of the earlier reports on mesa implantation for GaN based devices used protons, with the post-implantation mesa to mesa resistance being around 1 M ^ [44]. A second study by Binari et al. [45] achieved isolation in the fabrication of GaN MESFETS by using multiple-energy proton implantation.

One of the niche applications for GaN based devices is in high-temperature electronics. This implies that the implant-damaged regions should be thermally stabile at the device operating temperature. Since the isolation is generated through the introduction of electrically active defects or defect complexes by the incident energetic particles.

264 Ch. 8 ED. Auret and S.A, Goodman

these defects or defect complexes should be thermally stable at the operating temperatures to ensure that the material remains insulating. Exposing semiconductors, even those that are not considered as radiation hard as the III-V nitrides, to high energy electrons results in the formation of predominantly simple point defects. These point defects are generally removed by thermal treatments in the temperature range 250 to 400°C. This is considerably lower than the operating temperature of the high power, high temperature applications of the nitride based devices. In order to ensure that the insulating regions remain insulating at the operating temperature of the devices it is necessary to form more thermally stable defect complexes upon particle irradiation. These defect complexes are formed by irradiation with high doses of heavier particles or ions. Both H- and He-ion implantation have been used in GaN-based microelectronic processes [46,47], and it was found that He-ion implantation produced high resistivity GaN at a fluence that is compatible with photoresist masking techniques. The use of incident particles heavier then electrons for this purpose also allows the spatial tailoring of material properties (with respect to the semiconductor surface). However, in order to utilize ion-implantation effectively in the field of device processing it is critical that the intentionally and unintentionally introduced defect properties (electrical and thermal) be determined.

The first report on the electrical characterization of defects introduced by He-ion irradiation of GaN by DLTS was presented by Auret et al. [19]. They irradiated GaN with a free carrier density of (2-3) x 10^ cm~^, grown by MOVPE on sapphire, with alpha-particles (He-ions) from an ^ " Am radionuclide [48]. Before irradiation, ohmic contacts and Au SBDs were fabricated on the GaN as previously reported [34]. After assessing the diode quality by current-voltage (I-V) measurements, determining the free carrier concentration, N D - N A , by capacitance-voltage (C-V) measurements and recording control DLTS spectra, some of these Au SBDs were irradiated with 5.4 MeV He-ions to doses of between 0.4 x 10 ^ cm~^ and 2.5 x 10 ^ cm"^ at a dose rate of 7.1 x 10^ cm~^ s~^ Defects in the as-grown and irradiated GaN were characterized by DLTS in the 50-380 K temperature range using a lock-in amplifier (model SR830).

An important parameter during device isolation by ion-implantation is the amount of free carriers removed by defects and/or defect complexes introduced by the energetic ions. This will ultimately determine the efficiency of material isolation during this processing step. First, consider the He-ion irradiation induced reduction in free carrier density. For the dose range investigated, they observed a linear decrease of Np—NA with dose. The carrier removal rate, A(ND-NA)/(He-ion dose), calculated from this data, was 6200 zb 300 cm~^ at 300 K. This carrier reduction was found to be constant in the first half micron below the surface analyzed by C-V measurements using a reverse bias of up to 2 V. This observation is what can be expected because the range of 5.4 MeV He-ions in GaN is 25.3 |xm and there is little variation in the electronic and nuclear stopping in the first few microns of their path.

After exposing the GaN to 5.4 MeV He-ions, three prominent additional defects, ER3, ER4 and ER5, were observed (curves b and c in Fig. 6), of which only the ER3, with a level at Ec —0.20 eV, was previously detected after electron and proton irradiation of similar material [19,34]. The newly observed radiation induced defects, ER4 and ER5, were detected after recording DLTS spectra using a filling pulse frequency of 100 mHz,


re

CO

100 200 300 Temperature (K) ^=0.1 Hz

I . . . . I . . . . I

0 50 100 150 200 250 300 350 400

Temperature (K)

Fig. 6. DLTS spectra of unirradiated (curve a) and 5.4 MeV He-ion irradiated (curves b and c) epitaxial n-GaN, recorded using a reverse bias of 2 V, a filling pulse amplitude of 2.2 V, a filling pulse width of 0.2 ms and frequencies, / , as indicated.

i.e. an emission rate of about 0.23 s~^ The DLTS signatures of ER4 and ER5 were determined (Table 2 and Fig. 4) by using pulse frequencies of between 4.6 and 220 mHz. Note that under 'typical' DLTS recording conditions (emission rates of 50-200 s"^) the DLTS peaks of ER4 and ER5 would occur at (430-450) K and (470-500) K, respectively, which is probably why they were not previously detected.

The levels of ER4 (Ec -0.78 eV) and ER5 (Ec -0.95 eV) are the deepest radiation induced levels below the conduction band yet detected by DLTS. The only radiation induced defect-related transitions with roughly the same energies as the ER4 and ER5, are those reported by Linde et al. [29] after a photoluminescence (PL) study of electron irradiated GaN. These authors found that electron irradiation introduces two PL bands centered around 0.85 and 0.93 eV, respectively, and using optically detected magnetic resonance, they tentatively identified the latter level as belonging to a Ga^'^-complex. Due to the fundamental differences in the origin of DLTS and PL spectra, no direct comparison between their PL and the DLTS spectra of Auret et al. [36] is possible. However, since Ga interstitials are formed during irradiation, they, or complexes including them, are likely to yield deep levels that can be detected by DLTS. Alternative possibilities for structure of ER4 and ER5 is the N-interstitial, which was predicted to have levels near the center of the band gap [49], and the VcaNj" and VoaNf ~ states with levels calculated to be in the upper half of the bandgap [50].

The defect introduction rates, r\ = Nt/(He-ion dose), of ER3, ER4 and ER5, were determined after calculating the defect concentrations, Nt, by using the fixed-bias variable-pulse method [41] as 3270 ± 200 c m ' ^ 1510 ± 300 cm"^ and 3030 ± 500 cm ', respectively. We note that the combined introduction rate of defects that could ^-1

retain electrons at room temperature (ER4 and ER5) is about 25% smaller than the carrier removal rate at the same temperature. This implies either that the ER4 and ER5 concentrations measured here are lower than in reality or that there is another radiation


1.5

1.4

O O

1.2

1.1

. ' o ER5

: r=378K L f=0.1Hz L V;=2V, Vp=2.2V

h ^

r ^ o f o"" L ^ [ °

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o

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j y ^ \

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j y ' ' ^ \

^^^^^ j QO H

o j o ^

-

1.0 10-8 -10- 10-6 10-5 10^ 10-3 ^0-2 10-^

Filling pulse width (s)

Fi%. 7. DLTS signal (5(r) = ACjC) as function of log(r) for ER5. The error in 5(0 is about the same as the height of the symbols.

induced defect with a level deeper than that of ER5 that were not detected. As shown below, it is indeed difficult to determine the saturation peak height of ER5 due to its capture kinetics.

Capture cross section (an) measurements ER5 were performed using pulse widths, tp, of between 50 ns and 50 ms. Fig. 7 shows that the DLTS signal of ER5 increases monotonically with tp for the whole pulse width range investigated. If the DLTS signal, S, is proportional to the defect concentration, NT, then capture onto a point defect can be described by [9]

^ ( 0 = 5oo [1 - exp(-c„0] (1)

where 5*00 is the magnitude of the saturated DLTS signal, the capture constant is Cn = o (vth)w, and (vth) and n are the electron thermal velocity and concentration, respectively. Even when assuming a value of S^ larger than that obtained using tp = 50 ms, no linear plot of ln(l - S(t)/Soo) vs t could be obtained. Because the total concentration of radiation induced defects in the sample used for this measurement was much lower than the free carrier concentration, this incomplete filling of ER5 is not due to a competition for electrons between ER5 and the shallow donors. However, the presence of a straight line region in the plot of S(t) vs log(r) in Fig. 7 is similar to what has been observed for carrier capture by traps which are not randomly distributed, but which are arranged along lines [51]. In such a case the capture rate is limited by a Coulomb barrier which increases with increasing charge capture onto the extended defects. The data presented here strongly suggests that ER5 is a line defect, or an extended defect, where charge build-up governs the capture rate. Regarding the formation mechanism for such a defect, it should be noted that for a head-on collision 5.4 MeV He-ions can transfer sufficient energy to the GaN lattice to cause extended regions of disorder.

In an attempt to gain further insight into the nature of He-ion induced defects, we


P T — I — I — r — T — I — I [ t I — I — r — I — I I I I ] — I — r — I — i ; i i

0)

I 4

Q 2

I I I I I I u_j i_j L-j.

300 400 500 600

Temperature (K)

700

Fig. 8. Relative DLTS peak heights as a function of isochronal annealing for 2.0 MeV proton irradiation of n-GaN.

considered the annealing properties of the three major electron defects (ER2, ER3 and ER5). Fig. 8 depicts the relative DLTS peak heights of these defects and as-grown defects E02 and EOS present in unirradiated material. As expected, defects E02 and EOS remain unchanged in the temperature range used here. However, the concentration of the radiation induced defects ER2 and ER3 which are stable up to S40 K decreases rapidly to zero at 620 K. The removal of defect ERS begins at 540 K and at 660 K it is completely removed. The annealing experiment on defects ER2 and ER3 was repeated for the electron irradiated material with similar results. In order to monitor the quality of the metal SBD during the annealing cycles, current-voltage and capacitance-voltage measurements were conducted. In Fig. 9 the recovery of the reverse leakage current measured at 1.0 V as a function of annealing temperature is shown. Prior to annealing

10-° 1 <; > 10- 1 p

Z 10» C

^ O 10-9 0

0

1 10-10

; - ! 1

:

I

I

h 1 il

• ' 1 '••

!

. 1 . 1 J - . 1

. - r - , y

! *

..1 1 U -

^ ""

f

- 1 - J

' '

f

LJU

T 1

1 1

i \ 1 1 1 1 1

' ' ' ! • '

f 1

. . j - i .1 ..,

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f

JL-A-iJL

1 1 t 1-4

j

t

3

j

- J

,1 1 1 1 H

200 300 400 500 600 700 800

Annealing Temperature (K)

Fig. 9. Influence of annealing temperature on the reverse leakage current measured at 1.0 V of Au SBDs on n-GaN.

268 Ch, 8 KD. Auret and SA. Goodman

1.8

1.6

o

.7 1.4

(0

« 1 . 2

1.0

200

I [ t I I I I I I I { I I I I I I I 1 I I I I I

\ \ \ \ \ ^

• • ' > ' • ' • ' ' ' • • '

\ \

i i I t I I I I I I t t I

1.00

0.95

0.90 03 Q)

0.85 i-

0.80 ^

0.75 5 <

I H 0.75 5

300 400 500 600 700 Annealing Temperature (K)

0.70

0.65

0.60

800

Fig. 10. Influence of annealing temperature on the ideality factor (n) and barrier height of Au SBDs on n-GaN.

the irradiated material, the reverse leakage current was of the order 5 x 10"^ A, this improved more than two orders of magnitude to 2 x 10"^^ A at 760 K.

A similar trend is observed in Fig. 10 where the change in ideality factor and barrier height with annealing temperature is illustrated. The barrier height prior to annealing was 0.73 eV and at 760 K it increased to 0.94 eV. The ideality factor which was initially 1.5 approaches 1.05 at 660 K. It is interesting to note that the recovery of these parameters coincides with the temperature at which the removal of ER2, ER3 and ER5 is initiated. Care must be taken in the interpretation of the recovery of these SBD properties upon annealing, it must be noted that there was not an appreciable change in the free carrier density prior to and after annealing.

During the characterization of semiconductors using the DLTS technique and Schot-tky barrier diodes, a quiescent reverse bias and forward bias pulses are applied to the sample. The application of the reverse bias forms a space charge region, this region is characterized by the presence of ionized states or deep levels. It is generally assumed that the emission of carriers from these states or deep levels is a purely thermal process. However, this may not always be the case and inaccurate defect characteristics may be calculated if one assumes only thermal emission under certain experimental conditions. There is strong evidence that in some cases the emission rate of carriers from deep levels does depend upon the applied bias during the measurement cycle and also on the doping level of the semiconductor under consideration. The presence of an electric field in the space charge region may adversely affect the accurate determination of the defects electronic signature (position in the bandgap (Ej) and the capture cross-section (an) as well as the concentration (Nj) of the defect under investigation. On a positive note, accurate measurements of the field enhancement of emission rates can lead to a model of the localized defect potential of the deep center thus providing vital insight into the nature of the defect states in the semiconductor [52].

In the case of GaN the first paper on field enhanced emission from a deep level


105

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LU

10^

103

102

10

E

I

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L |-

Lx.j_

— Gauss, well(0.2O6 0V,6±1A) ^ ^ Square well (0.196 eV, 20 ±2 A) ^^

' " 3D Coul. well (0.196 eV) ^^ 0 Exp. emission rate ^^

•

3^ ' ' n 9 * : ^ ^ ^

1 1 1 1 1 1 I 1 1 1 1 1 1 1 i. 1 1 1 1 1 1 1 .1 1 i. 1 1 1 1

- r i - |

\

\

J -J

- U _

250 300 350 400 450 500 550

Electric field'- ' (V/cm)'' ^

Fig. 11. The experimental and modelled emission kinetics of defect ER3 as a function of electric field strength in the space charge region.

in GaN was by Goodman et al. [53]. In this work the electrical properties and the dependence of the emission rate on electric field strength of a deep level defect (ER3) introduced by 5.4 MeV He-ions in n-GaN was reported. Defect, ER3 was reported to have a 'low field' (7.6 x 10" V/cm) DLTS 'signature' of Ec -0.196 ± 0.004 and 3.5 zb 1 X 10~^^ cm^. In order to simplify the determination of the emission kinetics of ER3 at different electrical field strengths in the space-charge region, they made use of isothermal DLTS.

In Fig. 11 the experimentally measured emission rate of ER3 as a function of the square root of the electric field in the space charge region is shown. In order to establish the potential associated with this defect the experimental data was modeled making use of various simple defect potential models. It must be noted, that the one-dimensional calculation grossly overestimated the field enhancement, as is well known [54]. Therefore, the three-dimensional Poole-Frenkel description of electric field assisted thermal emission from a coulombic well was considered. According to this model [55], the emission rate can be described by:

e{F) = e{0) ' kT Y

1 + kT + 1

(2)

where e(0) is the emission rate at zero electric field, k is Boltzmann's constant, T is the absolute temperature and

^ = (£)• (3)

It is evident from Fig. 11 that this particular potential does not suitably explain the experimentally measured emission enhancement. It must be noted that the characteristic dependence of the emission rate {e) on electric field (F) in the case of the one-dimensional Poole-Frenkel effect for a coulombic well, namely that log e is proportional to


F^^, is frequently used by experimentalists to distinguish between donor and acceptor defects. The linearity of this dependence is characteristic of a charge leaving a center of opposite sign. In n-type material this would imply a donor type defect, whereas, in p-type material this would imply an acceptor type defect [52]. It must be noted that the determination of the electronic type should be approached with caution as was expressed in the paper by Buchwald et al. [56], who reported on the revised Poole-Frenkel effect for EL2 in GaAs.

Secondly, the gaussian well was considered as a possible potential description for ER3. The enhanced emission rate in this case is [57]:

^(F) = 27r^(0) + ]exp - ^^ ^' ^* kT I qFro

exp c^yi + 1 , (4)

where ro is the top of the distorted well where hE/hr = 0. The resulting equation is non-linear in ro, E, a and VQ, and has, therefore, been solved iteratively for each set of these values before calculating e{E) using Eq. 4. A good fit is obtained when a characteristic width of 6.0 ± 1 A and a potential of 0.206 eV is used.

Thirdly, the spherically symmetric square well potential of radius b was investigated. The variation of emission rate (e(f)) with electric field of a square well of radius b is [55]:

e(E) = e(0) [(kT/2qFb) [txpiqEb/kT) - l] + 1/2} (5)

Using a potential equal to the experimentally determined activation energy, namely, 0.196 eV and a well with a radius of 20 ± 2 A, a good fit is obtained between the experimentally measured emission rates and the modeled points.

It would appear that the square well and the gaussian well with their particular physical dimensions discussed both provide an adequate description of defect ER3 detected after high energy He-ion irradiation. In an attempt to understand how both potentials describe the experimental results, a comparison of the distortion of these potentials at a reasonably high (2.5 x 10^ V/cm) electric field strength was investigated. Fig. 12 schematically represents the distortion of a square and a gaussian well. It is clear from this figure that using either a gaussian or a square well with the specified physical attributes can adequately describe the enhanced emission kinetics of ER3. The fact that the field enhanced emission from ER3 can not be adequately described by a coulombic well indicates that ER3 is not a donor type defect but an acceptor type defect.

4. Defects introduced during low energy particle related processing

4.1, Low energy ion bombardment

Low energy ion bombardment may originate from ion beams or plasmas, consisting of reactive or non-reactive ions or molecules. It is routinely used to clean materials surfaces before Auger electron spectroscopy (AES) or X-ray photoelectron spectroscopy (XPS), or to erode the materials for depth profiling. Reactive or non-reactive plasma treatments are employed to clean semiconductor surfaces or etch away finite thicknesses of semiconductors for pattern definition. It has been shown that all these processes result


0.20

0.15 I

0.10

^ 0.05 I

S> 0.00

•I -0.05 [

1 - 0 . 1 0 ^ °- -0.15 [

-0.20 [

-0.25

-0.30

^' ' ' ' 1 ' ' ' ' 1 ' ' • ' 1 ' ' ' ' 1 ' ' ' ' 1 ' ' • ' 1 ' ' ' ' j

L Square well (b-20±2A.Ej = 0.196 eV) j f o Gaussian well (a = 6±1 A, E^^ 0.206 eV) 1

F

r 1 '

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^^^p AE^ 1.5x10^ eV A

\

1 F ! * - / ) - * ! F^2.5x 1(f V/cm i

-60 -40 -20 20 40 60 80

Well Width (A)

Fig. 12. The reduction in potential for a gaussian and a square well, when the electric field strength in the space charge region is 2.5 x 10^ V/cm.

in some or other degree of damage at and beneath the semiconductor surface. In the sections below, we describe the effect of this damage on the electronic properties of the semiconductor and on device performance.

4.2. Pre-metallization plasma treatments

Mistele et al. [58] reported on the influence of different pre-etch methods on the specific contact parameters of n-GaN contacts. For these investigations they used ex-situ chemically assisted ion beam etching and in-situ sputter etching before metal deposition. The electrical contact parameters were determined using the extended circular transmission line model. For nitrogen as an etching gas they obtained rectifying character (Schottky) of metal-n-GaN contacts compared with mostly linear (Ohmic) behavior for conventional etching gases such as Ar or Ar + CI2. They speculate that a decrease of N vacancies caused by the N2 treatment is responsible for the Schottky behavior of these contacts. Pre-etch sputtering with Ar ions reduced on the one hand the specific contact resistance, but on the other hand it resulted in an increase in the sheet resistance in near-surface region.

Cao et al. [59] exposed n-GaN Schottky diodes to N2 or H2 inductively coupled plasmas prior to deposition of the rectifying contacts. Subsequent annealing, wet photochemical etching, or (NH4)2S surface passivation treatments were examined for their effect on diode I-V characteristics. They found that, either annealing at 750°C under N2, or removal of about 500-600 A of the surface, essentially restored the initial I-V characteristics. There was no measurable improvement in the plasma-exposed diode behavior with (NH4)2S treatments. Cao et al. [60] examined the effects of H2 or N2 plasma exposure on the current-voltage characteristics of Ti/Au/n-GaN Schottky contacts as a function of source power and rf chuck power. Under all conditions they observed a severe degradation of the electrical characteristics of the GaN surfaces. This resulted in a strong reduction in diode reverse breakdown voltage and an increase in forward and reverse currents. These authors interpreted the results as being consistent

272 Ch. 8 KD. Auret and SA. Goodman

with creation of a thin (< 600 A) conducting n-type surface layer resulting from energetic ion bombardment. Further, they observed that heavier ions (Nj) created more damage than the Ughter (H^) ions, where damage accumulates without any concurrent etching of the surface. Much of the degradation in diode quality could be recovered by annealing in N2 at 750°C.

For p-type GaN, Cao et al. [61] used the reverse breakdown voltage of Schottky diodes to measure the electrical effects of high density Ar or H2 plasma exposure. They found that the near surface of the p-GaN became more compensated through introduction of shallow donor states whose concentration depended on ion flux, ion energy, and ion mass. At high fluxes or energies, the donor concentration exceeded 10^ cm"^ and produced p-io-n surface conversion. Based on electrical and wet etch rate measurements, the damage depth was established as about 400 A. Rapid thermal annealing at 900°C under a N2 ambient restored the initial electrical properties of the p-GaN, similar to the thermal stability of implant isolated p-GaN [47].

In summary, from the studies discussed above it appears that plasma processing results in a conductive n-type surface layer on n- or p-type GaN. It has been proposed that donor-like defects are responsible for the observed effects. Mistele et al. [58] speculated that these defects are related to N vacancies. However, in none of the studies discussed above were any mention made of electrical characterization of the plasma processing induced defects, and consequently their electronic properties are not yet known.

4.3. Metallization

The fabrication of electronic devices requires, among others, metallization for ohmic or Schottky contacts on the GaN. The metallization method chosen for this purpose should fulfil several requirements, including good adhesion of the metal to GaN, the ability to deposit compounds stoichiometrically and the ability to deposit high melting point metals at controllable rates. Most importantly, the metallization method should not introduce unwanted defects in the semiconductor. This latter requirement is particularly important for depletion layer based devices, such as metal field effect transistors. Defects that are introduced during metallization processes of semiconductors have, amongst others, been shown to give rise to modified rectification quality of Schottky barrier diodes (SBDs).

In Sections 4.3.1, 4.3.2, 4.3.3 and 4.3.4 below, we discuss some results that have been recently reported for the metallization of GaN using different techniques.

4.3.1. Resistive (Joule) evaporation This method has been recognized for a long time to be a 'defect-free' metallization method. The material to be melted is simply evaporated by passing current through a crucible of some form. This method, however, has at least one serious disadvantage: it cannot easily evaporate high melting point metals. On the other hand, it is perfect for evaporating metals like Au, Pd, Al and Ni, which are all frequently used for the formation of ohmic and Schottky contacts. In the DLTS data thus far reported for GaN, no mention has been made to any defects that could possibly have been introduced during resistive evaporation of Schottky contacts.


4.3.2. Sputter deposition Sputter deposition is a metallization method which is frequently employed because sputter-deposited layers exhibit better adhesion compared to layers deposited by other methods [62]. In addition, sputter deposition facilitates the stoichiometric deposition of compounds and controllable deposition of high melting point metals, and yields high deposition rates. However, due to the energetic particles involved, sputter deposition is damaging on an atomic scale and causes lattice disorder at and below the semiconductor surface [5].

Sputter deposition induced defects in semiconductors, and the influence of these defects on the rectification quality of SBDs, have been studied for many years. Generally, it has been found that these defects reduce the barrier height of SBDs on «-type semiconductors and increase it on p-type semiconductors. Using DLTS, it was shown that sputter deposition induces defects at and below the semiconductor surface, and it is thought that these defects are the cause of the barrier alteration [5]. The degree of barrier modification depends on the sputter conditions. Most of the pioneering studies regarding the electrical characterization of sputter induced defects and their influence on metal-semiconductor contacts have been performed using Si and GaAs, and little data is presently available for GaN.

Auret et al. [63] reported the characteristics, determined by DLTS, of defects detected in epitaxially grown GaN before and after sputter deposition of Au Schottky contacts thereon. For this purpose, they used epitaxial GaN with a free carrier density of (2-3) X 10^^ cm"^, grown by metalorganic vapor phase epitaxy (MOVPE). Before contact fabrication, the samples were cleaned employing wet chemistry [64]. Following this, Ti/Al/Ni/Au (150 A/2200 A/400 A/500 A) ohmic contacts were fabricated [65]. Prior to Schottky barrier diode (SBD) fabrication, the samples were again degreased and dipped in an HCl rHaO (1:1) solution. Thereafter, circular Au Schottky contacts, 0.5 mm in diameter and 1 jxm thick, were sputter-deposited on the GaN through a metal contact mask, as close as possible to the ohmic contact to minimize the diode series resistance. Sputter deposition was performed in DC mode at a power of 0.141 kW in an Ar pressure of 4.8 x 10~^ mbar at a deposition rate of 4.5 nm s~ . For control purposes, Au SBDs were resistively deposited next to the sputter deposited SBDs.

Current-voltage (I-V) measurements (Fig. 13) showed that for sputter deposited SBDs the current at a 1 V reverse bias was (1-2) x 10"" A, compared to the <10~^^ A of resistively deposited diodes on the same GaN. The forward log (/) vs V characteristics of the sputter deposited diodes were non-linear and no ideality factor could be accurately calculated. The barrier height estimated from the reverse I-V characteristics of these diodes was (0.47 ± 0.03) eV. These I-V measurements confirm that, as for Si [66] and GaAs [67], sputter deposition of Schottky contacts on n-GaN yields diodes with a drastically reduced barrier height and inferior rectification characteristics.

Fig. 14 depicts the DLTS spectra of control (resistively deposited) and sputter-deposited diodes. Curve a shows that the control sample contained two defects, labeled E02 and E05, at 0.27 ±0.01 eV and 0.61 ±0.02 eV below the conduction band, respectively [20]. The concentrations of these defects were found to be uniform throughout the region analyzed, indicating that these defects are a fingerprint of the GaN and that they are not introduced during metallization (Section 2). Curves b-d in Fig. 14 show

274 Ck 8 ED. Auret and S.A. Goodman

0.4 0.6

Bias (V)

Fig. 13. Forward (F) and reverse (R) characteristics Au Schottky contacts to OMVPE grown n-GaN: resistively deposited (curve a), and sputter deposited (curve b).

10

° 8 X

O

CD C u>

CO 4 CO

I ' ' ' ' I

E02

50 100 150 200 250

Temperature (K)

300 350

Fig. 14. Curve a: DLTS spectrum of resistively deposited SBD on OMVPE grown n-GaN. Curves b-d: DLTS spectra recorded from the sputter deposited Schottky contact using filhng pulse amplitudes of 0.9 V, 1.0 V and 1.05 V, respectively. All spectra were recorded at a lock-in amplifier frequency of 46 Hz, i.e. a decay time constant of 9.23 ms, a filling pulse width of 0.2 ms and a quiescent reverse bias of 1 V.

that after sputter deposition, defects labeled ESI, ES2/E02, ES3 and ES4 are detected. Curves b-d show that the peak heights of the sputter induced defects increase with increasing filling pulse height, indicating an increase of the concentration of the sputter induced defects towards the Au/GaN interface. This trend was also previously observed for defects introduced by sputter deposition of Schottky contacts on Si [66] and GaAs [67,68]. Note that E05 is absent in the spectra of sputter deposited SBDs. The reason


6 8 1 0 0 0 / T ( K ' )

10 12

Fig. 15. DLTS Arrhenius plots of defects in particle-processed and as-grown OMVPE grown n-GaN. Triangles, E-beam deposition; squares, sputter deposition; thick solid lines, high energy irradiation; broken lines, as-grown GaN.

for this is that the energy level of E05 is 0.61 eV below the conduction band whereas the barrier height of the sputter deposited SBDs is only 0.47 eV. Therefore, during the quiescent DLTS bias the £05 level remains below the Fermi level [69] and does not emit carriers.

For determining the defect signatures, the overlapping peaks in Fig. 14 were separated using different pulse conditions [63]. From Fig. 15 and Table 3, where the signatures of the sputter induced defects are compared to those of radiation-induced defects and defects in as-grown OMVPE GaN, it seems that two of the defects observed after sputter deposition may be the same as other defects previously reported in GaN. Firstly, ES2, with a level at Ec -0.30 ± 0.01 eV, appears to be similar to E02, with a level at EQ —0.27 ± 0.01 eV, which is present in as-grown GaN. However, it does seem as if sputter deposition resulted in an increase of the ES2 concentration towards the GaN surface. Secondly, the signature of ESI, with a level at Ec -0.22 ± 0.02 eV, is similar to that of the ER3 defect with a level at ^c -0.20 ± 0.01 eV, which was observed after 5.4 MeV He-ion irradiation (Section 3.3) and 2 MeV proton irradiation (Section 3.2) of the

Table 3. contacts

Electronic properties of defects introduced in n-GaN during sputter deposition of Au Schottky

Defect label

ESI ES2 ESS ES4

Ej

(eV)

0.22 ± 0.02 0.30 ±0 .01 0.40 ± 0.01 0.45 ±0 .10

o-a (cm2)

6.5 ± 2.0 X 10"^^ 4.4 ± 1.0 X 10"*^ 3.3 ± 1.0 X 10-^^ 8.1 ± 2.0 X 10-16

•'peak

(K)

^ 1 2 0 157 192 249

Similar defects

ER3 [19], E [24] E02[19],E1 [15], E2 [16]

--

^ Peak temperature at a lock-in amplifier frequency of 46 Hz, i.e. a decay time-constant of 9.23 ms.


same epitaxial GaN, and the E defects observed by Fang et al. [24] in electron irradiated n-type GaN. The ESS and ES4 defects, with levels at Ec -0.40 ± 0.01 eV and Ec -0.45 ih 0.10 eV, do not correspond to defects observed in irradiated or in as-grov^n epitaxial n-GaN. Their signatures also do not correspond to those of defects introduced by nitrogen implantation of GaN, where it was suggested that one of the defects thus introduced may be a N interstitial [22]. These observations suggest that ESS and ES4 are not related to the simple radiation induced point defects. This can be explained by the fact that, during sputter deposition, energetic particles, like Ar ions, enter the GaN and lose energy at a high enough rate to create defects in close proximity of each other. These defects then combine or interact to form larger defect complexes.

The peak shape and electronic properties of ES4 were found to be strongly dependent on the pulse height-increasing the pulse height resulted in a broadening of the peak and a shift to lower temperatures. The same behavior could not be seen when maintaining a fixed pulse level, and increasing the reverse bias, ruling out the possibility of this behavior being due to electric field assisted emission. This behavior of ES4 is similar to that of defects introduced during low energy Ar ion bombardment of GaAs where it was shown that those defects are located close to the surface and have a band-like energy distribution [68].

In a recent paper, DeLucca et al. [70] reported the properties of defects introduced in a 20 micron thick HVPE grown GaN layer with a carrier density of 1.5 x 10 ^ cm~^ by DC magnetron sputter deposition. After ohmic contact formation, photoresist patterned samples were immersed in 1:1 HCl: DI for ten minutes, rinsed with DI water, blown dry with N2 gas, and immediately loaded in the deposition chamber for evacuation to 10"^ Torr. After a pumpdown of at least eight hours, 500 A thick Pt layers were deposited followed by lift-off in acetone. Three different sputter conditions were investigated, with decreasing power {P) and increasing Ar pressure (/?) conditions, intended to reduce the energy of incident species on the GaN surface [71]. These conditions are (1) high-power low-pressure (P = 100 W, /? = 5 mTorr), (2) 'normal' (F = 6 W, /? = 5 mTorr), and (S) low-power high pressure (P = 6 W, /? = 15 mTorr).

Firstly, consider the DLTS results of contacts deposited under 'normal' sputter conditions. Curves a-e in Fig. 16 show the presence of at least four sputter induced electron traps, ES1-ES4. The peaks of ESI-ESS are not well separated and only ES4 could be accurately characterized. These spectra are very similar to those recently reported [6S] and discussed above for sputter deposited Au contacts on OMVPE grown n-GaN. In that case it was demonstrated that the ESI-ESS peaks could only be deconvolved by recording spectra using a wide range of pulse widths, extending from nano- to milliseconds.

Defect depth profiling was performed considering only the maximum (combined) peak height, ESC, of the ES1-ESS defect group, without deconvoluting the defect peaks. Fig. 17 reveals that the concentration profile seems to be composed of two parts: one part that increases sharply towards the interface, and another that extends much deeper into the GaN. This is the result of ESC being the superposition of unresolved defect peaks-one close to the surface and the other deeper. Because ES4 displayed a band-like behavior, it was not possible to extract its depth profile in the conventional way.

Next, consider the results for contacts deposited under high plasma pressure and low


150 200 250

Temperature (K)

300 400

Fig. 16. DLTS spectra of a Pt contact on HVPE grown n-GaN, sputter deposited under 'normal' conditions. Curves a-e were recorded using filling pulse amplitudes of 1.0. 1.5, 2.0, 2.5 and 2.9 V, respectively. All spectra were recorded using a filling pulse width of tp = 0.2 ms, a reverse quiescent bias of Vr = 2 V and a pulse frequency of f = 46 Hz.

10 5 L

c o O

0) Q

10^4

L V

i -T-r 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

- - ^ EO6:Ec-0.67eV - A - EOS: Ec - 0.61 eV - a - ESC = ES1+ES2+ES3

]

0.02 0.04 0.06 0.08 0.10

Depth below junction (microns)

0.12

Fig. 17. DLTS depth profiles of defects observed in HVPE grown n-GaN after depositing Pt SBDs 'normal' sputter deposition conditions. Note that ESC is the highest point on the compound comprising ESI, ES2 and ESS. The shape of its profile suggests the presence of at least two peaks with different depth distributions.

power conditions. Curves c and d in Fig. 18 that show that sputter deposition under these conditions does not seem do introduce any discrete level defects, except for ES2 in very low concentrations. However, the spectra c and d in Fig. 18 are characterized by a skewed baseline of which the offset increases with increasing temperature. This phenomenon is consistent with the presence of defects, located close to the interface, with a continuous energy distribution of which the concentration increases with the


10

^ o X

C) U

"co c D) (f) CO

b

8

6

4 -• (d)

: (c)

50 100 150 200 250

Temperature (K)

300 350 400

Fig. 18. DLTS spectra of a Pt contact on HVPE grown n-GaN, sputter deposited under 'low power, high pressure' conditions (curves c and d). For comparison we also include spectra of an electro-deposited Pt contact (curve a) and a resistively deposited Au contact (curve b). Curves a, b and c were recorded using filling pulse amplitudes of Vp = 2.2 V while for curve d, Vp = 2.4 V. All spectra were recorded using a filling pulse width of tp = 0.2 ms, a reverse quiescent bias of Vr = 2 V and a pulse frequency of f = 46 Hz.

depth of the level below the conduction band [68]. A further interesting phenomenon is observed when comparing curves c and d at temperatures above 350 K. It is clear that the increase in Vp (from 2.2 V for curve c to 2.4 V for curve d gave rise to a broad feature where the E06 is usually located. Its broadness indicates that this could be due to a band of defects close to the surface. Further low frequency or high temperature characterization is required to resolve this issue.

The results discussed here for sputter deposited SBDs on GaN follow the same trends as for Si and GaAs: firstly, the barrier height of sputter deposited is lower than those of contacts deposited by resistive deposition or electro-deposition (Section 4.3.4) — processes which do not introduce defects. Secondly, the barrier height of contacts deposited using a higher plasma pressure (15 mTorr) is higher than that of contacts deposited under 'normal' pressure (5 mTorr) conditions. In confirmation, DLTS revealed that 'normal' sputter conditions introduce more defects than high-pressure sputter deposition. This, in turn, can be explained by considering the energy of particles that impinge on the GaN during sputter deposition. Under higher pressures the mean free path of these particles are shorter and consequently the maximum energy that they gain before reaching the sample is lower. Consequently, particles from high-pressure plasmas create fewer defects in the GaN than particles from low-pressure plasmas.

In summary, sputter deposition of Schottky contacts on n-GaN generally results in SBDs with degraded rectification properties. The degree of degradation can be controlled by varying the sputter conditions, for example the gas pressure and sputter power. The SBD quality improves if they are deposited using low power and high-pressure conditions. Finally, remember that sputter deposition is frequently employed to provide better adhesion. The study of DeLucca et al. [70] showed that SBDs deposited at high


powers and low pressures exhibited good adhesion but poorer I-V characteristics, while for the diodes deposited at lower powers the opposite was true. It therefore seems that, depending on the application, a trade-off has to be made between obtaining good adhesion or good I-V characteristics.

4.3.3. Electron beam deposition It has been shown that, although sputter deposition is the method that yields the best metal adhesion to semiconductors, and is also useful in depositing stoichiometric compounds, it introduces defects at and below the surface of semiconductors, including GaN [63,70], which result in SBDs with degraded rectification properties. Electron beam (EB) deposition, on the other hand, is also widely used in the semiconductor industry, in particular where high melting point metals have to be evaporated. However, unless proper care is taken, it too introduces defects in the semiconductor because stray particles originating in the region of the filament or molten metal can impinge on the semiconductor surface. In this respect, the important difference between sputter- and electron beam deposition is that in the latter case defect introduction can be virtually eliminated by introducing proper shielding [71,72].

To study the defects introduced in GaN during EB deposition, Auret et al. [73] have used n-type GaN with a free carrier density of (2-3) x 10^^ cm~^, grown by metalorganic vapor phase epitaxy (MOVPE) on sapphire substrates. After conventional wet chemical cleaning, Ti/Al/Ni/Au (150 A/2200 A/400 A/500 A) ohmic contacts were fabricated [65]. Prior to Schottky barrier diode (SBD) fabrication, the samples were again degreased and dipped in an HC1:H20 (1:1) solution. Following this, circular Ru Schottky contacts, 0.6 mm in diameter and 50 nm thick, were evaporated on two identical GaN samples by EB deposition through a metal contact mask at a pressure of 2 X 10"^ mbar [73]. On the first sample, Ru was deposited at rate of 0.01 nm s"^ without shielding the GaN, and on the second sample it was deposited at a rate of 0.05 nm s~ whilst shielding the GaN from stray particles. For control purposes, Au SBDs were resistively deposited next to the EB deposited SBDs.

I-V measurements (Fig. 19) revealed that for unshielded EB deposited SBDs (curves b, the current at a 1 V reverse bias is 2 x 10"^ A. These characteristics are poorer than those of the resistively deposited Au diodes (curves a), but much better than those of a sputter deposited contact (curves d) on the same sample. The forward log (/) vs V characteristics of the unshielded EB deposited diodes are linear only between 10"^ A and 10~^ A. In this region the ideality factor and barrier height, calculated assuming thermionic emission, are 1.07 ±0.02 and (1.00 ±0.02) eV, respectively. From the shapes of curves b it is evident that in the low-current region recombination-generation (RG) currents dominate, whereas in the high-current region the series resistance limits the current. These I-V measurements confirm that, as for GaAs [71,72], EB deposition of Schottky contacts on n-GaN, without shielding it from stray particles originating at the filament, yields diodes with non-ideal rectification characteristics. Curve c in Fig. 19 was recorded from a diode that was shielded from the filament when metallizing at a deposition rate of 0.05 nm s'\ Its ideality factor and barrier height are 1.08 ± 0.01 and (1.08 ± 0.02) eV, respectively. No significant evidence of RG currents can be seen.

From a comparison of curves b and c in Fig. 19 it is clear that shielding the GaN from

280 Ch. 8 ED. Auret and 5.A. Goodman

0.2 0.8 1.0 0.4 0.6

Bias (V)

Fig. 19. I-V characteristics of resistively deposited Au contacts (curve a), EB deposited Ru contacts (curves b and c) and sputter deposited Au contacts SBDs (curve d) on n-GaN. 'F' and 'R' refer to the forward and reverse characteristics, respectively. Curve b and c are for contacts deposited at 0.01 nm s~^ without shielding, and at 0.05 nm s~^ with shielding, respectively.

the filament and depositing at higher rates, significantly improves the diode quality. This can be understood in that the GaN is exposed to energetic particles originating from, amongst others, a region close to the filament. These particles cause damage at and below the surface and this damage leads to the transport of charge by mechanisms in addition to thermionic emission, e.g. RG currents. When shielded from the filament and depositing at a high rate, the exposure of the surface to energetic particles originating at the filament is reduced and thus the concentration of defects that give rise to RG currents is reduced. On the other hand, when depositing without shielding the GaN from the filament and when depositing a low rate, the total particle dose on the GaN is higher and therefore more defects are introduced which, in tum, cause poorer I-V characteristics.

Fig. 20 depicts the DLTS spectra of control (resistively deposited) and EB-deposited diodes. Curve a shows that the control sample contained two defects, labeled E02 and E05, with energy levels at 0.27 ± 0.01 eV and 0.61 ± 0.02 eV below the conduction band, respectively (Section 2). Curves b and c in Fig. 20 show that after EB deposition, defects labeled Eel and Ee2 are detected. Note that in curves b and c the peak height of Ee2 has been reduced by a factor of ten with respect to that of Eel. These defects are produced by the particles impinging on the substrate during EB deposition. The energy and apparent capture cross section of Eel, as determined from Fig. 15, are (0.19 ± 0.01) eV and (1.2 ± 0.2) x 10"^^ cm^, respectively, while for Ee2 these parameters are (0.92 ± 0.04) eV and (7.9 d= 2) x lO'^^ cm^ respectively. As can be seen from Fig. 15 and Table 4, the DLTS signature of Eel matches that of ER3 well. ER3 is introduced in n-GaN during high energy (>MeV) proton [19] and He-ion irradiation [36]. ER3,


200

Temperature (K)

400

Fig. 20. Curve a: DLTS spectrum of resistively deposited SBD on epitaxial n-GaN. Curves b and c: DLTS spectra recorded from the EB deposited Schottky contact without and with shielding, respectively, using a filling pulse frequencies of 46 Hz and 0.1 Hz, as indicated. All spectra were recorded using a filling pulse width of 0.2 ms and amplitude of 1.6 V, superimposed on a quiescent reverse bias of 1 V.

Table 4. Electronic properties of defects introduced in n-GaN during electron beam deposition of Schottky contacts

Defect label

Eel Ee2

(eV)

0.19 ±0.01 0.92 ± 0.04

(cm^)

1.2 ± 0.2 X 10-^5

7.9 ± 2.0 X 10-^^

^peak

(K)

% 120 (46 Hz) % 350 (0.1 Hz)

Similar defects

ER3 [19], E [24]

^ Peak temperature at a lock-in amplifier frequency of 46 Hz, i.e. a decay time-constant of 9.23 ms.

in turn, is thought to be the same as a defect, labeled E, with a level at EQ —0.18 eV, observed by Fang et al. [24] after MeV electron irradiation of IVIBE-grown GaN. The energy level of the major EB deposition induced defect, Ee2, is similar to that of ER5 introduced during high-energy particle irradiation of GaN [36] which is as yet unidentified.

The depth distributions of Eel and Ee2 for unshielded deposited SBDs were calculated using the constant bias variable pulse DLTS technique. By applying a reverse bias of 1 V and increasing the pulse in steps of 0.1 V, a region up to 0.17 |xm below the interface could be probed. Fig. 21 shows that within this region the concentration of the prominent defect, Ee2, decreases from an estimated 1 x 10^^ cm"- just below the interface to 1 x 10 ^ cm~^ at 0.06 jxm into the GaN. Clearly, Ee2 will significantly reduce the free carrier concentration directly below the Ru/GaN junction at room temperature. Fig. 21 also shows that the concentration of Eel decreases from 2 x 10 ^ cm~^ just below the interface to 5 x 10 ^ cm"^ at 0.17 |jim into the GaN. The concentration of Eel is too low to significantly affect the GaN free carrier concentration. For shielded diodes deposited at 0.05 nm s~ the concentration of Ee2 is estimated (from Fig. 21) as about


1016

E

c

ro

C 1013 t

O

10^2

. Ee1:Ec-0.19eV

. EO2:Ec-0.27eV

. Ee2: E- - 0.92 eV

0.00 0.05 0.10 0.15

Depth below junction (microns)

0.20

Fig. 21. DLTS depth profiles of defects in as-grown n-GaN before EB deposition (E02), and after EB deposition without shielding (Eel and Ee2) of Ru SBDs.

