Epitaxial Growth and Design of Nanowires and Complex ......epitaxy, in which precursor molecules for the semiconductor material components are introduced in a low-pressure vapour

Epitaxial Growth and Design of Nanowires and Complex Nanostructures

Kimberly Dick

Doctoral Thesis 2007

Division of Solid State Physics Department of Physics

Lund Institute of Technology Lund University

Solid State Physics Lund University Box 118 S-221 00 LUND Sweden Copyright © Kimberly Dick, 2007 ISBN 978-91-628-7150-5 Printed in Sweden by Media-Tryck, Lund April 2007

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Abstract This thesis describes the epitaxial growth of III-V semiconductor nanowires using Au seed particles, and the design of more complex three-dimensional branched structures from these wires. Growth was performed by metallorganic vapour phase epitaxy, in which precursor molecules for the semiconductor material components are introduced in a low-pressure vapour. Nanowires grow epitaxially (with controlled crystal orientation) on a semiconductor substrate; diameter control is achieved via the Au particles, while length is controlled by growth parameters. Particle-assisted nanowire growth is used extensively today to achieve well-controlled structures. The current understanding of this growth mechanism was developed over forty years ago, and is known as the Vapour-Liquid-Solid (VLS) mechanism. This model indicates that a liquid alloy is formed between the seed particle and the growth material(s), and growth proceeds by precipitation from a supersaturated particle. The enhanced growth rate compared to the bulk growth from the vapour is typically attributed to preferential decomposition of precursor materials at or near the particle surface. Recently, however, several inconsistencies have been observed between this model, which was developed for Au-assisted Si whiskers (micro-scale wires), and particle-assisted growth of other materials. In particular, there have been many reports of nanowire growth at temperatures too low for a liquid alloy to form. As well, nanowire growth has been reported for systems where no precursor molecules are used, and thus growth enhancement cannot be explained by preferential decomposition. Other reports have given evidence that such preferential decomposition does not necessarily occur when precursors are used. The first part of this thesis presents the current understanding of particle-assisted growth, both generally and for the specific materials and growth systems used here. Semiconductor nanowires present the possibility for numerous applications, and many simple device components have been demonstrated. The development of practical applications of such prototypes may rely on the ability to assemble nanowires into more complex structures. The second part of this thesis presents techniques for the production of three-dimensional branched nanowire structures, including methods to achieve controlled structure and morphology. The assembly of branched structures into large-scale interconnected networks is also presented.

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Contents Abstract iii

Contents v

List of Papers vii

Abbreviations xi

Preface xiii

1. Introduction 1

1.1 Nanotechnology and Nanoscience ....................................................................1

1.2 Semiconductor Materials ..................................................................................2

1.3 Nanowires .........................................................................................................4

1.4 Nanowire Applications......................................................................................6

2. Epitaxy of Nanowires 9

2.1 Epitaxy: Concepts and Techniques ...................................................................9

2.2 Metallorganic Vapour Phase Epitaxy: MOVPE .............................................11

2.3 Nanowire Growth Techniques.........................................................................14

2.4 Au Aerosol Particles .......................................................................................16

3. Particle-assisted Nanowire Epitaxy 19

3.1 History of Particle-assisted Growth................................................................19

3.2 Growth Mechanism .........................................................................................21

3.3 State of Particle...............................................................................................25

3.4 Interaction of Au with III-V Materials ............................................................27

3.5 Precursor Chemistry .......................................................................................30

3.6 Surface Diffusion.............................................................................................35

3.7 Axial Heterostructure Nanowires ...................................................................37

4. Design of Complex Nanostructures 41

4.1 Branched Nanowire Structures: Nanotrees ....................................................41

4.2 Heterostructure Nanotrees..............................................................................44

4.3 Au-In Particles for Reduced Particle-wire Interaction...................................46

4.4 Height Control of Nanotree Branches ............................................................47

4.5 Position-control of Nanowires and Nanotrees................................................48

4.6 Nanowire Networks.........................................................................................50

Outlook 53

Appendix 55

References 65

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List of Papers This thesis is based on the following papers, referred to in the text by their roman numerals: I. Failure of the vapor-liquid-solid mechanism in Au-assisted MOVPE growth of InAs nanowires K. A. Dick, K. Deppert, T. Mårtensson, B. Mandl, L. Samuelson, W. Seifert Nano Letters 2005, 5, 761 II. A new understanding of Au-assisted growth of III-V nanowires K. A. Dick, K. Deppert, L. S. Karlsson, L. R. Wallenberg, L. Samuelson, W. Seifert Advanced Functional Materials 2005, 15, 1603 III. Growth of GaP nanotree structures by sequential seeding of 1D nanowires K. A. Dick, K. Deppert, T. Mårtensson, W. Seifert, L. Samuelson Journal of Crystal Growth 2004, 272, 131 IV. Optimization of Au-assisted InAs nanowires grown by MOVPE K. A. Dick, K. Deppert, L. Samuelson, W. Seifert Journal of Crystal Growth 2006, 297, 326 V. Morphology of axial and branched nanowire heterostructures K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross submitted to Nano Letters

VI. Synthesis of branched 'nanotrees' by controlled seeding of multiple branching events K. A. Dick, K. Deppert, M. W. Larsson, T. Mårtensson, W. Seifert, L. R. Wallenberg, L. Samuelson Nature Materials 2004, 3, 380 VII. Improving InAs nanotree growth with composition-controlled Au-In nanoparticles K. A. Dick, Zs. Geretovszky, J. N. Andersen, L. S. Karlsson, E. Lundgren, J. –O. Malm, A. Mikkelsen, L. Samuelson, W. Seifert, B. A. Wacaser, K. Deppert Nanotechnology 2006, 17, 1344 VIII. Height-controlled nanowire branches on nanotrees using a polymer mask K. A. Dick, K. Deppert, M. W. Larsson, W. Seifert, L. R. Wallenberg, L. Samuelson Nanotechnology 2007, 18, 035601 IX. Position-controlled interconnected InAs nanowire networks K. A. Dick, K. Deppert, L. S. Karlsson, L. R. Wallenberg, W. Seifert, L. Samuelson Nano Letters 2006, 6, 2842 The following papers are not included due to overlapping content or content beyond the scope of this thesis: X. Semiconductor nanowires for 0D and 1D physics and applications L. Samuelson, C. Thelander, M. T. Björk, M. Borgström, K. Deppert, K. A. Dick, A. E. Hansen, T. Mårtensson, N. Panev, A. I. Persson, W. Seifert, N. Sköld, M. W. Larsson, L. R. Wallenberg Physica E 2004, 25, 313 XI. Growth of one-dimensional nanostructures in MOVPE W. Seifert, M. Borgström, K. Deppert, K. A. Dick, J. Johansson, M. W. Larsson, T. Mårtensson, N. Sköld, C. P. T. Svensson, B. A. Wacaser, L. R. Wallenberg, L. Samuelson Journal of Crystal Growth 2004, 272, 211

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XII. Synthesis of branched 'nanotrees' for optical and electronic applications K. A. Dick, K. Deppert, M. W. Larsson, T. Mårtensson, W. Seifert, L. R. Wallenberg, L. Samuelson VDI-Berichte 2004, 1839, 7 XIII. Growth related aspects of epitaxial nanowires J. Johansson, B. A. Wacaser, K. A. Dick, W. Seifert Nanotechnology 2006, 17, S355 XIV. Crystal structure of branched epitaxial III-V nanotrees L. S. Karlsson, M. W. Larsson, J. –O. Malm, L. R. Wallenberg, K. A. Dick, K. Deppert, W. Seifert, L. Samuelson NANO 2006, 1, 139 XV. InAs nanowires grown by MOVPE K. A. Dick, K. Deppert, L. Samuelson, W. Seifert Journal of Crystal Growth 2007, 298, 631 XVI. Directed growth of branched nanowire structures K. A. Dick, K. Deppert, L. S. Karlsson, M. W. Larsson, L. R. Wallenberg, W. Seifert, L. Samuelson MRS Bulletin 2007, 32, 127 XVII. Electrospraying of colloidal nanoparticles for seeding of nanostructure growth P. H. M. Böttger, Zhaoxia Bi, D. Adolph, K. A. Dick, L. S. Karlsson, M. N. A. Karlsson, B. A. Wacaser, K. Deppert Nanotechnology 2007, 18, 105304 XVIII. Size-selected compound semiconductor quantum dots by nanoparticle conversion B. A. Wacaser, K. A. Dick, Z. Zanolli, A. Gustafsson, K. Deppert, L. Samuelson Nanotechnology 2007, 18, 105306

XIX. Targeted deposition of Au aerosol nanoparticles on vertical nanowires for the creation of nanotrees K. Bayer, K. A. Dick, T. J. Krinke, K. Deppert Journal of Nanoparticle Research 2007, in press XX. High-speed nanometer-scale imaging for studies of nanowire mechanics D. Hessman, M. Lexholm, K. A. Dick, S. Ghatnekar-Nilsson, L. Samuelson submitted to Small

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Abbreviations AsH3 arsine, precursor for As at. % A atomic % of component A CBE/MBE chemical beam epitaxy/molecular beam epitaxy CVD chemical vapour deposition DMA differential mobility analyzer EBL electron beam lithography ESP electrostatic precipitator MOVPE metallorganic vapour phase epitaxy PH3 phosphine, precursor for P PMMA polymethyl methacrylate SEM scanning electron microscopy Si2H6 disilane, precursor for silicon TEM transmission electron microscopy TMA trimethylaluminium, Al(CH3)3, precursor for aluminum TMG trimethylgallium, Ga(CH3)3, precursor for gallium TMI trimethylindium, In(CH3)3, precursor for indium UHV-CVD ultra high vacuum chemical vapour deposition VLS vapour-liquid-solid VPE vapour phase epitaxy

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Preface This thesis discusses work carried out during the period from September 2003 – January 2007 at the Division of Solid State Physics at Lund University. The aim of this work was to develop a thorough understanding of particle-assisted nanowire growth, and to develop techniques for arranging such wires into more controlled complex branched structures. Chapter 1 of the thesis deals with the fundamental concepts involved, including the idea of nanowires and potential nanowire applications. Chapter 2 describes the epitaxial growth of nanowires, including fabrication techniques, the particular growth method used for work in this thesis and the general idea of particle-assisted growth. Chapter 3 discusses the current understanding of particle-assisted nanowire growth in our system, from the fundamental mechanism to the specific processes involved. The design of complex branched structures, and the controlled production of increasingly complex structures for functional applications, is covered in Chapter 4. Accordingly, Chapter 3 and 4 comprise the original work developed during this period, roughly divided into the two areas of growth issues and design issues. This division is apparently natural, but of course both issues are important for the development of nanowire and nanostructure applications. The production of complex structures necessarily requires an understanding of growth processes, and the development of such structures can often give insight into growth mechanisms as well. Therefore, most of the papers included in this thesis involve a discussion of both topics. Papers I-V are grouped as primarily “growth” papers, since such issues comprise their main topics. However, many also include a discussion of branched structures and the special issues involved in their growth. Papers VI-IX are grouped as “design” papers since their major topics involve demonstrations of novel techniques; naturally, all of them also include discussion of the growth issues involved.

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Acknowledgements I have hesitated in writing these acknowledgements, for the difficulty in adequately expressing what should be said and the inevitability of forgetting someone or some contribution. I must apologize in advance then, for anyone I have left out. You are not forgotten, merely out of mind for a short moment. First I would like to thank Knut Deppert, who first took the chance on me and gave me the opportunity to come to Lund, and who has stood by me throughout the entire process of completing my PhD. I am incredibly grateful for this opportunity, and for all the support I have received over these years. I would also like to thank Lars Samuelson, for keeping the department running with an endless source of good ideas. It is sometimes difficult to find time for a conversation, but I always walk away from one with more enthusiasm, clarity of understanding and inspiration than I had before. Werner Seifert is also acknowledged for being an incredible source of knowledge about epitaxy, and for teaching me everything I know on this topic. The cohesion and success of the epitaxy group over the past few years has largely been a result of Werner’s influence, and he is very much missed since leaving the department. Reine Wallenberg is acknowledged for teaching me about electron microscopy, without which all the nice samples we have grown could not have been shown to the world. As well, he has been an incredible source of support and encouragement. Towards the end of my PhD I had the opportunity to travel to IBM Research Center in New York to visit the research group of Frances Ross, as well as to work with Frances in Lund during the last part of my degree. It has been such an honour to work with such a talented and knowledgeable scientist. I hope we will have more opportunities to collaborate in the future. I would also like to thank Suneel Kodambaka, a very skilled and enthusiastic scientist with whom I had the opportunity to work during my stay at IBM. Of course, I have had the opportunity to work with very many talented people here in Lund, without whom the work presented in this thesis could not have been achieved. Thomas Mårtensson is acknowledged for patient assistance with many

aspects of epitaxy, for endless interesting discussions about science and other topics (both at home and abroad), and for teaching about processing and EBL. Jonas Johansson is also acknowledged for all the conversations and interesting ideas, and for teaching me about thermodynamics. The other MOVPE growers, including Magnus Borgström, Niklas Sköld, Bernhard Mandl and Patrik Svensson, are also acknowledged; the incredible level of skill and knowledge that has been present in this group has enabled a lot of interesting results and made it a pleasure to work here. Magnus Larsson at Materials Chemistry is acknowledged for providing excellent TEM images and plenty of new ideas. I would also like to thank Lisa Karlsson for being both friend and coworker, and for her tireless and patient TEM work with so many of the samples I produced. A significant portion of this thesis would not have happened without her. Jan-Olle Malm is also acknowledged for providing TEM images and knowledge, as well as discussion and new ideas. Zsolt Geretovszky is acknowledged for all the work on the Au-In project (and our many less successful aerosol projects). As well, his astonishing skill and knowledge with the aerosol system are entirely responsible for the success we’ve had making aerosol particles in recent years. Martin Karlsson is also acknowledged for his patience in helping me to learn the aerosol system in the beginning, and for the friendship over the years. I would like to thank Brent Wacaser, with whom I have shared an office for several years, for being a confidant on all things ranging from science to Sweden. I have learned much from him, from running the aerosol machine to understanding crystallography. Linus Fröberg, my other officemate, has also been a great source of conversation, as well as knowledge about physics, growth and the Swedish system. I would like to thank Anders Mikkelsen, Edvin Lundgren, and Jesper Andersen at Synchrotron Radiation Physics, for teaching me all about surface science and providing so much useful data (and usually on quite short notice). In particular, their assistance with the Au-In project was very much appreciated. Søren Jeppesen is acknowledged for his phenomenal technical skill and for keeping our equipment operational. The technical crew for the processing labs, Ivan Maximov, Mariusz Graczyk, Lena Timby, David Adolf and Aline Ribayrol, are also acknowledged for tireless work in keeping these labs running. As well, Mona Hammar and Monica Pålsson are acknowledged, for keeping the department itself running. There have also been many people with whom I did not directly work, but whose presence made the work environment a much better place. First, I would like to

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thank Ann Persson for assistance with many of the challenges involved in working towards a PhD, and for being an inspiration to stick with things. I would also like to thank Sara Ghatnekar-Nilsson for all the support, for always being there to talk to (or laugh with) and of course, for proofreading this thesis. Monica Lexholm has been a great source of conversation and company, and never fails to brighten a room or a day. Jessica Eriksson has also provided much-appreciated companionship over this past year, when it has been most needed. I would also like to thank Johanna Trägårdh, Carina Fasth, Emelie Hilner, Anneli Löfgren, Vilma Zela, Gabriela Conache, and the rest of “the girls” for our regular lunch dates downtown; they have always been the highlight of my week. There are always many other people behind the scenes, whose support outside of the work environment has made it possible to complete this work and this thesis. In my case this includes not only people in Sweden, but also many back home who have stuck by me in chasing a dream partway around the world. I am still surprised, and touched, that so many have made the effort to stay in touch and remain interested in whatever it is I am doing over here. I won’t attempt to list everyone (you know who you are), but I would particularly like to thank Shire Ullah, Mitun Das, Kevin Hadley and Aye Nyein San, whose friendship has extended to making the trip all the way to Sweden to visit. I would also like to thank my family: my mother Susan, my father Paul, my brother Stephen, my grandmother Ann Morrison, and all of my aunts, uncles and cousins. They have offered unwavering support on this great adventure (sometimes against their better judgment), always believed in me, and kept me going through the more difficult times. My “second family”, Monica and Erling Thelander, have also provided assistance and encouragement throughout this thesis. Finally and most of all, I would like to thank Claes Thelander, who has been my inspiration, editor, therapist, partner and friend over these past few years. I literally could not have done this without you.

