JOONAS HILSKANOVEL METHOD FOR ARSENIC FLUX DETERMINATION IN MO-LECULAR BEAM EPITAXY

Bachelor of Science Thesis

Examiner: Tomi Leinonen

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ABSTRACT

TAMPERE UNIVERSITY OF TECHNOLOGYBachelor’s DegreeHILSKA, JOONAS: Novel method for arsenic flux determination in molecularbeam epitaxyBachelor of Science Thesis, 35 pagesNovember 2015Major: Teknillinen FysiikkaExaminer: Tomi Leinonen

Keywords: molecular beam epitaxy, gallium arsenide, arsenic flux

In this thesis, a novel method for the determination of arsenic flux in molecular beamepitaxy is presented. The method is based on the growth and ex-situ characterization ofa GaAs layer grown at a low temperature and under arsenic limited conditions. Growthunder these conditions results in excess gallium accumulation on the surface, which isproportional to the supplied arsenic flux during growth. Using ab initio calculations, adependency between the arsenic flux and the amount of accumulated surface gallium isderived, from which the arsenic flux is determined. The amount of accumulated galliumis determined from scanning electron microscope images, using a geometric modelbased on atomic force microscope measurements. A proof of concept is offered bycomparing results with the already established high resolution X-ray diffraction tech-nique. Additionally, an example calculation of the spatial arsenic flux distribution ispresented.

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CONTENTS

1. INTRODUCTION ................................................................................................ 11.1 Molecular beam epitaxy .............................................................................. 11.2 The aim of this work ................................................................................... 1

2. BACKGROUND .................................................................................................. 22.1 Basic description of MBE ........................................................................... 22.2 Gallium arsenide ......................................................................................... 22.3 MBE growth of GaAs ................................................................................. 32.4 Low temperature and arsenic limited growth of GaAs ................................. 3

3. EXPERIMENTAL SETUP AND CHARACTERIZATION METHODS ............... 63.1 MBE-system ............................................................................................... 63.2 MBE operation and sample growth ............................................................. 8

3.2.1 Flux measurement ......................................................................... 83.2.2 Sample growth ............................................................................ 10

3.3 Characterization methods .......................................................................... 113.3.1 Scanning electron microscopy ..................................................... 113.3.2 High resolution X-ray diffraction ................................................ 113.3.3 Atomic force microscopy ............................................................ 13

4. CALCULATION OF ARSENIC FLUX FROM ARSENIC LIMITED AND LOWTEMPERATURE GROWN GALLIUM ARSENIDE ................................................. 155. RESULTS ........................................................................................................... 18

5.1 Gallium droplet geometry ......................................................................... 185.2 Proof of concept ....................................................................................... 215.3 Spatial arsenic flux distribution ................................................................. 24

5.3.1 Applying the results .................................................................... 286. DISCUSSION AND CONCLUSION .................................................................. 297. REFERENCES ................................................................................................... 30

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LIST OF ABBREVIATIONS AND SYMBOLS

AFM Atomic force microscopyAlAs Aluminum arsenideBAG Bayard-Alpert ionization gaugeBEP Beam equivalent pressureBSE Back-scattered electronFEL Fast entry lockGaAs Gallium arsenideGaAsBi Gallium arsenide bismideHRXRD High resolution X-ray diffractionLT-GaAs Low temperature gallium arsenideMBE Molecular beam epitaxyRADS Rocking curve analysis by dynamical simulationSE Secondary electronSEM Scanning electron microscopyVLS Vapor-liquid-solid methodXRD X-ray diffraction

N Number of atomsA AreaNA Avogadro’s constantBEP Beam equivalent pressureρ DensityD DiameterF Atomic fluxh Heightγ Height to diameter ratioη Ionization efficiencyM Molar weightT Temperaturez ThicknessV Volume

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1. INTRODUCTION

1.1 Molecular beam epitaxy

Molecular beam epitaxy (MBE) is an epitaxial growth technique where materials aredeposited on a substrate in a vacuum. MBE enables the growth of various epitaxialstructures with a wide range of available deposition materials, such as metals, semicon-ductors, oxides and even organic materials. In particular, the growth of semiconductordevices, such as lasers, solar cells or transistors, is the predominant use for MBE in in-dustry as well as research. A key attribute of MBE that allows for the production ofthese devices is the precision in controllability of the material composition and dopingduring growth. With MBE it is possible to grow (i) materials with low defect concentra-tions, (ii) structures with abrupt interfaces and doping profiles, and (iii) quantum struc-tures. Owing to these properties, MBE has led major advances in the electronics indus-try as well as in material research. [1, 2]

1.2 The aim of this work

Enabling the successful MBE growth of the aforementioned semiconductor devicestructures it is required that the critical growth parameters, namely the growth tempera-ture and molecular fluxes, are precisely known and controlled. In this work, the focus ison gallium arsenide (GaAs) growth and, in particular, the accurate determination of thearsenic molecular flux. The growth of high quality GaAs films is usually achieved withhigh growth temperatures (~600 ºC) and with high arsenic overpressures [1]. As long assufficient arsenic overpressure is achieved, the quality of the GaAs film is essentiallyindependent of the arsenic molecular flux. Therefore, accurate control of the arsenicmolecular flux is often neglected. However, beyond this typical GaAs growth, the arse-nic molecular flux often becomes deciding factor in material properties. Importance ofarsenic flux control is evident in the growth of GaAs based alloys (e.g. GaAs1-xBix) [2],low temperature GaAs [3] and GaAs nanostructures (e.g. quantum rings) [4]. For thesecases, the precision in the control of arsenic flux is often insufficient, due to the pooraccuracy of arsenic flux measurements. For example, an accuracy of ~10 % is achievedin ion-gauge measurements of the arsenic flux [1]. The aim of this work is to establish anovel method for determining the arsenic flux based on growth and ex-situ characteriza-tion of a calibration sample, in conjunction with ab initio calculation. Furthermore, afew results gained by this method are also presented and discussed.

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2. BACKGROUND

2.1 Basic description of MBE

The basic technique of MBE was developed in the late 60s at Bell Laboratories by Al-fred Y. Cho and John R. Arthur. Although MBE technology has improved vastly fromthe early designs, the simple working principle of MBE remains the same. A sourcematerial is heated in a crucible in ultrahigh vacuum conditions, causing the source mate-rial to evaporate. The evaporated material forms a beam as it passes through the crucibleorifice. The beam is then directed towards a substrate material where some of the evap-orated atoms or molecules are adsorbed to the surface of the substrate. The vacuum en-sures that the source species travel to the substrate uninterrupted by other source or re-sidual gas particles. The species traverse in free molecular flow as opposed to a viscousone, because the vacuum is low enough for the mean free path of the species to be largerthan the dimensions of the chamber. Adsorption to the substrate is dependent on growthconditions, such as substrate material, other incident source material fluxes and sub-strate temperature (in this work referred to as growth temperature). In addition to theuninterrupted molecular flow of the source species, the vacuum environment ensuresthat the amount of impurity species in the chamber is minimized, which might be harm-ful to the properties of the grown layer if adsorbed during growth. To this end, thesource materials and substrates must be of high-purity. [1, 2]