4-5 times less than for unshielded diodes. The concentration of Eel (Fig. 21) is even more reduced than that of Ee2 with shielding and increased deposition rate.

Subsequently, the effects of forming Pt Schottky contacts on HVPE grown n-GaN with EB deposition have been investigated [70]. In this investigation no intentional screening was placed to protect the sample from stray particles. It was found that the I-V and C-V characteristics were poorer than those of electrodeposited contacts fabricated on the same epitaxial layer. DLTS showed that the same two EB induced defects, Eel and Ee2, that were detected in OMVPE grown GaN were also detected in the HVPE GaN after depositing the contacts. Their properties are included in Table 4.

In sununary, during EB deposition stray electrons impinge on the sample, introduce defects in it and result in degraded rectification properties of SBDs. The concentration of these defects, and thus the degree of device degradation, can be reduced by shielding the sample from these stray particles. When doing this, it should be borne in mind that the physical construction of EB deposition systems may be different and therefore each system has to be separately optimized. The governing principle here is that most of the particles originate in the region of the filament and molten metal. The effect of these stray particles can further be reduced by increasing the deposition rate. This reduces the particle dose onto the sample and hence the defect concentration, and consequently results in an increase in SBD quality.

4.3.4. Electrodeposition The motivation for employing this metallization method is two-fold [70]. First, it is thought that a cleaner, more intimate contact could be realized through the use of electrodeposition compared to physical vapor deposition methods, since electrodeposition could be performed in an acidic solution that could potentially remove the native oxide or other surface contaminants. Second, electrodeposition is a room-temperature process with extremely low processing energy (below 1 eV) [74]. DLTS results of


Pt Schottky contacts to n-lnP [75] and w-GaAs [76] indicated that concentrations of electrically active defects induced by the electrodeposition process are negligible compared to, for example, those of defects introduced during electron beam evaporation. In addition, the electrodeposited Pt/n-lnP contacts exhibited a much higher barrier height [75] than what is typically reported for contacts prepared by physical vapor deposition methods.

The suitability of electrodeposition for Schottky contact fabrication on GaN was recently demonstrated when Pt Schottky contacts, fabricated on the same HVPE grown n-type GaN by electrodeposition, electron beam evaporation, and DC magnetron sputtering, were studied [70]. The electrodeposited contacts were shown to produce significantly higher I-V and C-V barrier heights than most electron beam evaporated and sputter deposited contacts studied, with reverse currents reduced by three to four orders of magnitude.

In Fig. 22 we compare the DLTS spectra of Pt Schottky contacts deposited on the same HVPE grown n-GaN using DC magnetron sputter deposition, electron beam deposition and electrodeposition. This figure reveals that, whereas several defects are introduced during DC magnetron sputtering and electron beam evaporation, no detectable defects are introduced during electrodeposition.

The high barrier heights obtained using electrodeposition together with the fact that it

14 I I I I I I I I I I I I I I I r ' I

E02+ES3?

E06

( 3 ) , ^ ^ . . ^ . - ' ' ' ^ ^ ^

0 50 100 150 200 250 300 350 400

Temperature (K)

Fig. 22. DLTS spectra recorded using Pt Schottky contacts deposited on HVPE grown n-GaN by electro-deposition (curve a), electron beam deposition (curve b)), high-pressure low-power sputter deposition (curve c) and high-power low pressure sputter deposition (curve d). All spectra were recorded using a filling pulse width of tp = 0.2 ms, a reverse quiescent bias of Vr = 2 V, a filling pulse amplitude of Vp = 2.2 V and a pulse frequency of / = 46 Hz.


does not introduce defects, renders this method very suitable for the fabrication of high quality rectifying contacts to n-GaN.

5. Summary and conclusions

High energy particle irradiation introduces several electron traps in n-GaN with energy levels between 0.06 and 0.95 eV below the conduction band. Some controversy surrounds the nature of the most frequently level at 0.20 eV. It has recently been shown that the DLTS signal of this level can be deconvoluted into at least two levels. One of these is a shallow donor at EQ —0.06 eV which has previously been assigned to the VN-The origin of the deeper lying defects is not clear yet. All the observed high energy irradiation induced defects anneal out at 700 K.

Resistive (Joule) evaporation and electrodeposition of metals do not introduce defects in semiconductors. However, two other metallization processes, E-beam and sputter deposition, were shown to introduce electrically active defects in GaN. Both these processes introduce a defect with a level similar to that of ER3, believed to be related to the nitrogen vacancy. In addition, each of these processes introduces defects characteristic to the process. The concentration of these process induced defects can be minimized by optimizing the deposition conditions. For sputter deposition this can be achieved by minimizing the deposition power and maximizing the plasma pressure. In the case of E-beam evaporation, the geometry of the e-gun with respect to the sample position should also be taken into account. Finally, the thermal stability of these metallization induced defects has not yet been reported. This, in conjunction with the thermal stability of the Schottky contacts, is required to assess whether or not post-deposition annealing can remove the defects responsible for diode degradation.

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[61] X.A. Cao, S.J. Pearton, A.P Zhang, G.T. Dang, F. Ren, R.J. Shul, L. Zhang, R. Hickman and J.M. Van Hove, Appl. Phys. Lett. 75, 2569 (1999).

[62] L.I. Maissel. In: L.I. Maissel, R. Glan (Ed.), Handbook of Thin Film Technology, Vols. 1-4, 1970, McGraw Hill, New York.

[63] F.D. Auret, S.A. Goodman, F.K. Koschnick, J.-M. Spaeth, B. Beaumont and P. Gibart, Appl. Phys. Lett. 74, 2173 (1999).

[64] P Hacke, T. Detchprohm, K. Hiramatsu and N. Sawaki, Appl. Phys. Lett. 63, 2676 (1993). [65] S. Ruvimov, Z. Liliental-Weber, J. Washburn, K.J. Duxstad, E.E. Haller, Z.-F. Fan, S.N. Mohammed,

W. Kim, A.E. Botchkarev and H. Morkoc, Appl. Phys. Lett. 69, 1556 (1996). [66] E. Grussell, S. Berg and L.R Andersson, J. Electrochem. Soc. 127, 1573 (1980). [67] D.A. Vanderbroucke, R.L. van Mierhaegte, W.H. Lafrere and F. Cardon, Semicond. Sci. Technol. 2,

293 (1987). [68] F.D. Auret, G. Myburg, S.A. Goodman, L.J. Bredell and WO. Barnard, Nucl. Instr. Meth. Phys. Res.

B 67, 411 (1992). [69] Q.Y. Ma, M.T. Schmidt, X. Wu, H.L. Evans and E.S. Yang, J. Appl. Phys. 64, 2469 (1988). [70] J.M. DeLucca, S.E. Mohney, F.D. Auret, S.A. Goodman, J. Appl. Phys., submitted. [71] FD. Auret, G. Myburg, H.W Kunert and WO. Barnard, J. Vac. Sci. Technol. B 10, 591 (1992). [72] G. Myburg and FD. Auret, J. Appl. Phys. 71, 6172 (1992). [73] F.D. Auret, S.A. Goodman, F.K. Koschnick, J.-M. Spaeth, B. Beaumont and P Gibart, J. Phys. B

273-274, 84 (1999). [74] H. Hasegawa, Y. Koyama and T. Hashizume, Jpn. J. Appl. Phys. 38 (1), 2634 (1999). [75] H. Hasegawa, T. Sato and T. Hashizume, J. Vac. Sci. Technol. B 15 (4), 1227 (1997). [76] N.-J. Wu, T. Hashizume and H. Hasegawa, Jpn. J. Appl. Phys. 33 (1), 936 (1994).


CHAPTER 9

Residual stress in III-V nitrides

Nora V. Edwards

1. Introduction

A preliminary goal of this chapter is to convince the reader that residual stresses have a profound effect on nitride optical data. And since these materials are being heavily developed for opto-electronic applications, the presumption is that anything affecting nitride optical properties to such a large extent should be investigated, at the very least so that such perturbations can be eventually eliminated or exploited to improve nitride-based LED and laser diode performance.

Such an investigation will naturally center around the fundamental ways that stress affects the optical properties of a material, but we will also be concerned with the materials and growth parameters that produce such stresses in the first place. That having been done, we will also examine the extent to which it has been possible to manipulate residual stresses in these materials, with the goal of improving optical properties. We will focus on GaN films and will largely ignore the non-negligible role that defects and impurities (readers interested in this topic should see, for example, Kisielowski et al. [1] and Gorczyca et al. [2]) play in this drama. This is justified for the simple reason that the strain states of even the most rudimentary GaN heterostructures are not at all well-understood and that we must master the simplest case before proceeding to more complex combinations of materials. In short, we must learn to walk before we can run.

It is a simple matter to establish that residual stress readily perturbs GaN optical properties. We demonstrate with a collection of selected GaN low-temperature reflectance lineshapes [3] (Fig. 1) obtained from films grown under a variety of conditions. At the time of publication, researchers were interested in obtaining the 'proper' value of the critical point energies of the A, B, and C excitons — which are closely tied to the strain-sensitive valence band structure — from the extrema of the peaks shown. We immediately see that there is no simple recipe for extracting such information. The number and position of the peaks vary in almost each case, where each case again represents a GaN film grown under a different set of heterostructure design and growth conditions. The focus of this chapter will revolve around two seemingly simple questions: how is this selection of lineshapes possible for a single material? and more pointedly, why does this range of phenomena occur? We will, where possible, address these questions from both a phenomenological and fundamental perspective.

Prior to proceeding with the optical data, we maintain that it is absolutely crucial to

288 Ch.9 N.V.Edwards

3.40 3.45 3.50

E(eV) 3.55

Fig. 1. Selection of representative GaN reflectance lineshapes (10 K) designed to show that samples with different states of strain have different optical properties. Samples were grown under a variety of conditions representing different combinations of the following: substrates, buffer layers, growth temperatures, and growth techniques.

examine the physical structure of the samples that are being measured. Accordingly, the next section is a summary of the basic physical issues affecting the state of strain in the GaN films that were used to generate the seminal optical data. Because much has been learned lately about nitride physical properties and growth mechanisms — certainly since the first reflectance data were taken by Dingle et al. in 1971 [4] and even since the renewal of interest in such spectra in the mid-1990s — we in hindsight have the information necessary to decode these data that were largely unavailable to the workers initially investigating the problem. Indeed, during the course of this chapter we shall see that a lack of information about the physical properties of the material has been the source of considerable misunderstanding about strain behavior in the GaN literature. Indeed, we will use these structural and related materials issues to explain: • why the GaN optical data was an initial source of confusion; • why the trends in residual stress for GaN films were discovered to be contrary to

conventional wisdom; and • why unusual growth strategies — beyond what has been necessary to manage residual

stresses in traditional III-V strained layer systems — have been necessary to move the material forward technologically.

Residual stress in III-V nitrides Ch. 9 289

2. Basic physical issues surrounding GaN heteroepitaxy

2.1. Introduction

We will begin our discussion with a bit of history. To understand residual stress behavior in GaN films — and indeed to understand the evolution of the material from cracked, rough films to the foundation of viable commercial products — it is instructive to first tell the story of the humble AIN buffer layer that assisted this transformation. Though nitride stress-control methods have evolved beyond this relatively simple strategy, the story of the initial struggle to achieve specular GaN films highlights some crucial materials issues pertaining to residual stress behavior for a variety of nitride structures. Because GaN substrate material was not and still is not available commercially, it has been necessary to insert a thin layer of AIN between the GaN film and the two conmion substrate choices, Qf-Al203 or 6H-SiC. Other substrate materials have been tried but with less success. Among these are Si, GaAs, NaCl, GaP, InP, W, Ti02, ZnO, LiGa02, MgAl204, MgO, and ScAlMg04. See Hellman et al. [5] for more details. Not surprisingly, buffer layers are meant to minimize the considerable mismatch between film and substrate. But the physical structure of the constituents of nitride heterostructures often makes what should be simple mediation into a far more complex matter. In this section we will focus upon issues surrounding (a) lattice mismatch, (b) buffer layer morphology and initial film growth, and (c) thermal mismatch behavior for four materials: GaN, AIN, 6H-SiC and a-Al203. These are three interrelated issues that largely dictate the state of strain in GaN heteroepitaxial films.

While the materials issues surrounding the achievement of specular GaN films are naturally more our concern than the historical picture of its development, we mention nonetheless that GaN films were actually achieved as early as 1969 [6] in order to illustrate the importance of the AIN buffer layer. This is because further developments — beyond the initial growth of HVPE material [6] and other key achievements [7-9] in the early 1970s — were stymied until quite recently by poor morphology and difficulty with the control of impurities [10]. To be balanced in our treatment we must observe that the solution of the problems conceming the control of n-type conductivity [11] and with the activation of holes in Mg-doped material [12,13], were watershed innovations that enabled the current frenzy of nitride development. But before these issues could even be addressed, specular films needed to be achieved. Key developments in this area are summarized in Table 1 [11,14-21].

The buffer layer mediates mismatch by different mechanisms, depending on the substrate material. These differences, not surprisingly, are the source of the further differences that we will encounter between the two heterostructure systems with respect to both optical and residual stress behavior. For growth on 6H-SiC, the buffer layer appears to be a true mediator of lattice mismatch, while for growth on sapphire it acts more like a 'platform' for epitaxy. The high-resolution transmission electron micrograph of the substrate-buffer layer interface [10] for both materials shown in Fig. 2 is clearly indicative of differences in each that must be occurring during buffer layer growth. The transition between the AIN buffer layer and the sapphire substrate is abrupt and yet incoherent, though the AIN layer is still generally considered epitaxial. Indeed, the film

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quality manages to be quite high without a direct, one-to-one correspondence between the two lattices. In contrast the 6H-SiC/AlN interface is coherent and is indicative of the relative similarity in lattice structure between the two materials [10].

2.2. Lattice mismatch

The simplest way to view strain is from the perspective of lattice mismatch, where we are concerned with the quantity Aa/a or Ac/c, where a is the lattice parameter in the [1120] or the [1010] direction and c is its counterpart in the [0001] direction, given that the most common phase of GaN and AIN crystallizes in the wurtzite structure. The mismatch itself is defined as Aa/a = [ caN — ÂIN]/<ÂIN, for example, for the simple case of GaN grown on a layer of AIN. We will examine two heteroepitaxial systems (GaN/AlN/6H-SiC) and (GaN/AlN/AÔs), neither of which have lattice-matched components. In the simple picture of film growth advanced by Frank and van der Merwe [22], if an epitaxial layer is grown on top of a substrate that has a smaller (or larger) lattice parameter, growth will proceed pseudomorphically, that is, with the deposited film strained to have the same interatomic spacing as the substrate. The total elastic strain energy will increase with increasing film thickness until a critical thickness is reached, where a misfit dislocation that relieves this strain will be created. This extends along the interface in lieu of the plane of atoms that was removed (or inserted). One cannot remove or insert planes of atoms instantaneously, however. There will be a


boundary where the extra plane of atoms were removed (or added) and where the epitaxial layer has not yet relaxed. In the simplest scenario, this is called a threading dislocation, though other sorts of defects are possible [23]. Since all of these defects to some degree are detrimental to device performance, the issue of strain created by lattice mismatch is of keen interest to the nitride community.

In this discussion, we will be presenting lattice parameter data as a function of temperature (and later, coefficient of thermal expansion data as a function of temperature) as though they were a fait accompli; we do so to streamline the arguments concerning the physical origin of stresses in GaN films. In fact the reader should be armed with the preliminary information that this has been a controversial area of research since the achievement of specular nitride films. We refer interested readers to an excellent series of references that provide a de facto summary of the majority of the temperature dependent work done for the materials involved in GaN heterostructures: Wang and Reeber for AIN (theoretical calculation) [24]; Aldebert and Traverse for AI2O3 (neutron time-of-flight diffraction on polycrystalline material) [25]; Reeber and Wang for GaN (neutron powder diffraction plus theoretical calculation) [26]; and Reeber for SiC (calculation) [27] (see also Ref. [28]]. We will be primarily concerned with basal plane (i.e. tz-plane) values in this section, but c-plane values are contained in these references as well. Readers interested in single temperature measurements on epitaxial films that address the very significant problem of the variation of GaN lattice parameter with growth technique, substrate choice, and free electron concentration can consult, as a starting point, Leszczynski et al. [29] and a review by Kisielowski [30].

In Fig. 3a,b we have plotted the basal plane (a-plane) lattice parameters vs. temperature [24-28] for materials involved in growth on SiC and AI2O3 substrates, respectively. The scales are the same in (a) and (b) to allow for ready comparison; fine-scale plots for the individual materials are given in (c) through (f). The data in (a) readily indicate that AIN is a good choice for mediating the mismatch between the GaN and the SiC; in fact, this mismatch is reduced by around 1% across the temperature range shown, with a slightly larger reduction (1.5%) at the growth temperature (^^1350 K) [21]. Table 2 gives the specific values of lattice mismatch (e.g. mismatch = [acnN — ÂIN]/ÂIN) for this heterostructure at the experimentally relevant temperatures for producing strain in the system: (1) growth [^^1350 K], (2) cooling [298 K], and (3) measuring strain via optical data at low temperatures ['^10 K]. So instead of the full ^^3.6% the GaN actually experiences a ^^2.5% compressive mismatch to the AIN in the three temperature zones. Structurally, the match is almost ideal: GaN and AIN both have the wurtzite structure with the standard 2H stacking sequence while the SiC substrate has a hexagonal structure with a 6H stacking sequence. The physical arrangement of the lattices is shown in Fig. 4. Here only the SiC substrate and the AIN buffer are shown for clarity but nevertheless we know that the GaN would simply stack in a similar fashion above the AIN, as they have the same structure and stacking arrangement. This, of course, explains the coherent interface for AlN/SiC seen in Fig. 2.

By contrast the data in Fig. 3b clearly indicate that the AIN buffer is not a lattice mismatch-mediating layer for growth on sapphire. It must be serving a purpose of another kind. Indeed, for this case not only is the a-plane lattice parameter of AIN [24] far smaller than that AI2O3 [25], it is also slighdy smaller than that of


Table 2. Basal plane (a) mismatches using data from for GaN (Reeber and Wang, Ref. [26]), AIN (Wang and Reeber, Ref. [24]), and 6H-SiC (Reeber, Ref. [27,28])

a

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GaN [26]. To complicate matters further, the buffer does not even have the same crystal lattice structure as the substrate. While we have established that GaN and AIN both crystallize in the wurtzite structure, a-Al203 is actually rhombohedral, with an orientation relationship defined in Fig. 5. Take special note of the fact that the a-axis of GaN is inclined at an angle of 30° to that of sapphire, introducing additional complications. So, in addition to the rather sizeable lattice mismatch between buffer and substrate there is also a 30** basal plane misorientation with which to contend for this substrate choice. This physical arrangement casts doubt on a simple lattice mismatch picture of strain behavior for this system (and hence the omission of a corresponding mismatch table), though readers interested in this perspective can certainly calculate the mismatches at different temperatures from Fig. 3c-f. But before any effort is invested in such a calculation, it would be wise to proceed to the following section on buffer layer morphology and initial film growth mechanisms. It is certain to discourage a purely lattice mismatch-based view of the strain behavior in GaN/AlN/AliOs heterostructures.

2.3. Buffer layer morphology and initial film growth mechanisms

The mismatch scenario for growth on sapphire lends itself to a rather unusual buffer layer morphology (Fig. 6) [18] that at first glance has more in common with the amorphous low-temperature nucleation layers developed for heteroepitaxial growth of GaAs on silicon [10,31,32] than with the AlN/6H-SiC system. Indeed, at relatively low deposition temperatures (600*'C) AIN growth on sapphire is amorphous, but when the temperature is elevated to the growth temperature of the GaN layer (1030°C), the buffer crystallizes via solid phase epitaxy to become a layer with a high density of slightly misoriented columnar structures, each with a diameter of about 10 nm (Fig. 6,

294 Ch.9 N.V Edwards

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Fig. 4. Crystal structure and stacking arrangement of 6H-SiC and AIN. Figure courtesy of J. Birch, Linkopings University.

Step 1). These in turn act as nucleation sites for GaN, creating a 'faulted zone' of fine columnar crystallites similar in structure to the AIN. These extend for a thickness of around 50 nm, approximately the same thickness as the underlying buffer layer (step 2). It is believed that these crystallites undergo geometric selection via grain orientation competition mechanisms until an oriented domain structure emerges, with the columns arranged such that the c-axis of each is in the direction normal to the surface (step 3). As the growth front area of these crystals increases, trapezoidal islands emerge, as shown in step 4. Step 5 involves the lateral growth of these islands, where larger trapezoidal crystals engulf the smaller islands to form the 'semi-sound-zone'. It is proposed that the lateral growth proceeds at a much higher rate than growth along the c-axis, leading to the coalescence of the islands and eventually resulting in a smooth, uniform film, labeled the 'sound zone' in step 6 [18]. But the misorientation in the crystalline AIN layer is present in the overlying film as well, resulting in a GaN film with low-angle grain boundaries [33]. Interestingly, growth on sapphire with GaN buffer layers proceeds in an analogous fashion. In fact, growth mechanism models very similar to the one described for AIN buffers have been proposed and are generally accepted [34-37]. There have even been reports of constant levels of tensile strain during growth that remain invariant.


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(•^-^203) Fig. 5. Basal plane orientation of sapphire and GaN. Note the 30° misorientation between the two.

regardless of whether GaN or AIN buffer layers were used, for growth on sapphire [35]. Despite the open question regarding the origin of this strain, it nevertheless seems that the buffer in this system, regardless of material, acts more like a wetting layer or an epitaxial platform than a true mediator of lattice mismatch.

By contrast the morphology of AIN buffers grown on 6H-SiC substrates is relatively unremarkable, if the proper growth conditions are observed ([20,39], also see Ref. [40]). But if the dependence of AIN buffer layer morphology on growth temperature is investigated, we see ranges of behavior that actually have features in common with the mechanism for low-temperature AIN growth on sapphire. A key difference is that a window of growth parameters exists that eliminates the polycrystalline buffer layer morphology, presumably due to superior lattice matching in the AlN/6H-SiC system. This is achieved by depositing the buffer layer at high temperatures. Indeed, like growth on AI2O3, AIN layers deposited in the 500-1050°C range on 6H-SiC are polycrystalline. But unlike the sapphire-based system, GaN deposition on these layers yields random nucleation and growth of isolated islands that do not coalesce into a smooth layer. But at temperatures greater than 1100°C, monocrystalline buffers and films — without misorientation or low angle grain boundaries — are achieved ([20,39], also see Ref. [40]). This is presumably due to increased surface mobility of adatoms and the slightly decreased mismatch between GaN and AIN at the relevant growth temperatures (cf. Table 2 and Fig. 3a). The initial growths of these films have superficial similarity to the GaN films grown on sapphire in that the nucleation and coalescence of two-dimensional islands occurs after around 1 min of growth, with growth being layer-by-layer thereafter. The difference is that this process takes only about 400 A to occur on a 6H-SiC substrate ([20,39], also see Ref. [40]), as opposed to the --2000 A required for growth on AI2O3


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(cf. Fig. 6). This tendency toward island formation and lateral growth is an interesting aspect of nitride behavior that in the worst case has created confusion about strain behavior, stymied crystal growers and, as we shall see, in the best case made various schemes for stress management (in addition to quantum dot structures) possible.

2.4. Thermal stress

At the respective growth temperatures, then, GaN films in 6H-SiC-based heterostruc-tures are expected to be in compression, while those based on AI2O3 appear to grow


in tension. But it is well known that GaN films measured at room and low temperatures typically exhibit the opposite behavior: heterostructures with AI2O3 substrates are usually in compression [4,41-46] while those with 6H-SiC are typically in tension [41,47-50]. To explain these phenomena the thermal behavior of the respective materials must be invoked. The large scale needed in Fig. 3a,b to accommodate the dramatically larger lattice parameter of AI2O3 gives the impression that temperature effects might be minimal for these systems. They are actually quite dramatic, or rather, the growth and cooling processes span the temperature range where the most dramatic changes in the lattice parameters occur. This dependence is evident in a closer look at Fig. 3c through 3d, also from Refs. [25-28].

Another way to show these variations is to plot the respective basal plane coefficients of thermal expansion for AI2O3- and 6H-SiC-based heterostructure systems [25-28]. We show such plots in Fig. 7a and 7b, respectively. The first notable feature of any of the materials in either (a) or (b) is the nonlinear character of a over the relevant temperature range (10 K to --1400 K). This may not seem remarkable, but it means that the common practice of using room temperature values of of (of = 5.59 x 10~^/K over the temperature range from 300 to 900 K [6] for GaN is often used, for example) for each material in heterostructure strain analysis does not adequately convey the extent to which these materials expand and contract upon heating and cooling. This is the equivalent of using a linearized value of ot to calculate strain, in lieu of the more complete expression

^ \T2-TI JTI

that a nonlinear a requires. We will see that this simplified approach has been the source of misunderstanding about strain behavior for growth on 6H-SiC. The misunderstandings are discussed and analyzed in more detail in Edwards et al. [51]. Also see Sect. 'Stress trends for nitride heterostructures' of this chapter.

We can say at the outset that the thermal behavior of AIN makes it difficult in some cases to provide pat, easy answers about stresses originating from thermal mismatch in these heterostructures. More specifically, it seems to play a role more complex than simple mediation. In both Fig. 7a and 7b we see that for temperatures greater than 547 K, QfAiN > QfGaN- At tcmpcraturcs lower than this value, the reverse is true. We have stated that conventional wisdom in this field used to be that GaN grown on AIN/AI2O3 is in compression, while similar films grown on 6H-SiC are in tension. If we examine Fig. 8a, we see how this might be the case for growth on AI2O3. Here the basal plane a of AI2O3 dominates that of the AIN and GaN. Upon cooling, the AI2O3 layer experiences a greater rate of contraction than the two overlying layers, creating a considerable compressive strain, providing there are no significant relief mechanisms (e.g. cracking) to compensate. As we have noted, empirical evidence indicates that in spite of or the absence of such mechanisms largely leave the samples compressively strained [4,46-51]. We will see in Section 5 that residual stress states for growth on 6H-SiC has thus far proven to be more subtle. On the whole, we have a situation where the two overlying layers experience a faster rate of contraction than the substrate, creating a net tensile stress in the GaN layer. But being a closer thermal match to the


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Fig. 7. Coefficient of thermal expansion in the fl-plane for (a) for GaN (Reeber and Wang, Ref. 26), AIN (Wang and Reeber, Ref. 24), and 6H-SiC (Reeber, Ref. 27); (b) for GaN, AIN and AI2O3 (Aldebert and Traverse, Ref. 25); (c) and (d) are analogous data in the c-plane from the same references. Reprinted with permission.

Residual stress in III—V nitrides Ch. 9 301

D

«

Coefficient of Thermal Expansion (c)

--—6H-S1C''

-•— GaN'

400 800 1200 1600 2000

T(K)

Fig. 7 (continued).

3.40 3.44 3.48 3.52

ENERGY (eV)

3.56 3.eo

Fig. 8. The seminal low-temperature (2 K) reflectance lineshape for GaN. The relevant polarization state is the a (E ±c,k c), used to obtain the energy position of the A exciton £ A = 3.474 ±0.002 eV and A-B and A-C excitonic splittings AEBA = 6.0 and AECA = 20.5 meV, respectively. Reprinted with permission from Dingle et al. [9].


other layers compared to the sapphire case, the SiC layer does not always dominate; we will see that other strain states are possible, likely due to the interplay between GaN and AIN at the growth and at room temperatures. To make matters worse, this interplay is more exaggerated in the c-direction. As expected for anisotropic (i.e. non-cubic) materials, the materials do not even expand and contract in a similar fashion in the a-and c-directions. For all of the materials a« > ac, except AI2O3, where «« < occ, and for 6H-SiC, where «« > oic [24-28]. The result of this is a compounded degree of complexity in the GaN/AlN/6H-SiC system; as stated, the interplay between the ofs of the layers is even more complex in the c-direction, as seen in Fig. 7d. Here we see that there are two crossover points in this system instead of the one at '^547 K seen with AIN and GaN in the (^-direction (Fig. 7a,b). There is one with GaN and AIN, where at T < ~647 KÂiN < cifGaN ûd the reverse is true above this temperature and another at r = ^^1201 K, where asic < otQaN below this temperature and is greater above it. Since films and buffer are grown at 1323 K (1100°C) and 1373 K (1050X), respectively, the SiC-based system passes through both crossover points upon cooling. This, again, can be contrasted to the case of sapphire-based growth (Fig. 7c), where the a of AI2O3 is so mismatched, i.e. so much greater than the others, that the interplay between GaN and AIN is in all likelihood obscured by it in the majority of cases. However, the implications of how the c-plane behavior complicates matters through the considerable anisotropics that we have seen (and its impact on issues such as variations in nitrogen vacancy concentrations via disturbances in c/a, for example) are not yet clear and have been investigated by several research groups [29,30,44,52,53]. For our purposes, the simple message is: thermal behavior in even these basic heterostructures is complex and the understanding of it is incomplete, and predicting stress behavior in GaN films is a far larger matter than merely comparing room temperature values of a. We will now turn our attention to the impact that this and the other two interrelated origins of strain — lattice mismatch and island coalescence behavior — have on GaN optical data.

3. Stress-related ambiguities in GaN optical data

3.1. Introduction: discussion of problems

The optical behavior of GaN is quite similar to that of CdS, which was studied extensively by Thomas and Hopfield in the early 1960s [54,55]. For this material the triply degenerate (6-fold degenerate with spin) states at /: = 0 are split by a combination of the crystal-field potential and the spin-orbit interaction into three singlet levels (doublets with spin included) whose associated excitons are labeled A, B, and C in order of increasing transition energy.

The appropriate group theory and the general procedure for determining these levels in terms of the crystal-field and spin-orbit interactions were also detailed by Hopfield [56]. For GaN, if the crystal-field potential were the only operative interaction the selection rules for light normally incident along the c-axis are such that only the A and B excitons would be observed. With the spin-orbit interaction included the B transition becomes weaker and the C transition becomes allowed, but only weakly. The strain caused by biaxial stress in the plane of the surface for films with the c-axis normal to the surface


Table 3. Early excitonic splittings observed for GaN heterostructures

Ref.

[4] [57] [58] [41] [59] [60] [61]

Authors

Dingle et al. Monemar et al.

Harris et al. Shan et al.

Mohammed et al. Gil et al.

Pakula et al.

Year

1971 1974 1995 1995 1995 1995 1996

Â

3.474 3.4751 3.488 3.485

3.4831 3.4775 3.4780

EE

3.480 3.4815 3.495 3.492 3.4896 3.4845 3.4835

^c

3.501 3.493 3.506 3.518 3.518

3.5062 3.502

ÊBA

6.0 6.4 7.0 7.0 6.5 7.0 5.5

AEBC

21.0 12.0 11.0 26.0 28.0 21.7 18.5

has the same symmetry as the crystal-field potential and can be treated as an additive effect. Accordingly, researchers measuring this material generally expect to see three excitons in low-temperature optical data corresponding to these physical perturbations.

The seminal low-temperature reflectance data obtained by Dingle and coworkers [4] in 1971 conformed to this expectation. It is shown in Fig. 8 to illustrate. The relevant polarization state is the a (E ± c,k c), used to obtain the energy position of the A exciton EA = 3.474 ± 0.002 eV and A-B and A-C excitonic splittings A£'BA = 6.0 and AEcA = 20.5 meV, respectively. These were obtained, it seems, by assigning the values at peak extrema. Such values were representative of data obtained on 100 [xm thick samples that had free electron concentrations of ^^10^^ cm~^ and mobilities >300 cm^/Vs. They were grown by 'vapor epitaxy' on (OOOl)-oriented sapphire substrates, with no buffer layer [4]. Later research groups confirmed the observation of three free excitons, with some variation in peak positions and splittings, as shown in Table 3 [4,57-61]. The only conspicuous deviation in A^BA values is the one from Ref. [61]. By way of explanation we note that except for the data on bulk GaN obtained by Pakula et al. [61] all of the data were obtained on GaN heterostructures with sapphire substrates. On the other hand, among this seemingly similar material we see that the A^BC values given by Monemar [57] and Harris [58] are in some cases half as large as the other values, obtained on material producing a very broad linewidth for the C transition. Gil [60] noted that perhaps there was a misinterpretation of the data in these cases, but without a definitive lineshape analysis for the material, it was difficult to say which interpretation was correct.

New data for GaN growth with 6H-SiC substrates complicated matters further. We see that there was even a small amount of controversy surrounding the data taken from material on sapphire substrates, where interpretation of relatively similar lineshapes eased matters. For this new heterostructure, initially, only two excitonic features were seen. Some of the earliest data were taken with spectroscopic ellipsometry, where two broad, closely spaced excitonic features in the vicinity of the fundamental absorption edge were observed in narrowband (3.3-3.6 eV) room temperature spectra. Representative spectra are shown in Fig. 9a [62], with data taken on a sample with a sapphire substrate included for comparison. Here the imaginary part of the pseudodielectric function vs. energy of GaN layers grown on AI2O3 (upper curve) and 6H-SiC (lower curve) substrates is shown. Again, it is clear that GaN layers grown on different substrates have different optical properties: the excitonic features in the

304 Ch.9 N,V.Edwards

A CM

V

2 h GaN on 6H-SiC:

oh 18meV

3.35 3.40 3.45

E(eV)

3.50

3.44 3.46 3.48 3.50 3.52 3.54 PHOTON ENERGY (eV)

3.56

Fig. 9. Imaginary part of the pseudodielectric function of GaN layers grown on AI2O3 (upper) and 6H-SiC (lower). The spectra were taken with a resolution of 2 meV. Reprinted with permission from Edwards et al. [62]. (b) One of the first low-temperature reflectance lineshapes obtained for GaN grown directly on 6H-SiC. The relevant curve is the top in the series; the other two curves are derivative reflectance (middle) and photoluminescence spectra (bottom). Reprinted with permission from Buyanova et al. [47].


upper curve are separated by ^7 meV, consistent with other values reported in Table 3, while at 'ÎS meV the excitonic splitting observed for the material on 6H-SiC is much larger. Note the conspicuous lack of a third excitonic feature compared to the seminal lineshape shown in Fig. 8. Of course, the observed features were broad, as the data were taken at room temperature. But without a third excitonic feature, it was not possible to use emerging perturbation theory calculation [62] of the variation of the A, B, and C absorption thresholds as a function of crystal field and biaxial stress potential (the Hopfield Quasicubic Model [56]) to assist in spectral interpretation. This was the case because of the ambiguity associated with the fact that Vspin orbit is obtainable from the excitonic splittings only by solving a quadratic equation, by necessarily has two roots (See Ref. [62]). Further, it could be argued that there was simply not enough data — or rather, data with dissimilar enough strain states — to provide a solid basis for the fitting procedures in the calculations. (Interested readers can look ahead to the significant scatter in the values of fit parameters ACF and ASO prior to 1997 to confirm this; see Table 5.) In short, it was unclear whether the same optical transitions in both cases in Fig. 9a were being observed. Work at low temperatures, to try to resolve a third feature, was necessary to resolve this issue.

Shortly thereafter, Buyanova and coworkers [47] obtained low-temperature reflectance data on a 3.9 |xm GaN film grown directly on 6H-SiC. Surprisingly, they also could not find any evidence of a third resonance. The spectra are shown in Fig. 9b, the top curve in the series. This did not resolve the controversy, as it was not possible to determine whether the B-A excitonic energy separation with an unresolved C exciton or an unresolved B-A splitting with a resolved C were being observed. A coherent lineshape analysis for GaN was sorely needed, as were a greater variety of strained samples to lift the ambiguity from the perturbation theory calculations.

3.2. Solution: Fourier analysis plus heterogeneous sample set

Such a study was published a year later by Edwards et al. [3] that undertook this task. The problem was addressed first by studying GaN layers designed to represent the widest range of residual in-plane strain that were available at that point and second by analyzing lineshapes in reciprocal space, where critical point energies can be determined independent of baseline artifacts to ±0.5 meV. Fourier analysis is especially suited to the challenges presented by this particular problem, as the technique can be used to determine critical point (CP) energies even if real-space lineshapes are not known a priori. This follows because baseline effects, information, and noise are localized in the low, middle, and high Fourier coefficients, respectively, ensuring that spectral information can be extracted independent of baseline and noise artifacts. In reciprocal space, critical point parameters also divide into 2 groups: one associated with the amplitude and one with the phase, which reduces correlations during least-squares fitting. In particular, the parameter associated with the CP energy appears only in the phase. The Fourier coefficients, then, are typically described according to the complex representation C„ = C„ exp(—/$„), where C„ is the amplitude of the coefficients, and „ is the phase. Further advantages of fitting optical data with Fourier analysis and details of specific procedures are given elsewhere, by Yoo et al. [63] and by Aspnes [64].


0.25

0.20

^ 0.15

0.10

3.44 3.48 Energy [eV]

3.52

-2 I-

- T

E^ + 0.3 meV

E = 3.4764 eV

20 40

n 60 80

Fig. 10. (a) Reflectance data (points) and real-space fit results (solid line) from Baranowski et al. [65], obtained from a homoepitaxial GaN sample. Location of excitonic CP energies obtained by Fourier analysis, done in this laboratory, are indicated by the arrows. Vertical lines denote division of the spectrum into sections isolating CPs for more accurate analysis, (b) Top half, solid line: ln(C„) of the selected data segment under analysis. Dashed line: variation of ln(C„) for a single CP representation. Bottom half, solid line: „ of the segment. Central dashed line: „ for a single CP representation for EQ = 3.468 eV. Dotted lines: variation of „ for EQ = 3.4764±0.0003 eV. Both reprinted with permission from Edwards et al. [75].

To demonstrate the efficacy of the technique, we show the comparison of Fourier analysis results to that which is still is regarded as one of the more sophisticated real-space fits for GaN reflectance spectra. Fig. 10a features such a comparison. The points represent data obtained from a homoepitaxial GaN layer, taken from Baranowski et al. [65] and the thin solid line corresponds to the results of their relatively elaborate real-space fit, including polariton effects. (A more current 'strain-free' value of the A exciton can be found in Komizer et al. [66]. Strain-free is in quotation marks because there has been considerable discussion over the degree to which homoepitaxial films are without stress. See Monemar [67].) Further details of the fit are given elsewhere [68]. The vertical lines denote the division of the spectrum into sections isolating the CPs for more accurate analysis in reciprocal space.

Residual stress in III-V nitrides Ch.9 307

Excitonic CP energies from the real-space fit were EA = 3.4767, E^ = 3.4815, and Ec = 3.4987 eV, with no uncertainty specified. CP values determined by Fourier analysis are as indicated by the arrows in Fig. 10a: 3.4764, 3.4822, and 3.4983 eV, respectively, all determined to within ±0.5 meV. The degree of agreement with the real-space fit is excellent ( A £ A = 0.3 meV, AEB = 0.7 meV, and AEQ = 0.4 meV). Even so, to further demonstrate the capabilities of the technique, we show that Fourier analysis can be used to determine CPs to accuracies of the order of magnitude of these small differences, as illustrated in Fig. 10b. Shown is a plot of ln(C„) and §„ vs. n, the index of the Fourier coefficients. The linear behavior of both ln(C„) and ^„ implies for the former that the lineshape of the dominant exciton is Lorentzian and for the latter that this excitonic CP energy is the energy of the inversion origin, here 3.4764 eV. The dotted lines here demonstrate the degree of accuracy associated with this determination, quite conservatively expressed as Ep, = (3.4764 ± 0.0003) eV. Even a 0.3 meV derivation from the fitted EA value yields a line with a finite slope, in contrast to the zero slope that occurs when the inversion origin equals the CP energy. Uncertainties are uniformly given as 0.5 meV in the following discussion to account for the variation of the individual uncertainties of the 45 excitonic CP energies determined here; some uncertainties may actually be less than this value, as shown.

The same selection of reflectance spectra that was shown in Fig. 1 is shown again here (Fig. 11) with the excitonic critical point energies, as determined by Fourier Analysis, indicated by the points. The historical lineshape of Dingle et al. [4] is shown in (d) with the original assignments indicated by the arrows. Our lineshape analysis indicates that A^'BA and A^CA are closer to 5 and 23 meV, respectively, rather than the 6.0 and 20.5 meV they reported.

The lineshapes are arranged in order of descending excitonic energy separation AEB A = EB — EA- They were obtained from GaN layers grown by (1) metallorganic chemical vapor deposition (MOCVD) on AI2O3 substrates with 250 A GaN buffer layers, (2) Hydride Vapor Phase Epitaxy (HVPE) on AI2O3 substrates without buffer layers, and (3) MOCVD on 6H-SiC substrates with 1000 A AIN buffer layers. They were referred to by the authors as Category I, II, and III samples, respectively, shown in Table 4. Details of crystal growth are given elsewhere [19,69,70].

Fig. 11a is typical of reflectance spectra of Category (I) films. The feature farthest to the left is an interference oscillation; the excitonic features of interest lie to the right. Here AEBA and AEQA are 9.2 and 27.8 meV, respectively; however, real-space assignments for the same sample yielded AEBA = 11 m^V and A ^ C A = 34 meV. The other Category (I) samples exhibit similar discrepancies as a result of baseline ambiguities. Reciprocal space AEBA values are as shown in Table 4, but the real-space values for Category (I) samples were all ~11 meV. Reliance on real-space analysis in this case would have lead (the authors maintain) to the incorrect corroboration of the work of Orton [71], who, performing a Hopfield Quasicubic model [56] calculation on a few samples grown only on AI2O3 (nearly all of the excitonic splitting values published at the time, however) concluded that AEBA was invariant. Reciprocal-space analysis was sufficiently sensitive to detect the non-negligible variation of AEBA for a sample set varying by only 0.5 |xm in thickness.

We observe a similar pattern in a sample set within Category (III), a 1.32 ^ m


<

AEg^ = 9.2 meV AE.. s 27.8 meV

AEg^ = 3.4 meV

AEc. = 19.7meV

AEB4 = 2.5meV

AE..s18.7meV

• Reciprocal Space Analysis Results I

V-AEg^ s <2 meV AE.. = 18.9 meV

3.40 3.45 E(eV) 3.50 3.55

Fig. 11. Excitonic energy splittings A£BA and A£CA VS. energy position of the A exciton; data shown by points. Least-squares fit shown by solid lines. Note the nonlinear character of the fit. Reprinted with permission from Edwards et al. [75].