Chapter 1

1. Introduction

1.1 Nanotechnology and Nanoscience It has long been understood that sufficiently reducing the number of atoms in a structure can have dramatic implications for its properties, behaviour and potential applications [1]. The reduction in size of crystalline structures will ultimately mean that physical principles important to atoms, but normally negligible in bulk, begin to increase in importance [2]. The size reduction of mechanical components, and particularly electronic components, occurring over the past few decades has generated intense interest in understanding the unusual behaviour of very small structures. Size effects become important when at least one dimension of a crystal is reduced to the order of hundreds of atoms – the length scale of nanometers. This has instigated the explosive growth of the fields of nanoscience and nanotechnology – the study and manipulation of matter on the scale of tens of nanometers. The unique properties of nanostructures can be roughly separated into two primary categories – surface-related effects and quantum confinement effects. Surface effects arise because atoms at the surface of a crystalline solid experience a different chemical environment than other atoms, changing their behaviour. In bulk materials the proportion of surface atoms to bulk atoms is entirely negligible, and processes that take place at the surface of a material are usually of little consequence to the behaviour of the material as a whole. However, the surface-to-volume ratio of a structure on the nanoscale is considerably higher – high enough that surface effects often cannot be ignored. The increased reactivity of the surface compared to the rest of the material reduced the inertness of materials with high surface area. As well, the structure of the solid state can change somewhat to accommodate the high proportion of surface atoms, ultimately decreasing the stability of the crystal [3].

2 Chapter 1: Introduction


Quantum effects occur when the wavelength of an electron in a material is of the same order as a dimension of the material. This limits the motion of an electron in the material, which becomes quantized in that confining dimension. The density of states of the electrons is then determined by the number of dimensions in which electrons are quantized [4]. As understanding of the unique properties of nanostructures increases, so does the interest in and potential of practical applications that take advantage of these properties. To date, device components have been fabricated in laboratory settings that demonstrate the possibilities available. However, the transition from promising science to practical technology requires an even greater understanding and control of the function and effects of nanoscale structures. Since the properties and function of nanostructures depend so strongly on their structures, reliable and controlled means of fabricating such structures are necessary.

1.2 Semiconductor Materials Many of the results (and much of the interest) in nanotechnology today are focussed on applications of semiconductor materials. Semiconductors are materials in which the electrical conductivity depends on applied energy (for example, temperature), due to the electronic band structure of the material. Much as single atoms exhibit discrete energy levels that can be occupied by electrons, crystalline materials exhibit broad energy “bands”, which essentially represent energy ranges that electrons can occupy as they move between atoms in the crystal. When the highest occupied electronic level (the Fermi level) lies within an energy band, electrons can move easily through a material since a small amount of kinetic energy can move it upwards within the band. Such a material will conduct electricity well, and is thus known as an electrical conductor. When the Fermi level lies in the gap between energy bands, electrons cannot easily move through the material (without gaining a significant amount of energy to jump to the next band), and so the material is an electrical insulator. However, if the gap between bands is sufficiently narrow, movement of electrons into the next energy band may in fact occur with a reasonable probability. This allows the material to conduct electricity when sufficient energy is supplied, and thus such materials are referred to as semiconductors. Strictly speaking, the division between insulators and semiconductors is artificial, and even insulators will conduct when enough energy is applied (for example, at very high temperature). The classification of a material as a semiconductor is mainly based on the potential for practical application of its semiconducting properties (meaning the band gap is not too large).

Section 1.2: Semiconductor Materials 3

Kimberly Dick

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The electrical properties of semiconductors may be modified by the introduction of dopants (impurity atoms), making them very versatile. Semiconductors are of particular importance for electronics, since their conductivity can be dynamically modified through the use of electric fields. Silicon is the quintessential semiconductor, used throughout the microelectronics industry due to its superior temperature performance, naturally-forming native oxide (that acts as an insulating barrier) and high natural abundance. Other semiconductors tend to be closely related to Si, and include other group IV materials such as Ge, binary III-V materials such as GaAs, and binary II-VI materials including ZnO. The work in this thesis focuses primarily on four III-V compound semiconductors – GaAs, GaP, InAs and InP. With the exception of GaP (and unlike Si and Ge), these materials have direct band gaps, meaning that electrons and holes can combine directly while conserving momentum, a process that results in the emission a photon. This makes these materials interesting for optical applications [5]. With appropriate doping, GaP can exhibit a quasi-direct band gap; moreover, it is ideal as a “support structure” for optical components of the other materials and is nearly lattice-matched to Si [6]. All of these materials have a high electrical mobility as compared to Si; InAs, in particular, has a narrow band gap (0.36 eV) and very high electron mobility (20000 cm2 V-1 s-1) which make it ideal for high-frequency electronic applications [7]. All of these III-V materials typically exhibit a cubic zincblende crystal structure in the bulk, giving them interesting mechanical and electronic properties [8]. Reports of hexagonal wurtzite structure formed during controlled growth conditions can also be found for each of these materials [9-12]. As the band structure of some III-V materials has been reported to change when the crystal structure changes between zincblende and wurtzite [8], the ability to select between these crystal structures during growth raises interesting physics and device possibilities. More discussion of crystal structure can be found in Chapter 4. In addition, ternary and quaternary III-V compounds can be formed, with properties tailored to the desired application. However, it cannot be assumed that these four materials will behave the same way under similar conditions, and differences must be taken into account during nanowire growth. The lattice constants range from 0.545 nm in GaP to 0.605 nm in InAs [13]. Figure 1.1 shows the lattice constants and band gaps for selected III- V semiconductors. The enthalpies of formation at 298 K vary from -14.0 (InAs) to -25.0 (GaP) kcal/mol [14]. The melting points vary from 942 oC for InAs to 1467 oC for GaP [13]. GaP is also the least dense (4.13 g/cm3) and the hardest (9450 N/mm2) while InAs is the most dense (5.66 g/cm3) and the least hard (3300 N/mm2) [15]. Generally, InAs is the most reactive and most sensitive, while GaP is the most stable and easy to work with. In most cases the properties of GaAs and InP fall in between, making them the most practical options for many applications.



Figure 1.1 Bandgap vs. lattice constant for selected III-V semiconductor materials. Si is also included for reference. These thermodynamic and structural differences are of particular importance during growth of III-V heterostructures. The differing enthalpies of formation, vapour pressures and melting temperatures yield different growth temperature ranges and optimums. The wide variance between lattice constants makes strain a serious hindrance to epitaxial heterostructure growth. Nanowire growth, the subject of this thesis, is particularly advantageous as compared to bulk or epitaxial layer growth: the narrow nanowire diameter allows for a significant degree of heterostructure strain relaxation [16, 17].

1.3 Nanowires Nanowires are defined as structures with two dimensions in the range of tens of nanometers, and the third much longer, typically in the range of micrometers. In practice, nanowires are usually symmetric in the two smaller dimensions and have a round or regular polyhedral cross-section. Such structures are of particular interest for device applications, as they exhibit quantum confinement in two dimensions while the third is relatively unrestricted [18]. They also have potential to act as interconnects between functional nanoscale components; such components can even be fabricated sequentially within the same wire. In addition, nanowires have higher surface-to-volume ratio than similar-volume structures that have three dimensions of similar scale, making them potentially interesting for controlled solid surface reactions and sensing applications [19]. Several demonstrations of the device potential of nanowires have been presented, which will be discussed in the next section.

Section 1.3: Nanowires

Kimberly Dick

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Figure 1.2 Epitaxial nanowires composed of III-V semiconductor materials. (a) Scanning transmission electron microscopy (STEM) image of a single InAs nanowire containing thin barriers of InP (darker contrast). Image by M. W. Larsson. (b) Scanning electron microscopy (SEM) image of an array of InP nanowires grown from lithographically-defined Au nanoparticles. There are two general ways to produce nanostructures, including nanowires, referred to as “top-down” and “bottom-up” [16]. Top-down methods use bulk materials of desired composition, and achieve nanoscale dimensions by lithographic techniques that essentially carve the desired structure out of the material. Such methods have dominated materials processing over the last century, and are still of principle importance for production of electronic components. However, as the desired length scales of devices and applications shrink, this technique becomes less desirable [20]. This is partly a practical problem; techniques to carve out ever-smaller structures are difficult to find. More importantly, uniformity of bulk crystals on nanometer length scales is not very high, and quality of structures becomes difficult to control. Bottom-up production methods, on the other hand, mimic nature’s way of self-assembling atoms to form increasingly larger structures. Such techniques involve controlled crystallization of materials from vapour or liquid sources, typically yielding uniform and highly ordered nanometer-scale structures. Nanostructures can be fabricated in solution, as particles in a vapour, or on a solid support surface. Epitaxy is the general term for the oriented growth of a crystalline material on a single crystal surface [21]; nanostructures produced by this technique will exhibit identically oriented crystal structure. Epitaxial growth of nanowires has become an exciting and rapidly expanding field over the past decade. Such nanowires have controlled crystal structure and (usually) length, and in many cases controlled diameter. The chemical composition is also controlled, and can even be varied over the length of a nanowire, yielding axial heterostructures [22-24] (Figure 1.2a). Recently, position controlled epitaxial nanowires have also been reported using lithographic



positioning of metal seed particles [25, 26] – a method that combines the advantages of top-down and bottom-up processing to yield highly controlled nanostructures (Figure 1.2b). Atomic force microscope (AFM) positioning of nanoparticles as seeds for nanowire growth has also been reported [16]. Branched nanowire structures (“nanotrees”) can also be formed by sequentially growing successive generations of nanowires originating from the side facets of the previous generation [27, Paper VII]. Growth and design of epitaxially-grown nanowires and nanotrees form the main focus of this work.

1.4 Nanowire Applications The unique properties of nanowires, related to their large surface area and potential for quantum confinement, make them interesting for very many possible devices. The ability to incorporate functional heterostructures that would be difficult or impossible to realize in 2D systems also increases their application potential. To date, no production-scale nanowire applications have reached the marketplace, but very many simple device structures have been demonstrated, illustrating the possibilities that may be available in the future. Some of these are discussed here, but it must be emphasized that this list is by no means exhaustive. Electronic applications have dominated to date, driven by the need for new technology to accommodate rapid downscaling. For example, p-n junctions have been demonstrated both within single wires [18, 28, 29] and between wires in contact [30]. Field-effect transistors (FETs) have been realized in nanowires [18, 30-33], and considerable effort has gone into developing scaleable process technology for direct integration of nanowire FETs [34]. Nanowire heterostructure devices take advantage of the strain relaxation in nanowires to produce device components that would not be possible in bulk. Nanowire heterostructure single electron transistors (SETs), for example, have been produced [35]. Such devices may be useful for low power electronics or high sensitivity applications. Nanowire-based resonant tunneling diodes have also been demonstrated [36], the functionality of which could be enhanced by the use of optimal material combinations. Finally, memory devices based on nanowire heterostructure superlattices show enhanced write-speeds compared to conventional flash memory [37], and may lead to more efficient memory devices in the future. Additionally, much work has focused on the development of optical and optoelectronic devices. A major advantage of nanostructures in this regard is the tunability of the band gap with diameter [38, 39]. Light-emitting diodes (LEDs) have been realized for a variety of materials (and thus colours of light) [30, 40-42]; their high crystal quality leads to improved power efficiency and good scalability.

Section 1.4: Nanowire Applications

Kimberly Dick

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Single-nanowire lasers have also been reported [43, 44], exhibiting good electrical performance and efficiency related to their high quality. Photoresistors have been demonstrated for Ge nanowires [45]. Finally, nanowire-based solar cells have been reported, taking advantage of the high surface area of nanowires for photon absorption [46]. The mechanical properties of nanowires have also been used to demonstrate numerous device concepts. Nanowires can, for example, be used as mass sensors for particles of very small mass [47]; this may one day lead to the development of mechanical single-molecule sensors. Nanowire power generators have been demonstrated using the piezoelectric material ZnO, with a potentially high power output useful for powering nanodevices [48]. The piezoelectric properties of ZnO nanowires have also been used for the production of FETs [49]. Finally, chemical applications taking advantage of the surface area of nanowires have been investigated. Recently, Law et al. demonstrated nanowire-based molecular sensors [50]. As well, pH sensors based on Si nanowires have been realized [51].

Chapter 2

2. Epitaxy of Nanowires

2.1 Epitaxy: Concepts and Techniques Epitaxy is defined as the ordered growth of one crystalline material on another. This means that the structure and orientation of the growing crystal will be influenced by that of the substrate. We will use the terms “homoepitaxy” to refer to the growth of a crystal on a like substrate, and “heteroepitaxy” to refer to growth on a substrate of a different material. Some definitions [21] restrict the term “epitaxy” to growth on an unlike substrate, and use the term “homoepitaxy” and “heteroepitaxy” to refer to cases where the two crystals differ mainly in lattice mismatch (such as doped Si on undoped Si), and where the two crystals differ mainly in terms of chemical bonds even if lattice-matched (such as In0.47Ga0.63As on InP), respectively. However, this definition is not commonly used for epitaxial growth of nanostructures, and will not be used here. Crystal growth, whether epitaxial or not, is driven by thermodynamics, which also determines the parameter range in which growth is favourable. Growth occurs in the range where there exists a chemical potential difference between the precursor materials and the material to be grown. A stable steady-state nonequilibrium condition is established by the continuous replenishing of vapour-phase materials, yielding a constant chemical potential difference, or thermodynamic driving force.

⎟⎠⎞⎜

⎝⎛=−=Δ

osv p

pRT lnμμμ (2.1)

Here μv and μs refer to the chemical potential of the vapour and substrate, respectively. This expression refers only to a one-component system; binary systems, including III-V materials, are necessarily more complicated. In this expression p refers to the partial pressure of the component in the gas phase, and po to the equilibrium partial pressure of that component over the crystalline

10 Chapter 2: Epitaxy of Nanowires


material at the given growth conditions. When growing from a liquid phase, the partial pressures are replaced by concentrations. Liquid phase epitaxy (LPE) is the oldest of the techniques common today, and was used for much early work on semiconductor growth. This technique involves a very high-purity supersaturated melt, from which crystalline semiconductor material is precipitated. Growth takes place very close to equilibrium. The main advantage of this technique, in addition to the high purity material produced, is its simplicity, both conceptually and practically. However, this also serves to limit its functionality, and the range of materials and devices that can be produced is limited. Solution phase epitaxy (SPE) involves precipitation from a supersaturated aqueous solution in which appropriate precursor salts for the desired material are dissolved. This is a far more versatile system, as the range of material for which appropriate precursors can be found is very broad. Complex materials can also be formed by adding various ratios of several precursor materials to the same solution. It is also a relatively simple and inexpensive technique, and is often used to produce nanostructures. Vapour phase epitaxy (VPE) is very similar, but involves precipitation from a supersaturated vapour phase. This vapour may contain pure elemental material, but more often involves chemical precursors for the desired substance. A huge range of vapour-phase precursors can be found, making this technique extremely versatile. Moreover, the vapour can be continuously replenished in a controllable way, allowing for much greater control over growth of complex structures than can be achieved with the previous techniques. This technique is the most common one today for growth of semiconductor device structures, and also dominates for the growth of nanostructures. The major limitation is that both reactants and operation are considerably more expensive than previous techniques. Metal organic vapour phase epitaxy (MOVPE) is a subset of this technique which has been used for all the work in this thesis, and will be discussed in the next section. VPE is itself a subset of chemical vapour deposition (CVD), which is not necessarily epitaxial. Molecular beam epitaxy (MBE) is performed in a high vacuum environment, and growth material is supplied in the form of elemental beams of material that are directed towards the growth surface. This technique is conceptually simpler and potentially much more controllable than VPE, making it very useful as a research tool for understanding fundamental processes in crystal growth. However, it is considerably more expensive and generally far less versatile than VPE, limiting its use for commercial applications. Chemical beam epitaxy (CBE) is a related hybrid technique, where one or more beams contain precursor molecules, rather than

Section 2.1: Epitaxy

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elemental material. This technique is considerably more versatile than MBE, but still generally very expensive and time-consuming.