The growth of typical semiconductor device structures, where different alloys are grownon top of each other with well-defined interfaces and layer thicknesses, requires the ac-curate control of numerous different material fluxes simultaneously. To achieve this,MBE systems have several independently heated sources which, in turn, have individualmechanical shutters to block the molecular beams from the source when necessary.Layer thicknesses can be controlled with a precision of a single monolayer, due to therate of closing and opening the shutters being faster than the time it takes to grow a sin-gle monolayer at typical growth rates. [1, 2]

2.2 Gallium arsenide

Gallium arsenide (GaAs) is a compound semiconductor used in a wide range of applica-tions that are manufactured with MBE. As many other semiconductor compounds,GaAs forms a zinc blende crystalline structure as a solid, which is analogous to dia-mond with the exception that the two face centered-cubic lattices have different atoms,in this case gallium and arsenic. Due to its high intrinsic electron mobility, GaAs ena-bles the production of high-performance transistors with higher functioning frequency

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than typical silicon based transistors. GaAs is also an intrinsically resistive material be-cause of its relatively wide band gap of 1.424 eV (at room temperature) [5]. The widthof the band gap also results in good temperature tolerance for GaAs based devices.However, these intrinsic electrical properties can be controlled by introducing dopingmaterials or alloying GaAs with other elements. Another important material property ofGaAs is that the band gap is direct, which allows for efficient light absorption and emis-sion. This property makes GaAs ideal for optoelectronic devices. [5]

2.3 MBE growth of GaAs

The production of high quality films of GaAs with MBE is typically done by using highgrowth temperatures and high As/Ga material flux ratios. Although optimal growthconditions can vary for each MBE system, due to their individual geometry and compo-nents, growth temperatures of ~600 ºC and As/Ga flux ratios of over ~2 are typicallyused to grow GaAs with excellent optical, structural and electrical properties togetherwith smooth surface morphology. These properties are influenced by the incorporationof lattice defects, impurities and deep levels, which, in turn, are controlled by thegrowth temperature. Moreover, growth temperature also controls surface morphology,and therefore interface roughness, since adatom diffusion, adsorption and desorption areall temperature dependent. [1]

The role of the As/Ga flux ratio on the GaAs crystal quality has similar effects as thegrowth temperature. Growth kinetics at the surface are controlled by the ratio of the Asand Ga surface vacancies and the relative population of chemisorbed As and Ga precur-sors, which, in turn, are controlled by the As/Ga flux ratio. As a result, the As/Ga fluxratio influences impurity sticking and incorporation coefficients, thereby influencinglattice defect, impurity and deep level concentrations. Similarly, surface morphology,dopant surface segregation and diffusion are also influenced by the As/Ga flux ratio. [1]

The growth rate of GaAs under typical growth conditions is controlled by the galliumflux due to its unity sticking coefficient and negligible desorption from the surface fortemperatures below ~620 ºC [1]. Arsenic, however, is a more volatile species and itssticking coefficient is highly dependent on the available group V site concentration onthe surface. At typical growth temperatures, all excess arsenic will desorb from the sur-face, allowing the growth of stoichiometric crystalline GaAs [1, 6, 7].

2.4 Low temperature and arsenic limited growth of GaAs

GaAs grown at low temperatures, referred to as LT-GaAs, has been studied extensivelydue to its unique properties, which allow for the manufacture of highly resistive materi-al. At low growth temperatures of below ~400 ºC and above unity As/Ga flux ratios,excess arsenic can incorporate into the GaAs lattice forming arsenic anti-sites, AsGa, andgallium vacancies, VGa [8]. Furthermore, thermally annealing such defects results in

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AsGa diffusion in the bulk to form arsenic clusters, making the crystalline structure high-ly resistive. This, in conjunction with high carrier mobility and fast recombination life-time, allows for subpicosecond photoconductive device applications [9].

Concentration of the aforementioned point defects is a function of both temperature andthe As/Ga flux ratio. The concentration rises quickly when increasing the As/Ga fluxratio above stoichiometric conditions and eventually saturates to a constant value [3].On the other hand, under these arsenic rich conditions the concentration decreases line-arly when increasing the growth temperature [8]. An excess of roughly 1% arsenic canbe achieved using high As/Ga ratios and low temperatures [3, 8]. In this work, however,the focus is on growth conditions where an excess of Ga is supplied at low tempera-tures.

In the growth regime where the As/Ga flux ratio is below unity, the arsenic (As2) stick-ing coefficient has been found to be practically unity, due to the excess amount of groupV sites available at the surface [6, 7]. During growth, however, excess gallium nucleateson the surface forming liquid droplets [1]. The droplets are essentially pure gallium, asarsenic solubility in the liquid gallium at these low temperatures is negligible [4, 10,11]. As growth proceeds at these conditions, the gallium droplets grow larger as excessamounts of gallium accumulates. Formation of the droplets changes the fundamentalgrowth process of GaAs over and around the gallium droplets. On one hand, the galliumdroplets act as gallium reservoirs, which supply the surrounding areas with gallium ada-toms, enabling the nucleation of GaAs with the incident arsenic [7]. On the other hand,the arsenic that is incident directly on top of the droplets gets trapped on the dropletsurface from where it migrates to the edges of the droplet where GaAs nucleation isenergetically preferable [4]. It should be noted that arsenic diffusion through the drop-lets or vapor-liquid-solid (VLS) type growth mediated by the gallium droplets is negli-gible, due to the previously mentioned low solubility of arsenic into the liquid gallium.As the growth proceeds, the liquid droplets can freely move on top of the surface, whicheliminates the chances of droplets being buried. This, together with the high surfacediffusion rate of gallium on gallium rich surfaces [1], creates relatively smooth GaAssurfaces on the perimeters of the droplets.

The LT-GaAs layers grown under arsenic limited conditions are stoichiometric, as theGaAs phase diagram at these growth temperatures only indicates a stoichiometric GaAsphase and a liquid phase of practically pure gallium. This is supported by observationsof no strain between the LT-GaAs layer and the GaAs substrate in high resolution X-raydiffraction (HRXRD) measurements. The point defects formed during growth underthese conditions are not known, however, due to limited research conducted in thisgrowth regime. Nonetheless, some things can be deduced from proposed incorporationeffects. The AsGa anti-site defects are the main cause of compressive strain in As-richLT-GaAs [8] and as the As-limited LT-GaAs shows no strain, it can be deduced that theincorporation of this particular defect is rare (concentration below ~1019 cm-3) in this

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growth regime. Furthermore, if the VGa defect is incorporated as a part of a defect com-plex with the AsGa anti-site, it is likely that this point defect is rare as well.

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3. EXPERIMENTAL SETUP AND CHARACTERI-ZATION METHODS

3.1 MBE-system

The MBE-system used in this work is the VG V80H, which is a model often used forresearch purposes. This specific system has been configured for III-V epitaxy and hassources for aluminum, gallium and indium as well as nitrogen, arsenic and bismuth forthe group III and V species, respectively. Additionally, silicon and beryllium are pro-vided for n- and p-type doping, respectively. The group III and dopant sources, alongwith bismuth, are traditional Knudsen effusion cells (K-cell). These cells are simplethermal evaporators where the source material melt is in a heated crucible and the mate-rial flux is controlled by careful temperature regulation. All the K-cells are fitted withindividual mechanical shutters. As for the remaining group V cells, there are speciallydesigned sources.