Table 4. Summary of GaN samples and corresponding growth parameters (Reprinted with permission from Edwards et al. [3])

Sample, category

1,1 2,1 3,1 4,1 5,11 6,111 7,111 8,111 9,111

10, III 11,111 12. Ill 13, III 14, III

Growth technique

MOCVD MOCVD MOCVD MOCVD

HVPE MOCVD MOCVD MOCVD MOCVD MOCVD MOCVD MOCVD MOCVD MOCVD

Substrate material

AI2O3 AI2O3 AI2O3 AI2O3 AI2O3 6H-SiC 6H-SiC 6H-SiC 6H-SiC 6H-SiC 6H-SiC 6H-SiC 6H-SiC 6H-SiC

Thickness (|xm)

2.7 + 0.025 GaN buffer 2.7 + 0.025 GaN buffer 2.6 + 0.025 GaN buffer 2.2 + 0.025 GaN buffer

250 3.7 + 0.1 AIN buffer 3 .1+0.1 AIN buffer 2.0 + 0.1 AIN buffer 1.5+0.1 AIN buffer 1.4 + 0.1 AIN buffer 1.4 + 0.1 AIN buffer 1.3 + 0.1 AIN buffer 1.3 + 0.1 AIN buffer 1.0 + 0.1 AIN buffer

Film growth

temp. (°C)

1050 1050 1030 1050 1050 1050 1050 1050 975 1025 975 975 1075 975

Â (eV)

3.4857 ± 0.5 3.4900 3.4890 3.4876 3.4743 3.4724 3.4729 3.4767 3.4726 3.4651 3.4680 3.4709 3.4668 3.4668

A^BA (meV)

8.6+ 1 7.1 8.3 9.2 6.7 2.5 3.4 6.2 <2 <2 <2 <2 <2 <2

A£cA (meV)

26.5 ± 1 34.7 30.9 27.8 23.5 18.1 19.7 23.9 20.4 14.2 16.3 18.9 14.8 18.8


representative of which is shown in Fig. l lg. These samples all are in the 1.03 to 1.45 jjim thickness range, grown on 6H-SiC with 1000 A AIN buffer layers, and have A^BA < 2 meV with A ^ C A values ranging from 14.2 to 20.4 meV. For this set the growth temperature of each sample is given in Table 4, providing a rationale for the observed variation of A^CA- Reciprocal-space analysis confirmed these assignments by showing that in each case IA^BAI could not have exceeded 2 meV; temperature-dependent reflectance data undertaken in the same work also supported this interpretation. However, like the Category (I) samples, it was noted that it would be premature to conclude that A^BA had a single value for material grown on 6H-SiC. The spectra shown in Fig. lle,f were obtained from Category (III) samples 3.10 |xm and 3.71 |xm thick, respectively, and exhibit A^BA, AJE'CA values of 3.4, 19.7 and 2.5, 18.1 meV, respectively.

Though Category (III) samples tended to show smaller A ^ B A splittings than those grown on AI2O3, a general conclusion of this nature would have been premature. Fig. l ie shows a Category (III) sample with AEBA = 6.2 meV and A ^ C A = 23.9 meV. Such values are typical for GaN grown on AI2O3 [4,41,57-60,72] and are in fact similar to the 250 |xm thick Category (II) sample shown in Fig. 1 lb with A ^ B A = 6.7 meV and A^cA = 23.5 meV. This result indicated something that was controversial at the time: that there was no a priori correlation between substrate material and observed excitonic splittings.

Finally, it was important to solve one remaining problem that had previously been a hindrance in the interpretation of some of the GaN reflectance spectra. (See Ref. [62] for further discussion.) This was the problem presented by extended regions of surface damage known as 'excitonic dead layers' [73], especially an issue in many nitride samples because of material quality considerations. Excitons cannot exist this surface layer; the material in the layer is therefore electronically different from the excitonic-containing layer below. Such a difference introduces a phase interference problem in phase-sensitive absorption measurements and perturbs the spectra in a cyclic fashion. Like the Hopfield Quasicubic Model [56], this work was largely investigated in the context of CdS, in the 1970s.

Such cyclic deformation of real-space lineshapes adds an additional element of ambiguity to the process of making excitonic assignments — yielding in some cases, for example, B excitonic features that dominate the A feature with increasing temperature, puzzling since the oscillator strength is larger for the A transition (from internal calculations; also see Bir and Pikus [74]). Such a deformed lineshape is seen in Fig. 1 lb, and is similar to the lineshape reported by Shan and coworkers [41]. Even worse, according to Evangelisti [61], all samples have dead layers for extrinsic reasons, since the exciton cannot exist with its center of mass closer to the surface than its radius without serious deformation, meaning that the potential exists for all lineshapes to be deformed with respect to an 'ideal value', to some degree. Worse, this dead layer can be made much deeper by surface damage or oxidation. Since the extent to which dead layers are present in any given sample is difficult to quantify, it is even more difficult to accurately account for them in real-space fits.

But it was still possible to determine the excitonic CP energies for the sample of Fig. 3b to within d=0.5 meV. This is the case because dead layers only introduce an


:3

X)

9

I E(eV) ^

Fig. 12. False data calculation illustrating the invariance of critical point energies with increasing excitonic dead layer. Reprinted with permission from Edwards et al. [75].

offset to the phase of the coefficients. But the slope of the phase is the parameter of interest for CP energy determination; any offsets are irrelevant. This fact is illustrated in Fig. 12 [75], which is a false data calculation of a simple (6:2), comprised of a unit step edge, a ramp, and an exciton. The energy position of the exciton is specified in the calculation, and the position of the step edge gives the location of the second CP. A layer without the exciton is placed upon this 'material' via a 3-phase model calculation, thus creating an excitonic dead layer. The thickness of the dead layer is increased until a roughly similar lineshape emerges at 700 A; this is the so-called period of the dead layer. Note the distortion of this simple lineshape and the ambiguity introduced with respect to CP energy determination by mere inspection. The energies of the two CPs were determined for each layer by Fourier analysis; not only did the CP energies remain largely invariant for increasing dead layers but the CPs did not deviate from the energy positions specified in the calculation. The issue of quantifying the extent to which various samples contain dead layers in order to render ones real-space fit exhaustive has been completely avoided by Fourier analysis, resolving the last of the series of stress-related ambiguities in GaN optical data.


4. Quantification of residual stress from optical data

4.1. Basic logic

We have seen that residual stress has a large impact on optical data. Now we will show how residual stresses can be determined from optical data. This fact is predicated on a few simple arguments. Not only do these arguments establish the basis for stress quantification, but they also enable the determination of fundamental physical parameters related to bandstructure. This insight into bandstructure is the primary advantage of using optical methods to determine stress, compared to more direct methods like X-ray diffraction, which should be viewed as complementary rather than competitive means of stress measurement.

Recall that if excitonic features can be resolved near the GaN bandedge, then: (1) the separation between the features will mimic the separation between the GaN valence bands; (2) applied or residual stresses will produce corresponding strains that vary valence band separations and conduction band positions; (3) residual stresses can be varied by changing the physical properties of the samples, where said physical properties are determined by material and growth parameters.

So, the obvious conclusion is that given optical data that contain excitonic features and given accurate values of the energy positions of these critical points, not only can residual stress be quantified in a particular GaN sample, but the variation of GaN valence bands with residual stress can also be assessed. This will be the task undertaken in this section; the correlation of this behavior with sample material properties will be discussed in the next.

4.2. Estimating residual stress using optical data and standard elastic theory

Once the relationship between in-plane residual stress and strain is determined from the elastic constants of a given material, there is a quick approach for estimating residual stress from observed features in optical data. (This is another example of physical parameters being presented as a fait accompli when they actually have been the topic of much investigation. For an excellent de facto review of this activity (plus first principles full-potential linear muffin-tin orbital calculations of elastic constants and related properties of BN, AIN, GaN and InN), see Kim et al. [76].) It is based on the shift in spectral energy of these features with respect to critical point energy values of analogous features in bulk, unstrained material. We begin with the stiffness tensor for hexagonal materials:

{C} =

Cn

Cn

C,3

0

0

0

Cn

Cn Cl3

0

0

0

C,3

Cl3

C33

0

0

0

0

0 0

C44

0

0

0

0 0

0

C44

0

0

0 0

0

0

C66

(2)


This expression assumes that the hexagonal crystal under consideration is isotropic in the basal plane, a very large assumption for GaN, given that considerable evidence exists for anisotropic in-plane relaxation in these films [51]. Nonetheless, for simple strain estimates we can evaluate Eq. 2 using [46]

Cii = 2 9 6 x 10^ Pa

Ci2 = 130 X 10^ Pa

Ci3 = 158 X 10^ Pa

C33 = 267 X 10^ Pa

C44 = 24 X 10^ Pa

Cee = 83 X 10^ Pa

and the relation Cii — C\2

C(s = ^

We additionally specify that

/an 0 0 \

0 ail 0

^ 0 0 0 /

to meet the requirement for basal-plane isotropy. Since {C}~^ = {5},

(3)

(4)

{S} = [C]-' =

• 5.1 X 10- '2

- 9 . 2 1 0 - ' ^

- 2 . 5 X 10- '2

0

0

0

- 9 . 2 X 10-^3

5.1 X 10- '2

- 2 . 5 X 10-^2

0

0

0

- 2 . 5 X 10- '2

- 2 . 5 X 10- '2

6.7 X 10- '2

0

0

0

0

0

0

4.2 X 10-

0

0

Sij = Sijkidki becomes

"en""

£22

£33

£23

^31

- £ 1 2 _

__

" 5.1 X 10-^2

- 9 . 2 X 10- '3

- 2 . 5 X 10-12

0

0

0

- 9 . 2 X 10-13

5.1 X 10- '2

- 2 . 5 X 10-12

0

0

0

- 2 . 5 X 10-12

- 2 . 5 X 10-12

- 2 . 5 X 10-12

0

0

0

0

0

0

4.2 X 10-11

0

0

4.2 X 10-11

0

0

0

0

0

4.2 X 10-11

0

0

0

0

0

0

1.2 X 10-11.

(5)

o-ii

0 33

2(723

2^31

where 6:23 = 31 = 12 = 0, an = (Jii and a33 with the isotropy requirement. We find that

£11 = ( 4 . 2 x 10-^^1/Pa)aii

£22 = (4.2 X 10_i2l/pa)aii

£33 = - ( 4 . 9 x 10-^2l/Pa)aii

^•23 = cr3i = a i 2

1.2 X 10-11J \_2ai2j

(6)

0 in accordance

(7)

(8)

(9)


which gives the relationship between an isotropic in-plane stress (in Pa) and the correspondingly induced strains.

The hydrostatic and therefore the in-plane strain can be obtained within an additive constant EAO from the measured gap energy E/^ and the deformation potential a according to the empirical expression

£'A = EM + aen{\0)

If a ^ —10 eV (a typical value for most semiconductors) and ^H = AV/V = 11 + 22 + ^33, which is merely three times the hydrostatic strain and if we substitute

Eq. 7 into the standard definition of hydrostatic strain

^11+^22 + ^33 , , , , ^H = Z (11)

(12)

we obtain

.H = \A.2 X 10-'^ ( 1 + 1 - ^ y - f ^ j û = 0.28^,,

Substituting this relation into £'A = £'AO + asw and conforming to the convention that tensile strains are positive and compressive strains are negative, we find, for example, that if EAO is the unstrained value of the A exciton (here 3.4764 eV [65]) and if Ep, is the experimentally observed energy position of the A exciton, that the observed Ep, = 3.4697 eV, for example, corresponds to an = a^x = 1.95 kbar, tensile.

4.3. Analyzing stress behavior with the Hopfield Quasicubic Model

4.3.1. The fit to the data With the connection to s^x established, we will now demonstrate the utility of plotting the B-A and C-A splittings in Table 4 vs. the observed energy position of the A exciton for each sample, as shown in Fig. 13 [3]. We can obtain residual strain information from the excitonic splittings in a more detailed way by examining the behavior of the valence band structure, given the physical connection between the two. This is the Hopfield Quasicubic Model [56] mentioned earlier, which is the calculated variation of the A, B, and C absorption thresholds relative to the top of the valence band as a function of spin-orbit, crystal-field and biaxial stress potentials. Again, for GaN, if the crystal-field potential were the only operative interaction the selection rules for light normally incident along the c-axis are such that only the A and B excitons would be observed. With the spin-orbit interaction included the B transition becomes weaker and the C transition becomes allowed, but only weakly. The strain caused by biaxial stress in the plane of the surface for films with the c-axis normal to the surface has the same symmetry as the crystal-field potential and can be treated as an additive effect.

The results of such a calculation are also shown in Fig. 13. They are the solid lines that represent a fit to the data [3] based on the Hopfield Quasicubic Model [56]. Indeed, with the energies EA, EB, and Ec of the A, B, and C excitons known to ±0.5 meV over a wider range of in-plane strain than was previously observed (cf. Table 3), parameters such as the spin-orbit splitting Vso = 17.0 ± 1 meV could then be calculated with increased confidence. It is worth pointing out that these data [3] also unambiguously


q-U

> CD

< o

liJ < •a c CO

< CD

LU <

0

GaN 10K

•

T , , 1 r- I

• m ^

^^^^

• • J

AEcA 1

ÊBA

]

3.46 3.47 3.48 EA(eV)

3.49

Fig. 13. Excitonic energy splittings A£BA and A £ C A VS. energy position of the A exciton; data shown by points. Least-squares fit shown by solid lines. Note the nonlinear character of the fit. Reprinted with permission from Edwards et al. [3].

showed the nonlinear dependence of the excitonic energy splittings AEBA and AJEBC on the energy £'A of the A exciton, in contrast to the linear relationship found by another research group [60].

The connection between Sxx^ AEBA and A£CA can be written in the quasicubic model as

A£BA, A£CA = {E^ - EA) = 2A2 + i (Ai - A2 + 0 , )

[( A , - A 2 + 0 . + 2A^ (13)

using the then-current notation of Chuang and Chang [77]. There 0^ = ks^x is the shear term, Ai = ACR is the crystal-field potential, and A2 = A3 = l/3Aso, where Aso is the conventional spin-orbit splitting parameter. Since AE^B and AEAC are determined experimentally, and since the independent variable 0^ can be expressed in terms of Sxx, then Al and A2 = A3 are the adjustable parameters for the least-squares fit shown in Fig. 13 (solid lines). Best-fit parameters in this case were ACR = 9.8 =b 1 meV and Aso = 17 db 1 meV. Aso was significantly larger than earlier values reported at the time [4,71] and the current theoretical estimates [78,79], though it was similar to that of Gil et al. [60], based on a linear approximation to the correct variation of the valence band energies with strain. The data in Fig. 13 clearly could not be represented by a straight line, in contrast to the data and linearization formulas offered in Ref. [60]. That fact was


Table 5. Summary of crystal field and spin-orbit splitting obtained by various workers (note the scatter in the values)

Ref.

[4] [85] [60,80] [50]

[77] [78] [71] [86] [87] [88] [3]

Authors

Dingle et al. Suzuki et al.

Gil et al. Volm et al. 'unstrained'

'relaxed' Chuang et al.

Wei et al. Orton

Lambrecht et al. Skikanai et al.

Stepniewski et al. Edwards et al.

Year

1971 1995

1995, 1996 1996

1996 1996 1996 1996 1997 1997 1997

AcF

22.0 72.9 10.1

35.0 11.0 16.0 42.0 19.2 19.0 22.0 8.8 9.8

Aso

11.0 15.6 17.6

18.0 17.0 12.0 13.0 10.4 21.0 15.0 17.9 17.0

also recognized by Gil et al. [80] in a revision of their earlier work on this topic. (This work also serves as a good starting point for those interested in the extensive work done on nitride deformation potentials, as does the review by the same (leading) author [81]. It is beyond the scope of this work to review this important related topic, but interested readers can also refer to the following in order to get an introduction to the area: Kim et al. [82]; Fan et al. [83]; Chuang and Chang [77]; Shikanai et al. [87]; and IVlajewski [84].) However, the wider range of data in Ref. [3] had more scatter than the more narrow range of previous workers [60,80]. The justification was (1) that this scatter was due to partial violation of the 1:1 connection assumed between hydrostatic and shear strain, and (2) that it was logical to assume that any partial, anisotropic relaxation would occur differently for each sample represented in a set of dissimilar samples. We will see some support for this premise in Section 5. Best-fit parameters of other workers are shown in Table 5 [85-88]. We see a large variety of ACF and Aso values obtained from basically the same physical model, making the case that a fit to a wider range of data was indeed necessary.

4.3.2. The physics behind the fit Given Sxx as an adjustable parameter, the task is to express A£BA and A^CA data shown in Fig. 13 in terms of the crystal field, biaxial stress and spin-orbit interactions with the Hopfield Quasicubic Model [56]. The method requires an exact calculation for the valence band and a perturbation theory treatment of the conduction band. Moreover, the effect of the crystal field is treated as a perturbation of the corresponding problem in a zincblende crystal. It is common practice to use the standard upper valence and lower conduction band states of a zincblende material as a starting point. In this case there are one (two with spin) s-like lowest conduction band state and three (six with spin) degenerate p-like valence band states, and the goal will be to lift this degeneracy via the crystal field (CF), spin-orbit (S-O) and biaxial stress interactions. The general strategy of the calculation is shown in Fig. 14a and the associated bandstructure of the result is


E (l state)

C

(a

(3 states) r-

(Diamond)

(2)

(V

®CF (D Biaxial

Strain

0)

(1)

(r)

(DS-0 #1

(V

(1)

ni

®S-0 #2

couples bottom

band to middle

band

crystal E(k)

field 1

7 y'

^

Ec = E, + A,

E? = E?=A,,

E § = 0 '

-C

{b

(a) Without spin-orbit interaction

{A2=A3=:0)

"Er = E-+Ai +A7

= A,+A,

(b) With spin-orbit interaction

( A 2 = A 3 ^ 0 )

E(k)

(C

Fig. 14. (a) Overall strategy of the Hopfield Quasicubic Model [56] calculation, showing the beginning scenario (diamond valence bands) and demonstrating the action of the perturbation terms, (b) The results of the calculation shown schematically, using the familiar notation of Chuang and Chung [77], reprinted with permission, (c) A schematic representation of the valence band structure, showing the effects of the crystal field (top) and spin-orbit (bottom) potentials with the accompanying irreducible representations of group theory.

shown in Fig. 14b (in the notation of Ref. [77], i.e. in terms of the output of the Hopfield Model) and in Fig. 14c (in terms of the irreducible representations of group theory).

Beginning with the zincblende wavefunctions at A: = 0,

\xyz t>, \xyz i) (2 states) Ec

\yz t>, \yz I) \zx t), \zx i) \xy t)' \xy i)

(6 states) Ev

we will introduce the following perturbations: (1) the crystal-field, (2) the spin-orbit, and (3) the biaxial stress potentials.

The first, the crystal field (C-F) term, is relevant because materials such as GaN, that are of hexagonal or wurtzitic structure, have a lower symmetry than cubic materials. Hexagonal and cubic materials differ most notably on the atomic scale by 4th nearest


# As, N

Top, 4th n.n.

Ga

^ ^ ^ S <— 2nd & 3rd n.n.—» ^ ^ H

Fig. 15. An exaggerated look down the body diagonal or (111) direction in a GaAs (zincblende, left) and the equivalent direction in wurtzite (right).

neighbor interactions. This is best seen by looking down the body diagonal or the 111 direction for zincblende and the equivalent direction for wurtzite, as sketched for both crystal structures in Fig. 15. The 60° rotation of the 4th layer with respect to the first in hexagonal materials reduces the overall electrostatic energy by putting positive and negative ions closer together. So we can expect the C-F potential to shorten the c-axis relative to the zincblende equivalent.

In the Hopfield Quasicubic Model this effect is described approximately by the addition of a crystal field term, which has the schematic form

VcF (r) = ^ (X + >; + z) + ^ (yz + zx + xy) (14)

Note that this interaction has a symmetry identical to that of trigonal shear. The practical consequences are that for epitaxial GaN films with the c-axis perpendicular to the plane of the surface, the CF and biaxial strain terms cannot be distinguished without further information, such as the energy of the fundamental absorption edge in an unstrained (i.e. bulk) crystal. Note as well that the shortening of the c-axis relative to the zincblende case gives rise to a negative V25 for GaN, in this equation.

The spin-orbit interaction concerns the interaction between the spin magnetic dipole moment of an electron and the internal magnetic field of an atom (in the one-electron picture). This internal magnetic field is related to an electron's orbital angular momentum. For multi-electron atoms, these internal magnetic fields are quite strong, so the spin-orbit effect is usually quite strong as well. The perturbation term due to the spin-orbit interaction is given by

(15)

(16) I \i \j I z \u - 1 /

operates on the basis set

318 Ch.9 N,V Edwards

and

L = r X p

The coefficient ^ = §(r) depends on the radial derivative of the core potential. It is largest for heavy atoms, thus the dependence of the spin-orbit interaction on size etc. A full basis set at A: = 0 for the S-O splitting is

conduction band: \xyz t>» l^yz i)

valence band: \yz t ) , 1 - t>. 1-3 t)» \yz I ) , \zx 4), \xy i)

where, for example:

Ly\yz t ) = -i^(^^ - ^ ^ ) i^^ t> = +i^\xy t> (18)

i.e. x(d/dz) effectively replaces z with x, and the z(d/dx) operator yields zero. Likewise

LAyz t> = -ih (y^^ - z^^ yzt)=o (19)

since \y'^) and \z^) are not part of the set. Using the general linear combination ^ = ai\x \) -\-a2\y \) H-aslz t ) +«4|-^ i) +

aslx I) + ae\x 4), we can find the resultant eigenvalues and eigenvectors, shown in Table 6. These linear combinations are eigenfunctions of §L • S with the eigenvalues shown. Note (1) that ^ is usually negative, so the j = 1/2 (spin-orbit split) band lies below the j = 3/2 band, and (2) that the difference in eigenvalues is +3/2(fi§). Selection rules involving momentum matrix elements can now be calculated, allowing us to build the Hamiltonian matrix and calculated transition oscillator strengths. Note also that the non-degenerate bands (i.e. the lower conduction bands) are not affected by the spin-orbit interaction.

The final perturbation is the biaxial stress interaction. The actual interaction with the electronic wavefunctions of a material is via strain, not stress. The change in lattice constants cause the change in electronic structure, not the applied or residual stress itself. Of course, strain results from stress; hence the confusion that often arises. Strain and stress are connected by the compliance tensor, as given in the previous section.

Table 6.

J

Resultant eigenvalues and eigenvectors for the spin-orbit perturbation

rrij Wavefunction Eigenvalue

3/2

3/2

3/2

3/2

1/2

1/2

3/2

1/2

-1/2

-3/2

1/2

-1 /2

(X t +iy t)/^/2

(x I +iy i -2z V/Ve

ix t -iy t +2z ;)/V6

(X 4. -iy i)/V2

(X 4. +iy i +z t ) /V3

(X t -iy t -z i)/V3

-^2'iH -^hH -{hH - i s ^ i

-ift^t -^ft^l


The perturbation term usually used to describe the effect of strain was originally derived by Pikus and Bir

H' = EijPikj SijPiPj 4- SijVij (20)

where P/ is the /th component of the momentum operator, eij is the //th element of the strain tensor, and

At the zone center ^ = 0 and the first term vanishes. As with other perturbations the most efficient approach is to divide s into combina

tions satisfying certain symmetries; thus

sn = \Ti(e) = I (EJCX + Syy + Szz) = hydrostatic component (21)

T = zz - jTr (?) = |f,, - I [e^jc + £yy) = tetragonal shear (22)

£R = ^xy = ^yz — zx = trigoual (or rhombohedral) shear (23)

Note that the relative volume change is just Ss^. Tetragonal shear represents a flattening along z with no volume change (so x and y expand), whereas trigonal shear represents compression along the body diagonal, with no change in volume as well. If we make the appropriate substitutions into the Pikus-Bir Hamiltonian [89], we can determine the strain contribution from these three terms

(24)

hydrostatic: H^^^^^^ = I^H {P^ + P^ + P^) = ^^HP^ (25)

which is the same as the kinetic energy term p^/2m and hence this strain only shifts energy levels around by a constant, in accordance with conventional wisdom about the effect of hydrostatic stress on optical spectra. The other components of strain are the ones that modify the spacing between valence bands and hence the excitonic splittings. In general terms, the *other components' are typically expressed,

tetragonal shear: H^^^ = ^sj [ipl - p]- p]) (26)

and

trigonal/rhombohedral shear: H^ = 3£R {pyPz + PzPx + PxPy) (27)

Thus for the case of GaN, we can simplify Eq. 20 to (Pikus-Bir [42], k = 0)

Ve (r) = VH3Tr (,) 4- — 5 . ( ^ 4- — 4- — ) (28)

K ( . ) = f a ( 5 H 4 - 2 5 . ) T r ( , ) + - ^ 5 4 4 ( — + ^ + ^ j (29)

We further specify the conditions for biaxial stress perpendicular to the c-axis.


in the lab frame:

to 0 o\ 0 a 0 0 0 a /

in the crystal frame:

a. =

and apply the cubic approximation of the strain tensor:

' f a (5ii + ISn) - | a544 -|cr544 £ = — âS44

— âS44

a (Sn +25i2) — âS44

-|a544 lcr(Su+Si2)

(30)

(31)

(32)

where the Sij are as defined in the previous section. As noted earlier, the C-F and biaxial strain perturbation will be treated as additive, since they have the same <111> synmietry.

Given the proper forms of the perturbation terms, the general strategy is to rotate the wavefunctions |z f), |z |> so that they are parallel to the (111) direction.

\Z) = j ^ (\yz) + \zx) + \xy))

\x) = j ^ (\yz) - \zx))

(33)

(34)

\y) = j=,i\yz) + \zx)-2\xy)) (35)

where \z} has three-fold rotational symmetry like the r25 valence band, and |x> and \y) are orthogonal to |z). We must diagonalize the Hamiltonian matrix (given in Table 7) defined according to the general relationship Ho^ = W^. Ho is simply [p^/lm) + V (r), where the crystal field, spin-orbit and biaxial strain interactions will be introduced through V(r). Since we chose a rotated basis, the matrix in Table 7 is already diagonal in the crystal-field and trigonal shear potentials. The diagonalization is typically approached in two pieces: first by diagonalizing the lower right 4 x 4 block involving \x \),\x \r),\y \),\y \) with respect to the S-0 orbit interaction, which generates a pair of states that are not mixed by the C-F and strain terms, and then by diagonalizing the remaining 4 x 4 block that involves strain and the C-F interactions. It is customary to use a wavefunction built up from linear combinations of the rotated wavefunctions: ^ = a\z t ) + b\z 1) + c\x f) -}- d\z i) + e\y t> + f\y i). The final result of the diagonalization is given below. Readers interested in further detail are advised to see similar published calculations in Refs. [56,77], for example. Here we have merely set up the problem and given the results so that the interested reader can have an informed starting point.

Residual stress in III-V

nitrides C

h. 9 321

o

-8

o

a

^ I I >

^ 1

K

^

I I >

I

t^

1

JUJS

^7 C

^ r^

ttj

I I

Mr ^

+ + >

1

Mr

(N

1^7 - ^ (N

Mr 1

CM

""l O

O

Mr

r-i J^

+ '

•^ ^ C

N

Û

<D

^

a. (/3 1

)

^ *!

H

C

O

CO

^1 C

D

1)

""C^

(N

1 *

CO

II 1

«N

CO

!»

(Z) "^ 13 N?

.2 ^

c 0)

5 2

oo : -fa


\A+)

\A+) /W+

\B+)\

\A-)\ \B-)

\â)

\%)

0

0

0 0

V 0 where

W^ = \ (Wi.

Wi =

\B+)

0 w+

0

0 0

0

fW2):

£v + 2VR +

\A')

0 0

w-0 0

0

tVw

* ^ 2 .

\B~)

0

0

0

w-0

0

-W2f

\K) \%') 0 0 \

0 0

0 0

0 0 W^ 0

0 W^ )

+ 2h*^^

(36)

W2 = £ v - V R - ^ V 2 5 + in^^

w^ = £ v - V R - ^ y 2 5 - i ; i 2 ^

(37)

(38)

(39)

(40)

\A'

[^ (Wi - W2) ± [/] iz t> + — I [2/IJC t) + (1 - 0 |jc;) + V3 (1 + /) 13';)] 2x/6

[[\{Wi-W2)±uf + \tf^''\ 1/2

(41)

|B±)

[i (ivi - W2) ±U]\zi)-^ [2i\x 4.) + (1 + /) |jc t> + V3 (1 - /) \y t>]

j[^(W,-W2)±t/f+ i?iVJ 1/2

I*: „/-.;)=[V3|Art)+/|3't)-(l-Ol3';)]

I*-) = -L [V3|Ar ;) + (!+ 1) Ij t) - i\y 4>]

t/ = i (IV, - W2f + 2li^^^

(42)

(43)

(44)

(45)


Tension Compression

3.46 3.47 EA(eV)

3.48 3.49

—r--2

(kbar)

Fig. 16. Excitonic energy splittings A £ B A and A£cA vs. energy position of the A exciton; data shown by points. Least-squares fit shown by soUd lines. Note the wider range of samples than in Fig. 13. Reprinted from Edwards et al. [90], with permission.

5. Stress trends for nitride heterostructures

Once a trustworthy Hopfield Quasicubic Model calculation is achieved, workers taking optical data on GaN films had a template for interpreting data for films with non-standard strain states. We illustrate this with Fig. 16 [90]. Here the Hopfield plot from Fig. 13 [3] is shown with a much larger collection of samples than those initially investigated. Material grown on 6H-SiC substrates is shown by the circles; on sapphire by the triangles (we will postpone the discussion of the 'SMU until the next section). The zero stress reference point is given by the asterisk [65,75]. Applying the knowledge from Section 4 to calculate the associated in-plane residual stress values for these excitonic splittings, we find for the data of Fig. 16 that an ranges from about -3 .8 kbar compressive to 3.5 kbar tensile, suggesting, not surprisingly, that the epitaxial material can withstand roughly equal amounts of tensile and compressive stress. We also see that some material grown on 6H-SiC is compressive, contrary to the conventional behavior

324 Ch. 9 N.V Edwards

described in Section 2.4. This section will be primarily devoted to the explanation of this phenomenon, which will involve debunking some of the then-standard concepts about residual stress in GaN films. Accordingly, we will only discuss growth on 6H-SiC in this section, as films grown on this substrate have exhibited more 'non-standard' behavior thus far than their counterparts grown on sapphire. We will focus on 6H-SiC films in this section, partly due to space constraints. Although much has been published about stress for GaN grown on sapphire, only a few reports are systematic studies of the variation of stress with various growth parameters. However, these do exist, though the majority deal with variations in buffer layer parameters, after the seminal work by Detchprohm et al. [44] established the trends for the variation of stress in GaN layers with film thickness. Perhaps the most extensive work on buffer layer conditions is by Kisielowski [1,2,30] though a smaller but very interesting study by Lundin et al. [91] addresses buffer layer conditions as well, and actually finds a change in the sign of the residual stress in the c-direction for certain buffer layer thicknesses, unobserved until that time. Other references of interest in this area include the seminal work on cracking by Itoh et al. [92], a detailed study of relaxation and PL exciton energies by Gfrorer et al. [93], and stress measurements from wafer curvature by Skromme et al. [94]. And of course there is the novel in situ stress monitoring work of Heame et al. [38] that we have already mentioned in Section 2.4. Clearly, there are others, but it is beyond the scope of this work to do an inclusive review.

As evident from the wide range of excitonic energy positions that we saw in Table 3 and in Section 3, we can see that residual stress in GaN clearly manifests itself in optical data. Samples grown under different conditions yield reflectance spectra with different lineshapes and excitonic splittings due to different states of residual stress in the layers. However, this wide range has typically resulted from the use of two very different substrate materials, 6H-SiC and AI2O3, rather than from achieving a wide variety of stresses on a single type of substrate. It should be noted that Krueger and coworkers had recently (at the time of publication for Ref. 51) achieved an impressive range of compressive stresses on AI2O3 substrates by varying various growth parameters. However, these are still within the realm of expected behavior for this substrate choice. See Krueger et al. [95]. Optical data in the literature historically gave the impression that compressive stress is the inevitable result of growth on AI2O3 substrates [4,41-46], while the relative scarcity of data for GaN on 6H-SiC reinforced the impression that only tensile material could be grown on this substrate [41,47-50].

We will show in this discussion that such observations are simply a result of growth in the regime where GaN on 6H-SiC is tensile. Empirical trends in residual stress for selected growth parameters in simple 6H-SiC substrate/AIN buffer/GaN film heterostructures (which still represent the widest range of stress reported thus far for this substrate material) [3] will be examined [51]. We show that compressive GaN layers are indeed achievable on this substrate, further supporting the earlier hypothesis [3] that there is no a priori correlation between substrate material and residual stress.

We will illustrate with a set of thirty GaN layers grown by metal organic chemical vapor deposition (MOCVD) on 6H-SiC substrates. All of the samples we will show are undoped, were grown with the same III-V flux ratio, have 1000 A thick AIN buffer layers grown at 1000°C, and were subject to the same post-growth rate of cooling [20].


As described in Section 3, reflectance lineshapes were analyzed in reciprocal space to yield the energies EA, E^ and EQ of the A, B and C excitons associated with the TQ, Fj and V^ valence bands, respectively, to within ±0.5 meV [3,63]. Residual in-plane stresses axx — cFyy = cfw were estimated to within an additive constant EAO from the measured critical point energy E^ as described previously [3]. Finally, film thicknesses were measured in cross-section to within 5% using a JEOL 6400FE field emission scanning electron microscope (FE-SEM) and verified by the reflectance data below the bandedge.

As stated, by conventional wisdom simple structures grown on AI2O3 are in compression while those grown on 6H-SiC are in tension. It is usually assumed for growth on 6H-SiC that compressive lattice-mismatch stresses [45,46] are relieved after a few nanometers of growth [96] and tensile thermal mismatch stresses [45,46] persist thereafter. To investigate these issues we plot E^ and GXX values for the samples vs. film thickness in Fig. 17, vs. growth temperature in Fig. 18, and compare on-axis and vicinal samples in Fig. 19. From Fig. 17 it is apparent that we can classify these films as very thin (^0.7 jxm), moderately thick (~0.7 to -^1.9 |xm), or very thick (--1.9 |xm) according to their residual stress. Some global trends are evident in Fig. 17, independent of growth temperature or offcut angle. Contrary to conventional wisdom, very thin samples are generally in compression. Consistent with previously reported XRD and TEM measurements on these samples, though Perry et al. [97] found six compressive samples. Possible explanations are differing penetration depths of the probe beams and different measurement temperatures. Moderately thick samples are in tension with stress typically increasing with thickness up to a critical thickness somewhere near 2-3 |xm. Above this critical thickness samples are in tension at a reduced stress of ^ 1 kbar. It

3.49

3.48

> (D

3.47

Q.

E

3.46 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Thickness (^m)

Fig. 17. EA and a^x vs. thickness d for GaN films on 6H-SiC. Lines are shown to guide the eye. Reprinted from Edwards et al. [51], with permission.


3.490

3.480

> 0

LU

3.470

3.460

1 — -

L • <0.7Mm • >0.7-<1.9

[| A >1.9

L • 0.62 1 • 0.44

— 1 — 1

• 0.19Mm 1

J

\ 0.83 •

1 F A •

• " 1 " 1 .. J

D.61

161

•

tWn to thick

f 1-

-3

h-2

1000 1050 1100

Growth Temperature (°C)

c o '55 0)

Q. E o o

<0 .£3

1 t)

C o

Fig. 18. The data of Fig. 17 vs. growth temperature for on-axis 6H-SiC samples. The arrows denote the progression in tensile stress with increasing thickness for moderately thick films (squares) at 975°C and 1050°C. Reprinted with permission from Edwards et al. [51].

appears that the relaxation process occurs more gradually — or that lattice and thermal mismatch stresses are more complex — than expected for these materials.

We interpret this behavior as a progressive relaxation of compressive stresses until moderate thickness is achieved and an abrupt relaxation of tensile stresses when the films become very thick. The compressive range is consistent with a gradual relaxation of pseudomorphic growth, given that the lattice parameters of GaN, AIN, and 6H-SiC at the growth temperature are such that compressive stress is produced (recall Section 2.1 and we show the lattice mismatch/thermal mismatch relationships again for convenience in Fig. 20a and Fig. 20b, respectively). The tensile range is presumably a thermal contraction effect, since the AIN buffer experiences faster rates of contraction upon cooling than the GaN film (see Fig. 20b). The weakly tensile region for d > ^^2.5 |xm is consistent with the idea that for sufficiently thick films an underlying interface is no longer able to withstand the stress and an abrupt relaxation occurs.

Other evidence supports this picture. While cross-sectional TEM micrographs show that the AlN/6H-SiC and GaN/AIN interfaces of these films are heavily dislocated (~10^^/cm^) [98,99], and calculated critical thicknesses of these layers are 46 A [100] and 12 A [98], respectively, high-resolution micrographs show that the films are not


3.490

3.480 L 0.62

> 0

3.470

3.460

(0001) vicinal

• • 0.19nm

0.47 •

• 0.95 4 0.76

4 0.18 0.83 I

0.61

1.30.

^4 ' 0.59 0.64 4

1.20

0 rt n

V 1 '

Y 3

1000 1050 1100 Growth Temperature (°C)

Fig. 19. EA and CTXX VS. growth temperature for growth on (0001) and vicinal (3-4° toward [1120]) 6H-SiC. The numbers indicate film thicknesses in ixm. Sample pairs linked by dotted lines were grown at the same time under identical growth conditions. Reprinted with permission from Edwards et al. [51].

fully relaxed [98]. In fact, Perry and coworkers found additional evidence of residual compressive lattice mismatch strain in the high resolution TEM micrographs taken on these samples. It was in the form of rounded peaks and grooves in the GaN film within 50-80 A of the AIN interface. They maintain that this sort of behavior is typical of films under compression [97]. This observation is also supported by the scatter of the data in Fig. 16 [90], and by reflection-difference (RD) data taken on the same samples [101], which shows evidence for anisotropic relaxation. Further, calculated coherency stresses at the GaN/AIN interface (a cjc = 56.5 kbar and ayy = 54.8 kbar) [98], are sufficiently large to reasonably account for residual stresses of an order of magnitude less after initial relaxation processes occur. And a multiplicity of defects with different Burgers vectors have been observed within a selection of representative films [99], a possible indication that different slip mechanisms could be activated as forces accumulate within a heterostructure with increasing GaN layer thicknesses.

The effect of growth temperature on these processes is shown for on-axis (0001) 6H-SiC samples in Fig. 18, and the additional influence of substrate orientation is shown in Fig. 19. Three trends are apparent. First, from Fig. 18 the thickness at which compressive stress changes to tensile appears to vary with growth temperature. ~0.6 i m films are slightly tensile at 1050°C and are sUghtly compressive at 1000°C. And at llOO' C,


CO

Lattice Parameter (a) vs. Temperature

4.8 K

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2

3.0

(a)

6H-SIC'

-•-•-•-•-•-•-•-•-•-• ^ - ' - '

500 1500 2000 1000

T(K)

Coefficient of Thermal Expansion (a)

2500

400 800 1200

T(K)

1600 2000

Fig. 20. Basal-plane lattice parameters vs. temperature, (a); coefficient of thermal expansion, (b), for: GaN (Reeber and Wang [26]), AIN (Wang and Reeber [24]), and 6H-SiC (Reeber [27]). Reprinted with permission.

a moderately thick sample is compressive, unlike those grown at lower temperatures. Second, at 1050°C the tension in moderately thick samples increases with increasing thickness while the reverse appears to be true at 975''C. Third, we see that the range of stress over which these processes occur appears to increase with increasing growth temperature.

It seems plausible that at any given temperature any film will follow the same general trend of progressive relaxation shown in Fig. 17, although the specific values of thicknesses and range parameters will vary with growth temperature. Granted, we have not enough samples were examined to confirm this hypothesis (and further work needs to be done), but it would explain the apparently unusual progression of stress with increasing thickness at 1050°C as opposed to the behavior at lower temperatures.

The effect of substrate off-cut angle on the relationship between residual stress and

Residual stress in III~V nitrides Ch. 9 329

growth temperature is shown in Fig. 19. Data are given for 6 pairs, each of which consists of one sample grown on an on-axis substrate (squares) and the other on a substrate offcut 3-4° toward [1120] (diamonds). Members of each pair were grown simultaneously. In each case, the vicinal sample is more tensile (or less compressive) and thinner than its on-axis counterpart. Here, as in Fig. 18, higher growth temperatures yield greater stress differences for each pair. Vicinal substrates have more surface steps to act as sites for the generation of dislocations, and therefore for stress relief, yet a variety of stresses for the 6 vicinal samples are achieved. Initial relaxation mechanisms appear partial here as well. Indeed, for the same samples Perry and coworkers [97] found TEM evidence of the higher number of steps on the vicinal wafers — not surprising — but what is interesting is that these steps served as formation sites for inversion domain boundaries. Threading dislocation densities for this sample set were -^lO^^/cm^ and -lO^Vcm^ for GaN on AIN grown on vicinal and (0001) 6H-SiC wafers, respectively. They theorized that the on-axis substrates had less formation sites (i.e. less steps) for the formation of these lattice mismatch relief-generating defects at the growth temperature. This, then, is the source of the residual compressive stress in these films compared to their off-axis counterparts [96]. Additionally, growth rates are slower for vicinal samples, while the reverse is generally true for other materials. The difference between GaN on- and off-axis growth rates suggests that cation desorption is promoted by steps, whereas cation desorption is not generally a factor for non-nitride III-Vs where the growth temperatures are much lower.

Another study, by Nikitina et al. [102], of stress trends in the 6H-SiC-based heterostructure system involved the variation of residual stress with varying buffer layer growth and material parameters (something not addressed by the previously described study of Edwards et al.) [51]. They also found that the relaxation of mismatch stresses were not complete. They studied 19 samples, both without buffer layers and with AIN and AlGaN buffers (of various thicknesses, and compositions in the case of the AlGaN) and concluded: (1) that largest residual strains were actually observed in the layers grown directly on SiC; (2) that a thick (500 A) AIN buffer layer reduced the absolute value of strains; and (3) that AlGaN buffer layers caused further reductions in strains values and could change the signs of them depending on the composition and thickness of the buffer layer. From what we know of the thermal behavior of the heterostructure materials (cf. Fig. 20b), conclusions two and three seem reasonable; number one is contrary to expectations, as one would typically expect fully relaxed films for such a large mismatch. Further, Waltereit et al. [103] have also reported that a significant amount of compressive lattice mismatch remains as well in their GaN layers grown with 'thin (5 nm) coherently strained AIN nucleation layers' on 6H-SiC. Indeed, they found that up to 0.3% can remain even after 1 |xm of growth. But their GaN layers grown directly on 6H-SiC were relaxed, the opposite of what Nikitina et al. observed [102]. Unfortunately, they did not report if dislocation densities were reduced relative to the relaxed layers, so we are unable to draw any conclusions concerning relief mechanisms in the films. However, they did observe that the strain state of the overlying GaN was determined by growth mode. This is in turn determined by the degree of wetting of the underlayer rather than by lattice mismatch, reminiscent of growth on sapphire. These seemingly contradictory results are mentioned to demonstrate the complex — and as of

330 Ch.9 KV Edwards

yet, not fully understood — interplay between the interrelated physical mechanisms of lattice mismatch, thermal mismatch, and growth mode/islanding/coalescence behavior as origins of residual stress.

But we can observe the following. The complexity of the results indicates that because of the closer match in substrate, buffer and film physical properties (as opposed to the single-handed dominance exerted in similar scenarios by the very much larger a and a of sapphire) we are able to observe this subtle interplay between what appears to be compressive lattice mismatch and tensile thermal mismatch stresses. And in some scenarios, yet to be fully determined, these factors may change the growth mode of the system as well. And for other sets of growth parameters, we may see more of an interplay between the anisotropic thermal properties of the heterostructure components discussed in Section 2.4, making it difficult to predict thermal behavior of the heterostructure a priori. Thus it appears that the 6H-SiC substrate/high-temperature AIN buffer layer combination enables a wide variety of options for tailoring stress states in GaN layers, to an extent thus far superior to its sapphire-based counterpart.