2.2 Metallorganic Vapour Phase Epitaxy: MOVPE MOVPE is a subtype of the vapour phase epitaxy (VPE) technique, which uses a gas distribution system involving chemical precursors in a high-purity carrier gas [52]. The precursors are individually fed into a reactor cell, designed to achieve a laminar gas flow across the substrate surface. This produces a concentration gradient of materials above the substrate surface, which can be controlled by growth parameters. This in turn controls the growth of the desired material. In MOVPE, at least one of the precursor materials (typically the group III precursor for III-V materials) is a metallorganic species. Like all crystal growth techniques, MOVPE is very complex. A large number of fundamental processes are involved, roughly divided into thermodynamic and kinetic factors. As discussed in the previous section, thermodynamics provides the driving force for all crystal growth. The rate at which processes occur is typically governed by kinetics, which is subdivided into several categories. Mass transport describes the movement of material through the gas phase towards the growth interface. For a cold-wall reactor, in which the substrate is heated directly from below, this process will only be significant in the heated “boundary layer” near the surface. Surface effects describe the atomistic processes involved in nucleation, which may involve such factors as kink formation and surface reconstruction, and usually include diffusion of material on the substrate. Finally, chemical reactions involving the precursor materials play a significant role. These processes primarily relate to decomposition and can be very complex, potentially including homogeneous reactions in the gas phase and heterogeneous reactions on the substrate, and may involve adduct formation between two or more precursors. The adsorption and desorption of precursors, and fully or partially decomposed precursors, are also important. The introduction of metal seed particles (in our case Au) for nanowire growth further complicates the picture. The various physical and chemical processes are affected by temperature, system pressure, and partial pressure of the precursor materials. Examination of such factors as growth rate can give insight into the processes dominating in the growth system under specific conditions. If the growth is thermodynamically limited (meaning crystallization is the limiting step), then growth rate typically decreases with temperature for (typically exothermic) MOVPE growth. This occurs because the chemical potential difference decreases with temperature for exothermic processes. When mass transport processes are limiting, growth rate typically is temperature-independent. If chemical reactions limit the growth (that is, decomposition of the precursors), growth rate will

Chapter 2: Epitaxy of Nanowires


12

typically increase with temperature, as is discussed below. It should be emphasized that all processes will still play a role in growth (as will be discussed in Chapter 3), and different processes may dominate under different conditions. For any chemical reaction, the rate at which a reaction proceeds is defined as the rate at which reactants disappear with time, or the rate at which products form (the rate is identical for each reactant or product). For a simple chemical reaction (consisting of a single step) of the form wW + xX → yY + zZ, the rate is defined by

[ ] [ ]xw XWTkr )(= (2.2) where [W] denotes the concentration of W. For a gas-phase reaction, concentrations are replaced for partial pressures. Note that this only applies if the reaction proceeds by a single step; when several steps are involved, the slowest (rate-limiting) step determines the order of the rate equation. The coefficient k(T) is known as the rate coefficient or rate constant (although it is not a constant), and is defined by

RTEa

Aek−

= (2.3) Here Ea is the activation energy of the reaction, or the kinetic barrier which must be overcome for the reaction to proceed, and A is the prefactor, an empirical factor which is usually taken to be temperature-independent. Thus the rate of a chemical reaction depends exponentially on temperature, within a temperature range where the activation energy is constant (this will be determined by thermodynamics). If chemical reactions limit crystal growth, the growth rate will follow this temperature dependence. In our system the pressure is typically maintained at 10 kPa; the carrier gas used is H2. Our system uses a graphite susceptor to hold the substrates, which is heated by a radio frequency generator outside the reaction chamber. The RF heater coil is water-cooled, so only the susceptor is heated. This ensures that the chemical reactions involved take place near the substrate. The metallorganic materials trimethylgallium (TMG), trimethylindium (TMI) and trimethylaluminum (TMA) are used as group III precursors, while the hydrides arsine (AsH3) and phosphine (PH3) are used as group V precursors. As well, disilane (Si2H6) is available for doping and Si growth. Waste materials, including unreacted precursors, are carried out of the chamber and burned. A schematic of an MOVPE system is shown in Figure 2.1.

Section 2.2: MOVPE

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Figure 2.1 Metallorganic vapour-phase epitaxy system. Hydrogen gas is used to carry the hydride group V precursor and metallorganic group III precursor to the reaction chamber. The sample is placed inside the chamber on a graphite susceptor, which is heated by a radio frequency generator. Waste gases are burned before leaving the system. From an operational standpoint, the procedure by which epitaxial nanowires are grown in this system is generally straightforward. First, samples are heated under a constant partial pressure of the group-V precursor. The presence of this precursor is necessary to minimize decomposition of the substrate at elevated temperatures and is thus chosen based on the substrate material, not the growth material (i.e. AsH3 for GaAs and InAs substrates, PH3 for GaP and InP substrates). By constant, an overpressure of the group-III precursor would result in the precipitation of droplets of the group-III material on the substrate, and so an overpressure of the group-V material is necessary at all times. In some cases, samples are first heated to temperatures above the desired growth temperature to anneal the substrates. This step aids in the decomposition of native surface oxides, and was originally believed necessary to achieve an appropriate alloy or compound between the Au particle and the substrate material. The effect of this step will be discussed in later sections. After annealing, the substrate temperature is reduced to the desired growth temperature (when annealing is not performed, samples are heated directly to growth temperature). Generally, nanowires are produced between the temperatures of 380 and 550 oC; the appropriate temperature range and its effect on growth will be discussed later in terms of the processes involved. Once the desired growth temperature is reached, a constant flow of the group-III precursor is turned on, initiating growth; after the desired growth time (times between 5 seconds and 15 minutes were used for various studies) the group-III precursor is turned off, halting growth (if the appropriate group-V precursor was not used

Chapter 2: Epitaxy of Nanowires


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during heating, it is also turned on with the group-III precursor). Finally, the substrate is cooled to room temperature, sometimes under a constant flow of the group-V material to prevent nanowire decomposition. The effect of cooling conditions has also been investigated. It should be noted that temperature is measured by a thermocouple inserted into the susceptor directly underneath the growth substrates. This measurement is very accurate, but does not of course directly measure the temperature at the growth front. Since the graphite susceptor is heated radiolytically, it is expected that the temperature is constant through the susceptor for a given position with respect to the RF coil. There may, however, be a drop in temperature between the susceptor and substrate (substrates are held in place only by gravity), as well as through the substrate itself. Temperature drops along the nanowires as they grow may also be possible, but are unlikely to be significant due to the very small length scale [53]. In general, the temperatures reported for this system should always be treated as the maximum temperature at which a given process was performed.

2.3 Nanowire Growth Techniques The formation of one-dimensional structures can be accomplished by a variety of techniques. Unlike molecular structures such as carbon nanotubes, where the one-dimensional nature is a direct consequence of the atomic arrangement, semiconductor nanowires typically exhibit the same crystal structures as bulk semiconductors. The realization of one-dimensional structures thus depends on the enhancement of the crystal growth rate in one dimension, and/or suppression of growth in the other dimensions. In general, there are two main categories of nanowire growth: template-directed and freestanding. Template-directed growth confines the forming crystal to a pre-defined shape, essentially suppressing growth in other dimensions by physical confinement [54]. This type of growth may also involve preferential nucleation along the length of the template, as in v-groove templated nanowire growth [55]. Such techniques take advantage of existing lithographic technologies and are readily scaleable with potential for high throughput, as well as natural integration into existing device structures. However, versatility is limited in terms of potential material combinations, and the resulting structures are necessarily confined to the surface on which they are grown. Size limitations are determined by the resolution of the lithographic technique used (which may or may not prove entirely acceptable for device applications in the future). Freestanding nanowires are typically grown outwards away from a single nucleation point, with confinement due only to the relative growth rates of the different dimensions. The term “freestanding” is understood here also to include

Section 2.3: Nanowire Growth Techniques

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Figure 2.2 Particle-assisted growth of freestanding wires from a vapour. (a) Nanoparticles are deposited onto a substrate, which is placed into a vapour-phase epitaxy reactor. (b) The sample is exposed to vapour-phase precursor materials at an elevated temperature. (c) Freestanding nanowires grow from the substrate. nanowires grown in solution, although of course these are not “standing” in the conventional sense. Such nanowires have shown exceptional versatility in terms of material options, can be grown on a variety of surfaces (or no surface at all) and readily transferred to other surfaces/media after growth, and typically can be produced down to smaller sizes than template-directed nanowires. However, freestanding one-dimensional growth is more complex to understand, and device integration may not be as straightforward. The dominant category of freestanding nanowires is grown with the assistance of small particles of a foreign material (typically a metal). These particles do not participate in the growth directly (and are normally not consumed), but act to substantially increase the growth rate in one dimension. Growth conditions can then be chosen such that kinetic hindrance significantly reduces growth in the other dimensions (on the side facets of the nanowires); alternatively, the side facets may be passivated to prevent growth. However, lateral growth on the side facets of such wires often poses a problem for this type of growth. Particle-assisted freestanding nanowires can be grown from vapour or solution, with or without a substrate, with a very large range of potential particle materials in liquid or solid state (discussed in more detail in Chapter 3). A schematic of particle-assisted growth from a vapour is illustrated in Figure 2.2; this type of growth forms the basis of this thesis. Numerous other techniques exist for growing freestanding nanowires. One of the more common is oxide-assisted growth, in which a mobile oxide layer on the surface acts to passivate side facets while enhancing one-dimensional growth [56]. Another technique is selected-area epitaxy, optimized by the Fukui group to produce highly regular areas of nanowires over large areas [57, 58]. This technique uses a template to define the nucleation centers, while tailoring growth rates to suppress growth on certain crystalline facets, which form the side facets of the nanowires.

16 Chapter 2: Epitaxy of Nanowires


2.4 Au Aerosol Particles Most nanowires described in this thesis were seeded by Au aerosol nanoparticles [59]; exceptions are presented in Chapter 4. The choice of Au as a seed particle material is mainly one of convenience; most early work focussed on this material, and as such it is well-developed as a seed particle for many nanowire materials. Very many other materials (typically metals) have been used for nanowire growth, particularly since this material is a very undesirable contaminant in semiconductor processing. It should be noted, however, that in comparative studies Au typically outperforms other metals in producing oriented, size-selected nanowires [60]. The reasons for this are not entirely clear. Au is relatively inert and does not react with gas-phase carriers including nitrogen, hydrogen and oxygen. It also forms low-temperature liquid alloys with many materials of interest. However, as will be discussed in Chapter 3, Au performs well as a seed particle even for materials with which it does not form liquid alloys, or even solid intermediate phases. An understanding of the appropriate choices for seed particle materials may thus depend on the development of a thorough understanding of the role of these particles. In addition to the aerosol technique described here, nanoparticles may be produced by evaporation and annealing of thin films, colloid reduction techniques, and lithography/metallization. The production of size-selected Au aerosol nanoparticles is performed in an evaporation/condensation generator [61]. A schematic of the process by which these particles are formed is illustrated in Figure 2.3.The first step in this process is the production of Au primary particles. Evaporation of Au takes place in a tube furnace at temperatures ranging from 1800-1950 oC. The resulting Au vapour is carried out of the furnace by ultra-pure nitrogen. As the vapour cools after leaving the furnace, homogeneous nucleation of the vapour takes place. Afterwards, particles grow by homogeneous condensation and coagulation of Au primary particles, which leads to a polydisperse aerosol containing agglomerates. These agglomerate aerosol particles are then charged with a β-emitting Ni-isotope charger, yielding primarily singly charged (positive or negative) and uncharged nanoparticles. A monodisperse fraction of the negatively or positively singly charged particles is selected by a differential mobility analyzer (DMA) [62], which classifies charged particles according to their mobility in an electric field. Following size selection, the monodisperse agglomerate particles are reshaped at temperatures around 600 oC in a second tube furnace to yield compact, spherical particles. When reshaped at a sufficiently high temperature compact, almost perfectly spherical particles can be formed, mainly by solid state diffusion [63]. The reshaped nanoparticles pass another DMA that further narrows the size distribution of the final aerosol. To determine the particle concentration, the resulting aerosol is fed into an electrometer. Assuming that all particles are singly

Section 2.4: Au Aerosol Particles

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Figure 2.3 Setup for production of Au aerosol particles. Au metal is heated in Furnace 1 and the vapour carried out by N2 gas; the resulting polydisperse nanoparticles are charged, then size-selected in a differential mobility analyzer (DMA). The size-selected particles are then heated again to reshape, then size-selected again in a second DMA. The resulting monodisperse spherical particles are fed into an electrometer to be counted, or into an electrostatic precipitator (ESP) to collect on substrates. charged, the electrometer gives an accurate count of the number of particles per unit volume. Substrates are then placed into an electrostatic precipitator (ESP) [64], where a deposition voltage of 6 kV in an electric field of 300 kV/m is used to attract the charged particles to the substrate. When the aerosol flow is directed away from the electrometer and towards the ESP, a desired surface density of particles can be deposited by applying the deposition voltage for the appropriate time.

Chapter 3

3. Particle-assisted Nanowire Epitaxy

3.1 History of Particle-assisted Growth The spontaneous growth of one-dimensional microstructures has been observed for more than 50 years [65]. In the 1960s, it was first observed that such structures very often had a small metal particle at one end. Such particles typically had a diameter consistent with that of the wire (or whisker) on which they were observed, and their shape was typically a hemisphere or truncated sphere with the flat end in contact with the end of the wire. Wagner and Ellis first proposed in 1963 a mechanism by which these particles act as seeds for one-dimensional growth, which they named the Vapour-Liquid-Solid (VLS) mechanism [66]. Their work focussed on Si whiskers seeded by Au particles, and they noted that these two elements form a low-temperature liquid alloy which is stable in the temperature range at which their whiskers grew. They concluded that this alloy forms spontaneously when Au is in contact with Si at elevated temperatures, and acts as a preferential nucleation site for the growth of Si crystals. The reason for this was not entirely clear, but they proposed that vapour-phase precursor molecules, in their case SiCl4, stick preferentially to the surface of the liquid particle, and thus are more likely to decompose there. This will result in a small region of locally enhanced Si concentration around the particle. This decomposed Si may escape into the vapour, but may also become incorporated into the particle. Since the vapour is continuously supplied with an overpressure of Si precursor molecules, the particle will eventually become supersaturated with Si, which will precipitate out at the point at which nucleation is easiest: usually, on the solid substrate. The Au-Si binary system is a simple eutectic system [67]. This means that there is limited solubility in the solid phase (less than 2 at. % Si in Au, and less than 2 at. % Au in Si), but continuous solubility in the liquid (for further discussion of alloys

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Figure 3.1 Au-Si binary phase diagram and phase diagrams, see Appendix). The freezing point of the liquid binary is in fact lower than that of either Au or Si, and exhibits a sharp minimum between them – the eutectic melting point (see Figure 3.1). The eutectic reaction is one in which a binary liquid alloy, upon slow cooling, will precipitate two solid materials simultaneously that will remain stable as the temperature is lowered. In the case of Au and Si, there is a single eutectic point at 363 oC (636 K), at which point the composition of the liquid alloy will be 18.6 at % Si. When a liquid Au-Si alloy of this composition is cooled (slowly), solid Au and Si will precipitate out at the eutectic temperature. If a liquid alloy with, for example, 50 % each Au and Si is cooled, this alloy will precipitate only Si as it cools (following the liquidus line), decreasing the Si composition in the liquid until it reaches the eutectic composition. At this point, as mentioned above, both Au and Si will be precipitated (each containing trace amounts of the other material dissolved in the solid). More discussion of alloys and phase diagrams can be found in the Appendix. The Vapour-Liquid-Solid mechanism, then, assumes that a liquid Au-Si alloy forms above the eutectic point, which serves as a preferential site for the decomposition of the Si precursor – locally increasing the amount of Si in the vapour near the particle, compared to elsewhere on the substrate. Si will be dissolved into the particle until the composition reaches the liquidus line. Beyond this point, if the local concentration of Si around the particle is still higher

Section 3.1: History

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(thermodynamically) than that within the particle, small amounts of Si will continue to enter the particle. This increases the composition beyond the liquidus line (see Figure 3.1). Although this can occur kinetically, it is a thermodynamically unstable situation, and the particle will precipitate Si in order to re-establish the stable composition of Si and Au in the binary liquid alloy. Some decades later, in 1989 Hiruma et al. demonstrated the formation of very small one-dimensional structures composed of GaAs, deemed nanowhiskers or nanowires, when this material was grown in the presence of a small amount of Au [68]. Again, they observed small Au particles at the tips of their wires, and so they concluded that Wagner’s VLS model (or a related mechanism) also occurred in their system. Their results led to an explosion of new experiments by many groups demonstrating similar nanowires of many different compositions, using particles of various materials as seeds for their growth. Today, with so many possible applications for nanowires envisioned, particle-assisted growth remains the dominant process for its simple reproducibility and application to an enormous variety of growth and material systems. This has also increased the importance of understanding the processes by which these structures form.