Fig. 3.1 a) Schematic of a K-cell. b) Schematic of a valved cracker cell.

For arsenic, a valved cracker cell is fitted. This cell comprises two segments: a bulkstage where solid arsenic is heated to produce As4 and a cracker stage where the As4

molecules can be dissociated to create As2. Generally speaking, the arsenic source hastwo operation modes. One where the cracker stage is heated to a lower temperature tolet As4 molecules pass without dissociation and one where the cracker stage is heated toa high temperature to generate As2. In this work, the latter mode is used. The arsenicflux is controlled by a needle valve positioned between the bulk stage and the cracker.For nitrogen, a plasma source is fitted to the reactor in conjunction with a mass flowcontroller providing atomic nitrogen. However, as it is not used in this work, the speci-fications for this source are omitted here.

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Fig. 3.2 Schematic cross-section of the MBE system used in this work.

The MBE vacuum chamber is divided into three segments: a growth chamber, a prepa-ration chamber and a fast entry lock (FEL) chamber (see Fig. 3.2). The chambers areseparated with vacuum valves and have individual pumping systems. The loading ofsubstrates and samples between atmospheric conditions and the MBE-system takesplace via the FEL chamber. During loading, this chamber is filled with pure nitrogenwhile the FEL vacuum pumps are turned off. After reaching an atmospheric pressure inthe FEL chamber, substrates and samples wafers can be loaded in or out of the systemtogether with wafer holding blocks. The blocks are made of molybdenum due to theirexcellent thermal stability and inertness. The FEL chamber is then pumped down by aturbomolecular pump in conjunction with a diaphragm backing pump. After the FELchamber has been pumped down to ~10-7 mbar vacuum level, the substrates can bemoved with their blocks to the preparation chamber using a wobble stick and a mechan-ical trolley transfer mechanism. The wobble sticks are used in both the preparation andthe growth chamber to maneuver the blocks. They consist of a magnetically actuatingarm, to mimic movements made on the handle outside the chamber, with a spatula thatcan hold the blocks via an upright facing pin.

In the preparation chamber, the substrates are heat treated to promote desorption of im-purities, such as water and atmospheric particles, from the substrate surface. The prepa-ration chamber is pumped by an ionization pump and its vacuum level is typically ~10 -8

mbar. After the substrate has been heat treated sufficiently, i.e. the preparation chamberpressures are stable and have reached a reference pressure level, it can be moved intothe growth chamber. The growth chamber has the best pumping capability and pressuresof ~10-10 mbar can be reached when cells are at their idle temperatures. This chamber ispumped by a diffusion pump together with liquid nitrogen-filled cryopanel surroundingthe chamber. The diffusion pump is backed by two rotary vane pumps. The growthchamber is also fitted with an additional ionization pump and a titanium sublimationpump.

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3.2 MBE operation and sample growth

The day-to-day MBE operation involves flux measurement and sample growth. In thefollowing chapters, the specifics of these procedures are explained for the measurementsand growths relevant to this work.

3.2.1 Flux measurement

The flux measurement of the sources, as well as chamber pressure monitoring, is donewith nude Bayard-Alpert ionization gauges (BAG). In this particular system, the fluxmeasurement BAG is mounted on to the backside of the manipulator arm which can berotated so that it is in the path of the molecular beams (see Fig. 3.2). An ion gauge con-sists of three components: a filament (cathode), a grid (anode) and an ion collector(ground). A schematic drawing of an ion gauge is provided in Fig. 3.3.

Fig. 3.3 Schematic drawing of a nude Bayard-Alpert ionization gauge

The ion gauge working principle is simple. By driving current through the filament, itheats up and begins to emit electrons. These electrons are accelerated towards the posi-tively charged grid. The electrons travelling towards the grid can pass into the spaceenclosed by the grid. In this space, they can collide with gas molecules and ionize them,producing positively charged ions. These positively charged ions are then collected effi-ciently by the grounded ion collector which is connected to an electrometer. The currentgenerated at the ion collector, referred to as beam equivalent pressure (BEP) by conven-tion, is proportional to the amount of gas molecules inside the grid and thereby propor-tional to the molecular flux.

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Measurement of group III BEPs is straightforward, due to their tendency to adsorb tosurfaces present in the chamber. This means that when the beam is directed towards theion gauge, all the beam species pass the ion gauge grid only once and stick to the ma-nipulator arm and chamber walls behind the ion gauge. Therefore, when opening theshutter, the ion collector current quickly rises to a stable value, as seen in Fig. 3.4.Group III BEPs can be typically measured and reproduced to within about 0.5 % [1].This, however, is often not the case with group V species. The more volatile group Vspecies, such as As2 and As4, can reflect off the surfaces behind the ion gauge and makea second pass through the ion gauge grid. This results in the increase of BEP over timeand, since the sticking coefficient of the group V species to different surfaces in thechamber is essentially unknown, renders the measurement useless. However, this prob-lem can be circumvented by depositing a layer of Ga, Al or In on the surfaces behindthe ion gauge before measuring the group V BEP, because group V species tend to haveunity sticking coefficient on these clean group III surfaces. This way, the group V spe-cies initially stick with unity coefficient to the group III coating and subsequently startsaturating the available group V sites, resulting in reflection and BEP rise. Due to thetransient unity sticking coefficient and saturation of the coating with group V species,the accuracy in group V BEP measurements is poor. For example, when using typicalAs4/Ga ratios and a 60 s gallium pre-deposition, an accuracy of 10% is achieved inmeasuring the As4 BEP [1]. Furthermore, it should be noted that the group V BEP sta-bility over time is much more variable than the typical group III BEP, making the fluxreproducibility even worse [12].

Absolute BEP values are dependent on many factors, of which the most crucial ones areion gauge sensitivity, geometry of the grid and ionization efficiency of the molecularspecies. Therefore, flux ratios are related to BEP values by equation 3.1.

=/

3.1

In equation 3.1, the ionization efficiency , absolute source temperature and molecu-lar weight are denoted for species X and Y, with respective sub-indices.

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Fig. 3.4 Typical BEP measurements for Ga, Al and As (approximate BEP valuesshown by double-headed arrows). In the right hand graph, the (i) valve jog start, (ii)arsenic unity sticking coefficient transient and (iii) increasing BEP due to arsenicreflection are indicated. The initial decrease in the Al BEP is believed to be due to ashutter transient, caused by thermal instability of the cell after opening the shutter.

BEP measurements in this work were measured in the following way. First, Al wasmeasured for 3 min and after closing the shutter the background BEP was measured for1 min and subtracted from the averaged Al BEP. Second, Ga was measured three timesfor 30 s and 15 s for Ga BEP and background, respectively. Finally, As was measured atdifferent valve openings (by gradually jogging the needle valve to a set value) with eachmeasurement being preceded by an Al deposition of 2 min and BEP was tracked for 1min. Typical BEP measurement results are depicted in Fig. 3.4.