6. Conclusion: future directions, unanswered questions, and clever strategies for circumventing the status quo

We have seen the extent to which open questions exist, even for the simplest GaN heterostructures, composed of only three layers. Yet optoelectronic devices fabricated from far more complex combinations of materials than these, such as the InGaN multiple quantum well diode laser structure shown in Fig. 21 [104], have not only been demonstrated but in many cases have been brought to market as well. In fact, it is common knowledge that this has typically been done when many fundamental physical parameters were yet unknown. As one colleague, K.P. O'Donnell, noted during his presentation at one of the many annual nitride professional meetings, "Usually one speaks of 'reverse engineering'. In the nitrides, we are usually having to do 'reverse physics'." Issues such as the role of strain in these heterostructures are indeed managed in some fashion without being fully understood.

There are several examples of phenomenological strategies to manage strain in nitride heterostructures; one of the most successful is the Lateral Epitaxial Overgrowth technique [105]. Here, briefly, GaN is deposited on an underlying GaN layer through the windows of an Si02 mask. The deposited material first grows vertically on top of the mask then proceeds to grow laterally over the mask (and vertically as well) until the growth fronts from all of the windows coalesce into a continuous layer. What is remarkable about GaN films grown by this technique is the dramatic reduction in threading dislocation density observed in the films: the usual 10^ to 10 ^ cm" in the area beside the mask and less than lO'* cm~^ in the area above it. This startling difference is shown in Fig. 22. Since dislocations have their origins in lattice mismatch and are detrimental to device operation, the technique is an excellent example of engineering stress in order to enhance device performance. Indeed, the threshold current of Ill-Nitride lasers is substantially reduced using LEO 'substrates' and these lasers experience a corresponding and dramatic increase in lifetime [106].

Another fascinating aspect of this material is that (1) the amount of lateral growth

Residual stress in III-V nitrides Ch, 9 331

Multi-quantum-welt structure

P-AI008 Gao92 N

p-GaN

n-GaN

^-^Kim G^dj)^ N

Energy

Fig. 21. An InGaN multiple quantum well structure shown to illustrate the complexity of device heterostructures. Reprinted with permission from Nakamura et al. [104].

has been found to be strongly dependent on the orientation of the SiOi stripe, and (2) that the morphologies of the GaN layers on the stripe openings, grown on <liOO>, were a strong function of growth temperature [105]. The observed progression from a triangular to rectangular cross-section are reminiscent of the island behavior we saw for growth on sapphire (cf. Section 2). Indeed, it is attributed to an increase in the diffusion coefficient (and therefore in the flux of the Ga species) along the (0001) plane onto the {1101} planes with increasing growth temperature [105].

This information has been very helpful in understanding another stress control strategy, this involving a concept called a strain mediating layer (SML). The goal was to develop a strategy to control residual stress in nitride layers grown on 6H-SiC, not only to eliminate epilayer cracking but also to manipulate nitride valence bands to achieve optimally low laser threshold currents [107]. Recall that for GaN film/AlN buffer/6H-SiC substrate heterostructures, we observed a greater versatility in achievable residual stresses than predicted by conventional wisdom or observed thus far for films on AI2O3 substrates (cf. Section 5). There GaN films were shown to be mostly compressive for films less than about 0.7 |xm thick, were tensile up to about 2 |xm, then abruptly became less tensile with stress values near 1 kbar thereafter. Despite this increased flexibility, the thickness dependence meant that a given combination of growth and material parameters nonetheless dictated a unique value of stress in the overlying film. However, with the SML technique, researchers found that the inclusion of a negligibly


Fig. 22. Cross-section transmission electron micrograph of a lateral epitaxial overgrown (LEO) structure. Note the dramatic reduction in threading dislocation density above the masked region relative to the region on the left beside the mask. From Nam et al. [105], reprinted with permission.

thin (--375-750 A) layer of GaN or AlGaN between the AIN buffer layer and overlying GaN film could potentially circumvent these trends for moderately thick (~2 |xm) GaN layers (normally >4 kbar, tensile), yielding a range of stresses between 0 and —2 kbar, compressive, without altering the optical and structural properties of the film. Thus the SML, when used in conjunction with current buffer layer technology, has the potential to provide even greater flexibility than the AlN/SiC combination alone. In fact, it enabled otherwise unachievable combinations of growth temperatures, film thicknesses and residual stresses [107].

The impact of the SML is shown in Fig. 23, which is the stress trends curve we for growth on 6H-SiC (Fig. 17) with the SML samples included. Note that without the SMLs, these samples would have been as tensile as sample 5, the most tensile on the graph (as they were all grown under the same conditions). This impact can be seen as well from our earlier Hopfield Model Calculation plot (Fig. 16). The SML samples there are represented by the triangles. We see that the inclusion of a very small layer

Residual stress in III—V nitrides Ch. 9 333

o.*t»

3.48

< UJ

3.47

3 46

, , _ —— •

X 4

. . A

: ••• \ '

1 1 1

0.0 0.5 1.0 1.5

Thic

I — — 1 — — T 1

• Without SML X With SML

X 2 X 3

Sample 5

2.0 2.5

kness (îm)

J

J

r " L _2

1 •"•

1 ° 1

1 ^

1 ^

1 "

3.0 3.5 4.0

F/^. 23. EA and a jc vs. thickness d for GaN films on 6H-SiC. Points [•] represent samples without strain mediating layers (SML); X's represent samples with SMLs. Reprinted with permission from Edwards et al. [107].

grown at slightly different growth temperatures than the overlying layer has the capacity to reverse the sign of the expected strain state [107].

What was difficult to understand in this case was the relationship between SML sample growth properties and the associated GaN film properties. These are shown in Table 8. How could such a small change in growth temperature between SML and film reverse the sign of the strain? And strangely, samples with thin (<400 A) SMLs had an overlying GaN film whose growth rate had been cut in half. Samples 2 and 3 are by contrast the expected thickness, and their SMLs are >400 A. To explain this behavior we must consider the anticipated morphology of the SML. Initial investigations of GaN growth on the high-temperature AIN buffer layer determined that growth was layer-by-layer only after an initial coalescence of two-dimensional, flat-topped islands that occurs after -^400 A of growth [21]. It is plausible that the samples with reduced

Table 8. Properties of SMLs and associated GaN films

1 2 3 4 5

SML

Material

GaN GaN GaN

Alo.13Gao.87N

-

properties

Time at T C O

2 min 1000 6min 1120 4 min 1000 2 min 1000

-

^d

(A)

375 450 750 375

-

d (M^m)

0.9 2.1 2.2 1.2 1.9

Properties of associated GaN film

(^xx (kbar)

0.26 -1.02 -0.44 -1.98

4.63

PL linewidth

(meV)

3.56 3.27 4.26 4.35 8.13

XRD FWHM (arcsec)

53 56 59 59 52

AFM Rms roughness

(A) 3.95 4.49 6.85 2.72 2.61

Reprinted with permission from Edwards et al. [107].

334 Ck9 N.V.Edwards

growth rates had SMLs that were not fully planarized and that growth was in fact occurring on non-(OOOl) planes. Growth on such planes occurs at significantly reduced rates, due in theory to reduced Ga incorporation relative to that for the (0001) direction [108]. The degree of reduction of growth rate would then depend on the degree of coalescence of the thin SML. The finer details of how this occurs is still being investigated. However, after the progress made with LEO samples, the results seem more plausible. (As do similar results for growth on sapphire with low-temperature interlayers that reduce both etch pit density and dislocation densities [109,110].) In the LEO case, coalescence and lateral growth rate were also extremely temperature and orientation-dependent. But why the strain state is altered is an open question, as is much of the behavior we saw in the last section.

Unfortunately, a simple look at the thermal and lattice mismatch behavior of nitride materials still cannot neatly explain the wide range of stress-related phenomena observed, even for simple heterostructures. Not surprisingly the majority of unexplained issues are related to the failure of classical Matthews-Blakeslee thin film relaxation models. Some examples involve stresses formed by the coalescence of two-dimensional islands, stresses that cause growth mode changes and then in turn exert stresses, and the observation of what appears to be multiple slip systems in simple structures. These appear to play an important but as of yet unclarified role in the relief of residual stress in GaN films in a way that transcend simple lattice mismatch. Again, this tells us that though impressive optoelectronic devices have been demonstrated and commercialized in recent years, it has been done with only a rudimentary and indeed merely phenomenological understanding of stress. The big implication is that work is not yet finished with regard to relaxation phenomena in this materials system. Though much has been achieved with this phenomenological 'understanding', far more could be achieved if relaxation phenomena were thoroughly understood (and controlled) even in simple nitride heterostructures.

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I. Grzegory and S. Porowski, Phys. Rev. B. 56 (23), 15151 (1997). [89] G.L. Bir, G.E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors, Wiley, New York,

1974. [90] M. Suzuki, T. Uenoyama and A. Yanase, Phys. Rev. B 52, 8132 (1995).


[91] W.V. Lundin et al., Inst. Phys. Conf. Sen 155, 319 (1997). [92] Itoh et al., J. Appl. Phys. 58(5), 1828 (1985). [93] Gfrorer et al. In: Proc. E-MRS Spring Meeting, Strasbourg, June 4-7, 1996. [94] Skromme et al., Appl. Phys. Lett. 71(6), 829 (1997). [95] J. Krueger, G.S. Sudhir, D. Corlatan, Y. Cho, Y. Kim, R. Klockenbrink, S. Rouvimov, Z.

Liliental-Weber, C. Kiesielowski, M. Rubin, E.R. Weber, Proc. Mater. Res. Soc. 482 (1997). [96] K. Hiramatsu, T. Detchprohm and I. Akasaki, Jpn. J. Appl. Phys. 32, 1528 (1993). [97] W.G. Perry, Ts. Zheleva, M.D. Bremser, R.F. Davis, W. Shan and J.J. Song, J. Electron. Mater. 26,

224(1997). [98] Ts. Zheleva, R.F. Davis, unpublished. [99] F.R. Chien, X.J. Ning, S. Stemmer, P Pirouz, M.D. Bremser and R.F Davis, Appl. Phys. Lett. 68,

2678 (1996). [100] S. Tanaka, R.S. Kern and R.F. Davis, Appl. Phys. Lett. 66, 37 (1995). [101] U. Rossow, N.V. Edwards, M.D. Bremser, R.S. Kern, H. Liu, R.F. Davis, D.E. Aspnes, Proc. Mater.

Res. Soc. 449(1996). [102] LP Nikitina, M.P Sheglov, Yu.V. Melnik, K.G. Irvine and V.A. Dmitriev, Diamond Rel. Mater. 6,

1524(1997). [103] P. Waltereit, O. Brandt, A. Trampert, M. Ramsteiner, M. Reiche, M. qi and K.H. Ploog, Appl. Phys.

Lett. 74(24), 3660(1999). [104] S. Nakamura et al., Jpn. J. Appl. Phys. 79, L217 (1996). [105] O.-H. Nam, M.D. Bremser, T.S. Zheleva and R.F. Davis, Appl. Phys. Lett. 71, 2638 (1997). [106] B. Monemar, Summary of the Lateral Epitaxial Overgrowth Workshop, Junea, AK, June 2-5, 1999

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Aspnes, B. Monemar, MRS Internet J. Nitride Semicond. Res. 4S1, G3.78 (1999). [108] X.H. Wu, C.R. Elsass, A. Abare, M. Mack, S. Keller, PM. Petroff, S.P DenBaars and J.S. Speck,

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L316 (1998).


CHAPTER 10

Structural defects in nitride heteroepitaxy

M.E. Twigg, D.D. Koleske, A.E. Wickenden, R.L. Henry, M. Fatemi and J.C. Culbertson

1. Introduction

Gallium-nitride-based semiconductors have demonstrated the potential to serve as the basis of a new generation of optoelectronic, high-temperature, and high-power microelectronic devices [1-5]. Because of the difficulty in growing sufficiently large GaN substrates [6], GaN films must be grown heteroepitaxially on a variety of alternative substrates. Despite large differences in lattice parameters and thermal expansion coefficients, technologically promisingGaN thin films have been grown on c-plane (i.e. {0001}) sapphire [7-10], a-plane {1120} sapphire [11,12], and {0001} SiC [13,14]. As a consequence of heteroepitaxy, however, the resulting film suffers from a large density of extended defects. Differences in lattice parameter and coefficient of thermal expansion necessarily lead to large dislocation densities, whereas differences in surface and interfacial energies often lead to the formation of islands and planar defects. Het-eroepitaxial c-axis growth of a polar material like GaN also introduces the problem of inversion domain boundaries (IDBs), as well as the possibility that the deposited film may have one of two polarities: Ga-terminated or N-terminated [15].

Properly optimized MOVPE (metalorganic vapor phase epitaxy) growth of GaN has succeeded in producing GaN films with dislocation densities between 10^ and 10^/cm^. Advances in the understanding of the effects of substrate nitridation and vicinality, reactor pressure, and dislocation filtering have led to strategies for reducing dislocation density and increasing grain size. These strategies, in turn, have contributed to the growth of uniform GaN films with properties suitable for electronic and electro-optic devices.

2. Growth and microstructure

The group III nitrides have stronger chemical bonds than other III-V semiconductors. The Ga-N bond, for example, is estimated to be 4.2 eV [16], which is comparable to the C-C bond strength of 3.6 eV bond for diamond [17] and much larger than that of Ga-As or In-P, which is 2.0 eV for both semiconductors [16]. Because of these strong and largely ionic bonds, nitride lattice parameters are relatively small. The lattice parameter of zinc blende GaN is 0.451 nm [18], as compared with that of 0.565 for GaAs. This strong bonding results in the wide band gap characteristics, making nitrides useful in a wide range of electro-optical [1,2] and power semiconductor devices [3-5]. Such strong

340 Ch. 10 M.E. Twigg et al.

bonds also result in small cation surface diffusion lengths, so that step-flow growth in MOVPE can only be achieved at high growth temperatures (--lOOO^C) [19,20]. High growth temperatures are also mandated by the kinetic constraints of MOVPE growth, in that high temperatures are required for ammonia (NH3) cracking. Growing GaN directly on sapphire at elevated temperatures, however, results in a large-grained (~1 [xm grain size) film with a hexagonally faceted surface. This rough morphology can be traced, in turn, to nucleation of GaN islands with widely varying heights. This wide range in island height is due to the tendency for GaN islands to nucleate at different moments over the course of growth as well as to differences in island polarity (Ga or N termination). For GaN films grown on c-plane sapphire substrates, N-terminated films tend to be rough whereas Ga-terminated films have smoother surfaces [21].

MOVPE growth of GaN on sapphire at lower temperatures (' SOO^C) results in a fine-grained (~10 nm grain size) film with a smoother surface morphology. Smaller grains are expected at lower growth temperatures, since the cation diffusion length is smaller. A fine-grained film, however, suffers from an extremely large density of extended defects, and is therefore unsuitable for electronic and electro-optical applications.

Ultimately, it has become apparent that neither low-temperature nor high-temperature heteroepitaxial growth of GaN, directly on a sapphire or SiC, is suitable for depositing GaN films with good surface morphology. Thus Akasaki et al. and Nakamura et al. adopted a two-step growth process for GaN thin films [22,23]. The first step consists of AIN or GaN growth at lower temperatures (~600°C) in order to achieve a smooth, fine-grained film; the second step consists of GaN growth at higher temperatures (~1100°C). This initial low-temperature deposition, although extremely defective, establishes a growth template with a surface energy much closer to that of the desired large-grained GaN film; the resulting interfacial energy should be significantly less than that for heteroepitaxial growth of GaN on sapphire or SiC substrates. Because the initial low-temperature GaN or AIN layer has a surface energy similar to the subsequent high-temperature (HT) layer, the tendency for islanding associated with Volmer-Weber growth would be minimized [24,25]. Because the low-temperature layer provides an array of properly optimized nucleation sites for subsequent HT growth, it is often referred to as the nucleation layer (NL), although some authors refer to it as a buffer layer.

2.1. MOVPE growth conditions

In order to address the problem of extended defects in heteroepitaxial MOVPE-grown GaN with sufficient generality, we need to make a few observations regarding the reactors used in growing the films discussed in this chapter. MOVPE growth of GaN films at the Naval Research Laboratory (NRL) has been conducted in two types of vertical reactors: a conventional vertical (CV) reactor consisting of a water-cooled, inductively heated, quartz tube with the gas inlet located 10 cm above the sample, and a resistively heated, close-spaced showerhead (CSS) reactor with the gas inlet 1 cm above the sample (Fig. 1). In both reactors, trimethylgallium (TMG) is the group III precursor for GaN growth. The group III precursors for AIN growth in the CSS and CV

Structural defects in nitride heteroepitaxy Ch. 10 341

group III

group V

"showerhead" Injector

water cooling

graphite susceptor heater quartz liner

water cooled steinless steel wall

quartz tube

Advantages quartz rf-heated - Higher growth rates - Increased flexibility - Better nucleation layers - Higher temperatures

TMG + NH3 + H2

pyrometer I

Advantages close-spaced showerhead - Avoid pre-mixing of alkyls and NH3 - Fixed boundary layer - More uniform film growth - Large grain size - Better high temperature growth

quartz / glass tube

rf coil

exhaust

rotation

Fig. 1. Schematic diagrams of NRL's close-spaced showerhead (CSS) and conventional vertical (CV) MOVPE reactors.

reactors are trimethylaluminum (TMA) and triethylaluminum, respectively. Ammonia is the group V source, and hydrogen is the carrier gas. Silane or disilane serve as the dopant source for Si-doped films. Prior to growth of the high-temperature GaN layer, a --20-50 nm nucleation layer (NL) is deposited. For the CV reactor, only AIN NLs are used, whereas in the CSS reactor both AIN and GaN NLs have been investigated [26].

Typically, NRL's CV and CSS MOVPE reactors operate at a total pressure of 40-300 Torr. The sapphire substrate is annealed for 10 min in H2 at --UOO^C prior to growth. The substrate is then cooled to a temperature of 500-600°C for 4-5 min of nitridation using 1-2 SLM (standard liters per minute) of ammonia (NH3). At this same temperature the AIN NL is then deposited using 1.5 |imole/min TMA (or TEA), 1-2 SLM NH3, and 2.0 SLM H2. The growth of the NL is followed by a 2-min ramp to 1020°C, after which the NL is annealed in this same temperature range for 10 min. A GaN film is then grown at 1020°C using 26 |xmole/min of TMG, 1 SLM NH3, and 2 SLM H2. The GaN film is doped using 8 ppm Si2H6 in H2, at a flow rate of 0.2 seem (standard cubic centimeters per minute).

The V/III ratio for GaN growth must lie in a range where the desorption rate of N does not greatly exceed that of Ga, thereby achieving the so-called nitrogen-rich growth condition. The V/III ratio at 1030°C, for example, must exceed 10^ in order to prevent GaN decomposition and the formation of Ga droplets. Because desorption rates exhibit Arrhenius exponential behavior with respect to temperature, the logarithm

342 Ck 10 M.E. Twigg et al

of the V/III threshold can be plotted as a linear function of inverse temperature. This threshold has been shown to be well defined for a wide range of reactors and growth conditions. Above this threshold, the GaN surface of an MOVPE-grown film is capable of maintaining a smooth morphology. Below this threshold the surface is invariably rough [20]. According to the atomic force microscopy (AFM) study of Keying et al., this change in morphology is traceable to dislocation-mediated growth (i.e. the effect of dislocation pinning on step flow) [27].

We should also note that other research efforts, notably those at Nichia [23] and University of CaUfomia at Santa Barbara (UCSB) [28], have been carried out using horizontal-flow MOVPE reactors. Although these reactors use the same reagents as those at NRL, some of the gas jets are directed horizontally across the substrate wafer. Nevertheless, there are a number of similarities between GaN films grown in vertical reactors and those grown using horizontal reactors. There are also common features among GaN films grown on different substrates. The concepts explored here are therefore sufficiently general to be useful to most growers of MOVPE GaN films. It is with these thoughts in mind that we seek to provide growers with a number of microstructural landmarks to guide them through the welter of parameters that describe MOVPE nitride growth and the constantly changing reactor environment.

2.2, The nucleation layer

Because the nucleation layer plays a very important role in determining the morphology of the HT layer, the configuration of the nucleation layer is a topic of considerable interest. Much that is known about the NL comes from the study of its influence on the morphology of the HT layer. As shown in Fig. 2, we have used cross-sectional transmission electron microscopy (XTEM) to study the resulting thin (50 nm) HT film for two differently prepared NLs grown in the CSS reactor.

The two growth sequences shown in Fig. 2 differ in the temperature at which the a-plane sapphire substrate [29] is initially exposed to ammonia (i.e. the nitridation temperature). In each case, the nitridation procedure lasts for 10 min and is followed by the growth of a GaN NL at 550°C [11]. A smoother and larger-grained HT morphology, indicative of successful lateral growth, was obtained by nitriding at the higher temperature of 1065°C. The rougher and smaller-grained HT morphology was obtained by nitriding at 625°C. From the corresponding diffraction patterns shown in Fig. 2, we determined that the two nitridation conditions result in two distinctly different orientations for nitride growth on (2-plane sapphire. The 1065°C nitridation resulted in the orientation relationship GaN[2ll0]/sap [ll20]; GaN(0001)/sap(ll20). The 625°C nitridation resulted in the configuration GaN[1100]/sap[1100]; GaN(0001)/sap(li20) [30]. (Please note that the effects of nitridation on orientation relationships, in GaN films grown on a-plane sapphire, are given correctly in [30], but not in [11].)

In a second set of samples, the effects of different nitridation procedures were found to result in significant differences in the structure of the thicker coalesced films, as shown in Fig. 3. XTEM of the film using the higher-temperature nitridation process (800°C) reveals a dislocation density of less than 10^/cm^, as shown in Fig. 3a. The HT film grown following the lower-temperature nitridation condition (500°C), and subsequent


NitrJdation Crystallography and Temperature

GaN[2 T T0]/Sap[1 ToO] GaN[1 T00]/Sap[1 ToO]

Fig. 2. DF XTEM images of GaN films after 10 min of HT deposition, (a) HT deposition after high-temperature nitridation. Diffraction pattern corresponding to GaN[2iiO]; sapphire[1100]. (b) HT deposition after low-temperature nitridation. Diffraction pattern corresponds to GaN[ll00] zone axis.

NL deposition and annealing, suffers from poor grain alignment, with large dislocation densities (> 10^^/cm^) at the grain boundaries, as shown in Fig. 3b. There are additional differences in growth conditions between these two films: the film with the higher nitridation temperature was also grown at a higher reactor pressure (150 Torr) than the film with the lower nitridation temperature (76 Torr). Nevertheless, it is only in films nitrided at low temperatures (shown in Fig. 2 and Fig. 3b) that the GaN[1100]/sap[ll00] orientation was observed. All of NRL's MOVPE GaN films that were grown on ^-plane sapphire using the high-temperature nitridation procedure were found to have the orientation relationship GaN[2i 10]/sap[l 100]; GaN(0001)/sap(l 120) [30].

Further evidence of the impact of nitridation on film structure has been observed by researchers at UCSB, who have traced the effect of nitridation time on c-plane sapphire (i.e. the ammonia dose prior to NL growth). Sample A, the film with the lower ammonia dose (3 SLM for 60 s), was found to form well oriented grains giving rise to a film with a dislocation density of less than 10^/cm^. Sample B, the film resulting from the larger dose (3 SLM for 400 s), suffered from a dislocation density greater than 10^^/cm^, which appeared to have resulted from both larger grain misorientation and

344 Ch. 10 M.E. Twigg et al

1 jxm 0110

Fig. 3. XTEM of coalesced GaN films, (a) Following high-temperature nitridation: GaN[2ilO]/ sapphire[liOO]; dislocation density <10^/cm^. (b) Following low-temperature nitridation: GaN[liOO]; sapphire[liOO]; dislocation density >10^^/cm^.

smaller grain size [28,31,32]. Both films exhibited the familiar GaN[2110]/sap[li00]; GaN(0001)/sap(0001) epitaxial relationship. Preliminary TEM observations of Wu et al. indicated that the as-grown GaN NL of sample A consisted of well oriented faceted islands predominantly of the cubic zinc blende crystal structure, which transformed into


the hexagonal wurtzite phase upon annealing [33,34]. The as-grown NL for sample B, however, had a 2-5 nm thick wurtzite 'wetting layer' which covered the sapphire substrate; upon this layer a rough layer of faceted islands grew of mixed wurtzite and zinc blende polymorphs with significant stacking disorder [32].

A recent study of UCSB's A and B NLs using grazing incidence X-ray scattering, indicated that the NL of sample A is a mix of zinc blende and wurtzite phases, with a zinc blende to wurtzite ratio of 0.56 [35]. The large fraction of the zinc blende phase was ascribed, in part, to a high density of stacking faults, which are clearly observable in XTEM. The NL associated with sample B, however, was found to have a zinc blende to wurtzite ratio of only 0.17.

According to both theory and experiment, GaN has a low stacking fault energy [36,37]: 20 mJ/m^, as compared with 45 mJ/m^ for GaAs and 55 mJ/m^ for Si. The stacking fault energy indicates the cost in energy that must be paid when an atom assumes a position on a close-packed plane (i.e. (0001) for wurtzite; {111} for zinc blende) that does not correspond to the equilibrium crystal structure. A low stacking fault energy would allow deposited atoms to more easily sustain such a metastable configuration. A large stacking fault density, and the significant presence of the metastable zinc blende polymorph in a NL that is wurtzite in structure at equilibrium, suggest that the NL was deposited at a relatively low temperature. Therefore, the presence of the zinc blende polymorph in a nitride NL may be regarded as evidence of a suitably low deposition temperature for a given set of growth conditions.

It has been observed by Suda et al. that GaN deposited by metalorganic molecular beam epitaxy (MOMBE) on c-plane SiC favors the zinc blende phase when the surface is Ga-stabilized [38]. The Ga-stabilized surface is thought to result in a difference in the charge distribution at the film surface so that a very thin Ga-stabilized GaN layer is less ionic than in the bulk. Because it is the ionic nature of GaN that is thought to be responsible for the stability of the wurtzite polymorph [39], any tendency to reduce ionicity would contribute the formation of the zinc blende polymorph favored by less strongly ionic semiconductors (e.g. Si and GaAs).

The presence of the zinc blende nitride polymorph in the NL may also result from its tendency to reduce the polarization field. Spontaneous polarization (i.e. pyroelectricity) is absent in zinc blende nitrides. A polarization field cannot be maintained in an unstrained cubic crystal, such as in the zinc blende nitride polymorph, since such a direction would have to be a unique direction of high symmetry [40]. In wurtzite nitrides, the [0001] is indeed a unique direction of high symmetry, whereas the analogous zinc blende <111> directions are not. The presence of the zinc blende polymorph in a NL would reduce the polarization field because of its own lack of a spontaneous field, as well as the tendency for its piezoelectric field to counter the spontaneous field of adjacent wurtzite GaN for some cases of pseudomorphic strain [41].

The TEM study of Twigg et al. also linked the presence of the zinc blende phase in the as-grown NL to the quality of the subsequent HT layer [42]. In this study, an AIN NL was grown on a-plane sapphire by MOVPE in the CV reactor. Unlike the NLs described by Wu et al. [33], these NLs were flat from center to edge, rather than consisting of separate islands. The NL at the wafer edge was found to have a greater presence of the zinc blende phase than at the wafer center. Because the HT grain size

346 Ch. 10 M.E, Twigg et al

was larger at the wafer edge than at the wafer center, these observations support the conjecture that a successful NL should have a significant volume fraction of the zinc blende phase. It should be noted, however, that in these NLs, the wurtzite polymorph was always predominant over zinc blende, possibly because the AIN stacking fault energy of 200 mJ/cm^ is much larger than that of GaN at 20 mJ/cm^ [36,37].

2.3. Film uniformity and grain size

Many important aspects of extended defect formation in heteroepitaxial GaN films can be understood by considering center-to-edge differences in films grown on a-plane sapphire in the CV reactor. The sources of these differences are thought to be the variations in temperature and deposition conditions (i.e. gas flow dynamics) from wafer center to wafer edge, and which may be attributable to the geometry of the CV reactor: namely that the reactants are delivered by a single inlet directed at the wafer center. Throughout the wafer the dislocation density was found to be approximately 10^/cm^. It is apparent from XTEM, however, that the GaN grain size at the wafer edge is approximately 1 |xm, whereas the GaN grain size at the wafer center ranges from 0.1 to 0.5 |xm, as shown in Fig. 4 [42].

Wafer Edge

Wafer Center

1 [Am 0110

Fig. 4. XTEM of edge-to-center coalesced film grown in CV MOVPE reactor. GaN grain size at the wafer edge is approximately 1 jxm, whereas the GaN grain size at the wafer center ranges from 0,1 to 0.5 |xm.


Using XTEM, we have studied the as-grown NL as well as the NL following the 2-min ramp to 1030°C. From transmission electron diffraction observations, we have determined that at the wafer center both as-grown and ramped NLs are polycrystalline with little tendency towards the preferred orientation. In the as-grown and ramped NLs at the wafer edge, however, we find evidence of properly oriented zinc blende and wurtzite AIN. At the wafer edge, the as-grown NL is a mixture of zinc blende and wurtzite polymorphs, and becomes more predominantly wurtzite upon annealing. The apparent necessity for some fraction of the zinc blende polymorph in the as-grown NL, for high-mobility GaN films grown on differently oriented substrates (c-plane and a-plane sapphire) in differently configured reactors, suggests the importance of NL crystallinity over that of the nitride/sapphire epitaxial relationship.

In order to develop a better understanding of the influence of the NL on the subsequent GaN growth, we grew a nominally 20 nm HT GaN layer on a fully annealed 50 nm AIN NL. From XTEM observations, as shown in Fig. 5, we see that the HT GaN film nucleates in the form of 100-200 nm wide islands at the wafer center, while no HT GaN growth appears to occur at the wafer edge. This difference in island density, from center to edge, is also observed in AFM, as shown in Fig. 6. Although the NL layer in

Wafer Center

Wafer Edge

100 nm 0110

Fig. 5. XTEM of edge-to-center 10-min islands from CV reactor. A 20-nm HT GaN film nucleates in the form of 100-200 nm wide islands at the wafer center, while no HT GaN growth appears to occur at the wafer edge.

348

0.4 mm

Ch. 10 M.E. Twigg et al.

10 mm

1 7 mm

1 im Fig. 6. AFM of edge-to-center 10-min islands from CV reactor. It is clear that islands only nucleate near the wafer center.

this film is seen to consist of properly oriented wurtzite AIN, the extended defect density is extremely high. At the wafer edge the extended defect density is 10^°/cm^, which is still drastically lower than that found at the wafer center, where the extended defect density is over 10 Vcm^-

As shown by XTEM in Fig. 7, the islands at the wafer center appear to form at clusters of extended defects in the underlying NL, suggesting that these defect clusters are responsible for GaN island nucleation. The absence of such nucleation sites at the

Fig. 7. Island at wafer center nucleating on defect cluster, (a) XTEM of islands formed at cluster of extended defects in the underlying NL. The absence of such nucleation sites at the wafer edge allows the formation of a large-grained GaN film, (b) HRTEM image showing the defect clusters responsible for the island nucleation.


10 nm

10 nm GaN Nucleation Site in AIN NL

350 Ch. 10 M.E. Twiggetal

wafer edge allows the formation of a large-grained GaN film, whereas the presence of these clusters at the wafer center results in the formation of a smaller-grained GaN film. These observations are also consistent with recent studies addressing the influence of reactor pressure on GaN grain size [11,43]. Growing at higher pressures effectively suppresses grain nucleation in the HT GaN to such an extent that the overall grain size increases to well over 1 |xm, with the result that center-to-edge variation of film structure and electrical properties are effectively eliminated.

Another important observation relates to the nature of grain morphology. As shown in Fig. 8, the grain structure is well defined up to 1 [xm above the NL. In the region of the HT film greater than 1 |xm above the NL layer, however, the definition of the grains in the XTEM image begins to fade. In part, this loss of grain definition is due to dislocation annihilation with film thickness, since it is largely the threading dislocations

1 |im 0110

Fig. 8. Dark-field XTEM image of coalesced GaN film. Grain structure is well defined in the first 1 jjim from the NL. Farther from the NL layer the definition of the grains in the XTEM image begins to fade. This loss of grain definition is due to dislocation annihilation with film thickness.


that define grain boundaries in GaN films [32,44]. For this reason, GaN device structures are best grown on thicker and therefore relatively dislocation-free GaN films, at least to the degree allowed by the constraints imposed by thermal mismatch and the associated hazards of crack formation.

2.4. Threading dislocations

The line direction of threading dislocations in GaN films usually runs parallel to the c-axis. The Burgers vector for these dislocations may be 1/3<1120> (edge type), <0001> (screw type), or mixed (e.g. l /3<li23>). Edge dislocations occur at tilt grain boundaries, whereas screw dislocations occur at twist grain boundaries. A tilt boundary is defined as the interface between two grains that are rotated in a plane perpendicular to the grain boundary [45]. For the case of GaN grains in a heteroepitaxial film, tilt boundaries are formed when grains rotate a fraction of a degree from the nominal orientation, about an axis perpendicular to the substrate growth surface. Edge dislocations, which can be thought of as the line defining the end of an extra atomic plane inserted into the lattice, act to accommodate grain misorientation. Twist boundaries, on the other hand, occur when two adjacent grains are rotated out of alignment about the axis perpendicular to the grain boundary [45]. Screw dislocations, which are much like spiral staircases formed around an imaginary pole coincident with the dislocation line direction, are formed by the lattice offsets resulting from twist boundaries

Dislocations with screw components also occur in NLs. As is apparent in Fig. 9, NLs consist of a large density of small ('^10 nm) misoriented grains in which the c-axis for each grain is often not perpendicular to the substrate surface. Screw dislocations necessarily form at the boundaries of these adjacent misoriented grains. Dislocations with screw components are thought to serve as nucleation sites for HT growth [32]. Screw dislocations may also occur as 'pipes' (i.e hollow tubes wending their way through the GaN crystal) — the dislocation core remaining empty to eliminate the most highly strained part of the dislocation for the purpose of energy minimization [46].

2.5. Inversion domain boundaries

Like other compound semiconductors, GaN is polar. The existence of the cation and anion interpenetrating sublattices, offset in a direction perpendicular to the close-packed planes ((0001) for hexagonal; {111} for cubic), guarantees the polar nature of both wurtzite and zinc blende phases. In the TEM, this polar nature can be revealed by acquiring imaging and diffraction information from zone axes that include the {0002} reflections for the hexagonally indexed wurtzite phase. Although HRTEM elucidates the structure of the inversion domain boundaries (IDBs) that act as the interfaces between domains of differing polarity, the presence of such domains is more easily determined via dark field (DF) TEM imaging and convergent beam electron diffraction (CBED) [47].

For wurtzite and zinc blende materials, the convention for polar indexing regards the displacement from cation to anion along [0001] and [111] directions, respectively. Therefore, in following a given bond from gallium to nitrogen nearest neighbors in the wurtzite crystal, one imagines moving along the [0001] direction, in the positive sense


Misoriented grains AIN nucleal layer

ition^

AIN Nucleation Layer

a-plane Sapphire Substrate

AIN[2110] Sapphire [1100]

10 nm

Fig. 9. HRTEM of AIN-NL. NLs consist of a large density of small (-^10 nm) misoriented grains in which the c-axis for each grain is not quite perpendicular to the substrate surface. Screw dislocations form at the boundaries of these adjacent misoriented grains.

of the c-axis, as shown in Fig. 10. A GaN surface with the c-axis pointing outwards is necessarily Ga-terminated. Because the Ga atom terminating such a surface is held to that surface by three bonds, but linked to the next layer above it by only one bond, that surface has only one third the number of broken bonds as a similarly oriented crystal terminated by N. From an analogous argument, a surface with the c-axis directed inwards would be N-terminated. In Fig. 11, we see an example of such a determination using CBED. By recording the {0002} reflections of the CBED pattern as a function of XTEM specimen thickness, and matching them to the simulation of a CBED pattern [13,48], the polarity of the crystal can be determined. Using this procedure, we have determined that the film shown in Fig. 11 (like most of NRL's MOVPE-grown GaN films) is Ga-terminated.

Ramachandran et al. have observed that high levels of Mg doping lead to the formation of inversion boundaries in both MBE and MOVPE-grown GaN [49]. We have also observed one N-terminated film under high Mg doping, as shown by dark-filed TEM in Fig. 12. This Mg-doped film has a rough morphology and a high oxygen concentration, as determined by secondary ion mass spectroscopy (SIMS). NRL's other Mg-doped samples, with lower levels of Mg doping, exhibited neither the elevated oxygen concentration, nor the presence of IDBs.


GaN Polarity Q ^ . ^ ^ I Q

Ga-terminated N-terminated

[2TT0] Zone Axis

Fig. 10. Schematic definition of GaN polarity. For wurtzite and zinc blende materials, the convention for polar indexing regards the displacement from cation to anion along [0001] and [111] directions, respectively. Therefore, in going from gallium to nitrogen in the wurtzite crystal, one imagines moving in the [0001] direction, in the positive sense of the c-axis.

Convergent Beam Electron Diffraction (CBED) Determination of GaN Polarity

[2110] Zone Axis CBED Patterns

# 1 > A l : iî* i ^ i - ^ '^WSim ^^pfP

c-axis: [0001]

Thus: Ga-terminated

XTEM Specimen Thickness

120nm

140nm

160nm Fig. 11. Convergent beam electron diffraction (CBED) and GaN polarity. By recording the reflections of the CBED pattern as a function of thickness, and matching them to the simulation of a CBED pattern, the polarity of the crystal can be determined. Using this procedure, we have determined that this film is Ga-terminated.


c-axis

Inversion Boundary

c-axis f

Mg-doped GaN

g:{0002}

Fig. 12. Dark-field XTEM image showing inversion domain boundaries (IDBs) in heavily Mg-doped GaN film. The IDBs cause an originally Ga-terminated film to switch to N-termination, as confirmed by CBED.

Z-contrast STEM reveals that a single AlO octahedral layer defines inversion domain boundaries in AIN [50]. The presence of oxygen at AIN domain boundaries has also been suggested by energy dispersive X-ray spectroscopy (EDXS) in the STEM [51]. These STEM-based measurements suggest that each interfacial aluminum atom is surrounded by six oxygen atoms, in a configuration similar to that of an aluminum atom within an oxygen octahedron in sapphire [52]. The conjecture that oxygen is necessary for the formation of IDBs in nitrides is also supported by our own observation of an anomalously high oxygen concentration in a heavily Mg-doped sample containing IDBs.

There is also evidence for structure origins for IDBs. According to Wu et al., the presence of IDBs may also be traced to the morphology of the substrate surface [44]. Barbaray et al. have developed a sophisticated model, supported by detailed HRTEM imaging experiments, that addresses the role of c-plane sapphire surface steps of height c/3 in generating IDBs [53]. Rouviere et al. observe that IDBs may occur in GaN films grown on insufficiently thick AIN NLs grown on sapphire [54]. In this thin-NL condition, most of the HT film is found to be N-terminated rather than Ga-terminated. Such a film is characterized by a rough morphology as well as by the presence of IDBs.

The latter of these two structural mechanisms for IDB formation, however, may be attributable to composition. Using X-ray photoelectron spectroscopy, Cho et al. have observed the presence of oxygen as well as gallium and nitrogen in nominally AIN


layers (as identified by TEM) that form on sapphire during plasma source nitridation [55]. Using TEM-based EDXS measurements, Li and Zhu found that Al diffused up from the sapphire substrate and into the NL [56]. Because of the tendency for oxygen to promote the formation of IDBs in AIN, we conjecture that the polarity of some N-terminated GaN films is traceable to IDBs in the AIN NL. In the case explored by Rouviere et al., we might expect that thin NLs grown on sapphire substrates may be more easily saturated with oxygen and thereby give rise to IDBs and N-terminated HT GaN films.

3. Defect reduction strategies

Because heteroepitaxial GaN films evolve as a large number of slightly misoriented and coalescing grains, the film must necessarily contain a high density of grain boundaries and threading dislocations. In order to reduce the density of extended defects in such a heteroepitaxial film, researchers have devised a variety of schemes. Each approach involves one of three basic strategies: improving grain alignment, increasing grain size, or filtering threading dislocations. Improving grain alignment reduces the density of threading dislocations needed to accommodate the misorientation between adjacent grains. Promoting larger grain size reduces the density of grain boundaries as well as the density of threading dislocations that help define the grain boundaries. Dislocation filtering is accomplished through the deposition of specially engineered layers for enhancing dislocation recombination, where dislocations combine or annihilate as they thread to the film surface.

The approach to promoting grain size can be further divided into two rather different avenues: optimal pressure growth (OPG) and lateral epitaxial overgrowth (LEO). Both techniques rely on controlling grain nucleation at the onset of HT growth so that a lower density of grains succeed in nucleating. In the case of OPG, this control is effected by carefully controlling the growth parameters; in LEO, the growth surface is specially prepared to allow nucleation to occur upon only specific regions of the substrate.

3.1. Grain alignment via vicinal growth

Because the substrate in heteroepitaxy functions as the template for subsequent growth, the morphology of the substrate surface may influence the structure of the deposited film. In GaAs on (100) Si, vicinal substrates provide steps that act as island nucleation sites [57]. In addition, steps on vicinal surfaces influence the structure of interfacial dislocations, as has been observed for silicon on {1012} sapphire or CdTe on c-plane sapphire [58]. Weeks et al. have grown GaN on vicinal SiC substrates and arrived at a similar conclusion [59]. In this case, growing on a vicinal c-plane SiC substrate resulted in sufficiently good grain alignment to prevent the actual definition of grain boundaries when viewed using XTEM. For GaN films grown on c-plane sapphire, however, there is an absence of any correlation of GaN film quality with vicinality [60,61].

For GaN grown on ^-plane sapphire, we have found that the structure of the heteroepitaxial GaN film is strongly influenced by substrate vicinality. A detailed X-ray diffraction (XRD) survey, of a large number of GaN films grown on a-plane sapphire

356 Ch, 10 M.E. Twiggetal.

GaN on a- pi ane sapphi re: Effect of substrate vicinal angle on X- ray FWHM and Mobi I i ty

C JI

> < reooi

—»•: m-direction; f : c-direction

00000(25 Qo Qo ^^2M.2'' 0.5*' 1.5**

2 400h X

>200|-

';;r600| > | 4 0 0 h >-5 200

(A) (B) (C) (D) (E) (F)

Fig. 13. X-ray diffraction (XRD) FWHM and mobility vicinality experiment. For GaN grown on a-plane sapphire, the structure of the heteroepitaxial GaN film is strongly influenced by substrate vicinality. XRD reveals that films grown on vicinal a-plane substrates have a lower (0001) FWHM. Vicinally grown films also enjoy higher mobilities.

in the CV reactor at 50 Torr, reveals that films grown on vicinal a-plane substrates have a lower (0001) full-width at half maximum (FWHM) [62]. (Note that the orientation relationships for GaN on a-p\ane sapphire are not given correctly in [62]. The correct relationships are given in [30].) Furthermore, as shown in Fig. 13, these vicinally grown films also enjoy higher mobilities.

XTEM observations (shown in Fig. 14) indicate that the reduction in the XRD FWHM may be traced to better grain alignment in GaN films grown on vicinal a-p\a.nc substrates [30,62]. For samples grown in the CV reactor at 50 Torr, the density of edge dislocations in vicinally grown samples is less than 10^/cm^, as compared with an edge dislocation density of 5xlO^/cm^ for films deposited upon on-axis substrates. Because the density of screw dislocations is 5 x 10^/cm^ for both vicinal and on-axis films, the dislocation density in the former (5 x 10^/cm^) is half that of the latter (10^/cm^). It is our conjecture that steps on the vicinal a-plane sapphire surface provide a better template for grain alignment, which in turn leads to a lower density of the edge dislocations at the low-angle grain boundaries between adjacent grains.