3.2 Growth Mechanism It is useful to consider the thermodynamics of the crystal growth, following the introduction in the previous chapter. For any reaction to occur, the chemical potential of certain components (reactants), must be greater than that of other components (products) – in other words, a supersaturation must exist. The difference in chemical potential is the driving force for the reaction; kinetic factors may determine the rate at which the reaction occurs. As the reaction approaches equilibrium, the chemical potential difference approaches zero, and the reaction stops. If, however, a constant supply of reactant is maintained, the reaction can proceed continuously under steady-state conditions. This would be the case, for example, if Si was grown by MBE. If a constant supply of vapour-phase Si is maintained (above the equilibrium vapour pressure of Si at that temperature), a constant chemical potential difference would be maintained and steady-state growth would occur. In the simplest case, the reactions involved are reversible, and the products could re-form if the chemical potential difference were to be reversed (for example, if the Si vapour supply were to suddenly be shut off at high temperature, so that the resulting Si vapour concentration was below the equilibrium vapour pressure of Si). Normally, however, crystal growth is performed using molecular vapour-phase precursors, and the decomposition of these is not usually reversible. That is, once the precursors decompose to produce vapour-phase growth materials, these materials cannot be removed from the vapour except by growth (or, of course, by



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shutting off the precursor supply and flushing away the remaining vapour). Thus the chemical potential of the decomposed precursors must be considered to understand crystal growth. For example, when growing Si from SiCl4 precursor, the precursor decomposition is generally not reversible. At all times the chemical potential of the decomposed precursor (Si vapour) must be higher than that of crystalline Si for growth to occur. The introduction of another material, such as Au particles, complicates the picture somewhat. In order for Si to dissolve in the particle (that is, for binary liquid Au-Si to form), the chemical potential of the particle must at all times be lower than the surrounding vapour. However, the chemical potential of the particle must also eventually exceed that of the crystalline Si, so that this material forms by precipitation from the particle. This would lead to the conclusion that the chemical potential of the Au particle lies between that of the Si supply and the Si crystal being grown. However, since the chemical potential difference between the vapour and crystal would then be greater than the difference between the particle and crystal, this would lead to the conclusion that growth from the particle would be slower than growth from the vapour [69]. Clearly, thermodynamic arguments are insufficient to explain the growth of whiskers from seed particles, and kinetics must also be considered. Under equilibrium (or stable steady-state conditions), thermodynamics assumes that compositions everywhere are uniform. However, physical processes like diffusion also occur in growth systems, and these occur at a finite rate that can lead to inhomogeneities in the materials in the system. As described above, a local increase in the concentration of Si around the Au particle could lead to a higher chemical potential at its surface (and thus in the particle) than elsewhere in the vapour. The simplest possibility would be that the Au particles act as catalysts for precursor decomposition. A catalyst is a material that increases the rate of a reaction by lowering the activation barrier - by changing the pathway by which it occurs – without itself being consumed by the reaction. Catalyst materials react with the material being decomposed, but are then re-formed by secondary reactions and can thus react continuously with new material. If the reaction between the catalyst and the material being decomposed (the precursors in this case) has a lower activation energy than the decomposition without the catalyst, then the overall decomposition rate will increase. The change in activation energy between catalyzed and non-catalyzed decomposition is the hallmark of catalyst activity, and can be used to demonstrate its occurrence. In this example, if Au acted as a catalyst for the decomposition of SiCl4, it would change the activation energy of this process and thus increase its rate, leading to a locally increased Si concentration at the particle’s surface.

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However, Wagner et al. were able to demonstrate that the activation energy for the growth of their whiskers with Au particles was the same as that for growth of Si without Au [66]. This effectively demonstrated that Au was not catalytic in their system (although they did not state this explicitly). This led them to conclude that another process was leading to an increased local concentration at the surface of their particles, which they deemed an enhanced accommodation probability. In other words, physical surface processes were limiting in their model. This is an uncommon and difficult concept to explain or, more particularly, to demonstrate, but their model effectively described the process by which their Si whiskers grew. Compound nanowires, on the other hand, are more complex to understand than Si. Growth of GaAs, for example, requires the presence of two precursor materials, one for each of the Ga and As components. The ratio of these two materials influences the growth, as the chemical potential difference between the vapour and crystal is determined by both materials. Therefore, thermodynamic understanding is more complex and has less practical meaning. Another important question is whether the alloy particle must contain both materials for growth to be possible. Many binary compound materials do not form liquid ternary alloys with normal seed particle materials. GaAs is an exception; there exists a pseudobinary simple eutectic system between this material and Au [70]. However, the eutectic temperature for this system lies far above typical GaAs nanowire growth temperatures, suggesting that no As can dissolve in the particle during growth. In fact, no ternary Au-III-V phases or binary Au-V phases have been reported that are stable at temperatures below about 600 oC. Confirming this, As and P have never been observed in seed particles on nanowires by ex-situ post-growth investigation. For most compound materials, it appears that only one of the components must be dissolved in the particle; for III-V materials (as described in this thesis), this is normally the group-III material. Further discussion of alloys, phase equilibria and phase diagrams can be found in the Appendix. The dissolution of only one element in the seed particle poses some problems for our understanding of the growth mechanism. The most obvious question is how the second material (the group-V material in our case) reaches the growth interface. However, this may not be the largest problem, since it could easily be envisioned that it travels along the growth interface, or along grain boundaries if the particle is a solid (as will be considered in the next section). Indeed, very high diffusion rates for As along Au grain boundaries have been reported [71]. A more difficult question is what drives the growth in systems such as Au-Ga and Au-In. As will be discussed in the Appendix, both Ga and In exhibit very low melting points, far below typical growth temperatures. Therefore neither can be thought of as a true eutectic system, since there is no low-temperature melting point between the two elements (this is not strictly true, as discussed in the Appendix; however it can be taken as true for this discussion).



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Both Ga and In form a series of compounds with Au, all of which have moderate melting points (between those of Au and Ga or In). Local eutectic points exist between several adjacent compounds, and supersaturated liquid alloys in these composition ranges could be made to precipitate different Au-Ga or Au-In compounds. However, it is not clear how this could lead to growth of binary III-V compounds. The existence of a liquid Au-Ga or Au-In alloy, therefore, does not necessarily lead to the conclusion that growth of III-V materials should be possible by the conventional VLS mechanism. The question of catalysis must also be considered for these materials. As for Si, the formation of a supersaturated alloy from which growth will occur at a higher rate than nucleation from the vapour requires a locally-increased concentration on the vicinity of the particle. The most obvious possibility, again, is that the particle in some way catalyzes the decomposition of precursor materials at its surface. The first problem with this explanation is that GaAs nanowires have been grown by MBE [72], where no precursors are used and thus no thermally-activated process exists to be catalyzed. MBE growth of Si nanowires has also been reported, leading to the same conclusion [73]. As well, it has been shown that GaAs grown in MOVPE using trimethylgallium and arsine exhibits the same activation energy as (non-catalyzed) GaAs layer growth in the same system with the same precursors [74]. This will be discussed in more detail in section 3.5. Numerous groups, however, have reported activation energies which appear to differ from those for bulk material growth, suggesting catalysis may play a role in some cases [75, 76]. It is difficult, however, to determine the appropriate activation energy for comparison, since the rate-limiting step may depend on the materials present (carrier gas, other precursors, substrates and even the reactor walls), and in some cases may depend on growth conditions. It is difficult to find appropriate comparisons where all parameters are the same, particularly since epitaxial bulk growth typically takes place at very different temperatures than nanowire growth. For example, Verheijen et al. reported that GaP nanowires grown on oxidized Si exhibit a very different activation energy from the decomposition of PH3 on InP [76], which might be an indication of catalysis. However, given the significant role that substrate surfaces play in decomposition of precursors [52], it is difficult to compare such results. Paiano et al. have therefore presented a very interesting approach – they compared the activation energy of GaAs nanowires to the activation energy for growth on the side facets of the same wires, and determined that they are approximately the same [77]. In general, it can be concluded that particle catalysis may play a role in some systems, but it is not a general effect and is not sufficient to explain the general mechanism of particle-assisted nanowire growth. The actual role of the particle, therefore, is still very much under debate. It appears that the driving force for the enhanced growth (compared to bulk semiconductor

Section 3.2: Growth Mechanism

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growth) is neither thermodynamics nor chemical reaction kinetics. It seems, then, that physical surface processes must be of primary importance, in line with Wagner’s original idea of enhanced concentration by high accommodation coefficient. This idea is insufficient in itself for such techniques as MBE, where the accommodation coefficient may be taken as unity everywhere in the system. It may be, on the other hand, that the interface between the particle and the semiconductor acts as a preferential nucleation site, perhaps due to surface reconstruction. The development of a model to effectively describe all types of particle-assisted nanowire growth will be an important challenge in coming years.

3.3 State of Particle Wagner and Ellis concluded in 1964 that the Au particles at the tips of their Si whiskers were in fact binary liquid Au-Si alloy particles during growth. This conclusion was partly reached due to the shape of their particles, which were rounded with a hemispherical or truncated spherical shape. Additionally, the Au-Si binary system exhibits a low-temperature eutectic (far below their growth temperatures), and growth at temperatures above this eutectic point could allow for precipitation of solid Si from a supersaturated liquid alloy. More recently, observations of small particles at the tips of nanowires have often led to the conclusion that liquid alloy particles act as seeds for the growth of these wires by a mechanism similar to Wagner’s VLS. However, in some cases the possible existence of such a liquid alloy has not been carefully considered. An important point is that nanoparticles do not necessarily behave in the same way as bulk materials. The melting point of small nanoparticles has been investigated by many groups, all of which observed a strong depression in melting temperature at very small sizes. For Au, slight melting point depression occurs for particle diameters below about 20 nm; when particle diameters decrease below 5 nm, the melting points decrease very rapidly [78, 79]. As well, even solid Au nanoparticles have been shown to reshape at temperatures as low as 200 oC to form equilibrium shapes, without losing their crystal structure [59]. In other words, the mobility of atoms in small solid particles is high, and the distinction between solid and liquid particles is not always as clear. In 2004, Persson et al. observed that when Au nanoparticles at the tips of GaAs nanowires grown by CBE were heated to growth temperatures in vacuum, the amount of Ga and As absorbed into the particle was insufficient to form a liquid alloy [80]. They concluded that Au particles retain their crystal structure and solid state during CBE growth, and that growth occurs by a mechanism that they termed vapour-solid-solid growth (VSS). This was not the first suggestion of growth using a solid seed particle – Kamins et al. demonstrated in 2001 that Si nanowires can be grown from solid TiSi 650 K below the eutectic temperature [81], and the



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possibility of VSS growth (including the term) was first suggested 35 years ago by Bootsma et al. [82]. However, the work conducted by Persson et al. initiated an interest in further understanding the growth mechanism, and led to many investigations of the state of seed nanoparticles used for growth of many different types of nanowires. In 2005, we reported that InAs nanowires in MOVPE only grow in a temperature and compositional region where a solid Au-In compound would be expected in the seed particle (Paper I). The lower temperature limit for this growth has not been determined, but nanowires can be grown down to at least 360 oC. For reasons that will be discussed in the next section (and were briefly discussed in the preceding section), it is believed that group-V materials do not pass through the seed particle during III-V nanowire growth. Therefore only the Au-In binary system must be considered. It should be noted that In is a low-melting point metal; in fact, it would be expected to melt far below growth temperature. In other words, In could not be directly precipitated from a Au-In liquid alloy due to supersaturation. Moreover, any Au-In particle composition with less than 90 at. % In would be a solid up to 460 oC. The particle would have to increase near 10 times in size to absorb this much In, which is inconsistent with the observed wire diameter as well as ex-situ composition analysis. The temperature and compositional range in which InAs nanowires are grown thus suggests a solid Au-In particle. The same conclusion can be reached for InP nanowires, the growth of which has not been reported above 450 oC in MOVPE (Paper II). Growth of InAs and InP at such temperatures has also been reported by numerous other groups [83, 84]. Additionally, we have grown AlAs with Au particles at temperatures well below the lowest Au-Al eutectic (described in Paper V). GaAs can also be grown below the eutectic temperature using Au particles [85]. In addition to the studies discussed above, nanowire growth below the bulk eutectic temperature for the seed particle with the growth material has been reported for Si nanowires with Cu particles [86], Si with Al [87], Si with PtSi [88], Ge nanowires with Au particles [89, 90], Si and Ge nanowires with Ni particles [91, 92, from supercritical fluid], GaN with Ni particles [93, 94], ZnSe with Fe [95], and GaAs with Fe particles [96]. Furthermore, observations of GaAs with Au at sub-eutectic composition [97] or temperature [72] have led to further discussion of this mechanism. Despite the cases described above, where the applicability of the VLS mechanism is not clear, it still must be emphasized that this mechanism dominates for most nanowire materials and growth systems. This includes, for example, all Si nanowires grown using Au particles. Several suggestions have been proposed to explain the apparent solid-particle observations. For instance, nanoparticles are known to exhibit size-dependent melting point depression, as discussed above; this

Section 3.3: State of Particle

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has been proposed as an explanation for low-temperature nanowire growth [84, 89, 90, 95]. However, nanowires are usually grown with diameters larger than 20 nm, and sometimes as large as 100 nm, making size effects unlikely. As well, systems that use evaporated metal films usually require annealing at high temperatures to form the particles; a similar step is sometimes used to deoxidize the growth substrates. Melting/freezing hysteresis may occur in small particles, and could allow for undercooled liquid particles at sub-eutectic temperatures [72, 85]. However, not all observations of solid particles involve a high-temperature step (for example, the Au-assisted InAs discussed in Paper I does not). Also, growth sometimes occurs as much as 700 K below the bulk eutectic temperature, making undercooling unlikely. Very recently, Kodambaka et al. presented results for Ge nanowires grown by UHV-CVD from Au particles with in-situ TEM, that will largely solve the dispute regarding the state of the seed particle for nanowire growth [98]. They do not observe any size-dependent melting effects, but instead report three important observations: first, Au-Ge alloy particles show significant hysteresis in melting and freezing, allowing for sub-eutectic growth from undercooled liquid particles up to 80 K below the (observed) eutectic temperature. Second, they demonstrate that the Au-Ge phase diagram depends not only on temperature, but on pressure: a fundamental concept that is often forgotten, and is of particular importance for growth techniques far from atmospheric pressure. Finally, they demonstrate that Ge nanowires can be grown from Au particles in both liquid and solid state, and that these two states can even coexist (in neighbouring particles) due to the melting/freezing hysteresis. This effectively proves that VLS and VSS are both very similar and entirely valid mechanisms. It may in the future be possible to describe these by a single model, without explicit reference to the state of the seed particle. As a side note, it should be pointed out that it is not only the seed particle that can exist in different states. Numerous other particle-related mechanisms have been reported, the most common of which is solution-liquid-solid (SLS) [99], where the growth medium is replaced by a liquid solution. Also existing in literature are solid-liquid-solid (SLS again) [100], supercritical fluid-liquid-solid (SFLS) [101], supercritical fluid-solid-solid (SFSS, suggested above for Ni-seed Si and Ge) [91, 92], and vapour-adsorption layer-solid (VAdS) [82]. A consistent description of nanowire growth that allows for all of these possibilities would be of great interest to the nanowire community.