3.2.2 Sample growth

Sample growth is preceded by a standard cleaning process by heating the substrate in aspecialized outgassing stage situated in the preparation chamber at a temperature ofroughly 300 ºC. This heat treatment is done for two to three hours, depending on thewafer holding block and substrate cleanliness, until a reference pressure of 2×10 -8 mbaris achieved in the preparation chamber. After this, the sample is moved to the growthchamber and placed in the manipulator arm, which is kept at ~315 ºC.

Growth is initiated by starting manipulator rotation and a heating sequence of the sam-ple to ~620 ºC to remove the native oxide layer and any remaining impurities. An arse-nic overpressure is required during this heat treatment to prevent arsenic desorptionfrom the substrate, which would result in surface degradation. After 10 minutes of theheat treatment, the sample temperature is lowered to ~580 ºC while arsenic overpressureis maintained to grow a high quality buffer layer. A buffer layer of 150 nm thickness isgrown to ensure a smooth and clean surface on top of which the actual sample structureis grown. For this work, few different structures were grown; including a gallium depo-sition sample, three LT-GaAs samples, two AlAs/GaAs heterostructures and a single

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GaAs1-xBix alloy sample. The details of each sample are presented in the results anddiscussion chapter.

3.3 Characterization methods

3.3.1 Scanning electron microscopy

Scanning electron microscopy (SEM) works by tracing a focused beam of electrons in araster pattern across a sample surface and then producing an image by detecting the sig-nals that change in response to electron bombardment. SEM can provide information onsurface topology and composition for up to nanometer resolution. In this work, imagingis done by two detection modes, each of which provide unique information. Firstly, asecondary-electron (SE) detector is used. The secondary-electrons are low energy elec-trons (typically under 100 eV) that are ejected from the first few atomic layers of thespecimen, due to inelastic scattering interactions with the incident beam. This detectorprovides good insight into the topology of the surface, due to its high depth of field.Secondly, a back-scattered electron (BSE) detector is used. The back-scattered electronsare incident electrons that have elastically scattered from the specimen surface andtherefore have the same energy as the incident electrons, typically in the order of 100 to10 000 eV. The back-scattered electron imaging mode provides information on the sur-face composition, as the scattering efficiency is proportional to atomic number. [13]

In this work, the specific SEM system used is the Zeiss Ultra 55. All subsequent men-tions of the imaging detectors are denoted by SE and BSE for secondary-electron andback-scattered electron detectors, respectively.

3.3.2 High resolution X-ray diffraction

HRXRD is a versatile characterization method to determine material properties of crys-talline structures. Accurate information on thin film thickness, composition, as well ascrystal and interface quality can be achieved non-destructively. This, in conjunctionwith little to no sample preparation, makes it an ideal method for thin film research.

In X-ray diffraction (XRD), a collimated beam of X-ray radiation is incident on a crys-talline structure and, due to its wavelength being comparable to interatomic distances inthe crystal structure, it can diffract and constructively interfere to specific angles. Theseangles are determined by Bragg’s law and are depend on many factors, of which inci-dent angle with respect to the crystal planes and lattice plane separation are the mostcrucial ones. Moreover, in HRXRD the diffraction angles around a single diffractionmaximum (corresponding to a single lattice plane group) is measured with high angularresolution. In HRXRD, the aim of the measurement is to detect slight deviations fromthe ideal crystal structure, which form an intensity distribution around the ideal structure

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diffraction maximum, due to slightly different lattice plane separation in the differentparts of the crystal structure. For the case of thin films, this is particularly useful, as thelattice plane separation is proportional to the film’s composition. In addition to compo-sition determination, with HRXRD it is possible to determine thin film thicknesses, asthe film’s thickness causes additional interference fringes (Pendellösung fringes) aroundthe thin film peak which can be analyzed. A detailed analysis of the thin film parame-ters, such as composition and film thickness, is gained by fitting a model to the experi-mental data. In this work, this is done by Bede RADS (rocking curve analysis by dy-namical simulation) software, which uses a dynamical theory of X-ray diffraction for-mulated by Takagi-Taupin. In Fig. 3.5 there are two measurements and their corre-sponding simulation using the RADS software of two typical structures grown in thisstudy. [14]

Fig. 3.5 Examples of HRXRD measurements and simulations for structures grown inthis work. On the left, an AlAs/GaAs heterostructure and, on the right, a LT-GaAslayer grown under slightly arsenic rich conditions.

In this work, the XRD measurements are carried out with a Phillips X’Pert XRD sys-tem. In this specific system, the X-rays are Cu K-alpha (0.154056 nm) radiation whichare generated in a high power ceramic X-ray tube. The X-rays are then directed towardsan X-ray mirror that focuses the beam towards a four crystal Ge(022) monochromator.Past the monochromator, a triple-axis goniometer holds the sample in front of the fo-cused X-ray beam. The goniometer can be positioned in such a way that the diffractedintensity from specific lattice planes is directed towards the detector. The detector isfitted with an analyzer, which provides a narrow angular detection range. [15]

In this work the scans are so called ω-2θ triple-axis coupled scans, where both the sam-ple (i.e. goniometer) and detector are moved simultaneously (although with differentvelocities). The ω and θ angles refer to the incidence and diffraction angles, respective-ly, which are measured with respect to the lattice plane being measured. The GaAs(004) lattice planes are measured owing to their high structure factor, which governs thediffraction maximum intensity.

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3.3.3 Atomic force microscopy

Atomic force microscopy (AFM) is a method for measuring surface geometry three-dimensionally with nanometer resolution. AFM works by probing the specimen surfacewith an atomically sharp tip which is connected to a cantilever. When moving the tipcloser to the surface (in order of multiple nanometers) with a piezoelectric actuator, at-tractive forces, such as van der Waals, electrostatic and magnetic forces, are formedbetween the surface and the tip, which deflects the cantilever according to Hooke’s law.However, as the tip gets closer to the sample surface (sample-tip distance fractions ofnm) repulsive chemical forces deflect the cantilever in the opposite way. Adjusting thesample-tip distance while measuring the cantilever deflection by tracking laser lightreflection off the top of the flat cantilever head with a photodetector, yields informationof the interacting forces between the tip and the sample. Furthermore, raster-scanningover the sample surface while keeping, for example, the interaction force or tip heightconstant allows for accurate determination of the surface geometry. Depending on whatparameter is kept constant during the raster-scan, AFM can be divided into three imag-ing modes: contact, non-contact and tapping. In this work, the measurements are per-formed using the tapping mode. [16, 17]

In the tapping mode (also referred to as amplitude-modulation AFM), the cantilever isoscillated perpendicularly with respect to the sample surface near its resonance frequen-cy by a piezo element mounted in the cantilever holder. When lowering the oscillatingtip closer to the surface, the oscillation amplitude of the cantilever is decreased, due tothe interacting forces between the tip and the sample surface. Surface height is deter-mined by keeping the oscillation amplitude constant over the raster-scan by moving thecantilever up or down. The tapping mode has several advantages over the other imagingmodes of AFM for semiconductor research, for example no sample preparation is need-ed and sample surfaces are rarely damaged.

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Fig. 3.6 a) Diagram of AFM components. b) Artifact formation due to a dull probingtip. Adapted from reference [18].