3.2. Optimal pressure growth

Optimal pressure growth (OPG) improves film quality by increasing grain size in the HT layer. In an XTEM study of GaN films grown over a range of reactor pressures in the CSS reactor, grain sizes are found to be approximately 0.2 |xm for 39 Torr, 1 |xm for


Edge Dislocations

On Axis

Vicinal

1 \im 0110

Screw Dislocations

Fig. 14. Dark-field XTEM of GaN films grown on both vicinal and on-axis fl-plane sapphire substrates, (a) g = 0110, revealing 5 x 10^/cm^ edge dislocations in on axis growth, (b) g = 0002, revealing 5 x 10^/cm^ screw dislocations in on-axis growth, (c) g = 0110, revealing less than 10^/cm^ edge dislocations density in vicinal growth. (d)g = 0002, revealing 5 x 10^/cm^ screw dislocations in vicinal growth.

65 Torr, and 2 |xm for both 130 and 200 Torr as shown in Fig. 15 [12]. This trend is also followed in the CV reactor, where the grain size averages less than 0.5 |xm at a pressure 50 Torr or less, with a grain size of 1 ixm or larger at a pressure of 100 Torr or greater. As shown in Table 1, XRD measurements of the FWHM for both {0001} and {1102} planes also reveal the tendency for film quality to improve from 39 to 130 Torr. At 200 Torr, however, the (0002) XRD FWHM is seen to increase. The increase of the (0002) FWHM suggests the formation of screw dislocations and twist boundaries in the GaN film.

Table 1. Correlation of reactor pressure with X-ray diffraction data

Growth pressure (Torr)

39 65

130 200

FWHM (arc-s) ± 10

FWHM (arc-s) ± 10

326 325 340 420

610 608 517 510


Correlation of GaN Grain Size with Reactor Pressure

39 torr

65 torr

130 torr

200 torr

1 urn 0110

Fig. 15. XTEM grain size and pressure. Optimal pressure growth improves film quality by increasing grain size in the HT layer. Grain sizes are found to be approximately 0.2 ixm for 39 Torr, 1 |xm for 65 Torr, and 2 |xm for both 130 and 200 Torr.

An understanding of the increase in grain size, the corresponding decrease in the density of tilt grain boundaries, and the evolution of twist grain boundaries can be understood in terms of the influence of reactor conditions on grain size and morphology. According to Koleske et al. [43], higher hydrogen pressure promotes GaN decomposition, with hydrogen reacting with nitrogen on the GaN surface to form anmionia. Thus, enhanced desorption at higher pressures may retard grain nucleation, thereby resulting in larger grain size [11]. The dependence of growth rate on H2 pressure is shown in Fig. 16.

The presence of twist boundaries in the 200 Torr growth, suggested by the XRD data in Table 1, may be explained in part by the increasing diameter of HT GaN islands at higher pressure as well as by enhanced faceting. The enhanced faceting at higher


"kT*

=L

B CO

2 O

1

0.8

0.6

0.4

0.2

1 1 r~t

_

3

^

" 1 1 1 1

T~m "1^

1 1 1 1

1 1 1 1

i 1 1 1

~i I I I

t i l l

1 1 1 1 i _

' ' M " ) 50 100 150 200 250

Reactor Pressure (torr)

Fig. 16. Growth rate and pressure. Higher hydrogen pressure promotes GaN decomposition, with hydrogen reacting with nitrogen on the GaN surface to form ammonia. Enhanced desorption at higher pressures may retard grain nucleation, thereby resulting in larger grain size in GaN films.

pressures is apparent from Nomarski micrographs (Fig. 17) of GaN films grown directly on (2-plane sapphire (i.e. without a NL). Large faceted islands have a tendency to draw threading dislocations to the facets, thereby directing bundles of threading dislocations laterally. The extra atomic planes inserted (or removed) by these dislocation bundles give rise to crystallographic tilting [63].

Under the diffraction conditions employed in the dark-field XTEM images in Fig. 15, edge-type threading dislocations are in contrast. These diffraction contrast conditions are also sensitive to rotations of GaN grains about the axis perpendicular to the substrate surface. Such TEM imaging experiments resolve individual GaN grains flanked by tilt boundaries, and outlined by edge-type threading dislocations accommodating these in-plane rotations [45]. The dislocation density was seen to vary by less than a factor of two in the films, at a level near 10^/cm^. XTEM analysis of a Si-doped GaN film grown at 200 Torr indicated grains (mainly defined by tilt boundaries) of the same large size as the 130 Torr film. The GaN growth rate was observed to decrease with increasing growth pressure in this study, ranging from 0.5 to 0.7 |xm/h in the 39 and 65 Torr films, 0.5-0.6 |xm/h for the 130 Torr films, and 0.3-0.4 |jim/h for the 200 Torr films.

The variation in growth rate has been attributed in part to GaN decomposition, which is enhanced for pressures above 100 Torr in the CSS reactor geometry [11]. For other reactor configurations the optimal pressure for MOVPE growth may be as high as one atmosphere [64]. Enhanced GaN decomposition has been related to increased grain size by Koleske et al. [43]. It is suggested that small GaN nuclei suffer decomposition soon after their initial growth, bringing about a reduction in nuclei density and resulting in the lateral growth of large grains. The same mechanism would serve to limit GaN renucleation on the growing film surface. In addition to the decomposition mechanism, gas phase depletion of reactants at increased pressure may also be influencing the growth rate, and is a function of reactor geometry. The point at which the GaN growth rate decreases noticeably (e.g. by a factor of two) in the CV reactor is significantly higher, at pressures above 300 Torr. In both CSS and CV reactors, substantial sidewall deposits are seen at increased pressures. In the case of the CSS reactor geometry, the proximity


39 torr 130 torr

200 torr 300 torr lOOîm

Fig. 17. Un-nucleated growth and reactor pressure. Larger grain size and enhanced faceting at higher pressures are apparent from Nomarski micrographs of GaN films grown directly on (3-plane sapphire (i.e. without a NL).

of the gas injection showerhead to the heated susceptor may induce gas-phase depletion reactions at lower pressures than in the CV reactor geometry. These observations suggest a practical limit on the growth pressure that can be used to achieve large-grained film growth in the CSS reactor geometry, and a need to compensate for reduction in growth rate at higher pressures by increasing the total molar flows of the reactants.

While higher pressures are desirable for large GaN grains, this growth pressure regime is not optimal for controlled AlGaN growth. Fig. 18 illustrates the measured alloy concentration (as determined by cathodoluminescence spectroscopy) of 0.5-1.0 |xm thick AlGaN films grown at 1020°C, at pressures of 130 Torr and 65 Torr, with varying TMAl molar flow [12]. The films grown at 130 Torr are found to deviate from the expected gas phase composition [65] by a factor of two, and the growth rates were


I I t I I I I I I I I I I I I I I I I I I I I [ I I I I I I I I I

vapor composition

^ ^-P(growth) = 65torr -A

0 5 10 15 20 25 30 35

p.mol TI\ AI

Fig. 18. AlGaN growth rate with pressure. While higher pressures are desirable for large GaN grains, the growth pressure regime is not optimal for controlled AlGaN growth. This figure shows the measured alloy concentration of 0.5-1.0 |xm thick AlGaN films grown at 10200°C, at pressures of 130 Torr and 65 Torr, with varying TMAl molar flow. The films grown at 130 Torr are found to deviate from the expected gas phase composition by a factor of two, and the growth rates were half of those measured for growth of GaN at 65 Torr.

half of those measured for growth of GaN at 65 Torr. ^ A white deposit was observed in the reactor for the 130 Torr AlGaN growths, and increases as a function of TMAl molar flow. This deposit is ascribed to adduct formation between the ammonia and TMAl precursors [66-69,133]. Growth at 65 Torr pressure provides a reasonable fit to the expected gas phase aluminum content, with no evidence of adduct-type deposits. The fact that growth of AlGaN at 65 Torr proceeds without deposits, suggests that the aluminum is more effectively incorporated into the growing film at 65 Torr than for 130 Torr AlGaN growth. As a result of this study, the AlGaN films in recent AlOo.aGaojN/SiiGaN HEMT devices were grown at 65 Torr, upon highly resistive (HR) GaN films grown at 130 Torr. Device structures have been successfully grown using different reactor pressures for GaN and AlGaN layers [12]. The transport characteristics of these devices will be discussed later in this chapter.

3.3. Lateral epitaxial overgrowth

Similar in objective to OPG is the growth technique of lateral epitaxial overgrowth (LEO). In both cases the grower is trying to reduce the incidence of HT grain nucle-ation. In the case of OPG, this end is pursued rather subtly, by increasing the reactor pressure to a point where GaN decomposition frustrates HT grain nucleation. In LEO, the same end is achieved in a more obvious fashion, by masking off most of the nucleating surface [70]. As shown in Fig. 19, GaN grains are only able to nucleate on the

^ Gas phase composition was calculated using the vapor pressure equation: /oglOP(mmHg) = 8.224-2.134.83/r(K).


SiO, stripes

[xdtialGaMsabstiate

1). Grow GaN on sapphire

GftNgrovth

2). Pattern GaN with SiQ 7oids «3 gsBtinscoeitosce

3). Regrow GaN on Siq 4), Grow GaN until coalescence

Fig. 19. Schematic of LEO growth. In LEO GaN grains are only able to nucleate on the unmasked growth

template, followed by lateral growth over the masked region until coalescence occurs.

unmasked growth template, followed by lateral growth over the masked region until coalescence occurs. LEO in GaN is usually configured so that the lateral growth advances along the <10iO> direction, which allows faster lateral growth than the <li20> direction [70].

LEO shares the advantages of large grain size with OPG growth, namely that the density of grain boundaries, and the formation of dislocations at the grain boundaries are correspondingly reduced. There is an added potential advantage of LEO over OPG, however, in that the mask prevents threading dislocations originating at the NL and substrate interfaces from moving up into the HT layer; as a result these threading dislocations are completely blocked off. Most such threading dislocations then occur in large densities only in the immediate vicinity of the windows in the mask. Some dislocations originating in the unmasked region, however, seek the sidewalls rather than threading to the surface of the coalesced film [71,72]. In part, this circumstance can be traced to the general tendency for dislocations to seek out the nearest free surface in order to minimize strain energy. As in OPG growth, laterally directed dislocations act to induce lattice tilt, a tendency which increases with the overgrowth width (u;) to height (/i) ratio (w;//i) [63,73].

The lateral growth rate and the tendency to form sidewall facets is influenced by the V/III ratio. At a low V/III ratio, the sidewalls consist of inclined {1122} facets and the lateral growth rate is small. As the V/III ratio is increased, smooth vertical {1120} facets appear and the lateral growth rate increases. Continuing to increase the V/III ratio, however, leads to the formation of {1011} facets, a jagged morphology, and a fall in


growth rate [74]. A large lateral growth rate and smooth {1120} sidewalls are necessary for successful LEO growth of GaN, so that a value of the V/III ratio must be chosen that encourages both of these conditions.

The most technologically important aspect of LEO nitride growth, that of reducing the threading dislocations density, is illustrated by the AFM images in Fig. 20, where the surface at a LEO grain boundary is shown to be free of mixed dislocations. Dislocations with screw components act to terminate steps, a feature that is easily observable in GaN using AFM [73]. Unlike other semiconductors, GaN is relatively inert and is therefore without a thick native oxide that could mask surface structure [27]. AFM observations suggest that the dislocation density in regions of the LEO sample away from the windows in the mask may be less than 10^/cm^, although scanning electron microscopy (SEM), of some LEO samples treated with an UV-assisted KOH etch (i.e. photo-electrochemical etching, PEC) [75,76], suggests that 10^/cm^ is a more realistic estimate [77]. Thus, LEO may not always result in a significant improvement in film quality. It is apparent that a study using both PEC and AFM is needed to completely judge the efficacy of LEO. These two imaging techniques are complementary in that

Bulk GaN 10®- 10^° Dislocations/cm^

Step Terminations

LEO GaN <10®- 10^ Dislocations/cm^

No Step Terminations

lum Fig. 20. AFM of LEO growth and step terminations. The surface at a LEO grain boundary is shown to be free of mixed dislocations, whereas near the mask window the dislocations density is high. Dislocations with screw components act to terminate steps, a feature that is easily observable in GaN using AFM. AFM observations suggest that the dislocation density in regions of the LEO sample away from the windows in the mask may be less than 10^/cm^.


AFM is most sensitive to screw and mixed threading dislocations, whereas PEC is sensitive to edge and mixed threading dislocations [73,75,76].

Even in the case where none of the dislocations at the coalesced boundary thread to the film surface, LEO growth is faced with the problem of residual strains due to slight misorientations between coalescing grains. One approach to reducing such strains is that of Pendeo-epitaxy, a technique where lateral growth is seeded from <1010>-oriented stripes etched out of a conventionally grown GaN film [78]. The etching process removes several hundred nanometers of the SiC substrate as well, so that the growth proceeds from the {1120} sidewalls and remains suspended above the substrate, even after the film coalesces. In naming this approach Zheleva et al. adopted the Latin prefix pendeo, which is derived from the werh pendere, to hang on [78].

3.4. Dislocation filtering

Another novel approach to improving film quality is that of interrupting high-temperature growth with a series of low-temperature interfacial layers (ILs) grown under the same conditions as conventional NLs [79]. Weak-beam XTEM images of a GaN film, grown in NRL's CSS reactor at 130 Torr with AlN-ILs, are shown in Fig. 21 [80]. Diffraction contrast (g-b) analysis of the XTEM images indicates that the ILs primarily

1|lim

Fig. 21. Weak-beam XTEM images of a GaN film grown using multi-interfacial layer (IL) growth. Diffraction contrast {gb) analysis of the XTEM images reveals that the IL filters screw dislocations.


0002 0110 0112

1 im

Fig. 22. Weak-beam XTEM images of GaN/AlN IL interface of multi-IL structure. The orientation of the g vector (0002, 0110 and 0112, respectively) was varied to image: (a) threading screw dislocations, (b) threading edge dislocations, and (c) both screw and edge threading dislocations. Contrast if dislocations in the IL is seen in (a) and (c), but not in (b), indicating that the Burgers vectors of these dislocations are parallel to the c-axis (i.e. <0001>).

consist of dislocations with the Burgers vector perpendicular to the growth plane. This array of IL dislocations then act to annihilate threading screw dislocations, thereby reducing screw dislocation density to less than 10^/cm^.

Weak-beam XTEM images of the GaN film above the last AIN-IL of the 5 AIN-IL structure are shown in Fig. 22. Imaging conditions which highlight dislocations with <0001>, 1/3<II20>, or either of these two Burgers vector components are shown in Fig. 22 (a, b and c, respectively). Diffraction contrast analysis of the XTEM images indicates that the AlN-ILs consist primarily of dislocations, which, like threading screw dislocations, have Burgers vectors perpendicular to the growth plane (i.e <0001> Burgers vectors). This array of AIN-IL dislocations then act to annihilate threading screw dislocations, thereby reducing their density to less than 10^/cm^, as shown in Fig. 22a. A similar reduction in the screw dislocation density, using the IL approach, was also noted by Iwaya et al. [79]. Despite the large (2-6 |xm) GaN grain size in this film [11], the edge dislocation density measured in Fig. 22b is approximately lOVcml

In Fig. 22c, where dislocations with either <0001> or 1/3<1120> Burgers vector components are in contrast, a dislocation density of greater than 10^^/cm^ is revealed within the AIN-IL. The dislocations within the AIN-IL, however, arenot in contrast in Fig. 22b, indicating that the AIN-IL dislocations must not have 1/3 <ii20> components. Similarly, the dislocations that are incontrast in Fig. 22b, in the GaN layer just above the last AIN-IL, must have only l/3<Il20> Burgers vector components and are therefore threading edge dislocations. The screw dislocations appear to annihilate as they attempt to thread through the AIN-IL interfaces, thereby removing the screw dislocations


from the GaN film. As observed by Rouviere et al., for MOVPE-grown GaN, screw dislocations of opposite <0001>-type Burgers vector easily annihilate [54].

Despite the large (2-6 |xm) grain size in the 5 IL film, however, the edge dislocation density is ^10^/cm^. In contrast to screw dislocations, annihilation reactions involving edge dislocations seldom occur [81]. It was also observed that the XRD FWHM increased with the number of ILs. It may be that the lack of screw dislocations prevents strain relief between adjacent twist boundaries, with a corresponding increase in the XRD FWHM.

4. Defects and electrical properties

In contrast to essentially covalent semiconductors like GaAs and Si, GaN is strongly ionic [82]. One consequence of this strong ionicity is the wurtzite structure of the GaN lattice (as opposed to zinc blende of more covalent semiconductors). In wurtzite the distance between third-order Ga and N nearest neighbors is less than in zinc blende, which reduces the configurational energy derived from electrostatic forces [37]. For strongly covalent semiconductors, discontinuities such as surfaces result in dangling covalent bonds [83]. In strongly ionic materials like GaN, states associated with the lattice discontinuity at the surface are either few or energetically outside the band gap, so that the surfaces of GaN are not subject to fermi-level pinning [84]. Extended defects, such as dislocations, also act as lattice interruptions, and, like surfaces, do not generally have states within the band gap of strongly ionic materials [85]. Therefore, significant carrier recombination in ionic semiconductors like GaN is not expected to occur at dislocations. That is, extended defects in GaN should not act as deep electron traps. A possible consequence of such relatively benign extended defects is the ability of GaN-based light-emitting diodes (LEDs) to function despite large threading dislocation densities ('^lO^^/cm^) [86]. Although dislocations in ionic semiconductors are not efficient carrier recombination centers [87], they are highly negatively charged (as revealed by scanning capacitance microscopy [88] and therefore strongly scatter carriers [89,90]. This scattering, of course, acts to reduce carrier mobility in electrical devices.

4.L Point defects

The tendency for point defects to segregate to extended defects (and thereby influence the electrical activity of such defects) has been observed in other electronic materials [91]. Our objective is therefore to move from a general understanding of the role of extended defects in the electrical properties of heteroepitaxial GaN, to consider how specific problems due to extended defects affect electrical properties in GaN films, and develop strategies for minimizing their deleterious contributions.

Given the well argued conjecture that many of the extended defects in GaN are not intrinsically electrically active, we need to further examine the possibility that extended defects in GaN derive their electronic properties from associated point defects. There is a significant drawback to this approach, however, in that the role of point defects in the optical properties of GaN is not well understood. The configuration and


composition of the point defects responsible for yellow (2.2 eV) luminescence in GaN films, for example, are not clear, although there are a number of theories addressing the mechanism. Neugebauer and Van de Walle have used density-functional theory to calculate the formation energy of a number of defect configurations and have concluded that the Ga vacancy complexes Voa-Sica and Voa-ON are stable in n-type GaN and capable of functioning as the deep acceptor needed to generate yellow luminescence [92]. The photoluminescence study of Kaufmann et al. advances a convincing argument that yellow luminescence in their GaN films can be traced to Si [93]. In addition Kaufmann et al. show how blue (2.8 eV) luminescence can be traced to Mg in GaN and red (1.8 eV) luminescence to both Si and Mg in GaN [93].

4.2. Dislocations

To some degree dislocations can be thought of as internal surfaces. Eisner et al. adopt this viewpoint and observe that the low-energy {1010} plane serves as the internal surface for open-core screw dislocations and threading edge dislocations in GaN [94]. These two types of dislocations with {1010} internal surfaces are essentially benign and should not give rise to deep states within the band gap. There is also, however, a species of screw dislocations with a full (i.e. not open) core, as determined by the Z-contrast scanning transmission electron microscopy (STEM) imaging study of Xin et al. [95]. The strong distortion of the bonds at the core of a full-core screw dislocation are expected to give rise to associated states within the band gap [96].

Some of the attributes of dislocations in GaN have been addressed by SEM-based cathodoluminescence (CL) imaging of GaN films. Suguhara et al. used plan-view TEM and SEM/CL to study dislocations in MOVPE-grown GaN thin films [97]. Using panchromatic CL, Suguhara et al. imaged electron-transparent TEM samples held at ambient temperature and found that dark regions in the CL image are due to dislocations in the corresponding TEM image [97], indicating that these dislocations act as non-radiative recombination centers in GaN. From CL imaging experiments, Rossner et al. [98,99] and Salvanti et al. [100] conclude that dislocations act as non-radiative recombination centers in MOVPE and Hydride vapor phase epitaxy (HVPE) GaN, respectively. It should be noted that the SEM/CL experiment using an electron-transparent TEM sample, as conducted by Suguhara et al., has two advantages over CL measurements performed on a conventional bulk film: (1) the dislocations can be identified by TEM; (2) the thinner TEM sample allows for less broadening of the electron-irradiated area and hence better spatial resolution of the CL image [97].

Suguhara et al. estimated the hole diffusion length in n-type GaN as 50 nm by noticing that the loss of luminescence was most pronounced for regions where the spacing between adjacent dislocations was less than 50 nm [97]. This value stands in contrast to the 200 nm electron diffusion lengths measured in p-type GaN using electron beam induced conductivity (EBIC) measurements [101]. This small hole diffusion length may contribute to the ability of LEDs to function despite large dislocation densities.

In contrast to studies where dislocations are identified as non-radiative recombination centers, the CL observations of Ponce et al. indicate that yellow luminescence delineates grain boundaries in MOVPE GaN films [102]. The CL study of de Mierry et al. also


found that yellow luminescence is strongest at grain boundaries [103]. A CL study of grains in GaN grown by the sublimation sandwich method also found evidence for this tendency [104]. The CL observations of Christiansen et al., however, indicate that the intensity of yellow luminescence is uniform across GaN films grown by gas source molecular beam epitaxy (GSMBE) rather than concentrated at grain boundaries [105].

The rather great variety of outcomes in CL imaging of GaN films, especially regarding the optical signature of extended defects such as dislocations and grain boundaries, certainly deserves some comment. Even among GaN films grown by MOVPE, there is a lack of consensus on the identity of optical signatures for extended defects. One obvious explanation for the differences in these CL observations is that it is the impurities associated with the extended defects, rather than the extended defects themselves, which give rise to such optical features as yellow luminescence. Indeed, the calculations of Eisner et al., based on density-functional theory, indicate that most types of extended defects are not expected to generate the deep traps within the band gap that are necessary for these optical signatures [94,96]. These observations are in accord with the conjecture of Liliental-Weber et al., that screw dislocations configured as {1010}-faceted nanotubes derive their internal structure from the segregation of oxygen to the walls of the nanotube [106].

It should also be noted that optical properties improve with the lower threading dislocation density of LEO-grown GaN [107]. The use of LEO GaN has augmented the operating lifetime for laser diodes [69]. Furthermore, a study of p-n diodes fabricated on LEO GaN reveals a significant reduction in reverse-bias leakage current [108].

4.3. Grain boundaries

Scanning capacitance microscopy reveals that the edge and mixed-character dislocations, as well as the associated grain boundaries, are negatively charged [88]. This observation suggests that acceptors lie at these grain boundaries as well as at the dislocations defining these grain boundaries.

The electrical properties of a special class of grain boundaries in GaN have also been addressed by the TEM studies of Humphreys and coworkers [109-111]; in particular they have focused on double-positioning domain boundaries associated with the {1120} and {1010} habit planes, which are designated as DBl and DB2, respectively. Using electron energy loss spectroscopy (EELS) in the TEM, Humphreys and coworkers have compared spectra from DBl and DB2 with that of defect-free GaN. Like the dislocations built on {1010} surfaces, DB2 is benign and appears identical to bulk GaN in the EELS spectra. EELS analysis indicates that the {1120}-oriented DBl is heavily charged so that 1.5 electrons are bound to each atom at the boundary interface. It is the conjecture of Eisner et al. that these charges are the result of the trapping of Ga vacancies at DBl boundaries [94].

4.4. Carrier mobility

Although microscopy of individual extended defects and optical spectroscopy of point defects advance the understanding of the electro-optical properties of GaN, the mea-


surement of the aggregate properties of mobility and carrier concentration must have the final word on the suitability of such materials for electrical device applications. There is evidence that empirically derived values of carrier mobility and concentration values are consistent with carrier scattering by negatively charged dislocations defining the GaN grain boundaries [89,90,112]. The etching study of Youtsey et al. also suggests that dislocations in GaN are charged [75,76]. That GaN edge dislocations are negatively charged is supported by recent Z-contrast STEM and EELS measurements of Xin et al. [113]. Analysis of the Z-contrast images, however, suggests that the fraction of Ga vacancies in threading edge dislocation cores [114,115] is too small for the mobility reduction suggested by an analysis of electrical measurements [89,90,112]. Maximum entropy analysis of Z-contrast STEM images indicates that less than 15% of all possible Ga sites at the edge dislocation core are vacant [113]. This small fraction of Ga vacancies at edge dislocation cores therefore suggests that other impurities and point defects associated with the dislocation may be responsible for carrier scattering and the resulting reduction in mobility. It is also conceivable that carriers may be scattered by charged point defects that segregate to grain boundaries, as argued by Fehrer et al. [116].

As suggested by models of scattering by charged defects, the dislocation density must be less than 10^/cm^ before dislocations cease to significantly limit mobility [89, 90,112]. The existence of this threshold is supported by the observations of Watanabe et al. [97,117]. Using the PEC etching procedure of Youtsey et al., individual whiskers surrounding edge and mixed dislocations were revealed [75,76]. By determining the density of such whiskers using SEM observations, the density of edge and mixed dislocations can be accurately determined. Correlation of Hall mobility measurements and PEC/SEM observations agree with the claim that mobility does not increase significantly as the dislocation density falls below 10^/cm^. When the dislocation density falls below the 10^/cm^ level, other scattering mechanisms (such as those associated with point defects) have the opportunity to dominate [89].Changing the substrate nitridation procedure prior to NL growth has been shown to significantly alter carrier mobility as well as threading dislocation density [28,31,90]. It was found that reducing substrate nitridation time reduces the dislocation density from >10^^/cm^ tolO^/cm^. This reduction in the dislocation density leads to an increase in the carrier mobility at 300 K from 149 to 592 cm^/Vs. The effect of nitridation procedure on dislocation density and carrier mobility has also been investigated by Wickenden et al. [ll]._According to Wickenden et al., the preferred crystallographic configuration, GaN[2110]/sap[1100]; GaN(0001)/sap(ii20), for nitride growth on a-plane sapphire is brought about by nitriding at elevated temperatures (e.g. 1065°C). GaN films with this orientation were observed to have carrier mobilities of 500 cm^/Vs at ambient temperature [11,12]. Lower temperature nitridation (e.g. 625°C)_ results in the other observed configuration, GaN[liOO]/sap[liOO]; GaN(0001)/sap(li20), which suffers from poor grain alignment, with a resulting large dislocation density (>10^^/cm^) at the grain boundaries and carrier mobilities as low as 60 cm^/Vs. Similarly, Wu et al. found that c-plane sapphire substrates exposed to shorter nitridation times result in larger grains, fewer dislocations, and higher carrier mobilities as dislocation densities dropped from 10^^/cm^ to lOVcm^ [32]. It has also been shown by Fatemi et al. that by reducing the edge dislocation density from 5 x lOVcm^ to lOVcm^, while holding


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500

400

300 "^ o 3

200 ^ w

100

50 100 150 200 250 Reactor Pressure (torr)

Fig. 23. Electron mobility and concentration vs. reactor pressure. Si-doped GaN films grown at higher pressures exhibit increased mobility as pressure increases from 39 to 130 Torr.

screw dislocations density at 5 x 10^/cm^ the carrier mobility increases from 300 to 600cmVVs[62].

It is also conceivable that grain size may effect carrier mobility independently of dislocation density. For Si-doped GaN films grown in the NRL CV reactor, with dislocation densities that appear uniformly on the order of 10^/cm^, significant center-to-edge differences were found in mobility and carrier concentration at the center of a 2-inch diameter wafer recorded at ambient temperature (e.g. / = 83 cm^/V s and n = 2.34 X lO^Vcm^ at the wafer center; JJL = 192 cm^Vs and n = 6.0 x lO^Vcm^ at the wafer edge). The grain size at the sample edge was approximately 1 |xm, and 0.5 jxm or less at the wafer center. Smaller grain size may be the cause of the lower carrier mobility in the wafer center, due to enhanced carrier scattering at the grain boundaries [42].

It is not only in center-to-edge differences in electrical properties where grain size appears to play a role in electrical properties of GaN films. A characteristic relationship between growth pressure and structural morphology has been observed in films grown in both CSS and CV MOVPE reactor geometries by Wickenden et al. [11], with increased pressure resulting in larger grain growth. Si-doped GaN films grown at higher pressures exhibit increased mobility, within a specific range of pressure, as shown in Fig. 23. The Hall electron mobilities are plotted against temperature in Fig. 24. for samples grown at 39, 65, 130, and 200 Torr. The two higher-pressure films, in which similar large grain size was observed, appear to exhibit normal ionized impurity scattering behavior in the low-temperature regime.

The two lower-pressure films exhibit dramatically reduced mobility, which can be correlated to smaller grain structure of these films. The temperature dependence of the mobility of the lower-pressure films is consistent with models of charged edge dislocation screening [89,90,112].

The effect of screw dislocations on carrier mobility can be assessed from Hall measurements of GaN films grown with multiple AIN interlayers. Because of the significant decrease in the screw dislocation density in films grown using multiple AlN-ILs, the influence of screw dislocations on electrical and optical properties may be addressed by the study of these structures. Mobilities in excess of 700 cm^/Vs and carrier concentrations of ^ 2 x 10^^/cm^ were obtained in n-type Si-doped GaN

Structural defects in nitride heteroepitaxy Ch. 10 2,1 \

5

n o E

800

700

600

500

400

300

200

100

0

r - r - T - r y T - T I 7

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Fig. 24. Electron mobility vs. temperature. The Hall electron mobilities are plotted against temperature for samples grown at 39 Torr (diamonds), 65 Torr (squares), 130 Torr (triangles), and 200 Torr (circles). The two higher-pressure films, in which similar large grain size was observed, appear to exhibit normal ionized impurity scattering behavior in the low-temperature regime.

films grown using this multiple-NL approach. The relatively small density of screw dislocations may explain the superior electrical properties of this material. Similarly for Wu et al., the GaN material with the better electrical properties had a screw dislocation density of less than 10^/cm^ [32]. These data suggest that screw dislocations are deleterious to carrier mobility, as are edge dislocations.

Because Hall measurements reveal the bulk-like behavior of electrical conduction as a function of temperature in the Si-doped GaN, the improved electrical properties can be ascribed to improvement in the bulk GaN and are not due to the formation of a 2-dimensional electron gas (2DEG) at the AlN/GaN interface [118]. Over a narrow doping range {n ranging from 0.55 to 1.47 x 10^^/cm^), the mobility increases as the number of the AIN-NL increases. Yang et al. have also observed an increase in /x from 267 to 446 cm^/V s as the number of GaN IL increases from 1 to 4 [119].

4.5. Film resistivity

Because electrical devices such as field-effect transistors (FETs) and high-mobility electron transistors (HEMTs) require high-resistivity buffers to achieve pinch-off, the GaN buffer adjacent to the channel region must be highly resistive. Highly resistive GaN films are also important for device isolation. Growing highly resistive GaN films, however, is frustrated by unintentional doping (UID): the incorporation of impurities which act as dopants. In the case of GaN these unintentional dopants act as shallow donors. In order to achieve high-resistivity films, the deep acceptor concentration must exceed the shallow donor concentration. If the deep acceptor concentration greatly exceeds the shallow donor concentration in the HEMT, however, the 2DEG sheet carrier concentration will be lowered and device performance will be adversely affected.

Above a given growth pressure in MOVPE, which is reactor dependent, UID GaN films lose their highly resistive nature. In the NRL CSS reactor, this loss of high resistivity occurs as the growth pressure is increased from 39 to 200 Torr [12]. The


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200 torr

130torr

• ' • • * • ' • • '

65 torr

0.2 0.3 0.4 0.5 0.6 0.7 0.8

growth rate (jim/hr)

Fig. 25. Electron concentration vs. growth rate. The 300°K Hall electron concentration was observed to fall linearly with growth rate of the GaN/Si-doped films grown in the CSS reactor. The electron concentration would be expected to double as growth rate decreases from 0.72 |xm/h (at 39 Torr) to 0.38 mm/h (at 200 Torr), given a simple volume incorporation argument and a constant SiH4 dopant flow. The fact that the electron concentration at 200 Torr is six times that of the 39 Torr value suggests increased compensation and reduced donor concentrations in the films grown at lower pressure.

300 K Hall electron concentration was observed to fall linearly with the growth rate of Si-doped GaN films grown in the CSS reactor, as shown in Fig. 25. The electron concentration would be expected to double as growth rate decreases from 0.72 |xm/h (at 39 Torr) to 0.38 |xm/h (at 200 Torr), given a simple volume incorporation argument and a constant SiH4 dopant flow. The fact that the electron concentration at 200 Torr is six times that of the 39 Torr value suggests increased compensation or reduced donor concentrations in the films grown at lower pressure. Analysis of variable temperature Hall data for compensation levels was inconclusive in the Si-doped GaN films, due to the relatively high dopant concentration. The Hall electron concentrations are plotted against temperature in Fig. 26. The temperature dependence of the electron concentration is similar for the 130 Torr and 200 Torr films, but does not follow a simple exponential relationship in the 65 Torr and 39 Torr samples which were found to be much more resistive, even with relatively high 300 K electron concentrations. The variation of resistivity as a function of NL thickness has also been observed by Briot et al. [120]. The fact that GaN resistivity may be influenced by both growth pressure or NL thickness suggests that morphological structure is a common factor, in agreement with the grain growth mode of GaN growth proposed by Hersee et al. [121]. Edge dislocations defining grain boundaries may not directly affect compensation, but it has been suggested that their associated stress field may play a role in trapping effects [122].

The possible mechanisms responsible for the modulation of carrier mobility, carrier concentration, and donor compensation have been addressed by photoluminescence (PL) studies. In the series of Si-doped GaN films discussed above, yellow band emission (centered at 2.25 eV) is seen to be very strong in the 39 Torr film, less strong in the 65 Torr film, and very weak in the 130 Torr and 200 Torr films. Broad band emission centered at 3.0 eV is only significant in the 39 Torr film. These PL data suggest the presence of a deep acceptor that falls off with increasing growth pressure [12]. Yellow


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Fig. 26. Hall electron concentrations are plotted against temperature for samples grown at 39 Torr (diamonds), 65 Torr (squares), 130 Torr (triangles), and 200 Torr (circles). The temperature dependence of the electron concentration is similar for the 130 Torr and 200 Torr films, but does not follow a simple exponential relationship in the 65 Torr and 39 Torr samples which were found to be much more resistive, even with relatively high 300 K electron concentrations.

luminescence could be derived from electron recombination with deep acceptors trapped at threading edge dislocations as suggested by Eisner et al. [122].

The combined results of Hall and PL analysis suggest that the acceptor-type defects associated with the 2.25 and 3.0 eV bands are reduced at 130 Torr relative to the 39 Ton-film to a level that just compensates the intrinsic donor concentration, minimizing carrier scattering and increasing mobility in intentionally Si-doped films. SIMS measurements of the impurity levels in these samples indicate that the carbon concentration falls from 3 X 10^^/cm^ to 8 X 10^^/cm^ as the reactor pressure rises from 39 to 130 Torr. This fall in carbon concentration with increasing reactor pressure can be understood in terms of the enhanced probability that hydrogen reacts with the carbon on the film surface to form methane (CH4), thereby removing carbon from the film surface. As the compensating acceptor (possibly carbon) is further reduced at higher pressure, n-type conduction is enhanced, as seen by many groups in GaN films grown near atmospheric pressure. Because the carbon concentration is seen to decrease as the concentration of compensating acceptors decreases, it is reasonable to suggest that the carbon is acting as the compensating acceptor [123].

In a similar study of UID GaN films grown at varying pressures in the CV reactor, we observed that the conductivity of the films increased with pressure. When the HT layer was grown at 45 Torr, the films were found to be highly resistive, with a break-down voltage of greater than 1000 V. When the HT layer was grown at 250 Torr, however, the GaN film was found to be n-type (1 x lO^Vcm^) with high mobility (600 cm^/V s). XTEM analysis of these films also demonstrated that the films grown at higher pressure had larger grain size. The correlation between resistance and grain size is again in agreement with the multi-grained model of GaN growth [122].

Carbon concentration in GaN films grown in NRL's CV reactor is also seen to fall with increasing pressure. SIMS analysis indicates that the carbon concentration decreases from 4 x 10^^/cm^ to 1 x 10 ' /cm^ as the reactor pressure rises from 49 to 350


Torr. In a separate experiment GaN was grown in the CV reactor using variable pressure growth (VPG) such that high-pressure (250 Torr) growth was followed by low-pressure (49 Torr) growth. SIMS measurements of the VPG film indicate that the carbon level increased from 8 x 10^^/cm^ to 2 x 10 ' /cm^ with the fall in pressure. The Si concentration also decreased from 2 x 10 ' /cm^ to less than 1 x 10^^/cm^ whereas the grain structure and dislocation density of the film were unaffected by the change in pressure. This film was found to have a significantly higher breakdown voltage than in other films grown at 250 Torr in the CV reactor. In this case, the high breakdown voltage may be due to the fall in the Si concentration as well as to a decrease in the carbon concentration.

The effect of dislocations on film resistivity can be addressed by Hall measurements performed on GaN films with multiple ILs. Because the density of screw dislocations falls off with the number of AlN-ILs, carrier compensation due to screw dislocations can be assessed, to some degree by the way the calculated acceptor concentration AA decreases with the number of IL layers [80,124] in Si-doped structures. As the number of ILs increases from 1 to 5, A A falls from 1.74 x 10^^/cm^ to 0.51 x lO^Vcm^; the compensation ratio AÂ/A^D falls from 0.760 to 0.256. In the 5-IL film, PL measurements detect a lower intensity of yellow luminescence in the top 2 ixm layer, than in conventional MOVPE-grown GaN films. These PL observations then suggest that threading screw dislocations in this film (or the point defects surrounding these dislocations) contribute to yellow luminescence.

4.6. High-power device requirements

Requirements for nitride high-power microwave devices mandate highly resistive isolation layers, high mobility, and low trap density. Ideally, the GaN film is highly resistive (HR) when unintentionally doped (so that there are no significant shunting paths from source to drain [125]), and exhibits high mobility when intentionally doped. We have observed that MOVPE growth pressure profoundly influences the morphological structure and growth rate of GaN films, with a resultant influence on dopant incorporation and compensation level [123]. The growth rate and alloy composition of AlGaN films in HEMTs are also strongly influenced by the growth pressure, in agreement with reports of several groups [123].

Ambient temperature Hall measurements indicate that HEMT device structures fabricated on large-grained GaN films grown at NRL have been able to achieve high mobility (1500 cm^/Vs) and high sheet carrier concentration (1.2 x 10^^/cm^), which are necessary conditions for high transconductance [123,126]. Recently fabricated HEMT devices have achieved a transconductance of over 200 mS/mm [127,128]. The resistivity of the underlying HR-GaN buffer was found to be 10^ ^cm, allowing sharp device pinch-off [123,127]. On-wafer small-signal measurements have yielded a cut-off frequency ifj) of 90 GHz with a maximum oscillation frequency (/max) of 145 GHz: the highest values reported to date for a 0.15 |xm gate-length GaN HEMT [128]. In addition, trapping effects that have been known to cause drain lag (drain current transients in response to a drain voltage pulse) and current collapse (limitation of drain current due to electron trapping in the channel region) were significantly reduced in fabricated microwave devices [127].


In both of NRL's MOVPE reactors (CSS and CV), UID GaN films grown at low pressure (e.g. 40 Torr) are highly resistive, with typical breakdown voltages greater than 1200 V. When films grown at these low pressures are intentionally silicon-doped, however, they suffer from characteristically low mobilities. XTEM diffraction contrast imaging of these films shows small grains which are defined by threading dislocations. Within a certain pressure range, growth at increasing pressure results in larger grains and increased mobility of GaN:Si films, while simultaneously maintaining the capability for UID HR-GaN growth. At higher pressures, UID films become n-type, with high mobilities and low measured compensation [123].

AlGaN:Si/GaN HEMT devices have been grown with the HR-GaN layers deposited at 130 Torr in order to achieve large-grained films. As shown in Fig. 27, the GaN layer of the HEMT device has a large ('--5 jxm) grain size. The elimination of drain lag and the reduction in current collapse in this device structure may be due to the reduction of the density of grain boundaries, dislocations, or carbon contamination. The structure and composition of the AlGaN layer itself should influence the electrical properties of the HEMT as well. Many of the structural properties of the AlGaN layer can be determined by XTEM, as shown in Fig. 28. Here it is apparent that GaN/AlGaN interface suffers from approximately 5 nm of roughness. The lateral variation in the contrast of the

Fig. 27. XTEM of HEMT grain size. AlGaN:Si/GaN HEMT devices have been grown the HR-GaN under the 130 Torr pressure conditions favoring large-grained material. The GaN layer of the HEMT device has a large (~5 |xm) grain size. In the HEMT based on this material, drain lag has been eliminated and current collapse has been significantly reduced in fabricated devices.


100 nm 0002

Fig. 28. XTEM imaging indicates that GaN/AlGaN interface suffers from approximately 5 nm of roughness in this HEMT device structure. The lateral variation in the contrast of the AlGaN layer suggests segregation or clustering effects, such as would occur during spinoidal decomposition.

AlGaN layer suggests segregation or clustering effects, such as would occur during spinoidal decomposition [129-132,134].

5. Conclusions

Extended defects in heteroepitaxial GaN films grown by MOVPE scatter carriers, resulting in lower mobility, appear to surround themselves with point defects and impurities which act to compensate dopants. It also appears that point defects may be able to compensate dopants without associating with extended defects; the SIMS and TEM study of carbon in GaN films deposited by variable pressure growth supports this contention. In particular, it is interesting to consider carbon as a point defect involved in compensation, since it is an inevitable by-product of the MOVPE process which can be controlled, to some degree, by altering the reactor pressure.

Reactor pressure influences grain size as well as carbon concentration and there appears to be a reactor-dependent optimal pressure for growing grains that are large without the onset of faceting, or the onset of associated lattice tilting and twist boundaries. These reactor parameters for growing a film with the minimum extended defect density on a nucleation layer are similar to growth via LEO in that the lateral growth rate must be as large as possible without the onset of faceting. There is also reason to believe that both LEO and conventional growth can be optimized by the use of vicinal c-plane SiC or ^-plane sapphire substrates, in order to improve grain alignment and thereby reduce the edge dislocation density occurring at grain boundaries.


The role of the nucleation layer in heteroepitaxial GaN growth and the procedures for optimizing this layer are still not well understood. For some reactors, at least, it appears that the optimal nucleation layer goes down with a significant fraction of the film consisting of the zinc blende polymorph, which then transforms into the wurtzite phase upon annealing. Although there has been a preliminary effort to explain these structural constraints, there is not yet a sufficiently general understanding to guide a grower in achieving a good nucleation layer. There is some indication that optimizing the nucleation layer results in defining a specific film polarity (i.e. Ga-terminated) and that this desirable result may be achieved by reducing the oxygen composition and thereby eliminate oxygen-rich IDBs in the NL. It also appears that achieving a film with no inversion boundaries is frustrated by a rough substrate morphology.

Acknowledgements

This work was supported by the Office of Naval Research. We thank Larry Ardis and Bob Gorman for expert technical assistance. We also thank Evan Glaser and Steve Binari for helpful suggestions regarding the preparation of the manuscript.