3.4 Interaction of Au with III-V Materials The work performed during the course of this thesis focussed primarily on III-V nanowires grown using Au seed particles. In particular, the four materials GaP,



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GaAs, InP and InAs were studied (with most emphasis on GaP and InAs). Therefore, the discussion from here on will focus on these material systems. In order to understand the behaviour of these materials when they are grown using Au particles, it is important to understand the way that these materials interact. Far from being an inert catalyst, Au interacts significantly with the growth substrates and precursor materials at elevated temperatures, forming solid solutions, binary compounds and in some cases, eutectic melts [102]. Many stable binary compounds between Au and the group-III materials exist [103, 104], all of which have melting points intermediate between that of Au and that of the corresponding group-III material, Ga or In. There are also two metastable Au-P phases known, of which one (Au2P3) has been observed by numerous groups. No stable or metastable Au-As phases have been reported. Details of the equilibrium binary phase diagrams can be found in the Appendix. Interactions between Au and the substrate materials to form binary compounds may be critical to the metal-seeded growth of nanowires, as in the case of Si nanowires grown by the VLS mechanism. However, control of this interaction is necessary to obtain control of nanowire growth, at least in the case of III-V nanowires. Details of the interaction between Au and the III-V substrate, and its role in the growth of nanowires and nanotrees, are presented in Paper II. A brief summary is presented here. Both GaAs and GaP have been shown to be stable in contact with Au even when heated, provided a constant temperature and overpressure of vapour-phase group-V source material is maintained [105, 106]. By maintaining a constant pressure of AsH3 or PH3 gas we can simulate a closed system, allowing the substrates to be heated to high temperatures (annealing temperatures) without significant decomposition. Of the two systems, GaAs-Au has been investigated most thoroughly. In both cases, the tie-line between Au and the semiconductor is pseudobinary [106] (hence the stability observed), but only for GaAs is the nature of the pseudobinary system known. In this case, it resembles a simple eutectic system with a eutectic melting point similar to the eutectic of the Au-As system [70]. Unlike As, P does not form a eutectic with Au (see Appendix). Although both materials have high vapour pressures, in the case of P the sublimation occurs at such low temperatures that there is essentially no intermixing between P and Au. The pseudobinary GaP-Au is thus similarly stable; a eutectic point is likely, but probably exists at significantly higher temperature than the GaAs-Au eutectic. In an open system, the two materials behave very similarly when heated in the presence of Au. A solid-phase solution of Au and Ga (maximum Ga content 9 at. %) is observed to form under heating up to 475 oC [107], and further Au-Ga compounds form at higher temperatures [108, 109]. This instability however can be directly attributed to the loss of group-V material from the substrate; under overpressure of this material, such interaction is unlikely below the ternary eutectic point, since the composition will remain on the group-V rich side of the

Section 3.4: Interaction of Au with III-V Materials

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Figure 3.2 Interaction of Au particles with GaP nanowires during heating. (a) Ex-situ TEM image of Au particles on a GaP nanowire, which has been heated to 650 oC under PH3 overpressure. No interaction occurs. (b) In-situ TEM image of Au particles on a GaP nanowire. Interaction occurs when heating above 600 oC in vacuum. ternary system. Annealing studies of Au particles in contact with GaP nanowires have illuminated this effect. When this annealing is performed at 650 oC in the MOVPE chamber containing hydrogen and a significant flow of phosphine (molar fraction on the order of 10-2), no interaction between the particle and wire is observed by high-resolution TEM after cooling (see Figure 3.2a). When heating in vacuum with in-situ TEM, however, interaction between the particle and wire occurs at temperatures around 600 oC. In this case, Au diffuses into the wire accompanied by outgassing of the group-V material (Figure 3.2b). This diffusion occurs slowly, and melting is not observed. Also, no material transport proceeds in the other direction (into the particle), and so the particle retains its crystal structure until entirely absorbed. In our system, when a flow of TMG precursor is turned on, the equilibrium composition of the system changes and Au-Ga compounds may form. However, the incorporation of Ga into the Au lattice is known to be the rate-limiting step [110]. As well, so long as the group-V material is in excess, the steady-state composition of the system will still be on the group-V rich side of the ternary phase diagram. Thus the availability of other forms of Ga (i.e. the TMG precursor) should not result in the formation of Au-Ga compounds with greater than 9 at. % Ga, at least at temperatures below 475 oC. Recent ex-situ TEM and EDS investigations have determined that the final Ga composition of the particle after growth of GaAs nanowires at 375 oC depends on the cooling conditions: whether arsine is present, or TMG, or both, or neither. In none of these cases, however, does the Ga content exceed about 20 at. %, or approach the 30 at. % required to form a liquid alloy particle. Unlike the Ga-containing compounds, neither InAs nor InP is stable in contact with Au even at room temperature [105, 111]. Thus temperature-dependent interactions between these substrate materials and the Au particles would be



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expected to occur even when a constant pressure of group V material is maintained in the vapour. The compounds that form in these systems as the temperature is raised have been well-studied [112, 113]. For the most part the interactions between Au and InP and InAs are similar, forming a series of Au-In compounds with increasing In content as the temperature is raised. The Au-In γ phase (29-32 at. % In) is stable in contact with both materials in a closed system and is reported to be the final product in this interaction over the temperature range in which we are interested [114]. However, in the Au-InP system, the metastable compound Au2P3 has also been observed to form around 370 oC [115]; this compound is associated with the decomposition of the γ phase and formation of the higher-indium ψ phase (35-40 at. % In) for the Au-InP system [116]. Although the ternary phase diagrams of these compounds have not been thoroughly investigated at elevated temperature, no ternary alloys have been reported to form during heating to moderate temperatures (at least 500 oC). As well, the very limited interactions between Au and P or As suggest that low-temperature ternary eutectics are unlikely. Additionally, the absence of observed As or P in the particles after wire growth and cooling leads to the conclusion that these elements do not enter the particles in significant quantities. When samples are heated to annealing temperatures, the compound particle would be expected to melt, since all Au-In compounds with In content greater than about 20 at. % In have melting points below 600 oC [104]. Upon re-cooling to growth temperatures, the liquid particles may re-solidify, but melting/freezing hysteresis may play a role. In this case the composition and perhaps state of the particles will not be uniform over all particles on the substrate. By heating directly to growth temperature without annealing, the interaction between Au and the In-containing III-V substrate can be better controlled, allowing for more careful investigation of the nanowire growth. It is far more difficult to determine by ex-situ investigations the actual composition of In-containing particles during growth. The consistent observation of In in the particles after cooling (depending on growth conditions, but typically on the order of 30 at. %) clearly shows that In is not removed during cooling (at least not completely). This is confirmed by experiments that show that the difference in In content in particles on InAs nanowire after cooling with and without arsine is very small. It is therefore believed that the In content before and after cooling is similar.

3.5 Precursor Chemistry Growth of MOVPE involves molecular precursor materials, which necessarily makes the processes involved in nanowire growth more complicated. As discussed in section 2.2, the processes involved include thermodynamics, gas-phase mass

Section 3.5: Precursor Chemistry

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transport, chemical reactions, and physical surface processes. These processes will be discussed here for growth of GaAs, InP, GaP, and InAs nanowires. GaAs is the most thoroughly investigated system for MOVPE, and consequently much is known about the processes that take place in this system when growing with TMG and AsH3. When growing planar layers, the growth rate is observed to increase with temperature to about 550 oC, then be essentially constant in temperature until about 650 oC. Beyond this point it decreases [52]. This suggests that growth is chemical reaction limited at low temperatures (due to incomplete decomposition of the precursor materials), then mass-transport limited at intermediate temperatures (after precursors are completely decomposed). At higher temperatures competing reactions limit the growth, and decomposition plays a role. Since nanowire growth always occurs in the low temperature regime, it is assumed that growth is chemical reaction limited, unless Au plays a significant catalytic role in precursor decomposition. As has been previously noted, Borgström et al. determined that the activation energy for GaAs nanowire growth was approximately the same as that for GaAs bulk growth under similar growth conditions with the same precursors [74], as determined by Reep and Ghandi [117]. This indicates, first, that the growth is limited by chemical reactions (since a clear temperature dependence is observed), and second, that the limiting chemical reactions are the same for nanowire and bulk growth. An understanding of GaAs nanowire growth can be obtained from careful investigation of studies performed for bulk growth. It has been determined that, in the temperature regime of interest here, both precursors decompose primarily by heterogeneous (surface) reactions [118]. This is particularly true for cold-wall MOVPE, where only the susceptor is heated. When both precursors are present, the decomposition of both is enhanced [119]. It has been concluded that decomposition proceeds by the adsorption onto the surface of the two precursors (at specific sites), followed by the formation of a surface-based adduct between the two materials [120]. Decomposition then proceeds by the release of CH4 molecules from the adduct. The activation energy for this process is lower than that for the heterogeneous decomposition of the individual precursors [52], and is similar to the observed activation energy for growth of GaAs (both layers and nanowires). This would imply the formation of Ga-As dimers that can then be incorporated onto the surface. However at sufficiently low temperatures the dimers may be able to diffuse some distance on the surface before incorporating. Surface diffusion of the decomposed species is discussed in the next section. Above 475 oC, the growth rate of GaAs nanowires decreases with temperature [74]. This may be related to the increased growth of bulk GaAs, which will compete with nanowire growth and cause diffusing Ga-As dimers (or individual atoms) to incorporate before reaching the nanowire growth interface. It is also noted that the activation energy for both decomposition and growth (nanowires and bulk)



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decreases with V/III ratio [74, 121]; this dependence indicates that the precursors do not decompose independently. Finally, the growth rate generally increases with TMG flow, as is commonly observed for MOVPE growth. Growth of bulk InP with the precursors TMI and PH3 has also been well-investigated for MOVPE. Unfortunately, however, this is the least well-studied case for nanowires, so little understanding can be obtained about nanowire growth. In this case the decomposition behaviour of the two precursors differs significantly. TMI is known to homogeneously decompose (to completion) in hydrogen at temperatures as low as 350 oC [122]. Phosphine does not decompose homogeneously at temperatures reasonable for MOVPE growth [123]. It has, however, been shown to exhibit very enhanced decomposition in the presence of both InP and GaP surfaces [123]. Decomposition of the two precursors together, on the other hand, behaves very differently. Decomposition of TMI in the presence of PH3 has been shown to proceed to completion at only 300 oC [124]. More strikingly, the decomposition temperature for PH3 is lowered very significantly in the presence of TMI, up to several hundred degrees below the homogeneous decomposition temperature for PH3, depending on the V/III ratio [124]. As noted previously, for MOVPE growth, the group-V precursor is always in excess to prevent the homogeneous nucleation of group-III material on the substrate. Decomposition of PH3 in the presence of TMI thus exhibits a very interesting decomposition behaviour: a portion of it equal to the amount of TMI available decomposes at a particular low temperature (with a certain activation energy), while the remainder decomposes at a notably higher temperature (with a different activation energy). The proportion of decomposed In:P is found to be 1:1. This clearly indicates that the decomposition of the two precursors proceeds by interaction with each other, most likely in a similar manner as the GaAs precursors. It is also clear that the TMI is fully decomposed, since the activation energy of the TMI:PH3 decomposition process must be lower than that for homogeneous TMI decomposition, which is complete at temperature well below growth temperature. It is thus clear that the only chemical reaction that can affect the growth of InP is the heterogeneous decomposition of excess PH3. It should be noted that, although the decomposition of TMI:PH3 yields equal quantities of the two species, they may not reach the nanowire growth interface in equal proportions, since their surface diffusion properties are certainly different. In fact, it is well-known that group-III materials diffuse much further on semiconductor surfaces than group-V materials. Therefore, the heterogeneous decomposition of excess PH3 can influence the growth rate of InP nanowires. GaP bulk growth by MOVPE has not been investigated extensively, and so conclusions about the relevant processes must be deduced from GaP nanowire growth behaviour (which is discussed in Paper III) and from the understanding of InP and GaAs. It was noted above that the decomposition of PH3 increases


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significantly in the presence of both InP and GaP substrates [123], indicating that heterogeneous decomposition dominates in this case as well. It is furthermore reasonable to assume, based on the above cases, that TMG plays a role in the decomposition of PH3. It is noted that GaP nanowire growth exhibits very similar behaviour to GaAs, in that there is a clear temperature increase of growth rate peaking around 475 oC, then decreasing, and in that the growth rate increases with TMG partial pressure. However, the activation energy of the growth differs from both GaAs and InP, indicating that the decomposition proceeds by a somewhat different pathway. This is reasonable if all three systems exhibit mutual precursor decomposition. GaP nanowire growth, like GaAs, exhibits increased growth rate with increasing TMG partial pressure. InAs, like GaP, has not been extensively studied by MOVPE. However, nanowire growth is well-studied for this system; a general understanding of the growth process can thus be deduced from nanowire growth, together with information on the precursor decomposition (this is discussed in detail in Paper IV). The decomposition of TMI has been investigated for MOVPE conditions by Buchan et al. [122]. As was discussed above, complete decomposition of the In precursor, TMI, in hydrogen is reported at temperatures below our typical growth temperatures; we therefore assume the presence of elemental In on our substrates. As noted, however, arsine does not decompose homogeneously at temperatures below 500 oC under MOVPE conditions [125]. However, AsH3 decomposes heterogeneously in the presence of GaAs; similarly, both InP and GaP substrates enhance the decomposition of PH3 [123]. To our knowledge the decomposition of AsH3 on InAs and InP substrates has not been investigated, but it is probable that heterogeneous decomposition does take place. We do not observe significant differences in the temperature dependence of growth behaviour of InAs nanowires on these two substrates, suggesting that the dominant decomposition process is not simply heterogeneous decomposition on the substrate. Both TMI [126] and TMG [119] have also been reported to significantly enhance the decomposition of AsH3. If this occurs by heterogeneous adduct formation, similar to that suggested for GaAs and probably also relevant for InP, the substrate material may be less important. It is also important to note that we do not observe clear temperature dependence for the growth of InAs nanowires. Specifically, the temperature-dependent behaviour changes with the V/III ratio and the total gas flow. In general, there is little dependence of growth rate on temperature, except for the lowest V/III ratios. The growth rate peaks at a particular V/III ratio (approximately 100), above which the growth rate is temperature-independent. This may indicate that the proportion of AsH3:TMI adsorbed on the surface is 1:1 at this point. It can be assumed that all TMI will be decomposed at growth temperatures, whether or not AsH3 is present. At V/III ratios above 100, excess AsH3 may still be cracked by heterogeneous decomposition, but it will not participate in growth because there is no further In



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Figure 3.3 Dependence of InAs nanowire growth rate on V/III ratio at 420 oC. to combine with. However, at low V/III ratios, there will be excess free In, which can react with any AsH3 that cracks by heterogeneous decomposition. In this growth regime, a temperature dependence of growth rate will be observed, because heterogeneous cracking of AsH3 on the substrate is important. It is not clear, however, why only 1% of the available AsH3 will react with TMI. It may be considered that when TMI is in excess, it decomposes independently before coming into contact with an AsH3 molecule. Alternatively, two TMI molecules may form an adduct when TMI is in excess. Only when the proportion of AsH3 is sufficiently high can it be ensured that all TMI will decompose by forming an adduct with an AsH3 molecule. As the V/III ratio decreases (towards 100), the growth rate increases, most likely because decreased V/III ratio is associated with increased TMI (and therefore increased total decomposed material). Increasing the V/III ratio can also be achieved by decreasing the AsH3, of course, but this will generally not affect the growth rate. The average trend therefore is one of increase. Once the peak ratio of 100 is reached, all the AsH3 that can react with TMI already has. Beyond this, the growth rate will depend on temperature. If the temperature is high, and therefore significant AsH3 can be decomposed on the surface, the growth rate can actually increase. If the temperature is low however, this will not be the case. More In will be available, however, which may increase the probability of nucleation on the surface, competing with nanowire growth. A decrease in V/III ratio (below 100) that comes from decreased AsH3, rather than increased TMI, will also cause the growth rate to decrease because the total available As will decrease. The dependence of growth rate on V/III ratio for a sample temperature of 420 oC is shown in Figure 3.3.


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It should also be noted that, for very high V/III ratios (> 500), the growth rate approaches a constant. In other words, the growth rate does not depend on V/III ratio, total precursor pressure or temperature when there is sufficient AsH3 in excess. This implies that the surface sites for heterogeneous AsH3 decomposition are saturated, so increasing the AsH3 has no effect on the growth (nor would increasing the two precursors simultaneously). Since the relative rates of chemical reactions and mass transport are not affected, temperature still does not play a role. It has also been observed that tapering (lateral growth on the side facets) increases with both of the precursors. However, tapering generally decreases with temperature, particularly for low TMI pressures. This is in contrast to GaAs and GaP; in both of these cases tapering increases with temperature, indicating that bulk growth is also limited by chemical reactions under nanowire growth conditions (as expected). The trend for InAs clearly indicates that bulk growth, like nanowire growth, is not chemical reaction-limited at normal growth temperatures (and therefore, the increased axial growth rate cannot be attributed to a catalytic effect of the Au particle). The decrease that is typically observed with temperature is intriguing; it may be related to surface processes, as will be discussed in the next section.

3.6 Surface Diffusion As was noted in previous sections, transport of material along the substrate plays an important role for growth of III-V nanowires by MOVPE. This is a more specific case than the “mass transport” discussed in the previous section, which is dominated by transport in the vapour phase. However, decomposed precursor materials (the group-III and group-V components of the semiconductor) diffuse considerable distance on the surface as well. Although this process is not necessarily rate-limiting, it does significantly affect the dependence of growth rate on parameters including time, wire diameter, and interwire spacing. It is well-known that the growth rate of nanowires can be a function of the diameter [127]; the nature of this relationship will depend on the relative importance of processes occurring in the system studied. In MOVPE growth of III-V nanowires, the transport of materials along the surface to the growth interface is particularly important. This is modeled by assuming that the rate at which material reaches the surface is equal at the substrate, wire side facets and the Au nanoparticle [127]. In the early stages of growth, most material is collected from the substrate; as the wire grows, the collection area becomes smaller, and the growth rate decreases with time. When the wire length exceeds the diffusion length of the farthest-diffusing species (the group III species), the growth rate becomes constant.