However, compared to other microscopy techniques, AFM has some disadvantages. Asa microscopy technique it is considered to be slow, when compared to SEM, for exam-ple. When raster-scanning across the sample, the tip velocities are typically in the orderof µm/s, resulting in slow scan times over large areas. The resolution of AFM is limitedby tip geometry and imaging artifacts are possible, due to poor tip quality or steep sam-ple topography, as depicted in Fig. 3.6.

The AFM system used in this study was the Veeco Dimension D3100 with the Nano-scope IV control unit. Further analysis on the data was done by Veeco V613r1 andMatlab 2014a/2015a software.

a) b)

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4. CALCULATION OF ARSENIC FLUX FROMARSENIC LIMITED AND LOW TEMPERATUREGROWN GALLIUM ARSENIDE

In this chapter the method of calculating the arsenic flux based on the calibration struc-ture is presented. Additionally, the chosen growth parameters for the calibration struc-ture are explained. A motivation behind the derived analysis method is also discussedbriefly, which arises from the similarity of the structure and the substrate.

To calculate the arsenic molecular beam flux, a low temperature GaAs (~220 ºC) sam-ple is grown with below unity As/Ga flux ratio. The rationale for the low temperature isto prevent any desorption of the deposited As and Ga species. In the case of Ga, this isclear, as the desorption of Ga is negligible for even up to ~620 ºC [1]. In the case of As,it is bound to the excess amounts of Ga available forming GaAs, which is thermallystable for temperatures up to ~590 ºC [19]. The arsenic-limited growth mode on theother hand ensures that the sticking coefficient of the As2 species used is unity [6, 7].Based on these assumptions, a calculation of the arsenic molecular flux is possible fromthe thickness of the LT-GaAs layer grown, as it is directly proportional to the suppliedarsenic.

Measuring the grown LT-GaAs layer thickness directly is difficult, as its structure isvirtually the same as the buffer layer grown before it and therefore an accurate interfacelocation between the two is hard to determine. One way of circumventing this issue, isto grow a marker layer before the growth of the LT-GaAs layer from which the inter-face location between the marker and the LT-GaAs can be determined by various tech-niques. In this work, an AlAs marker layer is used for three reasons. First, its latticemismatch with respect to GaAs is low enough to enable relaxation free interfaces, buthigh enough to enable HRXRD analysis. Second, the elemental composition differenceenables the measurement of the interfaces directly by cross-sectional SEM measure-ments, for example. Third, growth of the structure is straight forward, as only group IIIspecies need to be controlled precisely. However, circumventing the problem of meas-uring the LT-GaAs thickness directly can be done without any marker layers by a de-tailed analysis on the amount of accumulated gallium at the surface.

Let us assume that a LT-GaAs layer is grown with a known As/Ga flux ratio, denotedby / , which is below unity with all incident species sticking to the substrate. Asdiscussed previously, some of the gallium is incorporated in the bulk LT-GaAs layer,denoted by , , while the excess gallium is accumulated on the surface as pure

16

gallium droplets, denoted by , . Arsenic, however, is only incorporated in thebulk, denoted by , . Since fluxes are proportional to amount of atoms deposited,the following relation can be written

= ,

, + , 4.1

Applying the knowledge that stoichiometry in pure GaAs is 1:1, i.e. , = , ,the previous equation can simplified to

=1

1 + ,,

4.2

Expressions for the quantities , and , are achieved by a simple densityand geometry calculation. In the following equations, the densities, , and molar mass-es, , are used for the atomic species . Avogadro’s constant is denoted by . For thegallium on the surface, individual gallium droplet volumes are summed over a samplearea giving some total volume of gallium in this area. The determination of droplet vol-umes by their shape is discussed in detail in the results chapter. Total mass of gallium inthese droplets is obtained by multiplying the total volume with density. Moreover, thenumber of gallium atoms is then achieved by multiplying with Avogadro’s constant anddividing by the molar mass of gallium.

, = 4.3

In equation 4.3, the summation of individual droplet volumes is done of droplets in-dexed up to that are located in some sample area, subsequently referred to as . Forthe bulk gallium, the number of atoms is proportional to the volume of the grown bulklayer in the sample area, denoted by . By a similar density and amount of substancecalculation, it follows that

, = + 4.4

From equations 4.3 and 4.4, the fraction in the denominator of equation 4.2 is given by

,

,=

( + )4.5

17

If now, postulating an imaginary scenario where an excess of As was supplied instead(assuming a formation of stoichiometric GaAs without any point defects), the Ga fluxwould be proportional to this imaginary (nominal) layer thickness, denoted by . Basedon this proportionality and, on the other hand, the proportionality between the As fluxand , it follows that

= =1

1 + ( + )∑ 4.6

Since the Ga flux is well-known and reproducible with accuracy [1], the quantity canbe easily determined. Furthermore, if an accurate calculation on the volumes of the gal-lium droplets over a measurable sample area is made, the only unknown in the aboveequation is . The latter equation in 4.6 can be solved analytically, with the fair as-sumption that ≠ 0 (i.e. some LT-GaAs is grown).

= −( + )

4.7

So in conclusion from equation 4.7, obtaining the real thickness of the arsenic-limitedLT-GaAs sample is possible if the gallium volume in the accumulated droplets is ob-tained and the nominal amount of gallium supplied is known. Moreover, from this cal-culated thickness it is possible to determine the arsenic flux from the following equa-tion.

= 4.8

In this work, investigation into the validity of this method is performed.

18

5. RESULTS

In this chapter, the results of this work are presented and discussed. First, the geometryof gallium droplets is investigated, as the method’s accuracy depends crucially on beingable to determine the volume of the droplets. Second, a proof of concept is offered bycomparing results between the method presented here and HRXRD analysis. Finally, anexample is presented, in which the arsenic flux profile over the substrate during growthis determined.

5.1 Gallium droplet geometry

The analysis method presented in this work relies on accurate evaluation of the accumu-lated surface gallium during arsenic limited growth, as seen from equation 4.7. To thisend, the geometry of the droplets was determined from AFM measurements performedon (i) a gallium deposition sample and (ii) an arsenic limited LT-GaAs sample.

The gallium deposition sample was grown by depositing pure gallium on top of theGaAs buffer layer for ~30 s at growth rate which was equivalent to ~0.35 µm/h ofGaAs. The deposition was performed at a growth temperature of ~220 ºC to preventgallium desorption. This resulted in droplet sizes of around 100 nm diameter. Further-more, the substrate rotation was stopped at the start of the gallium deposition, whichresulted in a variation in the total deposited gallium across the wafer surface due to theintrinsic non-uniformity of the flux, which will be presented in detail later.

The arsenic limited LT-GaAs sample had a nominal thickness of 250 nm and wasgrown at a growth rate of ~0.32 µm/h at a temperature of ~220 ºC. The estimated As/Gaflux ratio based on flux measurements was 0.55. However, as in the gallium depositionsample, the substrate rotation was stopped during the LT-GaAs growth and a gradient inthe As/Ga ratio over the wafer was formed. Generally speaking, one side of the waferhad As-limited conditions whereas the opposite side had As-rich conditions and be-tween these two sides a smooth gradient was formed.