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CHAPTER 11

Optical phonon confinement in nitride-based heterostructures

N.A. Zakhleniuk, C.R. Bennett, M. Babiker and B.K. Ridley

1. Introduction

The physics of semiconductor heterostructures and devices constituted, over the last two decades or so, one of the most exciting and rapidly developing research fields [1]. An important area of investigation, which was identified at the outset, concerned the main properties of the charge carriers and the lattice vibrations in heterostructures, as could be revealed experimentally, for example, using Raman measurements [2]. From a device application point of view, however, much effort was also devoted to understanding carrier-phonon interactions. Optical phonon scattering, in particular, has long been known to play the dominant role in determining the mobility in bulk III-V semiconductors [3] and it was only natural to contemplate how this key property would be modified in heterostructures.

At the nanoscale level, heterostructures present strongly inhomogeneous environments in which charge carriers and phonons coexist. This can cause confinement effects which should, in principle, lead to modifications of the physics relative to the homogeneous bulk. However, under these conditions not only that the gross properties of the charge carriers and the phonons would be subject to modifications, but, more importantly the carrier-phonon interactions themselves should suffer changes. The purpose of this chapter is to provide an account of carrier-phonon interactions and their manifestations in heterostructures with special emphasis on applications in the context of structures made of large-band gap semiconductors, most notably the nitride-based systems [4].

The characterisation of non-interacting carriers in heterostructures is relatively trouble free and has been successfully dealt with in terms of envelope function models involving an effective mass approximation [5]. In order to deal conveniently and practicably with phonons in heterostructures it seems reasonable to seek a continuum model which should be valid for long-wavelength vibrations and should essentially be analogous to the envelope-function model adopted for electrons. It turns out that in contrast with the case of electrons, constructing a continuum model for phonons in heterostructures is far from a straightforward matter.

The continuum model we must seek to obtain should correspond closely to the microscopic atomic models of lattice vibrations. This implies that within the limits

384 Ch. 11 N.A. Zakhleniuk et al.

where both theories are valid, the descriptions of a given phonon mode arising from the two separate (microscopic and continuum) frameworks should have the same frequency and the same field distribution, exhibiting the same spatial symmetry. Only when these basic requirements have been met can a continuum description of lattice vibrations be self-consistent and be confidently used as the basis for a broad range of phenomena, such as exist in Raman scattering or carrier-phonon interactions. A continuum model in the context of inhomogeneous systems has long been available for acoustic lattice vibrations [6], but not for polar optical (PO) phonons. As we explain later, dealing with polar optical vibrations presents analytical problems arising from the fact that these vibrations possess mechanical as well as electrical properties. The optical phonon fields must then experience jump conditions of both mechanical and electrical kinds at heterostructure interfaces. This necessitates specifying the correct forms of boundary conditions and applying them in derivations of the modes. To understand the basic issues involved in the construction of a consistent continuum model, it is useful to review briefly the development of the relevant work in this area.

The first significant work on polar systems was the phenomenological macroscopic theory of polar optical phonons in a homogeneous bulk polar material developed by Bom and Huang [7]. As is well known, the primary outcome of this theory was the derivation of the frequency-dependent dielectric function of the material. Once the dielectric function has been specified, the form of the electromagnetic modes can be found directly as solutions of a pure electromagnetic problem based entirely on Maxwell's equations and involving only electromagnetic boundary conditions. Because of this, the Bom and Huang model is often referred to as the dielectric continuum (DC) model. It should be noted that in the Bom and Huang theory the mechanical effects do play a role as they enter through the associated polarisation fields contributing to the dielectric function. In fact the treatment allows one to straightforwardly deduce the mechanical fields once the electromagnetic fields are known.

The Bom and Huang DC model was subsequently employed by Fuchs and Kliewer [8] to derive the modes of vibration for the inhomogeneous case of a layered medium. The central assumption of the Fuchs and Kliewer theory was that the dielectric function within a given layer is the same as that of the corresponding infinite medium, with adjacent layers possessing different dielectric functions. The allowed modes which are solutions of the wave equation in each region are specified in both spatial distribution and frequency after the imposition of electromagnetic boundary conditions which match the general solutions in adjacent layers. The main results of the Fuchs and Kliewer DC theory is the optical phonon confinement effect, which means that waves of specific frequencies can propagate only within the layers for which the frequencies are the bulk longitudinal or transverse eigenfrequencies of that material. A given wave in a layer of one material does not propagate in layers of the other type of material. Another important prediction of the Fuchs and Kliewer work is the presence of interface modes which have frequencies in the reststrahl bands of the materials and whose amplitudes decay away with distance on both sides of interfaces.

The Fuchs and Kliewer DC modes have been used in calculations involving electron-polar optical phonon interactions in layered semiconductor quantum well stmctures [9] and the theoretical results were compared with the corresponding results emerging

Optical phonon confinement in nitride-based heterostructures Ch. 11 385

from the bulk phonon model in which the quantum well electrons interact with the bulk phonons of one of the quantum well materials. It has been found that the Fuchs and Kliewer modes give rise to results exhibiting a better agreement with experimental results than do those emerging from the use of bulk phonons instead. This apparent success of the Fuchs and Kliewer theory should be contrasted with their failure when used to explain Raman scattering data. It has been found [10] that this theory failed to provide the correct interpretation of the Raman spectra from layered structures. In particular, the theory predicted the wrong symmetry of the confined modes identified in Raman scattering measurements [10]. It can thus be said that the Fuchs-Kliewer DC theory provides an adequate description of the phenomena in which individual separate modes do not play the key role but, rather, it is the total contribution from the entire set of allowed modes that is of significance. In the opposite case where single mode processes are observed, for example in Raman scattering, the Fuchs-Kliewer theory does not, in general, provide a reliable basis for comparison with experiment.

It has been suggested [10] that the conflicting roles played by the Fuchs-Kliewer theory in different physical contexts is due to employing macroscopic electromagnetic boundary conditions in the theory [8]. For confined modes such a step has the effect of imposing a zero electric potential at the interfaces with no restriction imposed on the mechanical field. Because the DC model does not incorporate any spatial dispersion effects, the mechanical equations of motion do not include any space derivatives of the ionic displacement field and so no mechanical boundary conditions need be specified. This is the reason why in the DC model the mechanical field is directly dependent on the electromagnetic field which is subject to the familiar electromagnetic boundary conditions.

On the other hand, it is physically obvious that at the microscopic level the mechanical motion of the atoms and ions at interfaces between different materials must differ from their motion away from these interfaces. At the continuum level, the influence of the interface must appear as boundary conditions imposed on the corresponding mechanical field. It turns out that these features can be taken into account by introducing spatial dispersion into the mechanical field equations [11] which then become differential equations and so have associated boundary conditions. This step puts the electromagnetic and mechanical fields in a polar medium on an equal footing and it also renders the model internally self-consistent and more advanced than the DC model. Because of the role played by spatial dispersion in this model it is appropriate to refer to it at this stage as the dispersive continuum model. As we explain later, when the dispersive continuum model is applied to heterostructures we obtain vibration PO modes which are, in general, a linear combination (hybrid) of longitudinal, transverse and interface-like solutions of the wave equation. This version of the dispersive continuum model has been referred to as the hybrid model.

The dispersive continuum model was initially applied to the GaAs/AlAs system [12-14] to evaluate the vibrational modes. This was followed by evaluations (based on the hybrid model) for electron-polar optical phonon interactions in quantum wells [15] and in the analysis of Raman spectra in GaAs/AlAs superlattices [16]. The results of these calculations turned out to be in very good agreement with the results of fully microscopic analyses of the PO phonons in GaAs/AlAs heterostructures [17].

386 Ch. 11 NA. Zakhleniuk et al

As we discussed at the outset, the general aim of the continuum theories is not just the enumeration of the vibrational modes, the derivation of their dispersion relations and the specification of their spatial distributions. In the context of semiconductor heterostructures the primary concern must be quantifying the carrier interactions with these modes, which is of importance for an adequate description of the performance of optoelectronic devices. For these reasons, both the carriers and the lattice vibrations need to be treated quantum mechanically. A rigorous quantization procedure for the PO vibrations using the DC model has already been developed [18], but there is need to extend the treatment to include the effects of the spatial dispersion in the theory, as contained in the dispersive continuum model mentioned above.

In this chapter we systematize the theory underlying the dispersive continuum model and apply it to describe the lattice vibrations in layered heterostructures, with particular emphasis on heterostructures based on III-V nitride materials. As we shall see, the nitride-based heterostructures have, in general, very special dynamical properties which distinguish them from the more traditional GaAs/AlAs heterostructures. The differences in properties between the two types of heterostructure are so significant that a more in-depth analysis of macroscopic lattice dynamics is required to deal correctly with the situation in nitride-based heterostructures. Another important question that we wish to address here concerns the mechanical boundary conditions. It turns out that the only rigorous self-consistent route to arrive at physically acceptable boundary conditions is to start from the microscopic mechanical equations which describe the vibrations of the separate ions and then carefully proceed to obtain the continuum limit. This is done here using the Keating model approach [19].

The general organization of this chapter is as follows. In Section 2 we present a brief description of the essential features of bulk nitride materials, particularly in relation to lattice vibrations and dielectric properties. In Section 3 we systematize a treatment of the quantum field theory of dispersive PO continuum modes in bulk nitrides, emphasizing the additional features introduced by the incorporation of spatial dispersion. This rigorous theory is presented here for the first time and applied in the context of electron-phonon interactions in the bulk. Section 4 deals with the application of the dispersive continuum theory to the situation in a heterostructure. Once more the inclusion of dispersion in the theory makes this section an original account presented here for the first time. In Section 5 we explore the microscopic origin of the continuum theory of PO phonons in heterostructures. In particular, we seek to shed some light on how the boundary conditions to be satisfied by PO modes at interfaces between different media emerge from a microscopic treatment when the continuum limit is carefully applied. In Section 6 we give a description of results emerging from the hybrid models, the double hybrid and extended hybrid models, in the context of electron-PO phonon interactions in double heterostructures and superlattices based on GaN systems. In Section 7 we highlight the existence of a sum-rule which holds whenever one is concerned with total contributions from the entire spectrum of allowed modes. This treatment too is presented here for the first time. The relationship between the dispersive continuum theory (in its hybrid model form) and the DC model is clarified. Section 8 contains a brief summary of the material presented.


2. Polar optical phonons in bulk nitride crystals

The very promising electronic and optoelectronic applications of nitride materials have fuelled many investigations of their physical properties particularly in low dimensional heterostructures. As far as the lattice dynamics of nitrides are concerned, much published research on the subject has appeared in recent years and it would be a difficult task to provide a complete review of all the current literature. In fact the number of publications continues to grow. Instead we shall aim to present here a general theoretical account of the macroscopic description of lattice vibrations in nitride-based heterostructures. We begin by outlining a brief description of the PO phonons in bulk nitride materials.

The most interesting structural property of the III-V nitride materials, such as GaN, AIN, InN, etc, is their ability to crystalize into two different crystal structures with different symmetries, namely, the cubic (zinc-blende ZB) and hexagonal (wurzite WZ) structures. Both of these crystal phases of nitrides have been successfully grown using Si or GaAs substrates for the cubic nitrides and sapphire substrates for hexagonal nitrides. The cubic crystals have two atoms per unit cell, whereas the hexagonal crystals have four atoms per unit cell.

Due to the cubic symmetry, the macroscopic parameters of the ZB crystals are isotropic. As a result of this the dielectric function S{(JO) is a scalar function:

2 2 CO^ — CO J

£(o}) = Soo-i f. (1)

Eq. (1) follows straightforwardly from the Bom-Huang model [7]. Here Soo is the high frequency dielectric constant, coi is the zone centre longitudinal optical (LO) phonon frequency which is related to the transverse optical (TO) phonon frequency CL>T by SOQCOI = Ssco^, with Ss the static dielectric constant. Substitution of the dielectric function in Eq. (1) in Maxwell's equations results in two PO phonon modes: a LO mode, whose frequency COL is given by the dispersion relation £((o) = 0, and a TO mode of frequency coj, which is given by the dispersion equation s~^(a)) = 0. There is nothing special here in the description of the properties of cubic GaN in comparison with, for example, GaAs besides the differences in the magnitudes of the dielectric constants and the values of the phonon frequencies. However, it is important to bear in mind that the difference in the numerical values of the corresponding parameters in these materials could have dramatic consequences for the electronic and optoelectronic device applications. For example, the Frohlich coupling constant and the LO phonon energy for GaN are af = 0.45 and hcoi = 92.8 meV, respectively. For GaAs we have Qf/r = 0.079 and Hco^ = 36.25 meV. The nitrides are then much more polar materials than the arsenides. As a result, the electron-PO phonon interaction in nitrides is almost an order of magnitude stronger than in GaAs.

The WZ crystals exhibit a uniaxial structure and have anisotropic properties. Due to the crystal anisotropy, the mechanical vibrations in which the atoms (ions) are displaced parallel to the c-axis have the frequencies COL (COT ) for the LO (TO) phonons and for the vibrations in which the atomic displacements are perpendicular to the c-axis

388 Ch. 11 N.A.ZakhleniuketaL

the corresponding frequencies are (JOIX_ {COTI) for the LO (TO) phonons. As a result the dielectric function e{(o) in the WZ crystal is a tensor function which is given by

(e^{co) 0 0 \ 8{a)) = 0 ex_{(o) 0 , (2)

with

e^{(o)

0 0

0 ex_{(o)

0

0 0

8 {(O)

% ,..2 (O"- — (O

£ ± M = £oo±^ 7^, (3) ft;; 'r_L

,2 _ ,..2 ft;^ — ft;; 'L e (ft>) = fioo - ; 2 ~ ' ( 4 )

where foo± and Soo are the corresponding components of the high frequency dielectric tensor. It is obvious that the description of the lattice vibrations using the dielectric function in Eqs. (2)-(4) in Maxwell's equations is far more complicated than in the isotropic case of cubic crystals.

The bulk wurzite-type crystals (mostly dielectrics like ZnO, ZnS, CdS, etc) have long been a subject for Raman light scattering analysis. As a result, the PO phonon modes in WZ crystals have been identified and extensively investigated both theoretically and experimentally. Much of the work done in the 1960s for wurzite crystals has now become relevant to WZ nitride crystals, like GaN, AIN, InN, etc. An excellent general analysis of PO phonons in WZ crystals was carried out in [20,21]. In these works, the Bom-Huang theory [1] was modified by including the anisotropy of the LO and TO optical phonon frequencies. The main result of this analysis of long- wavelength PO lattice vibrations in WZ uniaxial crystals is the identification of two types of phonons: one is the so-called ordinary phonon and there are two others called extraordinary phonons.

The ordinary wave has zero electric field E(r) = 0 (in the non-retarded limit) and the mechanical displacement vector u and polarization vector P are parallel to each other with both u and P simultaneously perpendicular to the phonon wavevector q and to the c-axis for any relative orientation of q and the c-axis. The ordinary phonons are transverse and their frequency is ft> = ft^j-x given by elîoS) = 0. Because the electric field of the ordinary phonons is zero, they do not couple to electrons.

For the extraordinary wave, the electric field E is always parallel to the phonon wavevector q (again this is true only in the non-retarded limit), the mechanical displacement vector u and polarization vector P have arbitrary orientation with respect to q and the c-axis and the dielectric displacement vector D is always perpendicular to q. The frequencies of both extraordinary phonons depend on the orientation of q with respect to the c-axis. In the non-retarded limit the angular dispersion of the extraordinary phonons is given by [20]:

6 (co) cos^((9) + 6^(0)) sin (6>) = 0, (5)

where 0 is the angle between q and the c-axis. This equation has two roots, in general.


which correspond to the two extraordinary phonon modes:

^1,2 = I [(î + ^ r i ) cos (6>) + (0)1^ + col ) sin (< ) ± ^(<^)]' (6)

where

D^{0) = [((w^ ^ ^2^) cos (6>) 4- (COIJ^ + 6t» ) sin (<9)]

+ 4(0)1 - ^T ) ( ^ L - ^T±) cos (6>) sin^(i9). (7)

Here we have neglected the anisotropy of the high-frequency dielectric constant by assuming sô ^ £oo± = oo-

The above equations can be considerably simplified if we take into account that, for strongly polar wurzite based nitride crystals, the differences between the longitudinal and transverse components of the frequencies, COL — COT and COL± — COT±, are large in comparison with the differences \a)L — COL±\ and Icoj — COT±\. Physically this means that the effect of the macroscopic electric field, which accompanies the PO lattice vibrations, is much stronger than the effect of the anisotropy of short-range mechanical, interatomic forces acting between the neighbouring atoms. In this case we obtain the approximate result D{0) = (col — col_^)cos^(0) + (colj^ — co\ )sin^(^) and the frequencies of the extraordinary phonon branches are [20]:

o)\ = (ol cos^((9)-|-(i;^j^sin^(6>), (8)

0)1 = 0)1 sin (6>) + o)\^ cos^((9). (9)

There is no simple polarization for the extraordinary phonon modes except for two special directions of propagation: q parallel to the c-axis (0 = 0) and q perpendicular to the c-axis (9 = 7r/2). For ^ = 0, the vibration with oî = a>i = ft;(Ai(LO)) is a Ai(LO) phonon and the vibration with 6t>2 = COT± = o)(Ei(TO)) is £'i(LO) phonon. When 0 varies from 0 to 7r/2 the above modes transform into Ei (LO) phonon and Ai(LO) phonons, respectively, with frequencies o)i = O)L± = o)(Ei(LO)) and 0)2 = o)T = o)(Ai(TO)), The mode of Ai symmetry is polarized along the c-axis while the mode of Ei symmetry is polarized perpendicular to the c-axis. Only in these two particular cases of propagation do the modes have proper LO or TO character and Ai or El symmetry [20]. In the case when the mode given by Eq. (9) has pure TO character (corresponding to either A\ or E\ synmietry) the associated electric field is zero and so the PO phonons do not couple to electrons.

For an arbitrary orientation of q, each of the extraordinary phonons, which are described by Eqs. (8) and (9), is a mixture of the LO mode (with Ai or Ei symmetry) and the TO mode (with Ai or Ei symmetry). It is obvious that the mode with frequency 0)1 is mainly LO-like in character because Eq. (8) contains the longitudinal frequencies o)L and o)L±, and that with frequency ( 2 is mainly TO-like in character because Eq. (9) contains the transverse frequencies O)T and O)T±. For these reasons, the electric field associated with the LO-like mode is of the same order of magnitude as in the cubic crystal, while the electric field associated with the TO-like mode is much smaller (approximately by a factor of \o)l - o)l^\/\o)\ - o)\j) and for <9 = 0 and 0 = n/2 the electric field is zero.

390 Ch. 11 N.A. Zakhleniuk et al

> 0 3

95

90

85

80

75

70

! " ' " ;

; ^ x

— ' 1 ' ' ' ' " "T •

Wurzite GaN

CO LL

J H

-]

]

-_

1 1 1 1 1 1 1 1 1 1 t . - . i

>

3

110

105

100

95

90

85

80

> ^ 65

3

60

30

en ' ' ' •

; % i

t '"TX

f . . . .

1 1 •

Wurzite AIN

1

'"u ]

i

^11 ' .

en ' '

''r

Wurzite InN

1

0 30 60 90

en Fig. 1. The angular dependence of the extraordinary wave phonon frequencies in wurzite GaN, AIN and InN.


Table 1.

GaN AIN InN

The phonon energies

hcoL (meV)

91.14 110.11 72.66

of the extraordinary waves

fiojLi. (meV)

92.13 110.98 73.53

for wurzite GaN, AIN and InN

hcoT (meV)

66.09 81.72 55.43

hcoTi. (meV)

69.56 83.20 59.02

The angular anisotropy of the extraordinary phonon frequencies is shown in Fig. 1 for GaN, AIN and InN. Table 1 shows the values for the PO phonon energies taken from the experimental results in [22] and [23]. The PO phonon spectra of GaN and InN are very similar in contrast to the AIN spectrum. As was noted in [24] this is not surprising since the cation masses (Ga and In) are about 5 and 8 times larger than the anion mass (N) and so the lattice dynamics are mainly governed by the motion of the nitrogen atom. In the case of AIN the cation/anion mass ratio is much smaller (about 2) and both the cation and anion motion govern the PO lattice vibrations. The angular dependences presented in Fig. 1 have been checked by ah initio calculations for GaN and AIN in [25], for GaN in [26] and for InN in [24] using dijfferent microscopic approaches. The calculations show an excellent agreement between the first principle data and the phenomenological Eq. (8) and (9).

The very small anisotropy of the LO modes in WZ GaN means that this will have little effect on the electron-phonon interaction. This was also recently confirmed by direct calculation of the electron-PO phonon scattering rate in wurzite Ga. The effects of the anisotropy on the scattering rate are larger in fact in the contributions due to TO-like phonons (Eq. (9)), but the overall scattering rate due to the interaction with LO-like phonons (Eq. (8)) is more than two orders of magnitude larger than that due to TO-like phonons. Therefore, the TO-like phonons can be safely omitted when calculating the electron scattering rate in a wurzite crystal.

The main conclusion [27] is that for wurzite nitrides it is a very good approximation to use the interaction Hamiltonian for a cubic structure ignoring all the angular anisotropics in the frequency dispersions. However, it must be emphasized that the complex angle- dependent structure of the wurzite phonon spectrum plays an important role in any Raman scattering investigations. The different symmetries of the Ai(LO, TO) and £'i(LO, TO) phonons facilitates their observation and easy identification in Raman spectra. This also facilitates not only the experimental verification of the phenomenological dispersion relations in Eqs. (8) and (9), but also the ability to deduce the zone-centre (F point) LO and TO PO phonon frequencies in the zinc-blende nitride structures once the Ai(LO, TO) and £'i(LO, TO) frequencies are known since the structural correspondence between ZB and WZ crystals has long been recognized [28].

The individual atoms have the same nearest neighbour configuration in both structures (the difference begins only in the third shell). The hexagonal WZ lattice can be obtained from the cubic ZB lattice by rearrangement of the planes of atoms perpendicular to the (111) axis [20,28]. Since the ZB crystals have two atoms per unit cell and the WZ crystals have four atoms per unit cell, the ZB Brillouin zone dimension


along the (111) direction is twice as large as the equivalent dimension in WZ along the [0001] direction. The main effect of this on the phonon dynamics is the folding of the phonon branches [29] at the new zone boundary. All frequencies at the symmetry point L of the ZB Brillouin zone are moved to the zone centre F point of the WZ Brillouin zone. The LO and TO zone-centre frequencies of the ZB crystal can be estimated as the angle-averaged values of the Ai(LO, TO) and EiCLO, TO) frequencies of the WZ crystal. This gives the following correspondence [26,30]:

coliT) <==^ I [co^ (Ai(LO)) + 2co^ (î(LO))], (10)

4 ( r ) ^=^ i [co^ (Ai(TO)) + 2co^ (î(TO))], (11)

where the left hand side gives the zone-centre frequencies for the ZB structure and the right hand side represents the corresponding modes of the WZ structure. The relations in Eqs. (10) and (11) are very useful for a quick estimation of the characteristic frequencies of one of the crystal structures if the frequencies of the other structure are known. A comparison of the results given by Eqs. (10) and (11) with the results of microscopic ab initio calculations [26,30] shows a very good agreement between them.

When the characteristic LO and TO frequencies of WZ or ZB structures are known at the high symmetry points, one can use this data for the calculation of the phonon dispersion curves (i.e. the dependence of the PO phonon frequencies on the phonon wavevector) along all the important directions within the Brillouin zone. The first principle, as well as phemonenological, calculations of the PO phonon dispersion in nitrides have been reported by a number of authors using different approaches (see, for example, [26,30-33] for GaN and AIN and [24] for InN).

The most interesting feature of the bulk phonon spectra in nitrides is the overlap of the dispersion curves for different materials. For example, the dispersion curves of GaN overlap with the dispersion curves of AIN and InN. This is because the LO phonon frequency of GaN lies within the reststrahl band of AIN and the LO phonon frequency of InN lies within the reststrahl band of GaN. This is the case for both ZB and WZ crystal structures. The overlap phenomenon does not arise in the GaAs and AlAs spectra where the corresponding reststrahl bands for each material are separated from the other by a frequency gap. This distinctive feature of the III-V nitrides spectra is due to the very small atomic mass of the anion (N) which is smaller than the cation mass (Ga, Al, In) for all the above nitride crystals. In the case of GaAs and AlAs the situation is different as the anion (As) mass is very close to the Ga mass and is about three times as large as the Al mass. The overlap of the phonon spectra for different nitride-based materials means that if these materials are in a heterostructure, PO modes excited in one of the materials can be transmitted through the heterostructure interfaces into the other material producing a propagating mode provided that the necessary boundary conditions [34] are satisfied at the interfaces. This transmission takes place only within the overlap range of the frequencies. Outside this range of frequencies there is practically no transmission unless the frequency is close to the classical interface polariton frequency [2] when an evanescent mode aides the transmission across the other material. Therefore, one can imagine three distinctively different regimes of the PO lattice dynamics in nitride-based heterostructures (with overlapping dispersion


curves) depending on the range of frequencies: one regime corresponds to the situation when transmission is possible with a totally propagating mode; another regime when there is transmission but in one material there is an evanescent mode; and a regime corresponding to the situation when there is no transmission at all. As we show later, these regimes require different approaches when calculating the frequencies and the normalized mode amplitudes of the PO lattice vibrations in heterostructures than used hitherto and we also need to examine the boundary conditions required.

3. Dynamics of dispersive polar optical lattice vibrations in bulk nitrides

3.1. General remarks

The lattice vibrations in the case of polar materials are a system of coupled mechanical and electromagnetic modes. Therefore, the PO modes are described by a set of mechanical field equations for the ionic displacements together with Maxwell's equations for the electromagnetic fields. When these modes are determined from the solution of the mechanical field equations and Maxwell's equations, any relevant application (for example, in the calculation of the electron-phonon interaction or the scattering intensity in Raman scattering) requires the evaluation of mode amphtudes. Since the field equations for mechanical and electromagnetic fields are linear equations, the mode amplitudes cannot be determined solely by these equations. The direct method for calculating the amplitudes is to follow the canonical quantization procedure of the fields [35]. This procedure is well described in the literature for acoustic and non-polar (deformational) optical phonons (see, for example, [36]). As to the theory of PO phonons, as far as we know, there exists no rigorous theory in the literature setting out the quantization of spatially dispersive polar lattice vibrations. Besides the clear importance of this issue from an academic point of view, it also has a practical value. Since various structures which consist of different polar materials (such as single heterostructures, double heterostructures, superlattices, etc.) are available for practical applications, it is useful to have a general expression for the PO mode amplitudes which can be applied to an arbitrary layered system. It is our aim here to show how such an expression can be arrived at within a rigorous and self-consistent approach. Although the theory is much more complicated for inhomogeneous heterosystems in comparison with the case in a bulk homogeneous medium, it turns out that it is very convenient methodologically to first develop the theory for the bulk material and use it as a starting point in considering the inhomogeneous layered systems.

3.2. Lagrangian and energy densities in a dispersive polar material

The most general and rigorous way to formulate a classical continuum description of polar lattice dynamics including spatial dispersion begins by introducing the Lagrangian density functional. As is well-known, the required Lagrangian density must reproduce, via the Euler-Lagrange equations, all the mechanical and electromagnetic field equations. At this stage we consider an isotropic, homogeneous system and so the treatment is more relevant to ZB than WZ crystal structures.


The Lagrangian density >C(r, t) for the system in question has the following form [13,37,38]:

2

C(r,t)='îw^-colw^) + — (-A + V0 j - (V X A)M - P • ( - A + V0 j

[-4pr] - iy22 (Â ^vA + i [î(V . w)^ + vl(V X w)^], (12)

where w(r, 0 = p^/û(r, t), u(r, 0 is the relative mechanical displacement between the positive and negative ions in the Wigner-Seitz cell at point r of the crystal at time r, p = m^_m_/iV(m4- + m_) with nin the ionic masses, N is the number of ion pairs per unit volume, COT is the TO frequency and 722 = ( 00 — l)/47r with oo the high frequency dielectric constant and c the velocity of light in vacuo. For simplicity we assume here that p is constant throughout the system. This is of course not necessarily the case for inhomogeneous systems and we will take into account changes in such properties when we consider inhomogeneous systems. The electric E(r, t) and magnetic H(r, 0 fields are given in terms of the scalar and vector potentials 0(r, 0 and A(r, t) by the equations

E(r,r) = - V 0 ( r , O - - A ( r , O , (13) c

H ( r , 0 = V x A(r,r) . (14)

The polarization field P(r, t) is expressed in terms of the mechanical displacement field w(r, t) and the electric field E(r, 0 by the following phenomenological equation [7]

P(r, 0 = yi2w(r, 0 + y22E(r, r), (15)

where yu = [sooicol — a;^)/47r] and coi is the LO phonon frequency which is related to COT by the relation col = ^^r^s/ôo with Ss the static dielectric constant.

The last two terms in the square brackets in Eq. (12) take into account the effect of spatial dispersion on the lattice oscillations. Here vi and vj are the velocity parameters which characterize the bulk dispersion of LO and TO modes and can in principle be determined from experimental measurements [16,37]. They are given by vl = c\\/ii and v\ = C44//Z where cn and C44 are the optical elastic constants [6] in the so-called reduced notation (cn = cim, C44 = C2323). In the literature the last two terms in Eq. (12) describing dispersion are given in a different form (see, for example, [13]):

J^dsp (r. 0 = I X I ^ -/it/ V; Wk V/ wi. (16) ijki

In the case of isotropic dispersion Z/y / is

'Zîjki = ^îjhi + BSikSji + C8ii8jk. (17)

The expression in Eq. (16) is not the same as the corresponding expression in Eq. (12). After a somewhat lengthy manipulation, L^sp can be presented as

Cdsp(r. t) = \[(A + B^ C)(V . vf + A(V x w)^]

UA + 5 ) V . [(V • W - W • V)w]. (18) 2


In accordance with the general properties of Lagrangians [39], the Lagrangian density is not unique. In particular, one can add to the Lagrangian density the divergence V • X of an arbitrary field X and this will leave all the field equations and total energy of the system unchanged. The last term in Eq. (18) satisfies this condition with X = -\{A + B)V • [(V • w — w • V)w] and, hence, can be dropped. The rest of the expression in Eq. (18) is exactly the same as the last term in Eq. (12) with (A + ^ + C) = i; and A = v^.

The Hamiltonian density of the polar medium follows from the Lagrangian density in Eq. (12) using the canonical procedure as

H(r, 0 = X ] ny(r, t)qj{v, t) - C(T. 0 , (19) j

where qjir, t) is one of the dynamical variables and Fly the momentum canonically conjugate to ^y(r ,0 ,

dqj{r,t)

Using the components of A and w as well as 0 as field variables, we obtain from Eqs. (19) and (20)

H(r, t) = Uw^ + (olw^) + - ^ rôo^' + H^] + T^D . V0

- ^ [ i ; i ( V . w ) 2 + i ;^(Vxw)2], (21)

where D is the electric displacement vector field,

D(r, t) = E(r, t) + 47rP(r, t). (22)

The expression in Eq. (21) is the desired energy density of the polar medium taking into account spatial dispersion.

3.3. The Hamiltonian of the whole polar system

In order to quantize the total energy of the system it is necessary to evaluate the total Hamiltonian

/ / = f n(r,t)d\. (23)

In order to carry out the above integration, we need the full set of field equations for the mechanical and electromagnetic fields in the polar material. These field equations follow from the Lagrange-Euler equation [39] for a canonical field variable q:

±(^\=.^- y ^ (24) dt\dqj) dqj ^£- d(V,qj)

396 Ch. 11 N.A. Zakhleniuk et ah

We obtain the system of Maxwell's equations

V . D(r, t) = 0,

V x E ( r , 0 = - - H ( r . O , c (25)

V . H(r, t) = 0, V x H ( r , 0 = - D ( r , 0 ,

c

together with the Newton equation of motion for the mechanical field w

w(r, t) = -ct>^w(r, 0 + yi2E(r, t) - vlv (V • w(r, t)) + vjv x (V x w(r, 0 ) • (26)

Substituting the Hamiltonian density given in Eq. (21) into Eq. (23) and using the first Maxwell's equation in Eq. (25) as well as Eq. (26) in the non-retarded limit (c -> oo, A = 0 and H = 0) we obtain

H = \ / [ i b ^ - w - w - vlV • (w(V . w)) - v^V • (w X (V X w))] d

In deriving the above equation we have also used the relations [33]:

V . (w(vlV ' w)) = vl(W . w)2 + w • V(i;2 V • w),

V • (w X (vjV X w)) = vj(V X w)^ + w • V X (u |V x w).

r. (27)

(28)

Within the bounds of isotropic continuum theory, the Hamiltonian in Eq. (27) is an exact result obtained taking into account the bulk dispersion of the optical vibrations. The interesting point about this result is that the integration of the last two terms in Eq. (27) gives exactly zero. To see this we need to use Gauss's theorem / V • Fd^r = ^^ F • da and the condition that F ^- 0 at the integration surface S which is taken at infinity where all the fields are zero. The final result for the Hamiltonian is

H=\ ( [ii;2(r, 0 - w(r, t) • w(r, r)] d\. (29)

Since the above expression contains not only w(r, 0 but also its time derivatives, w(r, t) and w(r, t), it is essential to work in reciprocal (Fourier) space. This is also important for the subsequent solution of the field equations. In the case of bulk homogeneous systems we use three dimensional Fourier transforms for all the fields which we denote as F(r, t) in the form

(30) F(r,r) = - i - r/*F(q)^'(^--"«''^j3^ + f ¥Hq)e-'^'^'-''''^d^q

Using Eq. (30) we obtain for the Hamiltonian

H = - ^ j a>>(q) • y^*iq)d'q. (31)

The components of the phonon wavevector q are quasi-continuous and take multiple values of the steps A^^ = In/La, a = x,y,z where Vb = L^LyL^ is the quantization


volume of the system. Thus we can apply Bom-von Karman substitutions

(27r)-j d'q <=> 5] , 5(q - qO ^=^ (^^Q^Q'' (32)

and present the Hamiltonian in Eq. (31) in the form

H = ^y]a>^w(q) .w*(q) . (33)

The Hamiltonian in Eq. (33) has exactly the same form as the Hamiltonian in Eq. (6.23) in [18] obtained for bulk non-dispersive homogeneous polar material. Of course, the vibrational frequencies coq are different in the cases of dispersive and non-dispersive media. The fact that the total Hamiltonian of the dispersive system does not contain explicitly the dispersion characteristics of the medium {vi and fr) is a reflection of the physical meaning of spatial dispersion. In general, the spatial dispersion is responsible for the redistribution of vibrational energy between all allowed modes, but it does not affect the total energy of all the modes within the medium.

The quantization of this Hamiltonian and the normalization condition for the mechanical displacement mode amplitude can be obtained by applying the following linear transformations

w(q) = K e ( q ) +«n(q) ] w;o(q),

w*(q) = K e ( q ) - /n(q)] w;*(q).

Imposing the mode amplitude normalization condition in the form

wô(q)-it;o*(q) = ^ , (35)

we obtain the Hamiltonian

^ = iEK2'(q) + n2(q)]. (36) q

This is the Hamiltonian for a system of independent classical oscillators and its quantization follows simply by the conversion of j2(q) and n(q) into the quantum-mechanical position-like and momentum-like operators <2(q) a d n(q) which satisfy the commutation relation [|2(q), n(qO] = iM^^^. The second quantized form of the Hamiltonian is obtained by introducing the annihilation a(q) and creation a^(q) operators which are related to (2(q) ^^^ n(q) by the relations

a{q) = ^j== Lqe(q) + /n(q)l, V 2 ^ L J (37)

aHq) = j = [a;qe(q) - /n(q)] ,

and which satisfy the commutation relations [^(q), <3^(q')] = ^q,q'- This leads to the Hamiltonian in the second quantized form

/f = ^ fk^q [a^ (q )a (q ) - f i ] . (38)

398 Ch, 11 NA. Zakhleniuk et al.

It is important to note that the normahzation condition in Eq. (35) is fixed by the requirement that the classical Hamiltonian of the system should have the canonical form in Eq. (36). It is only then that the second quantized Hamiltonian can be reduced to the canonical form in Eq. (38).

The quantum mechanical displacement field operator w(r, t) follows from Eqs. (30), (34) and (37):

w(r, t) = ^y] {2hco)'f^ [w;o(q)fl(q)^'^^'-"'''^ + wl{q)a\ii)e-'^'''-''-% (39)

3.4. Dielectric function of a dispersive polar medium and the electron-phonon interaction Hamiltonian

In order to investigate the coupling of the PO lattice vibrations to the electrons, it is necessary to evaluate the Coulomb potential operator 0(r, t) associated with the vibrations. To this end we need to establish the relation between the Fourier amplitudes 0(q) and w(q). This relation follows from the field equation Eq. (26), taking into account Eq. (13), which gives E(q) = —/q</)(q).

In the case of a dispersionless medium {vi = 0 and VT = 0) the required relation between 0(q) and w(q) can be obtained straightforwardly in a general form from Eqs. (12), (25), (26) and (30) as

-1-1/2

^ ' w;q(q), (40) 0(q) = - -An dcol

where we have used the notation u;q(q) = w(q) • Cq, Cq = (\/q. The dielectric function £(a>q) of the polar non-dispersive bulk material is obtained from Eqs. (15), (22), (25) and (26). We write

D(q) = f(c(;q)E(q), (41)

where 2 2

s{co^) = Soo-\ J. (42)

In the case of a dispersive polar medium {VL :^^ and vj ^ 0) the derivation of the dielectric function is not so simple. The Fourier transform of Eq. (26) gives

-yi2E(q) = {a)\ - 4 ) w ( q ) + iîq • (q • w(q)) - u^q x (q x w(q)). (43)

In order to obtain the dielectric function from Eqs. (15) and (22) we need to express w(q) in terms of E(q) by solving Eq. (43). This can be done by decomposing all the fields F(r, t) into longitudinal FL(r, t) and transverse FT(r, 0 parts as follows [40]:

F ( r , 0 = FL(r,0 + FT(r ,0 , (44)

where

V x F L ( r , 0 = 0, ( V . F L ( r , O ^ 0 ) ,

V . FT(r, 0 = 0, (V X FT(r, r) 7 0) .


It follows from Eqs. (45) and (30) that FL(r, t) is parallel to q and FT(r, 0 is perpendicular to q. In order to split Eq. (26) into two separate equations for the longitudinal and transverse fields, it is necessary to substitute Eq. (44) into Eq. (26) and take the curl and divergence of this equation [41] (or alternatively one can take the scalar (q •) and the vector (q x ) products of Eq. (43)). Next, using Eq. (45) together with the Helmholtz theorem [18,40], one obtains the equations for the longitudinal (A = L) and transverse (X = T) fields

-Ki2Ex(q) = [col -col^ vlq^] Wx(q). (46)

Finally using the equations in Eqs. (15) and (22) we obtain the expression

Dx(q) = Sx(co^, q)E),(q), (47)

where the dielectric functions 6x(cOq, q) of the longitudinal and transverse fields in the bulk dispersive polar material are

0)1- (JD\-V vlq^

Â((Wq, q ) = Soc—. 2 . 2 2 - ("^^^

Eqs. (47) and (48) represent generalizations of the Eqs. (41) and (42) to the case of a dispersive polar material.

In the case where the dielectric function is known, the problem of finding the vibrational frequency spectra becomes purely an electromagnetic problem which can be tackled by solving Maxwell's equations. Using the first two Maxwell's equations in Eq. (25) together with Eq. (45) we obtain for the electric displacement field V . DL(r, r) = 0 and V X DL(r, 0 = 0 and for the electric field V • ET(r, 0 = 0 and V X ET(r, t) = 0. In accordance with the Helmholtz theorem, this means that everywhere in the bulk homogeneous system

DL(r,0 = 0, (DT(r,O7^0),

ET(r,0 = 0, ( E L ( r , O ^ 0 ) .

Substitution of these equations into Eq. (47) yields the following equations

ei{o)q, q)EL(q) = 0 => Siioy^. q) = 0,

^r^^^q, q)DT(q) = 0 => £f k<Wq, q) = 0.

Therefore the frequency dispersion of the longitudinal and transverse fields is

Îx^^l-^W^ ^ = L,T. (51) The Fourier amplitude of the Coulomb potential of a dispersive medium is given by

1/2

WL(q). (52) 0(q) = - -1 dSLJCOq^q)

Alt dcol

where a>q = coî and wiiq^ = yfiiq) • Cq. In deriving Eq. (52) we have used the fact that E(q) = - / q0 (q ) , together with Eq. (49). This yields < (q) = /E(q)/^. Next we use the relation between EL(q) and WL(q), given in Eq. (46), and the expression for dielectric


function siicoq, q) in Eq. (48) to arrive at Eq. (52). The quantum mechanical operator of the Coulomb potential 0(r, 0 is obtained using Eqs. (39) and (52). The interaction Hamiltonian operator Heir, t) = -e4>(r, r), which effects the coupling between the electrons and the PO phonons, is

HAr, t) = -i J2 ^ ^ ^ ^ [a(q)e'<''-^-'"'> - a^(q)e-'«'-'-"">], (53)

where the interaction parameter ai (q) is

2dSLio)q,q) QfL(q) =

,2 _ ,.,2 , ,2^2

"^ a . ^ hxo.. (54)

where <Wq = <wi — iî^ • The Frohlich coupling constant r/^(q) which defines the strength of the electron-phonon interaction is given by TL(S\) = —/Vc^L(q)/^- Using Eqs. (48) and (54) we obtain

11/2

rL(q) = - -Ine^ o)}

Vo CO-y^ ( ) ^ q ^ (55)

This expression is a generalisation of the Frohlich coupling constant to the case of a bulk dispersive polar medium. In the non- dispersive medium we have o)î = coi and the expression between the square brackets in Eq. (55) no longer depends on q.

The analysis of the polar optical lattice vibrations which we carried out in this section is quite general and can be applied to any bulk polar material which exhibits spatial dispersion in the frequency of vibration. This is particularly important for the case of nitrides which do exhibit this property [30-33]. However, besides providing a rigorous derivation of the interaction Hamiltonian and the Frohlich coupling constant for a dispersive medium, the above analysis now forms the basis for developing the theory of polar lattice dynamics in inhomogeneous media, as we now discuss.

4. Continuum dispersive dynamics in semiconductor heterostructures

4.1. Hamiltonian function of a polar layered heterosystem

The continuum description of PO vibrations in semiconductor heterostructures has been the subject of a considerable number of studies in recent years (see, for example, [12-16] and [37,38] and references therein). These studies were focused mainly on the solution of the field equation to obtain an explicit form of the field distributions and mode frequencies of the PO modes in different heterosystems such as single and double heterostructures and superlattices. To the best of our knowledge, the important issues of mode quantization and mode amplitude normalisation in the presence of dispersion have not been addressed rigorously in the existing literature. These issues constitute the primary concern of this section.