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At this stage, the growth rate depends on the material impingement rate, on the diffusion length of precursor species (where the group III material diffuses the farthest), and inversely on the diameter of the growing nanowire (area where growth material is removed from the system). The material impingement rate is proportional to the difference in the reactant overpressure in the vapour and in the particle (which increases with decreasing size due to the Gibbs-Thomson effect). So long as the reactant pressure in the vapour is high, the Gibbs-Thomson effect in the particle will not be significant, and the inverse dependence on diameter will dominate the growth rate. This relationship has been investigated in detail for GaP nanowires [127], and the results of this study fit very well to this model. The relationship between the growth rate of InAs nanowires and their diameter at 440 oC is described in Paper IV. It is clear that there is a very large decrease in nanowire growth rate with diameter. This dependence is similar to that observed for GaP [127], but the effect is stronger at small diameters than for the nanowires studied in that work. By fitting this data to the model described in [127] (briefly described above), the diffusion length on the side facets can be determined. This data suggests that the critical diffusion length (that of the longest-diffusing species, most likely In) on InAs substrates is considerably higher than that of Ga on GaP substrates at the same temperature. The authors in [127] estimated a diffusion length at 440 oC of 250 nm, based on the fit of their data to the model. It has also been reported that the growth rate of nanowires depends on their density (that is, how closely spaced they are) [128]. This occurs because nanowires growing within one growth material diffusion length of each other on the substrate have overlapping collection areas. Material landing between the wires has an equal chance of being incorporated into each wire, which means that they “compete” for the material. This results in a lower amount of material available per wire as the wires become closer to each other, and so a decreasing growth rate. Previous results from chemical beam epitaxy growth of InAs nanowires [128] have suggested an In diffusion length of 650 nm at 440 oC on InAs (111)B substrates (arsenic diffusion rates are presumed to be smaller, and thus cannot be observed). This length will depend on growth conditions, but preliminary studies of InAs nanowires grown in MOVPE using EBL-defined Au seed particles suggest the same effect occurs for this system as well. Wires grown at a density of 0.5 per μm2 are on average much farther apart than this diffusion length, and so we can conclude that this effect will not be important for InAs nanowires in this study. However, it must be considered when growing more dense nanowire arrays. The long diffusion lengths inferred for the growth of InAs (estimated between 300 and 1000 nm in Paper IV) may help to explain some of the growth results discussed in the previous section. For example, it was noted that the nanowire

Section 3.6: Surface Diffusion

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tapering was observed to decrease with temperature, except at the very highest arsine pressures (V/III > 500). This is a surprising and uncommon observation, which is not reported for other materials. It is understood that when growth is limited by chemical reactions, tapering should increase with temperature as bulk growth rate increases with temperature (this is the case for GaAs and GaP). If growth is mass transport-limited (as appears to be the case for InAs), both the wire (axial) growth rate and the tapering (lateral growth rate) should not depend on temperature. This is observed for axial growth, but not for lateral growth. If growth is thermodynamically-limited, growth rate may decrease with temperature. This is an intriguing option, but not consistent with the low growth temperatures used. As well, it is surprising that lateral and axial growth do not show the same trend. It is possible then, that physical surface processes must be considered in order to understand the growth. Axial and lateral growth may be treated as “competing” processes. If the Au particle acts as a sink, from which material can not diffuse away once it dissolves, it may be inferred that all growth material that reaches the particle will contribute to axial growth. Any material which cannot diffuse far enough to reach the particle will contribute to lateral growth. Indeed, a diameter “step” is observed for InAs nanowire growth with high precursor flows (where tapering is significant); above this step, no tapering is observed (this is reported in Paper I). The length of the untapered region is observed to increase with temperature, corresponding to an increase in diffusion length with temperature (see Paper IV). If lateral growth rate is otherwise unaffected by temperature, the observed decrease in lateral growth may represent an increase in competition for material. This may also be an alternative explanation for the increase in axial growth rate with temperature for low V/III ratios.

3.7 Axial Heterostructure Nanowires Once a thorough understanding of the growth of homogeneous III-V nanowires has been attained, it is of interest to investigate the growth of heterostructure nanowires. Such structures can be prepared in two ways. First, axial structures can be formed by varying the composition in the growth direction during growth. Second, lateral structures, also known as core-shell structures, can be formed. In the lateral case, heterostructures are achieved by first growing nanowires by conventional techniques (as described in the preceding sections), then by changing the growth parameters so that bulk growth is favoured. In this way growth on the side facets of the wire will dominate, and shells will form [129, 18]. This type of growth is generally well-understood, and will not be discussed in this thesis. The other case, axial heterostructures, will be the focus of this section.



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It has long been understood that nanowires form an ideal system for the growth of heterostructures, since mismatched materials can be grown epitaxially on each other without misfit dislocations. This is possible because, when the diameter of a structure is narrow, strain can be relieved by coherent expansion of the lattice outwards (along the wire diameter), avoiding dislocations [17]. In fact, nanowire heterostructure superlattices have been demonstrated for a variety of material systems, with lattice mismatch as high as 3% [22, 24]. Calculations have been performed to determine the degree of mismatch that can be accommodated, and the critical (maximum) diameter allowable for a given mismatch [130]. Such numbers, however, depend very much on the particular materials considered, and to a lesser degree on growth conditions and techniques, and so will not be discussed in detail here. However, the growth of epitaxial heterostructures does not depend solely on accommodation of mismatch. The interface energies between unlike materials also play a role in the resulting heterostructure morphology. In the case of epitaxial layer growth, the relevant interfaces are between the two materials, and between each of them and the surrounding medium (vapor, solution or vacuum) [131]. Before growth occurs, the substrate material is in contact with the surrounding medium. When a monolayer of the second (adsorbate) material is added, two new interfaces are introduced: that between the substrate and adsorbate, and that between the adsorbate and medium. For layer growth to occur, the chemical potential for adsorption of the new material on the substrate must be negative; from this it follows that the Gibbs free energy per unit area of adsorbed layer must decrease with the number of adsorbed atoms per unit area (n):

dndG

=μ (3.1)

For n=0, G(n) is the free energy of the bare substrate, or in other words, the interface between the substrate and surrounding medium, σs. This will tend asymptotically towards the free energy of the bulk adsorbate, α, which at large n is equal to the interface energy between the adsorbate and medium, σa (obviously, adsorbate thickness increases with n). The intercept of the asymptote is equal to the sum of the two new interfaces, adsorbate-medium and adsorbate-substrate:

ia σσα +=∞ (3.2)

Therefore, the difference between the sum of the adsorbate-medium and adsorbate substrate interface energies, and the bare substrate-medium interface, determines the growth mode:

sia σσσσ −+=Δ (3.3)

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Figure 3.4 Schematic illustration of the model describing heterostructure nucleation. The energy balance AiB σσσσ −+=Δ determines the mode of growth, where σB is the interface energy between the first material (A) and the surrounding medium/Au particle, σi is the interface energy between the second material (B) and the first (A), and σA is the interface energy between material A and the surrounding medium/Au particle. For thin film growth: (a) Δσ < 0 results in layer-by-layer heteroepitaxial growth. (b) Δσ > 0 results in island growth of B on A. For nanowire heterostructure growth: (c) Δσ < 0 results in layer formation and straight nanowire growth. (d) Δσ > 0 results in the formation of an island at the three-phase boundary, and kinked nanowire growth.

If this difference is negative (Δσ < 0), then G(n) for the adsorbed layer must tend decreasingly towards the free energy of the bulk adsorbate, and the chemical potential for layer adsorption is negative – thus, as stated above, layer growth will be favourable [132].

If, however, the sum of the two new interface energies is higher than the substrate-medium energy (Δσ > 0), then the Gibbs free energy per unit area of a uniform adsorbed layer will increase as the number of atoms per unit area increases (towards the bulk adsorbate free energy). In other words, the chemical potential will increase as the number of adsorbed atoms per unit area of substrate increase. Island growth of the adsorbate material on the substrate, rather than layer growth, will then be favorable. These two growth modes are referred to as Frank-van der Merwe and Volmer-Weber [21], and are illustrated in Figure 3.4a,b. Generally, this means that the growth of heterostructures in one interface direction is easier



40

than in the other, since the surface energy of one will generally always be lower than the other. Such considerations also play a role in the growth of axial heterostructure nanowires. During growth, the interface between the growing material and the Au particle (or other particle material) is the one of importance; surfaces in contact with the growth medium (vapour/vacuum/solution) will not be considered. When the growth material is changed (to form a heterostructure), the sum of the interface energies between the two semiconductors materials, and between the new material and the Au, must be less than the interface energy between the Au and the first semiconductor for layer growth to be favourable. If this is not the case, island formation at the three-phase boundary will be favoured, which may lead to kinked nanowire growth (Figure 3.4c,d). This is described in more detail in Paper V. In general, we have observed that for a given combination of two materials (including GaAs, GaP, InAs, InP, AlAs, Si, and Ge) it is easier to form axial heterostructures in one direction than in the other. In the “more difficult” direction, nanowires tend to kink, or to wrap around and grow backwards on themselves, when a heterostructure is introduced. This poses significant problems for the growth of straight heterostructure nanowires which contain both interface directions. However, some combinations of materials, including GaAs-GaP and InAs-InP, have very similar surface energies, and tend to grow straight. As well, kinetics will play a role, and so growth conditions may be tailored to achieve high-quality heterostructure nanowires. Finally, modification of the interface energies by the introduction of surfactants may assist in heterostructure growth [133]. For example, removal of samples with GaP nanowires to air before growth of Si and InP at the top improves the formation of layers of these materials (which normally exhibit island formation when grown on GaP).

Chapter 4

4. Design of Complex Nanostructures

4.1 Branched Nanowire Structures: Nanotrees Complex branched nanostructures formed by sequential growth of generations of nanowires represent an important step in the controlled formation of nanoscale materials. The higher degree of complexity in such structures increases the potential for applications, by increasing the number of connection points and providing a means for parallel connectivity and interconnection of functional elements. In addition, such structures facilitate studies of certain growth parameters, such as nucleation, that are difficult to study in single wires. These structures, known as nanotrees, are presented in Paper VI. The production of branched nanotree structures involves at least two sequential nanowire growth steps, each of which uses metal nanoparticles to seed the wires. The first step in this process is the production of metal nanoparticles and their deposition onto the desired substrate, as described in section 2.4. Following the deposition of metal seed particles, semiconductor nanowires are grown from the deposited particles (Figures 4.1a). If the technique used for growing the wires allows for a constant growth rate, the wires will also have a narrow length distribution, and average length can be selected under constant experimental conditions by choosing the growth time. Under most conditions, the preferred growth directions of semiconductor nanowires are the <111>B directions (or the equivalent hexagonal [000 1 ] direction), so the use of (111)B substrates allows for the growth of nanowires aligned normal to the substrate. Following the growth of nanowire trunks with controlled length and diameter, a second set of metal nanoparticles is deposited onto these first-generation wires (Figure 4.1b) to serve as seeds for nanowire branches. Typically the diameter of subsequent sets of particles is smaller than that of the previous set. For all experiments presented here aerosol-phase nanoparticles were deposited, as they

42 Chapter 4: Design of Complex Nanostructures


Figure 4.1 Nanotree production process. (a) Nanowire trunks are grown by the process described in Chapter 2. (b) A second set of Au particles is deposited onto trunks. (c) Nanowire branches are grown by same growth procedure as trunks. can easily be distributed evenly over the first-generation (“trunk”) nanowires. A second MOVPE growth stage is then initiated, yielding second-generation nanowires branching off of the trunks (Figure 4.1c). This process is in principle limitless, and many subsequent generations of branching could in theory be produced. No more than three generations, however, are presented anywhere in this work. The resulting morphology of branched nanowire structure depends on the crystal structure of the grown material. All of the III-V materials discussed in this work exhibit zincblende structure in the bulk. This is a modified fcc structure with two atoms per lattice point (which can also be interpreted as two interpenetrating fcc lattices). In the <111> directions (of which <111>A denotes a group-III terminated surface and <111>B denotes a group-V terminated surface, for III-V materials), the structure is characterized by atomic bilayers with a hexagonal 2D structure stacked in three consecutive orientations (known as ABCABC stacking, see Figure 4.2a). When growing in this direction, however, the stacking sequence can be very easily modified (by kinetics) such that, for example, a B-type layer is followed by another A layer, rather than C. The closely related wurtzite structure is a hexagonal-type lattice which is characterized by hexagonal 2D layers identical to those in the zincblende structure, but stacked in only two alternating orientations (known as ABAB stacking, see Figure 4.2b). This direction is, however, the primary direction in this cell and labeled [0001] (or [000 1 ], which for binary materials such as III-Vs denotes terminated by the higher-index, such as group-V, material). Clearly, variations in the stacking sequence as the structures grow (known as stacking faults) can result in an intermixing of the two structures. Stacking faults are very common in III-V nanowire growth, and thus a mix of wurtzite and zincblende structures is usually observed. Generally, the zincblende structure dominates, but for InAs, wurtzite dominates under most growth conditions (note that this is not observed in bulk). Nanotrees grown from GaP, GaAs or InP, therefore, exhibit structure composed primarily of zincblende. In this structure, there are four equivalent <111>B directions, three of which are oriented downwards 109o from the original (trunk)

Section 4.1: Branched Nanowire Structures

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Figure 4.2 Atomic model of three layers of group III and group V atoms, in (a) the <111> direction in the zincblende structure, and (b) the [0001] direction in the wurtzite structure. Note that the first two layers are the same in the two structures, but while the third layer in wurtzite repeats the first layer (ABAB stacking), zincblende has a unique third layer before repeating the sequence (ABCABC stacking). Group-III atoms in the row designated “A” are yellow, those in row “B” are green, and those in row “C” are orange. Group-V atoms in all rows are blue. growth direction. Branches are thus observed to grow in these directions. Stacking faults from the original trunk are carried out into the branches, until this becomes incompatible with the growth direction. At this point a single crystalline section grows, followed by stacking faults perpendicular to the branch growth direction. Stacking faults in the trunk also serve to reverse the relative positions of the side facets (during growth), so six branch directions downwards from the trunk are observed when stacking faults are present. GaP nanotrees are illustrated in Figure 4.3. InAs nanotrees, however, exhibit somewhat different morphology. The hexagonal cell does not have four equivalent directions related to the [000 1 ]; this direction is in fact unique (but similar of course to the opposing [0001]). Therefore branches growing outwards from the trunk grow in the next-favoured direction, which is found to be [ 1 100], perpendicular to the trunk growth. Furthermore, there are six equivalent [ 1 100] directions, so stacking faults are not necessary for six branch directions to be observed. Finally, since branches grow perpendicular to the trunk, stacking faults in the trunk are carried out into the branches for their entire length. The growth behaviour of nanotrees is in principle equivalent to ordinary particle-assisted growth, and generally follows the trends discussed in the previous chapters. Certain special issues apply, however. For example, nanowire branches are typically much more densely spaced than are trunks, making proximity effects (as discussed in 3.6) much more important. Also, since branches grow at varying distances from the substrate, the collection area can vary with position, resulting in



Figure 4.3 Scanning electron microscopy (SEM) images of GaP nanotrees. (a) Single nanotree viewed at 45o from the surface normal. (b) Overview of nano-“forest” viewed at 30 degrees from the surface normal. (c) Nano-forest viewed from above. The six branch directions observed indicate the presence of stacking faults perpendicular to the trunk growth. a height dependence of growth rate (this has been observed for InAs). A special issue also for InAs is that branches grow in different crystallographic directions than trunks, and thus have different growth rates. The special growth behaviour of branched nanotree structures has been investigated in detail (in Papers XIV and XVI, not included in this thesis), but will not be discussed here.