The samples were chosen for analysis based on the sizes of the droplets, namely thegallium deposition sample had relatively small droplets compared to the LT-GaAs sam-ple, which had bigger droplets. Simultaneously, an effect of surface roughness on thegeometry was investigated, as the LT-GaAs sample had a somewhat rougher surface,which can influence the contact angle, for example.

19

Fig. 5.1 A planefitted AFM measurement of the gallium deposition sample.

To determine the geometry of gallium droplets, AFM images were measured from thesamples and a simple data analysis was conducted. Fig. 5.1 depicts a typical AFMmeasurement. The data was analyzed in the following way. First, the raw AFM data wasplanefitted with a 3rd order xy-plane to level the background, because typically the AFMtip is not normal to the specimen surface, resulting in a tilted raw image. Second, anappropriate cut-off height level was chosen to separate the background from the drop-lets. This cut-off was chosen to be slightly above to the background height value, so anyheight data above this value was likely to be measured from the droplets. Then, thedroplets were individually analyzed by height and area. Moreover, from the height andarea data of the droplet, the droplet volume and diameter were determined. The dropletvolume was approximated by the total sum of the height data for a single droplet multi-plied by the data resolution (i.e. a three dimensional Riemann integral). The diameterwas approximated based on an assumption that the droplet had a round base. This as-sumption was made based on SEM observations on the droplet shape, seen in Fig. 5.2.

Fig. 5.2 SEM images of the gallium deposition sample. On the left hand side, a SEdetector image. On the right hand side, a BSE detector image.

The first geometrical relation shown here is between the gallium droplet height and di-ameter. The height follows the diameter linearly, i.e. the height to diameter ratio is con-

20

stant, of about ~0.17, seen in Fig. 5.3. Similar relation has been observed for smallerand less dense gallium droplets on GaAs [20].

0 100 200 300 400 500 600

0

20

40

60

80

Gal

lium

drop

leth

eigh

t(nm

)

Gallium droplet diameter (nm)

Gallium deposition (A) Gallium deposition (B) Arsenic limited LT-GaAs Linear fit

Fig. 5.3 Gallium droplet height versus diameter calculated from AFM measurements.The deposition sample was measured from two locations (A and B) whereas the As-limited LT-GaAs was measured from one location.

Based on observations of droplet shapes from the SEM and AFM measurements, thedroplet shape follows the geometry of a spherical cap, i.e. a portion of a sphere cut offby a plane. Again, this conclusion has been made for smaller and less dense galliumdroplets on GaAs [20]. Volume of a spherical cap, , can be determined from the diam-eter of the base, , and the height of the droplet, ℎ [21]. Furthermore, if the height todiameter ratio, = ℎ/ , is constant, as shown previously, the spherical cap volume canbe simplified to be dependent on only the droplet area, .

=ℎ

634 + ℎ =

3√(3 + 4 ) / 5.1

In equation 5.1 on the right hand side, the power dependency of volume with respect tothe area of a spherical cap is seen, which is typical for other three dimensional geomet-rical objects on surfaces. The pre-factor is dependent only on the height to diameterratio, which is a constant, making the analysis on droplet volumes simple, as only theareas of the droplets are needed.

21

103 104 105

103

104

105

106

107

Gal

lium

drop

letv

olum

e(n

m3 )

Gallium droplet area (nm2)

Ga deposition (A) Ga deposition (B) Arsenic limited LT-GaAs Spherical Cap (h/D=0.17)

Fig. 5.4 Gallium droplet volume versus area based on AFM measurements. Meas-urements here correspond to the measurements in Fig. 5.3.

Fig. 5.4 shows the comparison between the data calculated from AFM measurementsand the analytical formula from equation 5.1. For large droplets the agreement is good.However, for smaller droplets, of around ~1000 nm2 area, there is some deviation. Here,this deviation is ascribed to the AFM measurement having two likely causes of error forthe case of the smaller droplets. Firstly, the data resolution of the AFM measurementswas in the order of ~2nm/px, resulting in smaller droplets being represented by fewerdata points. Secondly, the AFM tip geometry can be a factor in misrepresenting smallerdroplets accurately, as discussed in chapter 3.3.3. Nonetheless, this discrepancy can beneglected in cases where droplet volumes are relatively large, as is the case for samplespresented in this work where the method is applied. Furthermore, even if smaller drop-lets coexist together with big droplets, the majority of the total droplet volume can beascribed to large droplets, as seen in Fig. 5.2 from the relative population of larger drop-lets.

5.2 Proof of concept

To verify that the analysis method presented here is valid, a comparison between themethod in question and the already established HRXRD analysis was conducted. Asample with an As-limited LT-GaAs layer on top of an AlAs marker layer was grown.From this sample, the thickness of the formed LT-GaAs would be analyzed and com-pared between the two methods. The As/Ga flux ratio based on flux measurements wasestimated to be 0.66 for the LT-GaAs layer, which grown at a temperature of ~220 ºC.The AlAs layer thickness was ~50 nm (confirmed by HRXRD) and grown under typicalAlAs growth conditions, i.e. high temperature and high As/Al flux ratio. The LT-GaAslayer thickness nominal value was estimated to be ~232 nm, based on HRXRD meas-

22

urement and simulation from a previously grown dilute GaAs1-xBix alloy sample, grownwith the same gallium cell temperature. No major variation in the film thickness overthe wafer was observed (confirmed by HRXRD) for samples rotated during growth, sothis nominal value was used for the analysis over the wafer.

The droplet volumes, from which the thickness of the LT-GaAs layer would be calcu-lated using equation 4.7, were determined by an analysis on SEM images. The analysiswas done on BSE detector images with ImageJ software and conducted as follows.First, the image pixel size was set to correspond with the SEM image scale, so thatmeasurements from the image would be in nm. Second, the grayscale BSE image wasconverted to a binary image using an automatically applied threshold value. Third, noiseof the binary image was reduced by applying an outlier removal filter of typically 5 pix-el radius. The outlier removal replaces pixel values based on the median value of thesurrounding pixels inside a given radius. This was done for both white and black pixelsconsecutively, to reduce noise existing in the background and droplet areas, respective-ly. Fourth, as the outlier removal left edges of the droplets still noisy, a median filter of3 pixel radius was applied. Finally, a watershed function was applied, which separateddroplets that were connected to each other. Optionally, some touch-ups, such as cover-ing white pixels left inside droplets, were manually performed. The image from thisanalysis, i.e. a binary mask of the droplets, was then analyzed by ImageJ’s particle ana-lyzer function, which counted the droplets areas individually. A typical measurementand a result of the analysis are provided in Fig. 5.5. From the droplet area data providedby the image analysis, the droplet volumes were calculated and summed using thespherical cap model formulated in the previous chapter. This together with theknowledge of the sample area (SEM image area) enabled the calculation of the LT-GaAs layer thickness from equation 4.7.

23

Fig. 5.5 Droplet analysis conducted on a SEM BSE image. a) A raw BSE image fromwhich the droplets were analyzed, b) a binary mask based on the BSE picture and c)droplet outlines (numbered in red) overlaid on top of a SE image taken from the samelocation.