The type of inhomogeneous system we will consider here is in the form of multilayers of different materials separated by smooth planar interfaces. We assume that the z-axis is perpendicular to the interfaces with the x and y axes lying in a plane parallel to the


interfaces. This system, in general, does not possess translational symmetry along the z-axis, but the translational invariance property still holds in the x-y plane. This feature suggests that we should introduce, instead of Eq. (30), the two-dimensional (2D) Fourier transform

F(r, t) = ^ \J F(q , z)e'^^ ''--^ ^^d'q + j F*(q , z)^-^<^ ' - ^ ^^d'q ] ,

where x = (x, y) is the component of the position vector in the x-y plane. The three-dimensional Bom-von Karmen relations in Eq. (32) should now be replaced by their two-dimensional analogues

^/.»,«i:, .(,-,')«^.,.„ ,57,

where AQ = LxLy is the (large) area of an interface. The Hamiltonian defined in Eq. (27) is valid for any homogeneous or inhomogeneous

system. The only condition which has been used in deriving this expression for an inhomogeneous layered system is the continuity of the normal component of the vector D(r, O0(r, 0 at the interfaces between different materials [18]. This is satisfied by virtue of the continuity of Dn(r, t) and 0(r, 0- Thus we may start our derivation from the Hamiltonian in Eq. (27). In order to integrate the last two terms in Eq. (27) which describe the spatial dispersion effects, it is necessary to use the following form of Gauss's theorem

\ V • F ( r ) J V = X ] /" V • F(r)c/V = J Z /" F(r) • d^ r. (58)

Here F is either yf(viV • w) or w x (i^^V x w), where / runs over all the layers. Layer i has volume V, which is bounded by the surface 5/. Assuming that all fields are zero everywhere at the outer part of the surface (assumed to be infinitely large) a direct evaluation of the last integral in Eq. (58) gives AQ ^ - {^F^'^zd — F^^'^^z/)], where Fj^^^ are the normal components of the vector F taken on different sides of the interface z = z,. The integral in question disappears if continuity conditions hold at all interfaces for the following expression

vlw,{V . w) + 4 [u;,(V X w), - Wy{V x w)^]. (59)

Note that starting from the Lagrangian density in Eq. (12) we have assumed that p is constant everywhere. In the layered system p is constant only within each layer. It can, however, be seen that the layered system case can be dealt with by making the following substitution everywhere in the dispersive terms: w(r, t) -^ u(r, 0 and v\j -> IJLVJ^T-

The above condition in Eq. (59) are automatically satisfied if the mechanical displacement u and the acoustic-like stress tensor are continuous at the interfaces. These conditions can be obtained by direct integration of the equation of motion Eq. (36) across the boundaries [6,43] (note that the additional term F in the equation of motion in [6,43], which in the general case may also give rise to a contribution to the boundary condition, appears if one takes into account a real crystal structure for the medium, i.e.


we consider an elastically anisotropic medium. Here we assume from the beginning that each layer is elastically isotropic, so the function F in [6,43] is zero). Assuming that the above conditions are satisfied, we deduce that the integrals in Eq. (58) are zero when applying them to the last two terms of Eq. (27). Therefore the Hamiltonian in Eq. (29) which was derived for a bulk homogeneous polar medium is also valid for an inhomogeneous polar heterosystem.

Using the Fourier transform of Eq. (56) in Eq. (59), we obtain the Hamiltonian of a layered heterosystem

00

—oo

which can also be presented in the form

oo

^ = — X ! / ^q w(q , z) • w*(q , z)dz, (61) q

where we have used Eq. (57).

4.2. Quantization of the Hamiltonian

In order to quantize the Hamiltonian in Eq. (61) and to derive the normalisation condition for the mode amplitudes in the case of a layered heterosystem, we need to apply transformations as in Eqs. (34) and (37) where w(q) and wo{q) should be replaced by w(q , z) and u;o(q , z). The normalization condition imposed on the mode amplitude woiq , z) is

00

Woiq , z) • Wo(q ,z)dz = —Y- (62) q /

Using this condition together with Eqs. (34) and (37), we obtain the second quantized Hamiltonian

H = J2^<i [ (q )^(q ) + i] • (63) q

The second quantized quantum-mechanical operator of the lattice displacement is derived in similar manner to the case of a bulk homogeneous system. Using Eq. (39) we obtain

w(r, 0 = j ^ X^ (2ruo^ y^' [woiq )a(q )^'^^ " ' ^ > + u;*(q )aHq )^-'^^ ''-^^ ^>].

' ^ (64)

4.3. Electron-phonon interaction hamiltonian in layered heterosystems

Our aim here is to derive the interaction Hamiltonian Heir, t) = ~^0(r, 0- To this end it is necessary to obtain the Coulomb potential operator 0(r, t). There is a fundamental


difference between solving this problem for the case of a polar inhomogeneous layered system and solving it for the case of a bulk polar homogeneous medium. As we have already pointed out in the case of a bulk homogeneous system, the problem of evaluating the lattice vibrational modes can be solved as a pure electrodynamical problem. This was possible because we were able to derive an explicit expression for the dielectric function of the dispersive medium which is given by Eq. (48). In turn, this equation was derived using the field equation Eq. (46) for the Fourier amplitudes, which provides a relation linking Wx(q) to Ex(q). This relation shows that the connection between Wx(q) and Ex(q) is local, which means that the mechanical displacement Wx(q) at any point q of the Fourier space is expressed in terms of the electric field Ex(q) at the same point q. This is not the case for the inhomogeneous heterosystem which possesses interface boundaries. In this case the relation between Wx(q) and Ex(q) is non-local, i.e. the displacement field w at a given point z is determined by the electric field values E^ evaluated at every point z in real space.

In order to see this explicitly, we need to decompose all the fields in Eq. (26) into longitudinal and transverse parts, as in Eqs. (44) and (45) and take the Fourier transform of the equation obtained. This gives rise to the relation

1 Ex(q,z) =

Yn

^2 2 2 2 2 2 w,(q,z), (X = L,7). (65)

We see that Wx(q , z) is expressible in terms of ^x{q , z) by an integral relation. This is clearly different from what we had in Eq. (46) for the inhomogeneous infinite medium. The non-local form of the relation between Wx(q , z) and EA(q , z) does not permit one to introduce the dielectric function for the inhomogeneous system under consideration. As a result, the problem of calculating the lattice vibrational modes can no longer be presented as a pure electrodynamical problem. The solution of the mechanical displacement field equation is required in the first instance in order to determine the corresponding electric field modes. This problem will be considered in the next section. It will be shown that the longitudinal (A = L) and transverse {k = T) lattice vibrations are governed by the wavevector Q with components (q ,qx) where the confinement wavevector qx is defined by

2 2 2 2

ql = 5 . (66)

Using Eq. (66) we can present Eq. (65) in the following form

1 8ex(a)a , Q) Ex(q , z) =

-,-1/2 ,

47r dcol wx(q ,2) + -Ûx^ + ^ j W x ( q , z ) , (67)

where the derivative in the first term should be taken at the frequency satisfying

4 =col,=col-vlQ\ (68)

where Q^ = q^ -^ ql- In writing Eq. (67) we have formally introduced the following notation

col -^] ^ÎQ^ s,{<o^ , Q) = ôo-^ T-^2- ^ >


It should be emphasised that the expression in Eq. (69) is not the dielectric function of the inhomogeneous heterosystem. This is just a formal expression written here in a form similar to the dispersive dielectric function of the bulk polar medium given in Eq. (48). The reason for introducing ex(coq , Q) in Eq. (69) is that it allows a straightforward transition in Eq. (67) to the case of the bulk homogeneous medium. In this case d^/dz^ -> —q^ = -ql and, on making use of the relation Q^ = q^ -{-q^ = q^^ the last term in Eq. (67) becomes identical to the expression from Eq. (46) for the bulk homogeneous system. It follows from Eq. (67) that both the longitudinal EL(q , z) and the transverse ET(q , z) fields are not equal to zero for the inhomogeneous system (in the case of the bulk homogeneous system ET(q , z) = 0, see Eq. (49)). The explicit forms of these fields are as follows

EL(q ,z) = -1 a^x(^q,Q)

An 80.2

-1/2

WL(q , z) + K^'^S) WL(q ,z),

ET(q , z) = — U r + ^ ) T(q , z).

(70)

In the polar medium the electric fields are created by the mechanical lattice displacements and, therefore, the electric fields are zero if the displacements are zero. Note that the opposite is not necessarily true. For example, in the bulk homogeneous medium E j = 0 as can be seen from Eqs. (46), (49) and (51). In the case of an inhomogeneous medium the transverse electric field ET(q , z) is not equal to zero precisely because the dispersion of the lattice vibrations is taken into account (vj 7« 0). If the dispersion is ignored, then for both homogeneous and inhomogeneous media we haveET(q , z) = 0.

The Coulomb potential 0 ( q , z ) is obtained using Maxwell's equation V x E(q , z ) = 0, which gives E(q , z) = - V 0 ( q , z ) . The Fourier amplitudes are such that £ (q , z ) = -iq 0 ( q , z ) ; £^(q ,z ) = -9</>(q .z)l^z where E (q , z ) = q • E (q ,z)lq . Using Eqs. (64) and (70) we obtain the required expression for the interaction Hamiltonian operator for an arbitrary polar layered heterosystem in the form

.(r,0 = - / i E yJ^hXD^

Ao

1 a£x(<Wq , Q ) -1/2

An %co\ 'WL (q , z , x )

2 2

- V ^ ^ f A a ) i i x ( q , z , x )

(71)

'qL The subscript L in the first term indicates that the derivative is taken at tWq = o), (see Eq. (68)). Here we have introduced the following notation

Wx(q , z, X) = «;ox(q . z)a(q )e'*'' "-'"'- " - wlâHq )e-'<'' "-'""' '\ (72)

w(q , z, X) = WL(q , z, x) + WT(q , z, x), (73)

wx (q , z , x) = wx(q , z , x ) - e (74)


fx{z) = \+qf^^. (75)

The differential operator Tx{z) acts only on the mode amplitudes u xoCq > z) as can be seen from Eqs. (72) and (75).

The presentation of the interaction Hamiltonian operator in the form given in Eq. (71) is particularly useful as it explicitly displays the additional contribution to the interaction in the polar layered medium (the second term in Eq. (71)) due to the spatial dispersion. Also Eq. (71) facilitates a straightforward transition to the case of a bulk homogeneous polar medium. The dispersionless limit is achieved first by setting fxiz) = 0 and thus the entire second term in Eq. (71) vanishes. Next in the first term we set Q -> q; L(< q »Q) -^ ^L(<^q,q) ûd u'Ao(q ^ z) -^ u}xo(q)e^^'^ and finally we switch from a

2D to a 3D Fourier transform (which amounts to the formal substitution: q -^ q and ^0^ Ylq ~^ o~ Xlq)- These steps lead to the expression for the bulk as shown in Eq. (53).

It is also important to note that the bulk dispersion is present in Eq. (71), not just explicitly through the second term in this equation. Bulk dispersion manifests itself in the interaction Hamiltonian also implicitly in changes in the allowed vibrational frequencies and the corresponding solutions of the field equation for the allowed mode functions wxoiq » z). The allowed frequencies coq x and the mode functions wxoiq , z) are different in the cases of the dispersive and the non-dispersive (vx = 0) systems.

4.4. General solution of lattice dynamics field equations in a layered heterosystem

In order to arrive at an explicit form for the electron-phonon interaction Hamiltonian in Eq. (71), we first need to find the 2D Fourier components of the lattice vibration modes w xo(q »z). These modes should follow from a self consistent solution of Maxwell's equations displayed in Eq. (25) and the field equation Eq. (26). These equations are coupled and our aim is to derive the equation for the mechanical field variable w(r, t). One way to achieve this is to express all fields as a sum of longitudinal and transverse components, as in Eq. (44), and take the divergence and curl of Eq. (26). Eliminating the electric fields EL(r, 0 and ET(r, t) with the help of Eqs. (25), (22), (25) and (45), one obtains two equations for WL,T(r» t). An alternative and more transparent way for deriving the same equations for WL,T(r, 0 is to proceed as follows.

We begin by using the field equation Eq. (26) to write an expression for the electric field E(r,r)

j2 1 + a;2 + i;2 V(V.) - v^V x (Vx) w(r, t). (76) E(r, 0 = —

dt^

From Eqs. (22) and (76) we obtain an expression for the electric displacement field

J2 D(r, 0 = — [ ^ + a;i + i;iV(V.) - v^V x (Vx)

Yn Idt^ w ( r , 0 . (77)

The above expressions for the fields E(r, t) and D(r, t) should now be substituted in Maxwell's equations V x E(r, 0 = 0 and V • D(r, t) = 0. Further manipulation

406 Ch. 11 N.A. Zakhleniuk et ah

of the resulting equations requires decomposing fields into transverse plus longitudinal parts. Using Eq. (45) and bearing in mind that all the equations apply everywhere in the inhomogeneous medium, except at the boundary interfaces between regions occupied by different media (where only boundary conditions apply), and that within each medium the coefficients in Eqs. (76) and (77) are constants, we finally obtain the following equation for WL(r, t)

V . DL(r, r) = V . r ^ r ^ + a;2 + ^2^2! ^^^^^ ^

V X DL(r, r) = V X fe r ^ + a; -f vlvA WL(r, t)

Similarly for WT(r, /) we obtain the equations

V X ET(r, r) = V x — — + ( w ^ _ ^ 4 V^ WT(r, 0 = 0 ,

(78)

0.

V . ET(r, 0 = V . j — 1 ^ + 4 + vlvA WT(r, 0 1 = 0.

(79)

The second equation in each pair of the above equations is a direct consequence of Eq. (45). The crucial point in analyzing the above set of equations is to note that they are not applicable at the interfaces. To see this clearly let us consider the pair in Eq. (78). The first equation here V • DL(r, r) = 0 has been obtained from the Maxwell's equation V • D(r, 0 = 0 which is V • DL(r, 0 + V • DT(r, t) = 0. This is equivalent to V • DL(r, 0 = 0 only if we take the seemingly harmless step and write V • DT(r, 0 = 0 (see Eq. (45)). But this latter condition is not valid at the interfaces. Substituting from Eq. (15) into Eq. (22) we obtain D = ôoE + Anynyf and DL,T = £OOEL,T + 47ryi2WL,T' Taking the divergence of this expression gives V • DT = (Vsoo) • ET + fiooV • ET + 47r [(V)/i2) • WT + y^V • WT]. Since all the material parameters are constant within each medium and each parameter undergoes an abrupt change only at the interfaces (i.e. V oo 7 0 and Vy^ 7 0), it follows that V • DT(r, 0 = 0 everywhere except at the interfaces. Therefore, also V • DL(r, 0 = 0 everywhere except at the interfaces. Using the above expression for D we can further show that the second equation in Eq. (78) is not valid at the interfaces. A similar analysis can be carried out based on Eq. (79). Here the first equation V x ET(r, r) = 0 was obtained using the Maxwell equation V x E(r, r) = V x EL(r, 0 + V x ET(r, r) = 0 and assuming that V x EL(r, 0 = 0 (see Eq. (45). Again using Eq. (76) it can be shown that the latter condition as well as the condition V x ET(r, 0 = 0 are not valid at the interfaces.

Another important consequence of this analysis is that it follows that Eqs. (44) and (45) are applicable everywhere in the system except at the interfaces between different materials. This is because the equations that define the fields FL,T(r» 0 are not applicable at the interfaces. If Eqs. (78) and (79) were applicable at the interfaces as well, then integrating them, as usual, over a small Gaussian pillbox volume extending on both side of an interface, or over an Ampere's loop with parts on both sides of the interface, one would deduce that the normal and tangential components of the vectors


DL and Ex are continuous at interfaces. This means that the whole vectors DL and Ex themselves are continuous at the interfaces (and they are equal to zero at infinity). We thus conclude on the basis of Helmholtz theorem [40,42] that the vectors DL and Ex are zero everywhere. This also means that the expressions inside the large brackets in Eqs. (78) and (79) are equal to zero as well.

It is only because, as we argue above, Eqs. (78) and (79) are not valid at the interfaces that the vectors DL and Ex are not continuous there (more precisely, both components, the normal and the tangential vector components are discontinuous). As a result of this one cannot apply the Helmholtz theorem in order to conclude that DL = 0 and Ex = 0. We are thus forced to seek solutions of the equations

V . S x ( r , 0 = 0 , (80)

V x S x ( r , O = 0 ,

where A = L,T. These equations can be solved by introducing the scalar potential function Sx = — VO^. Using the Fourier transform, as defined in Eq. (56), we obtain the solution for a layered medium

Sx(q , z) = e (Axe^ ' + Â^"^ ') - ieMxe' ' - Bê-^ 0 , (81)

where SL(q , z) = DL(q , z) and Sx(q , z) = Ex(q , z). Using Eqs. (80) and (81) we can recast Eqs. (78) and (79) after taking Fourier transforms as follows

•^q + ^x + ^W + ^xl"? wx(q , z) = a^Sxiq , z), (82)

where ai = Yn/Soo and aj = yu. A general solution of the above equation for the ionic displacement field Wx(q , z) is

where

Wx(q.z) = G x ( q , z ) + , / , ^x^xCq.z). (83)

Gx(q,z) = C,^^'^^^+K,e-'^^^ (84)

In order to exploit the additional conditions V x WL(r, t) and V • Wx(r, 0 (see Eq. (45)) to obtain the solutions Wx(q , z), we introduce a coordinate system based on the following three orthogonal unit vectors in reciprocal space

q e = —, ex = Cz, Cs = ex X e . (85)

q These unit vectors facilitate mode classification in terms of p-polarization (with the

polarization vector in the (e , e2)-plane) and s-polarization (polarization vector along e j . The s-polarized mode is completely decoupled from the p-polarized mode. Note, the right hand side in Eq. (82) contains only the p-polarized function Sx(q , z) (see Eq. (81)). Thus we have the following expressions for G^'^\q , z):

G[^^(q , z) = e {CL e'^^^ + K^ e''"^'') + e^fid ^'^^'

Gi:^(q,z) (86)

408 Ch. 11 NA. Zakhleniuk et al.

Eqs. (81), (83), (86) and (87) constitute a general solution for the mechanical displacement field Wx(q , z). The electric field modes Ex(q , z) are found by substituting W; (q , z) from Eq. (83) into Eq. (70). This yields

EL^>(q , z) = - ^ i : ^ G { ^ - > ( q , z) + ; 7 ^ S , ( q , z), Yn ^(<^q) (88)

E^l\q,z) = 0,

E^^ \q , z ) = ST(q,z) , E^4^(q.z) = 0. (89)

These equations show that there is no electric field associated with s-polarized lattice vibrations. In deriving Eqs. (88), we have used Eqs. (68) and (69) and we also introduced the following notation

2 2

sico^) = Soo-^ J. (90) col ^^T

The electric displacement modes Dx(q , z) are found using the relation Dx = ÔOEA + 47r}/i2Wx. We obtain

Djf^(q,z) = SL(q,z) , (91)

D^^^q , z) = 4nynG^T'\q , z) + eico^ )ST(q , z),

D^^^(q,z)=47ryi2G;^\q,z).

It is useful to note that all the above p-polarized field modes W^P\ E^P^ and D^ ^ contain the vectors SL and ST in the same combination which we denote as D/

Di(q , z) = SL(q , z) + s(co^ )ST(q , z). (93)

The explicit form of I>/(q , z) can be found using Eqs. (81) and (93). We have

Di(q , z) = e (A/^^ ' + Bie'"^') - ieAAje"^' - Bie'"^'), (94)

where we have introduced new constants A/ and B/ instead of A^ and Bx such that Ai = AL -h e(cOq)AT and Bj = Bi+ s{a)q )BT. Because the equations of motion are linear and homogeneous, the solutions of these equations contain arbitrary multiplication factors which we denote as Cô and CSQ for the p- and s-polarized, respectively. Since the boundary conditions give only the ratios between the constants in the solutions without specifying the constants themselves, we can put Ci = Cpo, CTS = Qo» ^ L = kiCpo, KT = kfCpo, AI = ajCpo, Bj = bjCpo and Bjs = ^^Qo- The constants ki^krâi, bi and bs should be found from the boundary conditions and the constants Cô and C o are found from the normalization condition in Eq. (62). The s- and p-polarized solutions are decoupled from each other, so the s- and p-modes are normalized separately.


Using Eq. (93) we obtain for the total field modes

w\,'\q^ , z) = G['l{q , z) + G^^îq , z) - ^'^ ^(^q ){0)\ -0)^)

,M) (s), wi;\q,z) = G'o'i(q,z), (95)

7(P) (Or

Yn "^Gl^li^^z)^

e{coQ ) Doi(q ,z),

(96)

i(p) (P)/

Dô^(q,z)=4nynG^^liq,z), (97)

Here we have used the notation F^^'^^q , z) = F^ ' Hq , z)/C(s,p)o for all the above modes.

The above expressions for the total fields represent a general solution for the vibrational modes in an arbitrary polar layered heterostructure. These expressions are also needed in the boundary conditions in order to fix the numerical coefficients in Eqs. (86), (87) and (94).This is because the boundary conditions are imposed on the total fields rather than their longitudinal or transverse components.

4.5. An explicit form of the interaction Hamiltonian and the electron-phonon scattering rate

It is important from a practical point of view, to derive the explicit form of the interaction Hamiltonian using the solution obtained above for w(q , z) in Eqs. (83) and (95). We obtain from Eq. (71) the interaction Hamiltonian for the vibrational mode specified by q andcoq

HArj) = -ij:^^^^

(q.z)-Yn

^ ( ^ q ) ( ^ q -Ci>\) ^^

where the interaction parameter ap{q ) is

<>(q,^) m)e'''^-^'-HC

otp{q ) = Ine'^ 0)]

Ao o)} q Vôo ^s / ^ q <^Po(q ) '

with the normalization constant Cpoiq ) given by

Cpo(q ) =

oo -1/2

(98)

(99)

(100)


The parameters COLJ, Yn, £oo,s in Eqs. (98) and (99) are those of the material in which the electron interacting with the polar vibration is located.

The above expressions, together with Eqs. (94)-(97), can be applied to an arbitrary layered heterosystem. The only thing one needs to do in each particular case is to calculate the integration constants which enter the expressions for GoL,r(^ ' ^) ^^^ ô/(q » z). These constants are specified by the boundary conditions.

After the interaction Hamiltonian is derived, it is straightforward to obtain the expression for the transition rate W//(q ) for an electron scattering from an initial state i to a final state / due to the interaction with one vibrational mode

Wifiq ) = Y | (^/(r) l4(r) |vl / / (r)) | ' 8(Ef - E^ + hco^ ), (101)

where ^/ , / ( r ) is the electron wavefunction in the initial or final state and £"/,/ are the corresponding electron energies. The electron transition rate Eq. (101) takes into account the effect of the inhomogeneity of the layered heterosystem on the scattering rate. This effect is completely described by the interaction Hamiltonian in Eq. (98). Calculation of the total scattering process for GaN-based heterostructures will be given in Section 6.

4.6. Relation between the dispersive and non-dispersive theories of lattice dynamics

In considering the lattice dynamics in the preceding sections we took into account the spatial dispersion of the vibrations by including the last two terms in Eq. (26). Not including these terms in the mechanical field equation corresponds to the non-dispersive limit which is also known as the dielectric continuum (DC) model. Formally, the DC model limit can be obtained by setting i ^ = 0 and Vj = Q'm Eq. (26). In the case of an inhomogeneous layered medium this gives rise to two independent sets of modes [8], so-called confined and interface modes. The confined mode spectrum is degenerate since all the modes have the same constant frequency {COL for longitudinal optical (LO) and (JOT for transverse optical (TO) modes) and the mode amplitudes are non-zero only within layers of materials and have a frequency only as the LO or TO frequency. The interface mode frequency depends on a dispersion relation {co depends on q ) and the mode functions of these modes decay exponentially with distance from the interfaces between different layers.

From the solutions in Eqs. (95)-(97) for the case when the bulk dispersion is included, we have a superposition of the confined-like and interface-like parts, i.e. we have a mixing or hybridization of the modes [13,37]. In the dispersive theory the confined-like and the interface-like parts are not independent (contrary to the DC model). They have the same frequency which is given by Eq. (68). The allowed values of the confinement wavevector qx (see also Eq. (66)) follow from the characteristic equation which, in turn, follows from the boundary conditions. The main consequence of including bulk dispersion in the field equations is that, besides the hybridization of the modes, it lifts the degeneracy of the vibrational frequency. In this respect the bulk dispersion can never be considered as a small perturbation [13]. This can also be seen directly from the mechanical field equation Eq. (26). From a mathematical


point of view this is a differential equation the order of which is defined by the last two terms. If one makes the formal transition v\ -^ 0 and u^ -> 0 in the mechanical field equation, this would mean a change in the type of the equation, i.e. a transition from the differential equation to an algebraic equation. Obviously, the solution of this non-dispersive algebraic equation (from Eq. (26) with v\ = 0 and i; = 0) and the solution obtained as a limit of the general solution of the differential equation (Eq. (26) with vl ^ 0 and v^ 92 0) assuming i; -> 0 and Vj ~> 0, are, in general, completely different. They may coinside only in very special and particular cases. This is why one should treat with caution any theoretical analysis in the literature which considers the DC model results as a limit (vf -^ 0 and Vj -> 0) of the dispersive theory.

The DC theory of lattice vibrations is simpler than the dispersive theory which we considered here and it is very useful for applications as well. For example, we have considered here materials which have a cubic synmietry. The dispersive theory of nitride-based materials with wurzite synmietry has yet to be developed. The main problem with wurzite bulk materials and heterostructures is the anisotropy of the frequency spectrum [20]. Our present theory sets out a general method for quantizing the vibrational dispersive modes and, in this respect, it will be of direct importance when applying the theory to bulk materials and heterostructures with wurzite symmetry. At the same time, the DC model has been applied very recently to the study of anisotropy effects on polar optical phonons in quantum wells and superlattices based on GaN/AlN wurzite materials and also to the analysis of the electron scattering rate due to the interaction with PO phonons in these heterostructures [44,45]. These results will also be very useful for the future development of a self-consistent dispersive theory of phonon confinement in wurzite heterosystems.

5. Microscopic theory and continuum models

We have emphasized that a continuum model which is expected to accurately reflect the conditions at an interface must include dispersion — the variation of frequency with wavevector. Fortunately the acoustic-mode theory automatically has dispersion built in, leading to the familiar mechanical boundary conditions (BCs) of the continuity of both amplitude and stress (see, for example, [46]). Since a rigorous dispersive theory for optical modes, applicable to heterostructures as in Section 4, has not previously been available, the question of correct mechanical BCs for optical modes has remained unresolved. This section aims to provide an account of work exploring the microscopic origin of the continuum theory as applicable to lattice vibrations in polar media and consider the problem of the optical boundary conditions that are required in the context of heterostructures.

It is by no means obvious that a continuum model can ever be adequate to describe optical modes in an inhomogeneous solid containing spatially abrupt interfaces. It would seem that any description of ionic motion in terms of continuous envelope functions obeying a second-order differential equation where reduced mass and force constants change discontinuously cannot possibly provide an adequate description. Using the theory of microscopic lattice dynamics is in principle exact and it avoids the problem of BCs, though it is admittedly computer-intensive but, as we emphasized at the outset.


100 - ]

80 H

60

40 H

20 A

o4 -20 4

20 40 60

" T " 80 100 120

0.12 - i

0.10 A

0.08 A

0.06 4

0.04 4

0.02 4

0.00 4

-0.02 4

20 1^

40

1^ 60

1^ 80 100

I 120

Fig. 2. Quasicontinuum functions: (a) showing the displacement of one atom; (b) showing the variation of some property across an interface.

there are good reasons for constructing a continuum theory. The same perception applies to the use of envelope-function theory for electrons, yet there is good evidence that it works extremely well. Examples of envelope functions for an ionic lattice in a bulk medium and at an interface are shown in Fig. 2.

In fact, an exact envelope-function formalism can be developed to describe electron states [47]. The same is true for lattice vibrations as [48-50] have shown. In this case it is clear that any interpolation of ionic motion should not involve variations more rapid than the ionic spacing, which means restricting the envelope function to wavevectors within the first Brillouin zone. If this is done then it can be exactly and uniquely related to the ionic motion. The physical space of such functions is known as the quasicontinuum. Thus, quasicontinuum theory is capable of describing exactly the motion of ions in terms of envelope functions whose wavevectors are restricted to the first Brillouin zone. That being the case, continuum (or more strictly, quasicontinuum)


theory, being in principle as accurate as microscopic theory, is much more versatile and more generally useful, provided that valid mechanical BCs can be deduced. Certainly, there need be no qualms about its validity.

The classic theory of long-wavelength optical modes in polar material of Bom and Huang [7] does not include dispersion and so could not provide mechanical BCs. Fortunately, in the case of the most investigated system — AlAs/GaAs — the large difference of optical-mode frequencies suggested that the true mechanical BCs could be approximated by entailing that the amplitude vanish at the interface (u = 0), and this plausible approximation received support from the results of Raman scattering experiments [51-54] and from numerical models [55]. Combining this condition with the classic electrical BCs, continuity of both tangential electric field and normal electric displacement, led to the necessity for the optical modes to become hybrids of longitudinally-polarized (LO), transversely-polarized (TO) and polariton-like interface modes [14,56,57].

But the mechanical boundary condition u = 0 [14,56,57] could not be used for systems such as AlxGai_xAs, with x small, in which the frequency bands overlap. There were also earlier attempts to model mechanical BCs in terms of hydrodynamic BCs [11] in the context of Raman scattering theory or acoustic-like BCs [2,58]. However, investigations of this system have had to rely on the heavily numerical calculation of the microscopic lattice dynamics [59]. More recently, the increasing interest in the AlN/GaN system, where the frequency bands overlap, has added urgency to the problem of mechanical BCs. Other systems also pose problems. For example, the interface in the InAs/GaSb system can have the molecular character of InSb or GaAs, quite different from either binary, implying the existence of quite novel mechanical BCs [60,61] involving delta-function-like terms in the reduced mass of the ions and zone-centre force constants. A further characteristic of optical modes that make their mechanical BCs different from those of acoustic modes is that the optical stress tensor is not symmetric [61]. In the case of acoustic modes the stress tensor is symmetric as a result of the requirement for rotational invariance, but no such constraint applies for optical modes. As a result, optical-mode elasticity in zinc-blende materials requires 4 independent elastic constants instead of 3. This extra elastic constant does not play a role in a homogeneous material, but has to be taken into account in determining the boundary conditions.

It is clear that a continuum theory of optical-mode elasticity had to be significantly more complex than the equivalent for acoustic modes. In the next section we give the results of a three-dimensional analysis of optical-mode elasticity [62] which, although it contains simplifications for clarity's sake, successfully describes the principal features that makes optical-mode elasticity unique.

5.1. Long-wavelength vibrations

In order to focus on the mechanical aspects we ignore Coulomb effects and, for simplicity and convenience, take the two-parameter Keating potential for the zinc-blende lattice to describe the lattice dynamics [19]. This potential takes into account only the nearest-neighbour interaction via a central-force constant a and a second-neighbour


interaction via a non-central force constant p. Quasicontinuum theory is used to describe the discrete displacements of the atoms in terms of envelope functions and equations of motion for the two atoms A and B in the unit cell are derived from the Lagrangian. These equations are then converted to equations for acoustic displacement U and optical displacement u, where:

(102)

and m is the atomic mass and M is the total mass. This procedure entails that we extend the envelope function description to the mass parameters and the force constants in order to take account of their variation at an interface. A commonly used simplification is to assume that the force constants of different Group IV and III-V semiconductors do not vary significantly and that the parameter principally responsible for the difference in zone-centre optical-mode frequencies is the reduced mass. This simplification — the mass approximation — is assumed here. The equations are actually coupled, each involving acoustic and optical displacements, but they can be decoupled in the long-wavelength limit. When this is done the equation of motion for acoustic modes becomes:

0) pUa = —(CaXPti^p,fM),Xy

where p is the total-mass density, f/ , = dU^/dx^, A = 1 provided the subscripts occur in matched pairs, e.g. xxyy, xyxy, etc., and is zero otherwise and |£| = 1 provided the subscripts are all different, and zero otherwise. The nearest-neighbour separation is y/3a and the force constant P = (fi^ + P^)/2, i.e. the average of the force constants associated with each type of ion. Explicit results are:

r - . __^±^ 4a

C - c . = ^ " ^ (104)

^xyxy — ^xyyx — ^44 afi

a((x-^P)' which are the elastic constants derived by Keating [19].

The equation of motion for optical vibrations is:

a-\-B a-fi 1

+ âk^fifi + âfi^^x)

Cax^^ = ^ ( - ^ ) [(« - P)Kfix^ + Pi28^^Sx^ + 8^xh^ + 8^^8px)]

^' (a - ^f - -^(âX^fin + ân^^k) iTf^^ ~ ^(xx)(âphn + ôtn^fik). (105)

Optical phonon confinement in nitride-based hetewstructures Ch. 11 415

where /x is the reduced mass, pr is the reduced-mass density and p' = ^ -{- rAyS,

The optical elastic tensor has the symmetry c^x^^ = c^âx but, unhke the acoustic tensor, there is no rotational invariance, i.e. c^x^^j^ ^ Cax^^. Explicit results are:

_ / ^ \ ct + 3p _ ^

_ (j^\ ^ _ ^

(106) _ /ju X a 4 ^ ^ _ (a - pf

''^y^y -\M) Aa aco^M '

^' {ot - P) 2

<M/ 4a Sa aco^M

The tensor c^^ reduces to a straightforward force- constant in homogeneous material:

For a crystal inhomogeneous in the z-direction, the non-zero elements are:

__ a + P a + /6 ( ^ ) . . . - « - ' ' 4a^ 8a

a + fi a + 3)g / /xx ^, ,2-. ^^ 4a3

a- P - ^ < ^ ) - ^ < - > ^ ' - ^ -

C^y - ^3,^ - ^ ^ 2 ^'^

5.2. Homogeneous material

In what follows, it will be convenient to recast Eqs. (104) and (105) explicitly in terms of the non-zero elastic coefficients:

+ [Cl4(U,,y 4- Uy,,)ly + [Cl4(U,,Z + ^Z,.)],., (109)

CO^PrU,^ = CxxUx H- CjcyUy + C;,^^^ + [CnUx,x + Cl2(W3;,>; + Uz,z)Xx

+ kfll4Wjc,j + <:^^14Wy,;c)],y + [Cal4l^x,z + C^;14Wz,x)],z, ( 1 1 0 )

w h e r e C n = Cjcjcj j , C12 = Cxxyyt Q l 4 = ^jryjcy? ^Z?14 = (^xyyx-

Similar expressions exist for the y and z components.

• In an elastically isotropic material a = ^ and

• C i i — C12 = 2 C i 4 , Cii — C12 = Q l 4 + Cbl4,

416 Ch. II NA.Zakhleniuketal

and thus, in a homogeneous and isotropic material:

co^pV, = Cii[V . VI, - Ci4[(V X V X \])h, (111)

and

Co'^PrUx = CoWjc + C l l [ V • U],;, - Qi4[V X V X U)],;^. (112)

The form of these equations underiines the complete decoupling of longitudinally-polarized and transversely-polarized modes. Only one of the optical shear constants survives. The optical elastic constants that determine dispersion are equal to the acoustic elastic constants multiplied by the reduced-mass factor /x/M.

5.3. Boundary conditions

The similarity of the two Eqs. ( I l l ) and (112) has suggested to some that the boundary conditions for optical modes should be the same as for acoustic modes, i.e. the continuity of amplitude and stress. But this idea is entirely mistaken. Optical-mode displacements are related to the displacements of the individual atoms via mass factors, and it is the variation of these across an interface that is of supreme importance. At a heterojunction, the derivitives of the mass parameters that appear in the force constant Cap give rise to h- like functions. Also, in a no-common-ion system, such as InAs/GaSb, there is also a 8-like function in the reduced-mass density.

The BCs for the optical modes can be derived by first expressing Eq. (110) in terms of the optical-stress components T^ :

(O^PrUx = CxxUx + CxyUy -f- Cxz^z + Txx,x + Txy,y + Txz,z. (113)

where the 7,^ are the expressions in the square brackets in Eq. (110). Similar equations exist for the y and z components. We suppose that the interface is perpendicular to the z-direction and extends arbitrarily from —s to +6 where s is to be defined later. Integrating Eq. (113) across the interface allows us to relate the stress on one side of the interface to the stress on the other. Thus:

e

Txzi^) = Txzi-e) -I- / (a/prUx - CxxUx - CxyUy - Txx,x - Txy,y) dz, (114)

and similarly for Ty^ and T^z- Moreover, from the expression for stress we can relate amplitudes:

J \Cah Ux(s) = Ux(-s) + I [^-T,,-^-ÛzAdz, (115)

314 Cal4 /

and similarly for Uy and M . The amplitude in Eq. (115) was obtained by integrating the component of the stress Txz equal to Ca44 Ux,z' We label such components v^ = CaUa,z where for a = jc or y, Q = Q44, and for a = z,Ca = cu. The quantities to be connected across an interface are then the components of u and the components of v.

For brevity we consider only the situation in which waves approach the interface near normal incidence so that k^ ^ kx or ky. This means that the stresses in the integrand

Optical phonon confinement in nitride-based heterostructures Ch. 11 All

of Eq. (114) and the strain in the integrand of Eq. (115) are relatively small and can be neglected. Following [61] we solve these coupled integral equations using a perturbative expansion. To second order, we obtain;

£ £

Vct(£) = Va(-£)-^vpi-s) / Qafigîz. -s) dz + up{-e) / Qa^dz, (116)

and:

Uais) = Ua(-£) + U^(-s) / Qafigfi{£, z) dz + Va{-e)goc{£, s )

£ -£

+ V^{-£) I Qafigî£, z)ga{Z, -£)dz, (117)

where

£

ga(£,Z) = —dz, J Ca (118)

i/xx — ^ Pr (^xxi \ixy — (^xyt Hxz —

These relations include the spatial variations that exist in the absence of an interface and these must be subtracted in order to obtain the required connection rules that relate quantities immediately at one side of the interface at 0" to those at 0+. Bulk-like variations can be distinguished from interface variations by letting f{z) = f{h) •i-f(i)(z), where f(z) is any variable. Neglecting products of interface terms in the spirit of regarding the effect of the interface as a perturbation, we obtain the connection rules sunmiarized in the 6 x 6 transfer matrix, T:

(":)^°' =Kt) '' ' where

T = rfc(0+, £)T(e, -s)T(-s, O").

(119)

(120)

To lowest order we have

/l+fc. byx 0

'yx

0

\+byy

0

axy

ayy

0 0

l + ^ z . 0 0

b„

"yx

0

^xy

dyy

0

-bxy - bn

0 0

dzz 0 0

i-b,, J

(121)

418 Ch. 11 NA. Zakhleniuk et aL

The components are explicitly given by E

—e

£

Kp = I [-zpoc{b)Q,.fi{i) + zQap{b)pa{i)\ dz, (122) —£

dap = j [PaiOa + Pa{b)Qafiib)z^) " pl{b)Qap{i)z^] dz, —e

where pa = (Ca)~^. It is often possible to consider p-polarized waves (waves with polarization in the

plane of incidence) and s-polarized waves (waves with polarization perpendicular to the plane of incidence). In this case the transfer matrix factorizes neatly into:

(123)

In order to satisfy the continuity of energy flow we require the quantity w* v z — âKz to be continuous across the interface. This can be achieved by modifying the transfer matrix as follows:

(1 + bcca dcca \

Claa ^ -baa )

In order to work out the integrals in Eq. (122), it is convenient to invoke quasicontin-uum theory to describe the variation of the mass terms through the interface. Thus, for the common-ion case, we take the interface functions to be given by:

Q{i) = AQa(z) + QO8B(Z) + Gi5^(0, ^^25) p(i) = Apa(z),

where AQ = Q+- Q_, a(z) = :7r~^sgn(z)si(7r|z|/ao), si(A:) = f^ t'^ sintdt, 8B = sininz/ao), QQ = 2a and the prime on the delta-function denotes differentiation. The subscript B on the delta-function indicates that the wavevector range is limited to the first Brillouin zone. (If no common ion exists, eg. in the case of InAs/GaSb, extra delta-function terms appear.) We let the range of integration to be — oo to oo but define all integrals of the form f^ z^f(z) dz as lim f^ e'^^z^ f{z) dz in order to get

a->0"*"

convergence. We set the frequency, w, to the zone-centre frequency of one of the bulk constituents i.e. ccp- = 4(Q; H- P)/iJi± where ae+ (ae_) is the reduced mass to the right (left) of the interface, and obtain [63]:


_ a j ^ 2 {a + fi?r^r^np^ , {a + P)HÎJ-fpf

a + ^ _, , bxx = byy = — — [ p ^ r A r +:/r Âp^(Ar)^],

K. = ^ [ P / A r + ; r -Ap,(Ar)^] + ^p^^r, (126)

djcx = dyy = — pÂp.rAr -— ^ ,

2[(a-f3)g)r + A ^ / 2 ] ^ 4(a + ^) Ap.Afipf

The bar denotes the average of the right and left quantities. The force constants a and fi for most of the III-V zinc-blende compounds have been

listed in [64]. Here, we have assumed that they do not change across the interface (the mass approximation). As a consequence, the boundary conditions are dominated by the variation of the mass factors. These are (a) the ratio term r = {m^/M — m^/M)/2, (b) the reduced mass /x, and (c) the inverse of the optical elastic constant p, which depends on the reduced mass (Eq. (106)). For the perturbative treatment that has been used, these mass factors must not vary too much. Ideally, each of the factors appearing in the transfer matrix must, therefore, be small compared with unity. This is generally not true for interfaces separating different binary compounds such as AlAs/GaAs. In these cases the condition u = 0 is usually the appropriate condition to use. The connection rules derived above will find application to cases involving say a binary and its alloy, such as AlxGai_xAs/GaAs with x not too large, or to interfaces separating isotopic variants. It is clear, however, that optical-phonon connection rules are very different from the rules governing acoustic modes.

6. Electron-phonon scattering rates

Having obtained the field equation for optical phonon modes including a parabolic negative spatial dispersion and set out the generalised mechanical boundary conditions, we are now in a position to model the confined optical phonons assuming that the reststrahl bands of a two-material heterostructure overlap, as they do for nitride heterostructures. However, before we consider the full theory of optical phonons in the case of overlapping reststrahl bands, it is worth examining the results which have been obtained previously for the GaAs/AlAs system as these will be the limits of the results presented later for the GaN/AlN system when the reststrahl bands no longer overlap or the dispersion becomes small.

We begin by deriving the Coulomb potentials and electron-PO phonon scattering rates in a double heterostructure quantum well, of width d with material 1 (2) as the


z = -d/2 z = d / 2

x |

^<

z

',.'"''' -' .'•'^'"'"'i','-' •'.1''",

Fig. 3. A schematic illustration of the quantum well and the coordinate system used.

well (barrier) material and the interfaces at z = ±d/2 as shown in Fig. 3. We will compare three PO phonon models: the dielectric continuum (DC) model which is valid for both GaAs/AlAs and GaN/AlN systems; the hybrid model which is only valid for the GaAs/AlAs systems; and the extended hybrid model which, although applicable to any heterostructure system, is only required for systems with overlapping reststrahl bands such as GaN/AlN. We will also consider the phonon dispersion curves for a GaN/AlN superiattice using the extended hybrid model and compare these with the dispersion curves predicted by the DC model for the same superiattice.