4.2 Heterostructure Nanotrees The formation of branched nanostructures composed of multiple materials may be important for the applications of these structures. The incorporation of heterostructures into various levels of branching is an important step. This has been demonstrated for GaAsP segments inserted into the branches of GaP nanotrees. These segments have been shown to emit light at energies corresponding to the tunable composition of the GaAsP segment (Figure 4.4a). The growth of mismatched branches on nanowire trunks represents another type of heterostructure which may be of interest for device applications. This growth poses similar challenges to that of axial heterostructures – specifically, the balance of interface energies must be favourable for straight branch growth to occur. If this is not the case, island nucleation from particles on the side facets of nanowires will occur. In this situation, the particle will stay in contact with the trunk nanowire, and will be pushed along its surface as the “branch” nanowire grows. This will result in “crawling” nanowires growing along the surface of the original structure. Such behaviour has been demonstrated for InP nanowire branches growing on GaP nanowires (Figure 4.4b) (Paper V). Si branches grown on GaAs nanowires and Ge branches on GaP nanowires exhibit crawling morphology as well. It is noted that

Section 4.2: Heterostructure Nanotrees

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Figure 4.4 Heterostructure nanotrees. (a) Scanning TEM dark-field image of a GaP nanotrees containing segments of GaAsP in the branches (lighter in contrast). (b) SEM image of InP branches grown on GaP trunks. Note that branches wrap around the trunks rather than growing outwards from them. Previous investigation has shown that these “crawling” branches grow epitaxially on the GaP surface. Note, as well, that second-generation InP wires on the substrate also crawl. (c) SEM image of GaP branches on InP trunks. Unlike the branches shown in (b), GaP branches lift off and grow outwards from the trunk. Second-generation wires on the substrate also grow upwards (perpendicular to, and thus epitaxially from, the substrate). (d) TEM image of Si branches grown on a GaP trunk. The branches grow outwards perpendicular to the trunk. these two systems have approximately the same mismatch, but in different directions, indicating that mismatch direction is not responsible for this behaviour. On the other hand, GaP readily forms layers beneath Au particles on InP nanowires (see section 3.7), and therefore it is possible to form GaP nanowire branches on InP nanowires as well (Figure 4.4c). Obviously, the mismatch in this case is identical to that of InP on GaP, demonstrating that the magnitude of the mismatch is also not responsible for the crawling behaviour. Finally, we have also observed that Si nanowire branches grown on GaP exhibit straight morphology (Figure 4.4d). This is surprising given the results for axial heterostructure nanowires, which indicate that the Si-GaP interface is straight, but that the GaP-Si one is not. This may be related to the role of oxygen as a surfactant – branched nanostructures are always formed by the removal of trunk nanowires into air for deposition of a second set of Au particles, before the second growth stage. The thin oxide layer that forms on the surface may act as a surfactant for branch growth. By contrast, Si nanowires removed to air oxidize very significantly, and so GaP branches grown on Si nanowires grow nonepitaxially on top of a thick SiO2 layer. On the other hand, we have also observed the growth of a thin (< 5 nm) shell of Si grow on the side facets of a GaP nanowire during branch growth (of about 20 minutes). If this shell grows at a continuous rate, a 2-3 nm Si shell will already exist before the initiation of branch growth, which is observed to have an incubation time of about 10 minutes. This would mean that Si branches grow on top of a Si shell, and therefore would not be expected to crawl.



4.3 Au-In Particles for Reduced Particle-wire Interaction The degree to which Au particles interact with In-containing III-V substrates at elevated temperatures (see section 3.4) considerably limits the control we have over the nanowire morphology. This poses problems for the growth of InP and InAs nanotrees: Au particles deposited onto trunk nanowires interact so that growth of straight, properly oriented nanowire branches is difficult to achieve. Control of the Au-InP and Au-InAs interactions, therefore, is necessary to obtain control of nanowire branch growth. We have demonstrated that the addition of In to the Au seed particles before growth greatly improves the morphology of InAs nanowire branches. Details of this process are described in Paper VII. The improved growth can be understood by considering the interaction between the seed particles and the InAs nanowire trunks. We have reported previously that Au particles interact with InP and InAs substrates until a temperature-dependent equilibrium composition is reached, and that this effect is very significant when those substrates are actually trunk nanowires (see Paper II). When samples are annealed above growth temperature, no branch growth is observed, and the trunks themselves are observed to be “eaten away” by the Au particles. When no anneal step is performed, and samples are heated directly to growth temperature, it is possible to grow branches, but they are not as straight and rod-like as branches on GaP or GaAs trunks. This is a particular problem for InAs. Since Au interacts more readily with InAs than with GaP and GaAs, it is clear that this interaction hinders the growth of nanowires. The addition of In to the Au seed particles during particle production should limit the interaction between the substrate/trunk nanowires and the seed particles. Kinetic barriers limit the degree to which Au and InAs interact at low temperatures; as the temperature is raised, interaction proceeds only until equilibrium between the InAs and the Au-In alloy is reached [116]. We have previously reported that particles must contain 25-30 at. % In (γ phase) to be stable in contact with InAs, at least up to about 500 oC. Thus, by adding In to the particles during production, less In from the substrate/trunks needs to be incorporated to stabilize the particle under growth conditions. Any additional In present (particularly in samples with nominal In composition greater than 30 at. %) may evaporate, become incorporated into the nanowire, or be deposited onto the substrate. However, significant improvement in trunk nanowire morphology was not observed when using Au-In particles. This is not surprising since the substrate was not significantly damaged even when pure Au particles were used, providing the temperature was low enough. We have previously attributed this difference between trunks and branches to the smaller particle size (higher surface reactivity) and much higher surface density (10-20 times more) of Au particles for branches.

Section 4.3: Au-In Particles for Reduced Particle-wire Interaction

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As well, it is noted that while trunk nanowires nucleate on the zinc blende (111)B substrate, branches nucleate on wurtzite ( 1 100) trunk side facets. Wurtzite-structure InAs has only rarely been observed, and so the interaction of Au with such facets is unknown; it may in fact be much greater than that with the zinc blende (111)B surface.

4.4 Height Control of Nanotree Branches For device applications further control of nanowire structure may be important, including better control of the position of branching points on a nanotree. The distribution of Au aerosol nanoparticles on vertical nanowires depends on the electric field under which they are deposited, the diameter of the deposited particles, wire (trunk) parameters including diameter, length, and interwire spacing, and forces acting between the particles and trunks. The effect of these parameters on the resulting particle (and thus branch) distribution has been thoroughly investigated (reported in Paper XIX, not included in this thesis) and will not be discussed further here. For device applications, however, more precise control of the height of branching points may be desired. It is possible to position the height of Au nanoparticle-assisted branching points on vertically aligned nanowires. This is achieved by masking the lower portion of the vertical nanowires to a desired height with a spun-on polymer; we have demonstrated this using polymethyl methacrylate (PMMA). Au aerosol nanoparticles are then deposited onto the entire sample. Following this the PMMA layer is dissolved, leaving nanoparticles only on the unmasked area of the vertical nanowires. Since branching only occurs where Au particles have been deposited, the position of these sites on the trunks is thus selected. By varying the concentration of the initial PMMA solution and the rotation frequency at which is it spun on, it is possible to controllably choose the thickness of the polymer mask. First generation nanowires (trunks) are grown by conventional techniques described elsewhere (Figure 4.5a,b). After removing the samples from the MOVPE chamber, a drop of PMMA solution was applied. Samples are then baked to polymerize the PMMA layer. This step is illustrated in Figure 4.5c. A second set of Au particles can then be deposited onto the samples with vertical nanowires and PMMA mask (Figure 4.5d). Following Au particle deposition, the PMMA mask layer is lifted off by dissolution in acetone and cleaning in isopropanol. Figure 4.5e shows the sample after the removal of the PMMA layer. The final step is the growth of position-controlled branches by MOVPE. Typically branch growth conditions are the same as for trunk growth, but this need not be the case. Figure 4.5f shows a sketch



Figure 4.5 Schematic illustration of the process for producing position-controlled nanowire branches on first-generation trunk nanowires. (a) Au aerosol nanoparticles are deposited onto a (111)B substrate by electrostatic precipitation. (b) Epitaxial nanowires are grown from these Au seed particles, normal to the substrate in the [111]B direction. (c). A layer of polymer is spun onto the sample, burying the nanowires to the desired height. (d) A second set of Au aerosol nanoparticles is deposited onto the sample. (e) The polymer layer is removed, taking with it any nanoparticles that did not land on the upper (unmasked) part of the nanowires. (f) A second nanowire growth stage is initiated, producing second-generation nanowires (branches) at defined angles to the first-generation nanowires (usually the <111>B directions). of the sample after growth of position-controlled branches. We have demonstrated this technique for nanotrees composed purely of GaP grown by MOVPE, but it is not fundamentally material dependent. To produce a second set of height-controlled branches, a second PMMA layer may be deposited onto the nanotree sample, at a height that covered the first generation of branches. The second set of branches can then be produced exactly as before, by Au particle deposition, PMMA liftoff, and MOVPE growth.

4.5 Position-control of Nanowires and Nanotrees Although most of the results in this thesis involve nanowires randomly distributed over a substrate, ordered arrays of nanowires and nanotrees can be also produced (Figure 4.6). To achieve this, nanowires are seeded by lithographically-produced arrays of gold particles; electron beam lithography (EBL) is the most common

Section 4.5: Nanowire Networks

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Figure 4.6 Fabrication of Au particles by electron beam lithography (EBL), metallization and liftoff. (a) The substrate is cleaned, before deposition of a polymer resist. (b) The polymer resist is exposed to an electron beam in a desired pattern, and then the exposed resist is dissolved to form holes. (c) A layer of Au is deposited over the surface. (d) The polymer is dissolved, removing with it all deposited Au except that in the EBL-defined holes. means of achieving these particles, but nanoimprint lithography (NIL) can also be used for large-scale production of patterned samples [26]. After position-controlled nanowires have been produced, branch growth can be achieved using exactly the same procedure as for random distribution. Positioning of nanowires in defined patterns allows for the study of such factors as growth directions and diffusion effects, and offers the possibility for device applications. The process is illustrated in Figure 4.6. Substrates are first cleaned sequentially by acetone and isopropanol. Following this a thin layer of PMMA photoresist is added by spin-on deposition, and baked. The pattern of dots is then defined, typically by EBL. The EBL-defined pattern is next developed in methyl isobutyl ketone (MIBK) and rinsed in isopropanol (IPA), and samples are briefly treated with oxygen plasma to remove any resist residues from the exposed areas. After plasma treatment the samples are etched in hydrofluoric acid to remove surface oxide, and immediately transferred to a vacuum chamber where a thin Au film is deposited by thermal evaporation. Metal lift-off is achieved by dissolution of the photoresist layer in hot acetone, followed by rinsing in hot IPA. This process results in an oriented pattern of Au particles. After the fabrication of Au particles, growth by MOVPE is performed following the same process described throughout this work. It is expected that all results described in this work can be easily extended to ordered nanotree arrays; we have chosen to use aerosol seeds for the trunks for most nanotree studies, as they are quicker and easier to produce. Growth results lithographically-seeded nanotrees typically coincide with those achieved using aerosol particles, but systematic study of any differences has not been undertaken.



Figure 4.7 Schematic illustration of the procedure for producing interconnected nanowire networks. (a) Top view of InP (111)B sample with position-controlled InAs nanowires, seeded with lithographically positioned Au particles. (b) Tilted view of substrate with position-controlled InAs nanowires. Note that nanowires grow perpendicular to the (111)B substrate, in the wurtzite [000 1 ] direction. (c) Crystallographic directions in the zinc blende (cubic) cell indicated in black, with the corresponding wurtzite (hexagonal) directions indicated in blue; these directions are illustrated with respect to the top-view images (a) and (e). (d) Tilted view of sample as in (a), showing InAs nanowires after deposition of Au aerosol particles. (e) Top view of the sample after growth of branches, which followed deposition of Au aerosol particles (Figure c). (f) Tilted view of sample after growth of branches. The total number of branches shown has been reduced (compared to (e)) to make the image more clear.

4.6 Nanowire Networks When substrate position, branch height, and crystallographic growth direction of branched nanostructures can be understood or controlled, the next step is the production of increasingly complex architectures of one-dimensional components. The method discussed here presents the possibility to interconnect position-controlled epitaxial nanowires, incorporate functional elements into specified positions, and prepare the structure to be connected electrically to allow for its incorporation into more complex devices. This is achieved by combining all of the techniques described in the preceding sections to obtain optimal control over each aspect of the network design. First, position-controlled Au particles are needed, as described in the previous section. If the pattern of dots is oriented with reference to the sample edge, the crystallographic directions of the dots with respect to each other can be selected (Figure 4.7a, c). It is known that InAs nanowires grow in the [000 1 ] direction of the hexagonal cell, normal to the zincblende ( 1 1 1 ) substrate. Branches are known to grow in hexagonal < 1 100> direction, perpendicular to the nanowire trunks. Zincblende substrates are known to cleave along { 1 10} directions, which are the lowest-energy nonpolar surfaces. As can be seen in the figure, the < 1 100>

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growth directions are parallel to the substrate side facets (perpendicular to the < 1 10> directions), allowing for easy alignment of positioned Au particles with respect to the side facets. Following the production of position-controlled Au particles, nanowires are grown by MOVPE, as described earlier in this thesis (Figure 4.7b). For the growth of branches, aerosol nanoparticles are used (Figure 4.7d). To achieve optimal branch growth, Au-In binary particles are used, as in section 4.3 These particles will typically distribute over the wires and substrate, which may be prevented by masking the substrate with a thin polymer layer before growth. Branch height control may also be achieved with this technique, as described in section 4.4. Branch growth then proceeds by the usual technique described earlier in this chapter. If the positions of the trunk nanowires have been properly aligned, branches will grow towards neighbouring trunks and connect with them, yielding interconnected nanowire structures (Figure 4.7e,f). This technique has been demonstrated for pure InAs nanowires, but is not in principle material-dependent. Different materials could be used, including heterostructures incorporated into various positions in the branched structures. With proper development of heterostructure nanotrees, levels of branches may also be composed of entirely different materials, maximizing the potential for functional devices.

Outlook The understanding of the growth of one-dimensional nanowires using seed particles has advanced tremendously in the past decade, and particularly in the last few years. Wire growth has been demonstrated in a huge variety of material systems, using various growth techniques. Consistent explanations have been proposed for many of these systems. However, to date there is no cohesive model that can explain all types of particle-assisted nanowire growth, regardless of the growth technique, phase of the source material, or phase of the particle. Such a general model should not only be applicable to the huge variety of results already demonstrated, but should be predictive in terms of the expected growth behaviour for different materials systems. The next step will be to move beyond fundamental science, towards applications of nanowires in functional devices. A variety of prototypical components have been demonstrated, as discussed in Chapter 1 of this thesis. However, extensive processing and development will be required to make such applications profitable. This still leaves much to be done from a materials science perspective. More material flexibility would be greatly advantageous, for example in the development of semiconductor doping sources and novel heterostructures. The development of nanowire growth in directions other than <111>B (already demonstrated for selected systems) would be advantageous to many applications. As well, it is of great interest to find a particle material to replace Au, without sacrificing controlled morphology for a large variety of materials. To date, such development has largely followed a trial-and-error approach, as it is not clear which materials will work well in combination with which others, and under which growth conditions. It is hoped that a more consistent and predictive model of particle-assisted growth will allow for more informed choices and more efficient realization of device requirements.

Appendix Structural Phases, Phase Equilibria and Phase Diagrams The term “phase” refers to a distinct identifiable state of matter in which a given substance may exist [134]. The structure of a material phase is determined by the stable arrangement of the atoms under a given set of parameters, including composition, pressure and temperature, and serves to determine its physical and chemical properties. Solid phases of a given composition can have an ordered atomic arrangement (crystals or crystalline materials) or a random, disordered arrangement (glasses). Liquid and gaseous phases of a material typically have a disordered arrangement. The maximum number of phases that may be present at equilibrium for a given material is determined by the Gibbs Phase Rule. This states that the number of phases plus the number of degrees of freedom is equal to the number of components (types of atoms) plus two (accounting for temperature and pressure): P + F = C +2 (A.1) For the simplest case of a one-component (unary) system, such as a simple atomic metal, at an arbitrary temperature and pressure, the number of components is one, and the number of degrees of freedom is two (pressure and temperature), so the number of phases coexisting in equilibrium is one. However, two phases of a unary material (such as liquid and solid), may coexist under a specific temperature and pressure range, where a variation in temperature must be accompanied by an appropriate change in pressure. In other words, by reducing the number of degrees of freedom, the number of phases that coexist in equilibrium can be increased. It is also possible in a unary system for three phases (for example solid, liquid and gas) to coexist if the number of degrees of freedom is reduced to zero. That is, both pressure and temperature must be specified exactly. For many materials, four or more phases may exist. For example, carbon has two stable bulk solid forms (for different pressure ranges): graphite and diamond. Additionally, liquid and gaseous states exist. It is not, however, possible for four phases to coexist at equilibrium.