An important thing to note from Fig. 5.5 is that some of the droplets which lay at theedges of the image are cut-off. This causes some error in the droplet volume calculation,as the volume of a cut-off droplet is calculated as a droplet with a smaller base area.However, this error can be significantly reduced by choosing an appropriate SEM imagemagnification, so that the number of droplets cut-off by the image edges is outnumberedby the total amount of droplets in the picture, as is the case in Fig. 5.5.

The small deviation in lattice constants between the AlAs and GaAs layer enabled theHRXRD analysis of the sample, an example measurement and simulation is provided inthe left hand side of Fig. 3.5. The sample was measured and analyzed by both of themethods over the wafer at 5 mm intervals to compare their agreement, seen in Fig. 5.6.

a)

b)

c)

24

0 5 10 15 20204

206

208

210

LT-G

aAs

thic

knes

s(n

m)

Distance from wafer center (mm)

Droplet analysis HRXRD

Fig. 5.6 Comparison between LT-GaAs layer thickness over the wafer from dropletanalysis and HRXRD simulation.

In Fig. 5.6, the agreement between the methods is good. Surprisingly, even the absolutevalues agree well, with absolute relative error average of ~0.3 %. However, it should benoted that even the HRXRD analysis has error, which is dependent on the structure be-ing analyzed, so here the main point is that the analysis method gives consistent resultsand is within reasonable bounds when compared to HRXRD. Additionally, the As/Gaflux ratio calculated by the method averages to about 0.89, which is considerably differ-ent from the estimated flux ratio of 0.66. This discrepancy will be discussed in chapter6.

5.3 Spatial arsenic flux distribution

To investigate the arsenic flux distribution during growth, two LT-GaAs samples weregrown with As-limited conditions without rotation. The samples were grown withAs/Ga flux ratios of 0.7 and 0.55 for the first and second sample, respectively. Theseflux ratios were estimated from flux measurements. However, due to the non-uniformityof the fluxes and not rotating the sample during growth, an As/Ga flux gradient formedover the wafer. This previously mentioned gradient is depicted schematically in Fig.5.7.

25

Fig. 5.7 Top view of the flux gradient for samples #1 and #2. Two surface phases areindicated by color: (i) an area with As-limited conditions forming droplets and (ii) anarea with As-rich conditions forming smooth surfaces. The labelled boxes representthe molecular source positions with respect to the wafer orientation during growth(estimated from manipulator position) and the arrow represents the measurementaxis. The schematics are drawn based on optical microscope, SEM and diffuse lightscattering observations.

Fig. 5.7 shows, that the directionality for the As/Ga flux gradient is well defined andreproducible. The interface between below unity and above unity As/Ga flux ratio isperpendicular to the gradient, indicating that flux variation is only significant along theaxis depicted in Fig. 5.7. A rough illustration of how the As/Ga flux behaves is depictedin Fig. 5.8, where the droplet size decreases going towards the positive side of the axis.

Fig. 5.8 SEM images taken from sample #1 with the SE detector along the flux gradi-ent axis. The positions along the axis are: a) -15 mm, b) -5 mm and c) +5 mm.

Analyzing the arsenic flux based on equations 4.7 and 4.8 required the accurate value ofthe nominal thickness (i.e. the gallium flux) along the same axis. Therefore a referencesample was grown where a typical high temperature (~580 ºC) and high As/Ga fluxratio (~5) GaAs layer was grown without rotation on top of an AlAs marker layer. Fromthis sample, the grown GaAs layer thickness, which is proportional to the gallium flux,was determined along the flux gradient axis by HRXRD.

As

Ga

As

Ga

Sample #1 Sample #2+ +

- -

(i)

(ii)

(i)

(ii)

0 mm 0 mm

a) b) c)

26

-20 -10 0 10 20200220240260280300320

-20 -10 0 10 20120

140

160

180

200As/Ga > 1As/Ga < 1

Measured Linear fitG

aAs

thic

knes

s(n

m)

Distance from wafer center (mm)

Nominal Measured

LT-G

aAs

thic

knes

s(n

m)

Fig. 5.9 On the left, the measured thicknesses along the flux gradient axis of theAlAs/GaAs reference sample and a linear fit. On the right, the nominal thickness cal-culated for sample #1 based on the reference sample with a few measured thicknessesfrom the As-rich side where HRXRD analysis was possible. The red dashed line indi-cates the location of the interface between the two surface phases.

In Fig. 5.9, the measured GaAs thicknesses for the reference sample show a clear linearrelationship across the wafer, indicating that the change in the gallium flux across thewafer is linear, too. The nominal thicknesses for samples #1 and #2 were calculatedusing the proportionality of thickness and gallium BEP, i.e. the ratio between the LT-GaAs nominal thickness and the reference sample GaAs thickness was equal to the ratioof the gallium BEPs used in the growths. The right hand side of Fig. 5.9 shows the nom-inal thickness of the LT-GaAs based on the reference sample in comparison with themeasured thickness by HRXRD. The thicknesses from the As-rich side of the wafercould be determined by HRXRD due to the compressive strain induced by the pointdefects incorporated in As-rich growth. An example HRXRD measurement and simula-tion from sample #1’s As-rich side is shown in the right hand side of Fig. 3.5.

SEM measurements were made across the flux gradient axis with 5 mm intervals andthe droplet volumes were analyzed from the images as described in the previous chap-ter. From the droplet volumes and the nominal thicknesses, the real thickness of the As-limited LT-GaAs layer was determined using equation 4.7. Furthermore, the galliumflux was calculated from the nominal thickness and using equation 4.8 the arsenic fluxwas calculated. The flux distributions obtained are depicted in Fig. 5.10. Furthermore,using the arsenic and gallium flux distributions, the As/Ga flux ratio was determined,depicted in Fig. 5.11.

27

-20 -10 0 10 201.6x1014

1.8x1014

2.0x1014

2.2x1014

2.4x1014

2.6x1014

Ato

mic

flux

(ato

ms

cm-2s-1

)

Distance from wafer center (mm)

Ga flux: Sample #1 Sample #2

As flux: Sample #1 Sample #2

Fig. 5.10 Calculated gallium and arsenic fluxes across the flux gradient axis.

-20 -10 0 10 200.75

0.80

0.85

0.90

0.95

1.00

As/

Ga

flux

ratio

(dim

ensi

onle

ss)

Distance from wafer center (mm)

Sample #1 Sample #2

Fig. 5.11 Calculated As/Ga flux ratios across the flux gradient axis along with linearfits.

In Fig. 5.10 it is shown that the arsenic flux is almost constant throughout both the sam-ples. The arsenic flux has an average slope of −4 × 10 atoms cm-2s-1/mm whereas thegallium slope of −3 × 10 atoms cm-2s-1/mm is an order of magnitude higher. Thisresults in gallium being the controlling factor in the total As/Ga flux distribution, whichcan be seen in Fig. 5.11. Consequently, as the gallium flux was shown to be linearacross the wafer, the As/Ga flux ratio distribution is linear, too. The slope of the As/Gaflux ratio from the linear fit is approximately the same for both samples and has an av-erage value of ~0.0057 mm-1.