6.1. Dielectric continuum (DC) model

The basic formalism underiying the DC model, the field equations (Sections 3 and 4.6), the normalization condition (Section 4) and boundary conditions, have already been described here and elsewhere [6,9,18]. The results of applying the DC model to the case of a quantum well are well known [6,9,18]. They are presented here for completeness and for comparison to corresponding results arising from other models and/or applications to other systems. We display the second quantized electric potentials and the electron-phonon scattering rates for intrasubband and intersubband scattering. There are three sets of PO phonon modes which interact with electrons in the double heterostructure quantum well. Confined phonons in material 1, for which the quantized Coulomb field (CI) is given by

^ci(r,z) = ^ n,q L

001^ iq\

y/q^ + (nnd)^ CSn ( —ZJ^„,q + HC izl < 2- (127)

These satisfy the dispersion relation si{(o) = 0, i.e. co = COLI and their Coulomb potential vanishes in the barrier regions. In material 2 the Coulomb potential (C2) for a


semi-infinite material is appropriate,

c2(r,z) =

E x / F T ^ sinUj^-|zMJa<,^,, + //C d

(128)

These satisfy the dispersion relation Siico) = 0, i.e. co = a)i2 and their Coulomb potential vanishes in the well region. Finally there are interface (IF) phonons for which the Coulomb potential is either symmetric (S) or antisymmetric (A) with respect to the centre of the well. We write - 5 a),p(x,z) =

E Aoqsmh{qd)Ds{o)Xs,^)

^-^^/2cosh(^z) Izl <d/2\

cosh(^^/2)e-^'^' \z\ >d/2\ axs^^ + HC (129)

^jp(\.z) =

E 47r2fi ^ / '' ' ^-^^/2 sinh(^z) \z\<d/2\

Aoq sir\h(qd)DA(o)x,,q) sgn(z) sinh(^J/2)^-^'^' |z| > J /2 I ax,n + / /C

(130)

These interface modes have the dispersion relations 6i(co)/62(co) = — coth(^J/2) for the synmietric (S) modes and £i(a))/s2(co) = — tanh(^J/2) for the antisymmetric (A) modes. In Eqs. (127) and (128) we have introduced 0 ^ = Anhcouil/Sooi — 1/^5/)/Vb/ where Voi is the volume of the quantum well such that Vbi = ôd, with AQ the large area of an interface, while Vb2 is the volume of the barrier (assumed to be large) and n is a discrete index characterizing the quantization for the confined phonons in the z-direction. The function cs„(;c) is cos(jc) if n is odd or sin(x) if n is even, HC stands for hermitian conjugate, at is the annihilation operator for a mode with the indices /, ^.5,^ represents the number of modes, symmetric or antisymmetric, satisfying the dispersion relations for the interface phonons, Ds,A(o)x,q) = [dsi/dco — Si/£2d62/dco]a)^^, q is the quasi-continuous wavevector in the plane and q^ is the quasi-continuous wavevector in the z-direction for the semi-infinite barrier phonons. Fig. 4 shows the well-known dispersion curves of the DC model applied here to the GaN/AlN double heterostructure quantum well system.

For convenience, we assume that the depth of the quantum well for the electrons is infinite. Thus, the wavefunctions are given by

(131) T / X / ^ ikX / " ^ \

^n,k(x, Z) = JTT^^'A-T^) ' V Vbi \ d /

the corresponding energy eigenvalues are given by En = fi^n^n^/2m*d^ and the wavefunctions are zero outside the quantum well so the semi-infinite modes in the barrier, Eq. (128), do not contribute to the interaction with the quantum well electrons. The total phonon emission rate rii(£'/) arises from Fermi's golden rule (which is

422 Ch, 11 N.A. Zakhleniuk et al.

the integration over all modes of Eq. (101) and uses an interaction Hamiltonian He = ^0(r, z) similar to Eq. (98)). For intrasubband scattering within the ground state subband from an electron state with kinetic energy Et = h^kf/2m* it is obtained as

1/2

ZL^ 'rr2„2(yj2 _ n odd

n'^rfi{ri^ / 4) dq [1-/Zn(g)]

(^rf)2 + (n7r)2

- 1 / 2

1/2

^>0 l/Xcll(9)l<l

tanh(^rf/2)

(132)

(qdmqd)^ + (47r)2]2a>z.iD5(a;x„q)

Here Foi = ^^(l/ôo - lSs)^/2m*coii/h/h is the scattering rate for bulk material 1, finiq) = (q^-\-2m*(Ou/h)/2kiq, fx^niq) = {q^ -^2m*(D^^Jh)/2kiq and only the symmetric modes contribute to the intrasubband scattering. We may approximate the integrals in Eq. (132) by assuming that the initial kinetic energy is the same as the phonon energy which we also assume to be fixed. Setting £/ = ho) we have

q % ^2m''cjolh and

I f dq[\-f(q)]-'^' ' 71.

q>0

This is the threshold approximation used in [15] since it takes the value of the wavevector and the integral at £/ = hco, the onset of emission. Below £/ = hco the integral is zero. The intersubband rate r2i(£'/) from the bottom of the second subband to the ground state subband by emission of all possible PO phonons in the double heterostructure is given by

.1 /2

r2i(£i) = 256roirfl m E 2n=

!rHn'-lXn'-9) /

-1/2

dq

g>0 \fL2im0 IA^2l(9)l<l

qd coth(qd/2)

[(qd)^^7r^f [(qd)^ + {9jT)^f COUDA(CO^,,^)

(133)

Optical phonon confinement in nitride-based heterostructures Ch, 11 423

3 3

l.*f

1.3

1.2

1.1

1

\ 1 ,

- ^ 2

' "L ,

**" — — —

1 1 '

b j J

\

^

-

-- n> z

1 1 i

0.5 1

qd 1.5

Fig. 4. The frequencies of the DC interface phonons against qd in (a) a GaN/AlN quantum well and (b) a GaAs/AlAs quantum well of width d. The solid curves are the symmetric modes and the dashed curves are the antisymmetric modes.

where the functions are {q^ + 2m*{ha)x^,q - AE)/n?) /Iktq, while A£ = E2 - £i = 3h^7t^/Im'^d'^ is the sub-band energy difference. Only the antisymmetric modes contribute to this intersubband scattering. Since the initial kinetic energy is zero, the integral over the wavevector in the plane can be approximated as

1 I dq[l^fHq)] - 1 / 2 ?^ 7T

q>0

\fm<i


with q = y/2m*(AE -hco)/h^ assuming that the subband energy difference exceeds the phonon energy, otherwise the integral is zero.

The above results in Eqs. (132) and (133) are quite general and do not depend on the material system (other than through the parameters). We will compare to these results later. The simplicity of the DC model is a positive feature and, as we show later the DC model often gives accurate results for total scattering rates.

6.2. The hybrid model

As discussed in previous sections, the hybrid model assumes that the oscillations in one material are uncoupled from the oscillations in an adjacent different material and that it is a good approximation to assume that the relative displacement vector u at any interface is zero [15,65]. This is justifiably ideal for the GaAs/AlAs system but, as we discuss, is not so if the reststahl bands of the two materials overlap, as in the GaN/AlN system.

The theory underlying the hybrid model is outlined in several papers [14,15,65] and its results for scattering rates of electrons in quantum wells interacting with so-called double hybrids can be found in [15,65]. The reader is referred to these papers for fuller discussions. In general, the solution in one of the materials is the sum of the displacements of the longitudinal optical (LO) and interface solutions which produces a solution in the adjacent material of a decaying electric field associated with the interface solution. The original theory included a transverse optical (TO) component (producing so-called triple hybrids) but the TO component was shown to be irrelevant for the electron-phonon scattering rates and this led to the adoption of double hybrids. The boundary conditions are those of electrostatics with the parallel component of the electric field and the perpendicular component of the electric displacement field continuous. The relative ionic displacement field perpendicular to the interface is also taken to be zero. This leads to two sets of solution, each with a frequency value lying on the bulk LO dispersion curve of one of the materials. For the modes of material 1 there is a dispersion relation while for the modes due to material 2 the dispersion relation is that of a bulk mode with its associated normalized bulk amplitude providing the remaining unknown constant when solving for the boundary conditions.

The dispersion relation for synmietric modes due to material 1 is

"(^)fe-(f)-']-"^(T) = »' (134)

with the second-quantized Coulomb potential given by

I S . i(x,z) =

Z ^ I ^Ll V

he] 1/2

PlVoi<w/5,

qixsi%m{qd 2) , , , , , d cosiqiiz) + . cosh(^z) z < -

q sinh(qd/2) 2

qei sin(^J/2)^-^^l^l-^/2^

-h / /C \z\>

i Cli q.^Li

(135)


Hereof = 47TPi((jol.-ojli),a/ = col^-vlîq^ + ql^), fs = H-3sin(^z.i^)/^Li^ + 4sm'^(qiid/2) coth(qd/2)/qd + (q/qiOÛ + sin(^£iJ)/^£i J ] and all the other parameters are those for material 1 as defined in Section 4. For the antisymmetric modes in material 1 the dispersion relation is

^L\Sl

-'(¥)[|-(f)-]—(T)=«' (136)

and the corresponding Coulomb potential is given by

<t>,(x,2) =

E qii XPiVoicofAj

siniqiiz) -qiisi cos(qd/2)

sinh(^z) |z| q cosh(qd/2)

^'^^''^^gna)cos(^J/2)^-^(l^'-^/2)

+HC qsi

\z\> > a, q.^Li

(137)

fA = l-3sin(qud)qLid + 4cosîqud/2)tSinh{qd/2)/qd

+ (q/qu)^ [1 - sin(^z.i^)/îi^] •

Fig. 5 shows the dispersion of the double hybrid modes due to material 1. The curves form straight lines joining the frequency values where the mechanical wave fits the quantum well width at small wavevector to frequency values where the Coulomb potential wave fit the quantum well width at large wavevector [15]. The value (and the boundary condition that produces it) at small wavevector is the same as in the hydrodynamic model [11] while the value at large wavevector is that given by the

0.98 h

0.96 h

0.94

0.92

Fig. 5. The frequencies against qd of the double hybrid modes due to material 1, the well material, for a GaAs/AlAs double heterostructure. The dashed curves are the symmetric modes and the solid curves are the antisymmetric modes. The dotted curves are the DC interface phonons for the same system.


condition used in the DC model [15]. The only deviation from this is where the curves cross a DC interface phonon dispersion of the same synmietry where anti-crossings occur [15].

The modes due to material 2 are given in terms of an incoming amplitude, ALI^ of the Coulomb potential wave which is normalized in the same way as a bulk wave (see Section 4.2), thus [65]

42 -hej

(138) 2p2Vo2Coiq^-hql2)'

where co^ = C0I2 ~ '^lii^'^ + ^L2)- Hence, after applying the boundary conditions, the electric potential is given by

*2(x,z)=Xl q,^L2

Atie iqx

y+e -QZ Y-e qz

^ ^ ^ 1 îQL2(z-d)

qilSlSl

\z\ < d/2 z < -d/2

z>d/2 ^fL^qu -\-HC

(139)

with

L £2 V qiisij

i

\ V £2/ \qL2S2S2) I ^±qd

From Eq. (139) we may find reflection and transmission coefficients [65]. For brevity the scattering rates are not displayed or discussed here since a full

account can be found in [15] [65]. The main conclusion was that the hybrid model provides results for the scattering rates which are very close to those obtained from the DC model. The agreement is attributed to the negligible effects of spatial dispersion in the GaAs/AlAs system [15]. This situation will be contrasted with that in the GaN/AlN system, which we discuss next.

6.3. The extended hybrid model

We now apply the hybrid model to the case of GaN/AlN heterostructures. The theory in this case becomes quite involved and it is more instructive to provide an outline description of the essential steps. For further details the reader is referred to [66,67].

First we must determine the bulk dispersion curves. For this we have taken the frequencies at the F and X points from [68] and fitted a parabolic negative dispersion relation. The appropriate parameters are shown in Table 2 and the corresponding bulk dispersion curves are presented in Fig. 6. Note that this step of fixing the bulk dispersion is essential, but need not be accurate. The parabolic approximation is only made here because it is consistent with the order of the equation of motion. Also, some papers display the TO branch of GaN exhibiting a positive dispersion [33,69]. Again this feature does not affect the overall essential structure of the solution.


Table 2. The parameters associated with bulk GaN and AIN phonons assuming a parabolic dispersion. The values at the T and X points are taken from [68].

Material VL (ms"') VT (ms'O Symmetry Point hcDL (meV) h bar COT (meV)

GaN

AIN

10600

16000

2080

7380

r X

r X

92.76 79.24 114.08 86.92

69.69 69.19 83.08 76.14

It turns out that we cannot ignore any component of the solution as done in the double hybrid case. Hence, in every region we must include ionic displacements for the LO, TO and interface-like (IF) components with the associated electric and electric displacement fields. If the frequency of the mode lies outside the bulk dispersion band of a particular component of the solution, the wavevector becomes imaginary and the solution evanescent. For example, if coij(X) < co < coijir) then kij is real and a propagating solution is taken but if COL,T(X) > co > coLj{T),kij becomes imaginary and an evanescent solution should be included for that component. If the frequency lies above the bulk dispersion curve, the nature of the solution is determined automatically through the dispersion relation; for a frequency lying below the bulk dispersion curve an evanescent solution must be included artificially, i.e. by writing a decaying or growing exponential rather than a plane wave solution.

The extended hybrid model demands fixing six boundary conditions at each interface. Four of these are provided by the electromagnetic boundary conditions and the continuity of the perpendicular and parallel components of the relative displacement at each interface. In the preceding section we have seen how microscopic theory was used to try to find the two additional boundary conditions from the mechanical field equation. This work is still ongoing, so in order to investigate the importance of these boundary conditions we will consider two separate possibilities. It has been shown that the two

q(7t /a^)

Fig. 6. The bulk dispersion curves using a parabolic approximation and the parameters in Table 2 for GaN and AIN for the entire Brillouin zone. The shaded region is where the reststrahl bands overlap.


z = -d /2 z = d / 2

T01 T01 IP1 IP1

L01

£,(»)

'4^-f '

'tp^'<-

Fig. 7. A schematic illustration for the components of the mode when a L02 mode impinges on one surface of a quantum well. The LOl mode is also propagating in this example but the T02 and TOl modes are evanescent. There are also interface-like modes propagating parallel to the interfaces.

additional continuity conditions had to be such that [6,43]

cnV.u- (c44 + ^ ) -dx

and C44 h b dz dx

(140)

be continuous at the interfaces. Here we have assumed that the propagation in the plane is in the x-direction with the interfaces perpendicular to the z-direction, and b' is unknown [6,43]. There are two special cases of the conditions in Eq. (140). First we set y = C44 giving rise to the continuity of acoustic boundary conditions,

c n V . u - 2 c 4 4 ^ and 44 ( ^ + - ^ j , (141)

Secondly we set b' = —C44, giving rise to the continuity of the so-called optical boundary conditions,

cii V . u and C44(V x u)^. (142)

We are now in a position to determine the amplitudes associated with each component of the solution. The most efficient way to do this is to assume that a mode, either LO or TO, is propagating in region 2 as done in the case of the phonon tunnelling problem of the hybrid model [65]. This is illustrated in Fig. 7. For the LO mode the amplitude of the mechanical wave is fixed from the quantization procedure of a bulk wave in the form

Al2 = - , ^ , (143)

while for a TO mode the corresponding amplitude is fixed as

A2 ^ L (144) 2p2Vo2Coiq^-^ qJ2)

We now apply the boundary conditions at each interface. For a double heterostructure this gives twelve equations which may be solved to find the twelve unknown amplitudes (three reflected, three transmitted and six in the well region) in terms of the incoming amplitude. As before [65], the frequency is that of a bulk mode in material 2.


6A. Electron-phonon scattering

The electron-phonon scattering rates arising from the application of the extended hybrid model using the acoustic (Eq. (141)) and optical (Eq. (142)) boundary conditions as well as those arising from the application of the dielectric continuum model are shown in Fig. 8. As can be seen at once, it is very difficult to distinguish the curves, particularly the scattering rates due to the two forms of the extended hybrid model, suggesting that in this case the choice of additional boundary conditions is not important. Also shown are the corresponding scattering rates arising from the emission of the bulk phonons of the two materials. It can be seen that all the scattering rates invariably lie between

CM

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

\ \ A \

— \ -

1 ' '

X

\

' 1 '

^\ • ^ •

1 , ,

' 1 '

" -

. ' ^

• • ^ - -

1 1 1

a --

-

-

20 40 60 d(A)

80 100 120

120

Fig. 8. The electron-phonon emission rate for (a) intrasubband scattering in the ground state subband with an initial electron energy of Ihbarcou and (b) intersubband scattering from the first excited state subband with zero initial electron kinetic energy to the ground state subband at a temperature of 300K in a GaN/AlN quantum well. The solid curves are the results using the DC model which almost coincide with the results using the extended hybrid model with acoustic (dotted curves) or optical (dashed curves) additional boundary conditions. The chained curves are the emission rates due to bulk phonons with the higher (lower) curve using AIN (GaN) bulk phonons.


M CM

1.5

1 h

0.5

0

1 1 , 1 1 1 r - T - r - T - t 1 , , . , , , ,

_\ Interface

V L V 1 V

\^,>^ Confined

1 1 1 1

a J

k r ' ' . 1 1 1 1 1 1 1 1 1 1 1 7 T T T T " T T I 1- 1' ^

0 20 40 60 80 100 120

d(A)

0.5

0.4 h

f- 0.3

J 0.2

0.1 h

b

/ /

/ ^ /A Confined^^-^ /I \

^^.-<'^^_^-;^;::s:.^-'^^lnterfacei

-

1^1 , , , 20 40 60

d(A) 80 100 120

Fig. 9. As in Fig. 8 but with the DC model and extended hybrid model results separated into modes confined in the quantum well (the mode frequency on the dispersion curve of the bulk LOl branch in the extended hybrid model) and interface modes. The results due to bulk phonons are not shown in this figure.

these two bulk phonon scattering curves, a result which has been pointed out previously [9,13,18] and one which we will comment on further in the next section.

Fig. 9 displays the same scattering rates but the separate contributions of confined and interface modes are shown. Note that, for the extended hybrid model, by confined we mean any mode which has a propagating LOl mode as one of its components, i.e. the frequency of the total mode lies on the LOl bulk dispersion curve, otherwise it is considered to have the character of an interface mode. Again, the choice of additional boundary conditions is unimportant. However, there are different contributions from each type of mode when comparing with the DC mode even though the overall rate is the same.

In order to understand the new features arising from the extended hybrid model. Fig. 10 shows the variation of the transmission coefficient of the incoming phonon wave (L02 or T02) against its frequency. There are two sets of two resonances on each side of the graph which occur when the frequency of the mode is at resonance with any


c CD O

*if—

CD O O c o CO CO

E CO c en u .

0.8

0.6

0.4

0.2

^ y \ ^

-

--

-

-

L

^ 1

II 11

II l|

TTT V T T

V U 1 I 1

\ \ \V

\ II \ 1

-T~

1 1 1

\l

]/

L

- 7 ^

'•1 1 \ 11 1

il 1

, \ 1 . , r -

1 ;

I

1 ' 1 / \ / \ /

A-j

1 ' 1 H

-\ 1 ' 1 ~ 11 ;

1 1 -

-

-

1 1

u 0.8 0.9 1.1 1.2

co/co. LI

Fig. JO. The transmission coefficient of an incident L02 (frequencies above 0.9(OLI) or T02 (frequencies below 0.9(0L\) mode impinging onto a GaN/AlN quantum well of width d = 20A (dashed curve) and d = 40A (solid curve).

of the DC interface phonons (Fig. 4). The central peaks in the figure occur when an integer multiple of the wavelength of a propagating LOl mode fit into the quantum well width; this is the reason why there are more transmission peaks in the case of the wider well. We conclude that these resonances are equivalent to the confined phonons of the DC model or the modes due to material 1 in the hybrid model (although the symmetry agrees with the hybrid model not the DC model).

Fig. 11 shows the intrasubband scattering rate as in Fig. 8, but for a mode of specific frequency, evaluated for two well widths. Also in this figure, we show the corresponding result of the hybrid model applied to the GaAs/AlAs system. In the case of GaAs/AlAs it is seen that there is an enhancement of the rate when the frequency of the mode is at resonance with the interface phonons of the DC model. This also occurs in the extended hybrid model but for this model there are additional resonances occurring when there is an overlap with a propagating LOl mode, as expected from the behaviour exhibited by the transmission coefficient (Fig. 10). We also note that the incoming T02 mode does not contribute significantly to the scattering rate.

Finally, Figs. 12-15 show the relative displacement and the corresponding Coulomb potential for various frequencies. The resonances with the DC interface phonons (Figs. 12 and 15) and the LOl phonons (Figs. 13 and 14) are shown clearly whatever incoming mode exists in material 2. However, due to the orthogonal polarizations of the LO and TO components there is little coupling between them. Also note that the TO component does not have an electric field or Coulomb potential associated with it so it does not interact with the electrons.


1000 E

^ 100 k

'c 13

CO 10

CO C 1

0.1 t c

S 0.01 k

0.001

:

L-t r

h k I

t 1 1 1 pi C 1

L 1 J t /

t /

IL

- T ^

I I 1 \ 1 \\ ^

N

_i L_

s:^ 1 \ - ^ xj

T '

"^

f

/ ^ \ \ 1

1 •

1 1 1 —

. 1 ~ -A

J \

V

y— 1 \ \ \

— - \^ "

_ J i \

^ ^ ^

y

y i ^

J

I — 1 —

y / / / r

1 — 1 —

T \ \ \ \ \

a \ \ 1 I 3 \ g

\ ] \ J \ |

\i = ~~

-5

J ^

0.8 0.9 1

C 0 / ( 0 .

1.1 1.2

LI

1000

j2 'C 100

CO

3, •o

c s c

10

1 V

2 ' ; 1.4

1.35

- 3

z - 1.25

" 1 2

z C

'-_

, ) I

I _ -

^"S^ r

-,

' • ' - - , . ^

, . - • - • '

_j i___ 0.5

J L.

1

s

T 1 r-

A

. 1

1

qd

1

_ 1 ,

1.5 J

y>^ ,0^

J 1

1 1 1

^y^ / y ^ -" ^ / y

y

\ . 1

-1 1 ^ a

-b =

^ \ : \ ^ •

\ ^ ' \ ^ ~ \ " \ -\ J

\ :

^ 1 . J

1.24 1.26 1.28 1.3 1.32 1.34 1.36 1.38

Fig. 11. The intrasubband scattering rate of an electron in the ground state with initial energy Ihbarcou against the frequency of the phonon mode emitted at a temperature of 300 K for a quantum well of width c? = 10 A (dashed curve) and <i = 40 A (solid curve) using (a) the extended hybrid model (with either set of additional boundary conditions) in a GaN/AlN quantum well and (b) the hybrid model in a GaAs/AlAs quantum well. The inset in (b) shows the resonance condition with the interface mode dispersion (from Fig. 4(b)) of the two curves on the main graph.


Fig. 12. An example of (a) the relative displacement component in the plane parallel to the interfaces Uxiz), (b) the relative displacement component perpendicular to the interfaces Uziz) and (c) the Coulomb potential 0(z) in a GaN/AlN quantum well using the extended hybrid model with the frequency of the mode within the range (o^[^ < co< o^^^. In this range only L02 is propagating.


Fig. 13. As in Fig. 12 with the frequency within the range a)^^2 < ^ < ^ L 7 ^îch is when both L02 and LOl are propagating.

Optical phonon confinement in nitride-based hetewstructures Ch. 11 435

Fig. 14. As in Fig. 12 with the frequency within the range J/^^^ < co < a)\{ which is when both T02 and LOl are propagating.

436 Ch. 11 NA. Zakhleniuk et ah

Fig. 15. As in Fig. 12 with the frequency within the range (i>j2 < ^ < ^L\ which is when only T02 is propagating.

optical phonon confinement in nitride-based heterostructures Ch. 11 437

We will explore similarities between results arising from different models when we look into the issue of an approximate sum-rule which the DC model satisfies. Here it is instructive to see the connection between models by considering the case of a single heterostructure. Assuming that material 2 occupies z < 0 we have the solution

u = [ALiiqq - iqL2i)e'''' + Ar2(^r2q - iqi)e'^''' + Ajjqiq - iz)e^'] e^^\ (145)

and with material 1 occupying z > 0 we have the solution

u = [Aixiqq + / ^LIZ)^"^^" + A n ( ^ n q + iqi)e~'^''' + Anqiq + ii)e~'^'] e'^^^ (146)

In these solutions we have assumed that all the LO and TO modes are evanescent, but our aim is to show how the boundary conditions will produce the corresponding DC phonon results. The application of the two general boundary conditions, Eq. (140), gives the equations

AL2 [qîai -b2-\- b'^) + qljî] ~ q(b2 + ^2) [qriATi + qAn] =

All [q^(ai -bi+ b[) H- qlâi] - q(bi + b[) [qriAri + qAn],

Anqqiiibi + b'^) -h ^7-2(^72^2 + q'^b'^) + Anq^{b2 + b'^) =

Auqquibi + b[) + Aniqj^bi + q^b[) + AnqHbi + b[).

We now assume that the reststrahl bands of the two materials are separated and we are considering a mode of frequency close to that of material 2 LO and TO frequencies, i.e. qii and QTI are larger than any of the other wavevectors. We see that under these conditions the first equation in Eq. (147) gives the solution An ^ 0 and the second AT\ ^ 0 . This would be valid even if these modes were propagating (they just have to have the largest wavevectors) and this is also true when a propagating L02 (AIN) mode is impinging on a quantum well. Although the L02 branch overlaps with the LOl (GaN) branch, the wavevector associated with it qn is very large and, hence, the solution reduces to that of the hybrid model, which in tum, is close to the DC model. We also note that alternatively we can remove the TO components from the solution and disregard the two boundary conditions of continuity of the parallel component of u together with the second equation in Eq. (140). This procedure yields similar results to those discussed above.

6,5. Phonons in GaN/AlN superlattices

Next we investigate the polar optical modes in a GaN/AlN superlattice, for which the mode frequencies and scattering intensities can be experimentally determined using Raman scattering. A schematic illustration of the superlattice is shown in Fig. 16. In each region we include the forward and backward propagation of all components (LO, TO and IP) of the mode and apply Bloch's theorem, connecting different unit cells of the superiattice by multiplying by the factor e'^^ where \Q{d\ + d2)\ < n with Q the Bloch wavevector and di (^2) the widths of the GaN (AIN) layers. This, together with the boundary conditions, leads to a twelve by twelve determinant for the dispersion relation.


n = -2 n = -1 n = 0 n = 1

'-' xi

%w

> z

< X >•

a cs 2 1

F/g. 76. A schematic illustration of the GaN/AlN superlattice.

1.2

1.1

3" ' - 3

0.9

0.8

0.

- —

-

1 1 1 1 1—1—1—r—1 r r— i i i i i i i

^^^'^;r^r^^^^^^^ \

-1 J

= F=

\ —i^ -— ._ J

^ — — Z - " - - ^ _ _ ^

-

01

— ^

0.1 1

Fig. 17. The frequency against qd\ for the extended hybrid modes (solid curves) of a GaN/AlN superlattice in the case of zero Bloch wavevector Q with î = IDA and d2 = 20A. The dashed curves are the interface modes from the DC model for the same system.

Fig. 17 shows the dispersion curves for zero Bloch wavevector across the frequency range of the GaN and AIN reststrahl bands. Also shown are the dispersion curves of the DC phonons in the same system. As we have shown earlier (Fig. 5) in the case of the hybrid model in GaAs/AlAs, the curves form straight lines joining the frequency values where the wavelengths of the mechanical wave fit the quantum well width at small wavevectors to the frequency values where the wavelengths of the Coulomb potential


wave fit the quantum well width at large wavevectors (the latter is the condition on the wavevector for the confined modes of the DC model). The only deviation from this is where the lines cross a DC interface phonon of the same symmetry when anti-crossings occur.

Again, it can be shown that the issue as to which additional mechanical boundary conditions to apply is not of importance since the same results are obtained. This is explainable along the lines used in the case of the scattering rates. Also, ignoring the TO or LO modes when they are not propagating in a region is possible with similar results being obtained.

7. The sum-rule

We have shown that the extended hybrid model, like the hybrid model for GaAs/AlAs before it, gives similar results for the total electron-phonon scattering rates as predicted by the DC model. There are still symmetry differences between the sets of modes belonging to different models, but when all the modes are involved it appears that the results come out to be the same order of magnitude. Why is this? An explanation for this observation is clearly needed. It has been argued previously that the DC model follows an approximate sum-rule [6,9,13,18]. Here we will attempt to provide a more formal basis of this result and show how, and why, the results arising from one model come to be the same as those based on another model when all of the modes are involved in each case.

To this end we must introduce the Green function involved in the solution of the mechanical field equation, Eq. (26). Since we are working in the non-retarded limit and the electrons only interact with the Coulomb potential, we need only solve the Green function for the longitudinal fields with the transverse fields only featuring in the boundary conditions. The relevant Green function for the Coulomb potential satisfies the equation

V^ [i;2 v2 + {0)1 - a?)] G(r, r') = - — [u^V^ + ( ^ _ ^2)j ^^^ _ ./ ^43^

The solution of this equation is found by expanding the delta function as a Fourier series. Thus we obtain the mixed Green function in a system with inhomogeneity in the z-direction as

_ [vl{q^+ql)-{col-o?)\e''^--e''>^' 0(x, q, z, q,) - 2^^^^^^^ ^ ^^^ ^^3 ^^^ ^ ^^^ _ ^^, _ ^3^j . U4y)

The Coulomb potential in a region of the inhomogeneous system is given by

cD(x, q, z, q,) = [Aie'"^'' + BLe''"^'' + Aje^^' + Bje-^'] e''^'' + G(x, q, z, , ) , (150)

where <? = {co\ - o?)/vi - q^- If the bulk spatial dispersion is ignored by setting VL -> 0, the equation to be solved is

v2Goc(r , r ' ) = - 4 ^ 5 ( r - r ' ) , (151) e(a>)


which is the initial equation of the DC model. Thus

^Dc(x, q, z, qz) = [Ae'' + Be-^'] ' " + G(x, q, z, ^ , ) . (153)

Note that, although it is not clear at first sight, the confined modes are properly included in this solution. This is because when the summation over all the modes is performed exponential terms appear which look like interface modes but which have a normalization constant appropriate for the confined modes.

It can be shown that the Fourier transform of the Coulomb potential Green function is also given by [70]

(x, x', z, z') = Y <Pl,^ ,(x, z)0,,,„x(x', z)-^^^^^^^, (154)

where </>q, .,x(x, z) are the normalized Coulomb potential functions for the mode found earlier, coq^q^^x is the frequency of the mode and we have used a phonon propagator [70]. Using this expression it can be shown that we may write the electron phonon scattering rate as rif(Ei) =

^J J J (155)

where \l/(z) is the normalized electron wavefunction in the z-direction. We have essentially removed all the elements associated only with the phonons and placed them in the function

oo

Siq, z, z', CO) = Triz)4>(z).^ ^^ , , = [ iz, q,)e-''>--Uq„ (156)

where ^{z,qz) is the same as <t>(x, q, z, ^^) but does not include the exponentials containing q. It is Eq. (156) which becomes our more formal version of the sum-rule. Ignoring the frequency and material parameter dependence leads us to the same sum-rule put forward by Mori and Ando [9].

We note two points. Firstly, the Green function is a classical correlation function of the Coulomb potential and, as such, does not depend on quantum mechanics. Indeed, the only quantum mechanical concept used is that of the fluctuation-dissipation theorem [3,70] to connect the correlation function with the scattering rate. Finally, the Green function is constructed from a complete set and, hence, so is our solution. This feature has been pointed out elsewhere [13] and it has also been shown that missing parts of this complete set can produce misleading results [71].

Although we cannot prove that the sum-rule in Eq. (156) is approximately valid for every conceivable phonon model, we can show that if all the modes are taken into account the result for the DC or hybrid model will lie between the two bulk material phonon results, as seen in the previous section. Also the term in Eq. (156) will appear in


every calculation using the phonon potentials, so if a result is found for one application (electron-phonon scattering fo r example) then it will also apply elsewhere (polaron effects, coupling to the electron gas, etc). Note also that this sum-rule does not depend on the electron states whereas it does in [9]. The point is that, as long as the electron states remain unchanged, any phonon model should give a similar result.

We can also see why the hybrid and extended hybrid models give the same results as the DC model when contributions from the entire set of modes are included. We note that the TO component will only appear in the boundary conditions, i.e. it does not directly change the oscillator strength of the Green function and can only affect the coupling at an interface. Also, whenever a resonance occurs between either the LO or interface-like terms and the source term a similar oscillator strength will be produced whether the terms are coupled or not. However, this is only true because we are generally very close to the LO frequency of one material and the bulk dispersion is small. If the dispersion velocity or the value of the parallel wavevector were much larger this would not necessarily be the case.

8. Conclusions

Our original aim in this chapter was to present a general account of optical phonons and their interaction in nitride-based heterostructures. However, as must now be clear, we found that the task would have been incomplete without a presentation of a quantum field theory of the dispersive continuum model of optical phonons in the bulk and in heterostructures. The treatment is presented here for the first time and we feel completes the picture of the continuum description of dispersive polar optical modes and their interaction with electrons in heterostructures. The issues of boundary conditions have also been explored in depth here from a microscopic point of view and the application of the theory to double heterostructures and superlattices has been presented. One important conclusion that has been reached is the existence of a sum-rule which applies whenever the interaction of electrons with phonons involves the full set of optical phonons irrespective of the model that has been used to describe the PO modes in the heterosystem.

Acknowledgements

We thank the Engineering and Physics Sciences Research Council, UK and the Office of Naval Research, USA for funding for this work.

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Subject index

alloy fluctuation, 182 AIN buffer layer, 53, 54, 290 AlN/sapphire interface, 55 angular dispersion of phonons, 388 anisotropic relaxation, 315 as-grown defect state, 203 atomic force microscope, 348, 363 AX center, 157

band edge PL emission, 167 basal plane coefficients, 299 basal plane isotropy, 312 basal stacking faults in GaN, 65 Bom-Huang DC model, 384 buffer layer morphology, 293 bulk phonon scattering, 430 Burgers vector, 365

Ca-ions in GaN, 195 capacitance-voltage measurements, 264 carrier capture barriers, 156 carrier mobility, 368 carrier-phonon interaction, 383 close-spaced showerhead reactor, 341 common crystallographic defects, 51 composition modulation enhanced doping, 42 compressive strain, 299 concentration of Ga vacancy, 140 conventional tube furnace annealing, 212 conventional vertical reactor, 340 convergent beam electron diffraction, 351 critical point energies, 305-310 crystal field splitting, 315 crystallographic defects in GaN, 61

damage and damage distribution, 198 damage buildup and amorphization, 203 damage recovery, 212 dark conductivity, 154 dark current, 161 dark field XTEM, 357 defect reduction, 355 deep level transient spectroscopy (DLTS), 9, 153,

251 deep positron states at vacancy, 116 defect annealing, 267, 268 defect concentradons, 125 defect engineering, 2, 51

defect evelution, 200 defect introduction rates, 265 defect-related transitions, 26 defects and doping in GaN, 126 defects in electron beam deposition, 281 defects in GaN, 77 defects in GaN, 252 defects introduced during growth, 254 dielectric function in wurtzite crystals, 388 diffusion, 40 diffusion coefficient. 111 diffusion in solids, 110 dislocation filtering, 364 dislocation in GaN layers, 141 dislocation loop, 201 dislocations, 62 DLTS and electron irradiated GaN, 258 DLTS and proton irradiated GaN, 261 dopant, 2 Dopant in GaN, 17 doping, 216 doping during growth, 41 doping technique, 40 Doppler broadening spectroscopy, 113, 114 DX center, 152 DX center in GaN, 169

EDMR, 5 elastic recoil detection analysis, 218 electrical compensation, 125 electrical properties, 34 electrical properties of dislocation, 367 electrodeposition, 282 electroluminescence, 227 electron beam deposition, 279 electron irradiated GaN, 102 electron irradiation, 257 electron spin resonance (ESR), 4, 77 electron-phonon interaction Hamiltonian, 398 electron-phonon interaction in layered heterosys-

tem, 402 electron-phonon scattering, 429 electron-phonon scattering rate, 409, 419 electron-PO phonon interaction, 386 energy band structure, 83 Er-doping, 33 ESR study of shallow donors, 87-89

446 Subject index

ESR study of AIN and BN, 103 ESR study of deep acceptors, 93-96 ESR study of deep donors, 90-93 estimated residual stress, 311 Euler-Lagrange equations, 393 Exciton linewidth, 23 excitonic splitting, 303 excitons, 21 extended hybrid model, 426

field effect transistors (FETs), 151 Film resistivity, 371 film uniformity, 346 formation of Ga vacancy in GaN layer, 141 Fourier analysis, 305 free exciton, 27 Frohlich coupling constant, 400

Ga vacancy, 124 GalnAsN, 175 gamma irradiation, 257 GaN heteroepitaxy, 289 GaN/AlN/sapphire system, 291 GaN/MN/SiC system, 291 GaN/sapphire interface, 69 GaN/SiC, 57 GaNiEr LED, 33 GaN:Mg, 2, 73, 112, 127 GaN:Si, 20, 133 Ga-Rich condition, 59 grain alignment via vicinal growth, 355 grain boundaries, 368 grain-size, 346 Green function, 440 growth and microstructures, 339 GSMBE, 368 g-value, 82

Hall effect measurements, 35-39 Hall electron concentrations, 372 Hall mobility, 36, 370 Hamiltonian for polar system, 395 Hamiltonian function for a polar layered het-

erosystem, 400 He-ion irradiated GaN, 262 HEMT, 361, 371, 374 heterojunction bipolar transistors (HBTs), 18 high frequency dielectric constants, 389 High-power device requirements, 374 H-Mg complex, 2, 39 homoepitaxial growth, 23 Hopfield quasicubic model, 313 HREM, 71 HRTEM, 351

HVPE, 34, 35, 307 hybrid model, 424 hydrogen related defects, 261 hydrostatic pressure, 173 hydrostatic strain, 313 hyperfine splitting, 79

identification of defects, 4 identification of native vacancies, 123 identification of vacancies, 130 implantation induced defects, 203 implantation-induced optical activation, 228 impurity concentrations, 121 impurity luminescence, 227 impurity redistribution, 217 influence of channehng, 198 influence of radiation enhanced diffusion, 196 influence of sputtering, 196 inhomogeneous system, 400 initial film growth mechanisms, 293 interdifussion of atoms in GaN, 144 intrasubband scattering, 429 inversion domain boundaries, 66, 339, 351 ion depth distribution, 195 ion implantation process, 194 ion implantation, 8, 40, 193 ion implantation at liquid nitrogen temperature,

204-212 ion implantation range, 194 ion implantation range distribution, 194 ion implantation and devices, 242 iron, 97 irradiation-induced defects, 257 isolation by implantation, 235 isothermal DLTS, 269

k.p perturbation theory, 82, 103 Keating model approach, 13, 386 Kinchin-Pease relationship, 198 kinetic trapping model for positrons, 119

Lagrangian and energy density in a dispersive polar materials, 393

Lagrangian density, 394 large lattice relaxation, 152 lateral epitaxial overgrowth (LEO), 11, 12, 361-

364 lateral overgrowth, 60 lattice dynamic field equations, 405 lattice mismatch, 3, 291 lattice site location, 216 fight emitting diodes (LEDs), 1, 17, 32, 58, 366 LO phonon replica, 22 localized positron density, 117

Subject index 447

long wavelength vibrations, 413 low energy electron beam irradiation (LEEBI), 17,

39 low energy ion bombardment, 270

magnetic resonance, 77 magnification factor, 84 manganese, 97 Mathews-Blackeslee thin film relaxation model,

11 Maxwell equations, 384 MBE,20,34,51 mean projected range, 197 metallization, 272 Mg-acceptors, 17 Mg-compensation, 29 Mg-doping, 28, 38 MgO, 43 microcracks, 70 microscopic theory and continuum models, 411 misorientation, 297 MOCViD, 5, 20, 34, 153, 307 molecular doping, 42 MOMBE, 345 momentum distribution of positrons, 115 Monte-Carlo simulation, 199 MOVPE, 12,51,52,340 MOVPE growth conditions, 340

nanotubes in GaN, 70 Native point defect in GaN, 109 native vacancies in GaN, 121 nature of DX center, 168 negative ions in GaN, 121 nitration, 59 n-type doping by ion implantation, 219-223 nuclear reaction analysis, 216 nucleation buffer, 18 nucleation layer, 342 N-vacancy, 124

observation of native vacancies, 129 ODMR, 5, 77, 153 optical ionization energies of the DX center, 168 optical ionization energy, 173 optical memory effect, 166 optical phonon confinement, 383 Optical properties, 21 optimal pressure growth, 356 other dopants, 34 oxygen donors in AlGaN, 170

PC Spectrum, 25 Persistent photoconductivity (PPC), 7, 151

phonon energy for wurtzite GaN, AIN, and InN, 391

phonon properties, 10 phonons in GaN/AIN superlattices, 437 Photoconductivity (PC), 19 Photoconductivity spectrum, 168 Photoluminescence (PL), 19 photoluminescence excitation, 227 photoluminescence of ion implanted rare earth

ions, 230-235 Pikus-Bir Hamiltonian, 319 pinholes in GaN, 70 planar defects, 63 PO phonons in bulk GaN, 387 point defects, 366 point defects and growth conditions, 137 polar optical phonons, 384 Poole-Frenkel effect, 270 positron annihilation, 123 positron annihilation spectroscopy, 109, 110 positron implantation, 110 positron lifetime, 111, 122 positron lifetime spectroscopy, 112 Positron states, 115 positron trapping at point defects, 118 positron wave function, 115 post-implantation annealing, 201 PPC and metastable defects, 160 PPC buildup and decay kinetics, 155 PPC effects on UV photodetectors, 180, 181 PPC in GaN:Mg, 154 PPC in heterojunction devices, 177-179 PPC phenomena, 151 PPC possible mechanisms, 153 p-polarization, 407 pre-metallization plasma treatments, 271 Prismatic stacking faults, 67 proton irradiation, 259 proton irradiation-induced defects in GaN, 262,

263 Pt Schottky contacts, 283 p-type doping by ion implantation, 223-227

Q-factor, 84 quantification of residual stress from optical data,

311 quantization, 402

radiation effects, 8 radiation effects, 251 radiation enhanced diffusion coefficient, 197 Raman spectra, 385 rapid thermal annealing, 95, 202, 212 rare-earth doping, 31

448 Subject index

RBS, 199 reflectance, 288, 306 reflection difference, 327 residual stress, 287 resistive evaporation, 272 Resonance technique, 78

Secondary ion mass spectroscopy (SIMS), 218 self-consistent dispersive theory, 411 shallow positron states at negative ions, 118 Si doped AlGaN, 174 Si-doping, 27 small angle grain boundaries, 62 Spin Hamiltonian, 78, 80, 81 spin-orbit perturbation, 318 spin-orbit splitting, 315 s-polarization, 407 sputter deposition, 273 sputtering deposition of Au Schottky contacts, 275 sputtering-induced defects, 274 stacking faults, 63 standard elastic theory, 311 STEM, 354 stoichiometry of the MOCVD growth, 137 stress, 10, 56 stress trend, 323 stress-related ambiguities in GaN optical data, 302 structural defects, 339 structural Properties, 10 Structure of GaN grown on foreign substrates, 52 Structures of buffer layers, 59 sum rule, 439 superhyperfine structure, 80

TEM, 51, 326 TEM image, 54, 332 theory of dispersive polar continuum nodes, 13 thermal processing of GaN, 193 thermal stress, 298 threading dislocations, 351 transition group ions, 96 transition metal ions in GaN, 98 traps, 253 trimethylaluminum, 341 trimethylgaUium, 340 two-dimensional electron gas (2DEG), 152

undoped n-type GaN layers, 128 unintentional doping, 371 UV-blueLEDs, 151

Volmer-Weber growth, 340

weak beam XTEM, 365 wurtzite structure, 86, 387

x-ray diffraction, 206 XTEM, 342

yellow luminescence, 135-137, 165, 171

Zeeman interaction, 79, 80 Zeeman splitting, 79 zinkblende wave function, 316, 387 Zn-doping, 30

Documents

Manasreh, III-Nitride Semiconductors - Electrical, Structural and Defects Properties 0444506306 Elsevier 2000)