Appendix


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Figure A.1 Simple one-component (unary) phase diagram, for a system exhibiting only one solid phase. Phase transitions are indicated. Point T is the triple point, where solid, liquid and vapour coexist. Point C is the critical point, beyond which liquid and vapour are indistinguishable. The structural phases existing at equilibrium over a given parameter range can be illustrated by use of a phase diagram. For a unary system, which has only two parameters (degrees of freedom), the phase diagram will have only two dimensions and can easily be illustrated on paper. An example of a simple unary phase diagram consisting of solid, liquid, and gaseous phases is illustrated in Figure A.1. A phase diagram is assessed for a closed system, meaning that phases are not removed as they form. This is particularly important for gaseous phases, which may easily escape. If components are removed as they form, equilibrium will never be reached, and the phase diagram does not have meaning. It should be emphasized that phase equilibria and phase diagrams are determined only by thermodynamics; that is, they describe only the equilibrium situation. Transitions between phases, such as melting and vapourization (as illustrated in Figure A.1), are governed by kinetics. Thus, phases may persist long after parameters have been changed such that the phase equilibrium changes, if the rate of conversion between phases is slow. Such phases are known as metastable phases. This phenomenon is particularly important during conversion between two solid phases of different structure. For example, diamond, which is formed under very high pressures under the surface of the Earth, is metastable at pressures even far above atmospheric pressure. Nevertheless, diamond persists for millions of years at atmospheric pressure. The addition of a second component increases the number of degrees of freedom by one (the relative composition of the structure). A phase diagram for a two-

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component (binary) system thus has three dimensions. It is usually most instructive to consider “slices” of the phase diagram where one parameter is held constant. For example, if composition is held constant, a diagram similar to Figure A.1 may be drawn. Such a diagram is considered “pseudo-unary” if the two components form a unit that does not change over the parameter range illustrated. For example, a pseudo-unary phase diagram can be drawn for water, which exhibits three phases (solid, liquid, and gaseous) with the same stoichiometric component. However, at very high temperatures, water will separate to form molecular hydrogen and oxygen. At this point the pseudo-unary phase diagram no longer has meaning. More common are binary phase diagrams where pressure is held constant (isobaric phase diagrams), since most work with two-component systems has been performed at standard (atmospheric) pressure. Several types of phases exist in a two-component system. The most common are solutions, which may exist as solid, liquid, or gaseous phases. In such phases, composition is not fixed, but forms a stable range over a given temperature. Similarly, solutions are normally stable over a broad range of temperatures. Most materials exhibit full solubility in the gas phase, while solubility in liquid and solid phases may be limited. Liquid metals typically are continuously soluble (over the entire compositional range between the two pure materials), but may exhibit a solubility gap for intermediate compositions if they are very different in atomic size. Solid solubility is typically continuous for materials that have very similar crystal structure and atomic size. More dissimilar material may exhibit limited solid solubility, with a gap for intermediate compositions, while very dissimilar materials may have extremely limited (negligible) solid solubility. Unlike pure materials, which melt and freeze congruently, solid and liquid solutions melt and freeze over a range of temperatures, giving rise to a two-phase region in the phase diagram (bound by lines known as liquidus and solidus). Two materials with limited solubility may also form compounds, which are congruently-melting solid phases with fixed stoichiometry. This phase will typically have a different crystal structure than the two pure solids. In some cases, intermediate phases may also form that are similar to compounds, but exhibit a range of composition and melt incongruently. Intermediate phases and compounds formed from two metallic compounds tend not to have metallic properties. Congruently melting intermediate phases (compounds) serve to divide a complicated isobaric binary phase diagram into simpler sub-systems. When two materials exhibit limited solid solubility but continuous liquid solubility, they may exhibit three-phase reactions. This is possible because, when the vapour pressures of two materials are very low, it is possible to ignore pressure as a degree of freedom for an isobaric phase investigation (this will not always be appropriate, as will be discussed below). This means that two phases can coexist in

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Figure A.2 Simple eutectic phase diagram for the binary system A-B. The A-rich solid solution is labeled α, while the B-rich solid solution is β. TA represents the melting point of component A, TB the melting point of B, and Te the eutectic melting point. equilibrium over a range of temperature and composition (resulting in incongruent melting/freezing, as described above), and that three phases may coexist at temperature-composition combinations. This means that a liquid phase may coexist with two solid phases at a unique temperature over the compositional range through which the two solids are mutually insoluble. The reactions by which compounds are formed in such systems generally fall into two categories: eutectic and peritectic. Eutectic reactions typically occur when the melting points of the two components (or compounds) are similar. In this case, the liquidus exhibits a sharply-defined minimum at an intermediate composition, known as the eutectic point (eutectic temperature, eutectic composition). When a liquid alloy composed of two components, A and B, is cooled below the liquidus, it will precipitate solid solution rich in A, labeled α (if the composition is on the side of the eutectic closer to A) or rich in B, labeled β (if it is on the side closer to B). The composition of the liquid alloy will thus change as the temperature is lowered, moving closer to the eutectic composition. The eutectic composition will be reached at the eutectic temperature. At this point, both solid solutions will precipitate, with their relative compositions determined by the eutectic composition. A simple eutectic system is shown in Figure A.2.


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Figure A.3 Simple peritectic phase diagram for the binary system A-B. The A-rich solid solution is labeled α, while the B-rich solid solution is β. TA represents the melting point of component A, and TB the melting point of B. When the two components in a binary system have very different melting points, a peritectic reaction is more likely. For such a system, the minimum of the liquidus will typically be the lower-melting pure component. A liquid alloy of peritectic composition will precipitate A-rich solid solution upon cooling below the liquidus (where A is the higher-melting component) until the peritectic temperature is reached, at which point the remaining liquid will react with the precipitated A-rich solid solution (α) to transform it into B-rich solid solution (β). A melt containing more of component A than the peritectic composition will proceed similarly, except that some α solution will remain after the peritectic reaction. If the composition is more B-rich than the peritectic composition, then the reaction between the α and the liquid will not consume the liquid, which will continue to precipitate β solution as it cools. Such a system is illustrated in Figure A.3. Complex systems exhibiting many solid phases will typically exhibit several eutectic and/or peritectic points (as noted above, if congruently-melting compounds are formed, the system can be subdivided for simpler interpretation). In addition, solid-phase reactions may occur. These include the eutectoid reaction, which is analogous to the eutectic reaction, but involves the precipitation of two solid phases at a unique temperature from a third solid phase. As well, there exists a peritectoid reaction, in which one solid phase will precipitate another while cooling, but then react with it to produce a third solid phase.

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The addition of a third component (atom type) further complicates the situation. Such ternary systems have four degrees of freedom: temperature, pressure, and the relative composition of the three components with respect to each other. The relative compositions are of course not independent of each other, because the total composition must add up to 1 (or 100%). Nevertheless, four dimensions are necessary to fully illustrate an entire ternary phase diagram. Obviously, this is never actually attempted. The composition of the system is typically illustrated by a triangle bound at each corner by the three components. Temperature represents the third dimension, upwards from the triangle. In principle pressure represents a fourth dimension, but in practice, investigations of the pressure dependence of ternary systems are extremely rare. As noted above, when the vapour pressures of materials are small, pressure can be eliminated as a degree of freedom from isobaric diagrams. Sections of ternary phase diagrams are typically illustrated either as isothermal slices, or as constant composition slices. Constant composition slices resemble isobaric binary phase diagrams, but show the compositional range between two binary compositions; typically this does not have meaning unless the binary compositions represent congruent phases (one of which may be a pure elemental phase). Such a system is referred to as “pseudo-binary” if the two binary phases can be treated as units, and thus do not alter their stoichiometry when interacting with each other. When a constant composition ternary slice is not pseudobinary, the diagram becomes more complicated, and the phases present will depend on the process by which the investigation was made (such as cooling route). Isothermal ternary phase diagrams have primarily been investigated at room temperature. Typically, in such cases, only solid phases exist. Lines join pseudobinary combinations (where only two phases coexist over a compositional range) while ternary phases may occupy compositional ranges in the middle of the diagram. Up to three phases may coexist in equilibrium (and typically do in the absence of ternary phases). At higher temperatures, liquid phases may also be present over certain compositional ranges, giving rise to ranges where liquid and solid phases coexist. It should be emphasized once again that all phase diagrams represent only the equilibrium phases that coexist under a given parameter range. Such systems are typically investigated by forming melts of a particular composition, and investigating the phases that form upon slow cooling. Kinetics may significantly affect the phases that are observed, giving rise to metastable phases that persist under nonequilibrium conditions. In particular, transformations between solid phases may be very slow, which is of particular importance as the number of components in a system increases. Additionally, the processes of melting and freezing may be kinetically hindered, resulting in undercooled liquids and


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element atomic number

atomic mass

atomic radius

lattice structure

lattice constant

melting point

boiling point density

Al 13 26.98 1.43 fcc 4.05 660 2519 2700 As 33 74.92 1.39 rhomb. 4.13 817 603 5730 Au 79 196.97 1.46 fcc 4.08 1064 2856 19320 Ga 31 69.72 1.41 ortho. 4.51 29.7 2204 5910 Ge 32 72.59 1.37 diamond 5.66 938 2833 5323 In 49 114.82 1.66 tetragonal 4.59 156 2072 7310 P 15 30.97 1.28 cubic 7.17 44 280 1820 Si 14 28.09 1.32 diamond 5.43 1414 3265 2330 Table A.1: Physical properties of selected elements. Atomic mass is measured in amu, atomic radius and lattice constant in Å, melting and boiling points in oC, and density (of the solid at 298 K) in kg/m3. Note that properties of phosphorus are for white phosphorus, and those of arsenic for grey arsenic. The “boiling point” indicated for arsenic is the sublimation point, while the “melting point” is measured at 28 atm. superheated solids; this process occurs primarily in systems of very small volume, such as nanostructures [134]. A summary of some of the systems relevant to the work described in this thesis follows here. The vast majority of binary systems for any given two elements have been investigated, at least for standard pressure and for temperature ranges where vapour pressure need not be considered. Compilations of binary phase diagrams have been published by a variety of authors and organizations [67]. Most of the information presented below is based on the Landolt-Börnstein [135], which is particularly useful for its regularly-updated online content [136]. Since the investigation of ternary phase equilibria is much more complicated, and vastly more material combinations exist, a much smaller subsection of ternary systems has been investigated. Typically, room-temperature isothermal slices have been investigated, and less often higher-temperature slices [137]. Even more rarely, constant compositional slices have been investigated, most often for important pseudobinary systems. For the sake of brevity, the details of the investigations leading to the assessed phase diagrams will not be discussed here; details can be found in the references above. Only isobaric diagrams are discussed, although for the cases of As and P, the vapour pressures are quite high at moderate temperature, and care must be taken when interpreting the phase diagrams. Physical properties of the various elements discussed are listed in Table A.1. The Au-Si system is one of the most well-investigated binary systems; it is also one of the simplest. This system is a simple eutectic, exhibiting a eutectic point at 363 oC and 18.6 atomic % Si. There is very low solid solubility for both elements, with maxima less than 2 at. % on both sides. The Au-Ge system is very similar,

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exhibiting a eutectic point at 361 oC and 28 at. % Ge. The maximum solubility of Ge in Au is about 3 at. %, while the maximum solubility of Au in Ge is less than 1 at. %. The systems Au-Ga, Au-In and Au-Al are more complicated, since binary compounds and intermediate phases form for all of these systems. Additionally, the very dissimilar melting points for the first two systems complicate things. The Au-Ga system exhibits two congruently melting binary compounds (AuGa and AuGa2) exhibiting intermediate melting points, which form a eutectic subsystem. Additionally, several incongruently-melting intermediate phases form (all Au-rich). The solid solubility maximum for Ga in Au is 12.4 at. % (at 415 oC); there is no solubility of Au in Ga. In total this system exhibits three eutectic points, two peritectic points, and two eutectoid points. The liquidus minimum is pure Ga, followed by the eutectic between AuGa and the intermediate phase γ (at 339 oC, 34 at. % Ga). The Au-In system is similar but somewhat more complicated. Again, two congruently melting compounds, AuIn and AuIn2, exist, with melting points intermediate between Au and In. Also, there are numerous intermediate phases. One of these, φ, is not stable at room temperature. There is considerable solid solubility of In in Au, associated with structural changes that divide it into three distinct phases. The maximum solubility of In in the primary solid solution is 12.7 at. %; the solubility in the ζ phase is 23 at. %. There may be trace solubility of Au in In, although this is not well investigated. In total the system exhibits four eutectic points, four peritectic points, three eutectoid points, and three peritectoid points. The liquidus minimum is the In-rich eutectic, at 99.8 at. % In, 0.5 K below the In melting point. The Au-Al system includes a large number of intermediate phases with compositional variation; one of these, Al2Au, melts congruently (close to the melting point of pure Au). The system exhibits three eutectic points and two peritectic points. The solubility of Al in solid Au is 16 at. %; there is negligible solubility of Au in Al. The liquidus minimum is the lowest eutectic (at 525 oC and 20 at. % Au), which lies between the phases Al2Au5 and AlAu4. The system Au-As is complicated by the high vapour pressure of As; the sublimation point at atmospheric pressure is 603 oC, while the melting point of As under its own vapour pressure is 817 oC (pressure around 28 atm). The assessed Au-As phase diagram, therefore, cannot be determined for constant pressure, but for a closed system under the equilibrium vapour pressure of As. The system exhibits a eutectic melting point at 636 oC and 56.5 at. % Au. The solubility in both solids is negligible.


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Similarly, the Au-P is complicated by very high vapour pressure, as well as multiple structural phases, of P. The boiling point of the most common (“white”) solid phase of P is 280 oC, allowing for very little intermixing between Au and P. There is very limited liquid solubility at temperature above 935 oC and lower than 12.8 at. % P. Two metastable binary phases have been reported, AuP and Au2P3, although the stability range of these compounds is not clear. The As-P system is peritectic, with one intermediate phase (AsP) of broad composition, and significant solid solubility (20 at. % P in As, 30 at. % As in P). There are two peritectic points dividing the three phases (As, AsP, P). The Al-Ga system is simple eutectic, with eutectic temperature at 26 oC and 97.9 at. % Ga. The maximum solid solubility of Ga in Al is 9 at. %. The Ga-In system is similar, with eutectic temperature of 15 oC and 86 at. % Ga, and maximum solid solubility of Ga in In of 3 at. %. The Al-In system, on the other hand, exhibits a large liquid miscibility gap between 5 and 89 at. % In. There is a eutectic point on the Al-rich side of the miscibility gap, at 639 oC, and a peritectic point on the In-rich side. The Ga-As phase diagram exhibits a single congruently-melting intermediate phase, GaAs, with a melting point of 1240 oC, well above the melting points of the two pure phases. The Ga-P system is similar (although complicated slightly by the polytypism of P); the single intermediate phase GaP melts at 1467 oC. In-As exhibits one intermediate phase (InAs, melting at 942 oC) as well as a eutectic point at 12.5 at. % As and 731 oC. In the In-P system there is again only one intermediate phase, InP, melting at 1067 oC. Of the relevant ternary systems, the room-temperature isothermal slices of Au-Ga-As, Au-Ga-P, Au-Al-As, Au-In-As and Au-In-P have been investigated to varying degrees. No ternary intermediate phases are reported. For the first three systems, the Au-IIIV constant-composition slices are reported to be pseudobinary [100,101]. For InAs and InP, however, the corresponding Au-InAs and Au-InP compositional slices are not pseudobinary [100,106]. The pseudobinary Au-GaAs system has also been investigated [67]. Strictly speaking, this system is not a truly pseudobinary, because the considerable solubility of Ga in Au varies with temperature. However, it can be approximated as pseudobinary if the entire Au-rich solid solution is treated as a single phase, and the As released by the formation of this phase is considered negligible. This system appears to resemble a simple eutectic, with a eutectic composition of about 75 at. % Au (i.e. 12.5 at. % each Ga and As) and melting temperature around 630 oC. Very precise determination of this temperature has not been achieved. Additionally, the shape of the liquidus was investigated [67]. As expected, there is a sharp drop towards the Au-Ga binary that occurs for Ga content greater than

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25 at. % and As content less than about 2 at. %. Otherwise, the low point in the liquidus extends from the Au-Ga binary around 25 at. % Ga to the Au-As binary, near the eutectic (43.5 at. % As), with a melting point in the range of 600 oC. The ternary eutectic point (low point on the ternary liquidus) is situated very close to the Au-As eutectic (with about 5 at. % Ga), and has a melting point around 585 oC.

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