28

5.3.1 Applying the results

To further examine if the calculated As/Ga flux ratio gradient agreed with observationspublished in the literature, a few different samples where As/Ga was a deciding factor inmaterial properties were grown and analyzed. The growths of the layers analyzed wereconducted without rotation in order to form a flux gradient. The flux gradient was ob-served to be orientated in the same direction as those of Fig. 5.7, albeit with some varia-tion in the absolute interface position due to the different nominal As/Ga flux ratio usedfor each growth.

The first dependency examined here, is the AsGa point defect concentration in As-richgrown LT-GaAs, which can be seen in the left hand side of Fig. 5.12. The AsGa concen-tration was determined from the linear dependency on compressive strain that the defectinduces in the lattice [8], which was determined by HRXRD. The relationship agreesqualitatively with that found in the literature [3].

0.95 1.00 1.05 1.10 1.15 1.200.00.51.01.52.02.53.03.5

0.90 0.95 1.00 1.05 1.10 1.15

1

2

3

4

AsG

aco

ncen

tratio

n(1

019cm

-3)

As/Ga flux ratio (dimensionless)

Bif

ract

ion

(%)

Fig. 5.12 The AsGa concentration and GaAs1-xBix alloy bismuth fraction as a functionof As/Ga flux ratio in left and right hand side, respectively.

The second dependency examined here, is the bismuth incorporation into GaAs, form-ing the GaAs1-xBix alloy. Generally speaking, to incorporate bismuth into the GaAs lat-tice, low growth temperatures and near stoichiometric As/Ga flux ratios are required [2].On the right hand side of Fig. 5.12, the dependency on As/Ga shows the critical natureof arsenic flux control in GaAs1-xBix growth.

29

6. DISCUSSION AND CONCLUSION

In summary of the results shown here: (i) the gallium droplet geometry has been re-solved, (ii) a proof of concept test for the method has been carried out and (iii) themethod has been applied to gain information on arsenic flux distribution. The resultshave shown good consistency with HRXRD and agreement with results published in theliterature. However, one discrepancy has been observed between As/Ga flux ratio val-ues given by the method and flux measurements. In fact, during the early testing of thismethod, a motivation was to show that As/Ga values determined from the two methodshad at least a linear dependence. However, the flux measurements consistently gavelower As/Ga estimates and a linear trend was not evident.

The discrepancy for As/Ga values can arise from multiple factors. As discussed in chap-ter 3.2.1, there is a lot of uncertainty in the As flux measurement which complicatesfinding a linear trend, especially from the small sample size (4) used in the early testing.An important factor is also brought up by the volatile nature of the As species. Duringthe growth process, an excess As pressure is used before growing the LT-GaAs layer.This results in a background As pressure in the growth chamber and can affect the realflux value being higher than intended from flux measurements. This residual pressure isalso present after growth and might consume some amount of the gallium droplets,again resulting in a higher As/Ga estimate when compared to flux measurements. How-ever, to investigate this discrepancy further, a more systematic study with a bigger sam-ple size would be needed to establish a relationship between the method presented hereand flux measurements.

There is some room for future development in the analysis process. Automating theimage analysis and calculation processes would enable a faster analysis, although thesample growth and measurement processes would still be the dominating components interms of time consumption. Some minor improvements, such as accounting for cut-offdroplets correctly and confirming the spherical cap model for small gallium droplets,would result in a more accurate analysis.

In conclusion, a novel method has been presented for analyzing the arsenic flux fromex-situ measurement and calculation of a grown calibration sample. Results show goodagreement with established methods and literature.

30

7. REFERENCES

[1] R. F. C. Farrow, Molecular Beam Epitaxy, Elsevier, 1995.

[2] M. Henini, Molecular Beam Epitaxy: From Research to Mass Production, Elsevier,2012.

[3] A. Suda and N. Otsuka, “Arsenic flux dependence of incorporation of excessarsenic in molecular beam epitaxy of GaAs at low temperature,” Applied PhysicsLetters, vol. 73, p. 1529, 1998.

[4] X. L. Li, C. X. Wang and G. W. Yang, “Thermodynamic theory of growth ofnanostructures,” Progress in Materials Science, vol. 64, p. 121, 2014.

[5] “Wikipedia: The Free Encyclopedia,” Wikimedia Foundation Inc., [Online].Available: http://en.wikipedia.org/wiki/Gallium_arsenide. [Accessed 2ndDecember 2014].

[6] C. T. Foxon and B. A. Joyce, “Interaction kinetics of As2 and Ga on (100) GaAssurface,” Surface Science, vol. 64, p. 293, 1977.

[7] E. S. Tok, J. H. Neave, J. Zhang, B. A. Joyce and T. S. Jones , “Arsenicincorporation kinetics in GaAs(001) homoepitaxy revisited,” Surface Science, vol.374, p. 397, 1997.

[8] X. Liu, A. Prasad, J. Nishio, E. R. Weber, Z. Liliental-Weber and W. Walukiewicz,“Native point defects in low-temperature grown GaAs,” Applied Physics Letters,vol. 67, p. 279, 1995.

[9] S. Gupta, M. Y. Frankel, J. A. Valdmanis, J. F. Whitaker, G. A. Mourou, F. W.Smith and A. R. Calawa, “Subpicosecond carrier lifetime in GaAs grown bymolecular beam epitaxy at low temperatures,” Applied Physics Letters, vol. 59, p.3276, 1991.

[10] M. Tmar, A. Gabriel, C. Chatillon and I. Ansara, “Critical analysis andoptimization of the thermodynamic properties and phase diagrams of the III-V

31

compounds,” Journal of Crystal Growth, vol. 69, p. 421, 1984.

[11] J. C. DeWinter and M. A. Pollack, “Ga-As liquidus at temperatures below 650 C,”J. Appl. Phys., vol. 58, no. 6, p. 2410, 1985.

[12] J. Puustinen, Setup and growth parameter determination for molecular beamepitaxy of GaAsBi, Tampere University of Technology, 2014.

[13] R. F. Egerton, Physical Principles of Electron Microscopy: An introduction toTEM, SEM, and AEM, Springer, 2005.

[14] Bede Scientific Instruments Ltd. , Rocking curve analysis by dynamical simulation:User guide, 1998.

[15] PANalytical B. V., X'Pert PRo User's Guide, 2007.

[16] F. J. Giessibl, “Advances in atomic force microscopy,” Reviews of modern physics,vol. 75, no. 3, p. 949, 2003.

[17] N. A. Geisse, “AFM and combined optical techniques,” Materials Today, vol. 12,no. 7-8, p. 40, 2009.

[18] “Wikipedia: The Free Encyclopedia,” Wikimedia Foundation Inc., [Online].Available: https://en.wikipedia.org/wiki/Atomic_force_microscopy. [Accessed 9thNovember 2015].

[19] C. E. C. Wood, K. Singer, T. Ohashi, L. R. Dawson and A. J. Noreika, “Apragmatic approach to adatom-induced surface reconstruction of III-Vcompounds,” Journal of Applied Physics, vol. 54, p. 2732, 1983.

[20] M. Jo, T. Mano, Y. Sakuma and K. Sakoda, “Size-dependent contact angle of Gadroplets on GaAs,” Journal of Crystal Growth, vol. 378, p. 5, 2013.

[21] A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers andScientists, Chapman & Hall/CRC, 2007.