Physical Properties of Indium Nitride: a Highly Cation-Anion Mismatched Compound

Home , Indium nitride

Physical properties of indium nitride: a highly cation-anion mismatched compound

Louis Frederick John Piper

Thesis

Submitted to the University of Warwick

for the degree of

Doctor of Philosophy

Department of Physics

May 2006 Contents

Acknowledgements vii

Declarations viii

Abstract xii

Abbreviations xiii

Chapter 1 Introduction 1 1.1 Motivation for the thesis ...... 1 1.2 Organisation of the thesis ...... 3 1.3 Electronic properties of a semiconductor ...... 4 1.3.1 Deﬁnition of a semiconductor ...... 4 1.3.2 Various semiconductors ...... 5 1.3.3 Band structure approximations ...... 6 1.3.4 Carrier statistics ...... 10 1.4 Semiconductor interfaces ...... 11 1.4.1 Early studies of Schottky contacts ...... 11 1.4.2 Fermi level pinning ...... 13 1.4.3 Semiconductor free surfaces ...... 19 1.5 Space-charge calculations of free surfaces ...... 20 1.6 Summary ...... 23

Chapter 2 Experimental 25 2.1 Semiconductor surface spectroscopies ...... 25 2.2 Introduction to XPS ...... 25 2.3 Features typical of an XPS spectrum ...... 26 2.3.1 Background ...... 27 2.3.2 Core-level peaks ...... 28 2.3.3 Valence bands ...... 29

iii CONTENTS iv

2.4 Introduction to HREELS ...... 31 2.5 Semi-classical dielectric theory ...... 35 2.5.1 Program outline of HREELS of multilayers ...... 35 2.5.2 Evaluating the classical-loss probability for HREELS ...... 36 2.5.3 Dielectric functions and collective excitations ...... 37 2.5.4 HREEL simulations and Poisson-MTFA ...... 39 2.6 InN samples ...... 39 2.7 Atomic hydrogen sources ...... 42

Chapter 3 Indium arsenide 43 3.1 Surface preparation of indium arsenide ...... 43 3.1.1 Introduction ...... 43 3.1.2 Experimental details ...... 45 3.1.3 Core-level spectra ...... 45 3.1.4 Valence band spectrum ...... 47 3.1.5 Conclusion ...... 50 3.2 Space-charge proﬁles of indium arsenide ...... 50 3.2.1 Introduction ...... 50 3.3 Experimental details ...... 51 3.4 HREEL spectra ...... 52 3.5 Analysis ...... 54 3.5.1 InAs(100)-(4 2) ...... 56 × 3.5.2 InAs(110)-(1 1) ...... 57 × 3.6 Discussion ...... 59 3.7 Conclusion ...... 63

Chapter 4 Indium nitride: surface preparation 64 4.1 Introduction ...... 64 4.2 Experimental details ...... 65 4.3 XPS spectra ...... 66 4.4 Angular dependence ...... 68 4.5 HREELS ...... 70 4.6 Conclusion ...... 71 CONTENTS v

Chapter 5 Indium nitride: valence band structure 72 5.1 Introduction ...... 72 5.2 Experimental details ...... 73 5.3 Experimental results ...... 74 5.4 Comparisons with theoretical calculations ...... 78 5.5 Conclusions ...... 80

Chapter 6 Indium nitride: origin of the electron accumulation 81 6.1 Introduction ...... 81 6.2 Experimental studies of clean InN surfaces ...... 82 6.2.1 Experimental details ...... 82 6.2.2 HREEL Spectra ...... 83 6.2.3 Space-charge calculations ...... 84 6.2.4 Discussion ...... 88 6.3 Ab initio calculations of the electronic structure of InN ...... 91 6.4 Origin of the electron accumulation ...... 93 6.4.1 Chemical trends of III-V semiconductors ...... 93 6.4.2 Surface state density of InN ...... 93 6.4.3 Physical nature of the surface states ...... 94 6.4.4 Conclusion ...... 95

Chapter 7 Indium nitride: Fermi level stabilisation by low energy ion bombardment 96 7.1 Introduction ...... 96 7.2 Experimental details ...... 97 7.3 Results ...... 97 7.4 Analysis ...... 99 7.5 Conclusion ...... 101

Chapter 8 Indium nitride: origin of the high unintentional n-type conductivity 102 8.1 Introduction ...... 102 8.2 Experimental Details ...... 103 CONTENTS vi

8.3 Results ...... 104 8.4 Discussion ...... 104 8.5 Conclusion ...... 109

Chapter 9 Indium nitride: electron tunnelling spectroscopy of quantized states 110 9.1 Introduction ...... 110 9.1.1 Electron tunnelling spectroscopy ...... 110 9.1.2 Calculations of surface-bound quantized states ...... 113 9.2 Experimental details ...... 116 9.3 Experimental results ...... 117 9.4 Analysis ...... 119 9.5 Conclusion ...... 122

Chapter 10 Epilogue 123 10.1 Importance of the branch-point energy ...... 123 10.2 Indium nitride: a highly mismatched compound ...... 124

Appendix A EMRS Fall meeting 2005: the current status of InN 127

Appendix B Fermi level pinning at oxidized InN surfaces 132

Appendix C Eﬀects of the inhomogeneous electron distribution of InN 137

Bibliography 140 Acknowledgements

I would first like to thank my supervisor. I have to thank Professor Chris McConville for providing three fantastic opportunities. Firstly, he helped to organise my first summer placement at QinetiQ Ltd. Malvern; where, under the guidance of Dr. Harvey Hardaway and Dr. Tim Ashley, my interest in semiconductors began. Secondly, Chris is thanked for welcoming me into his group at the University of Warwick. I was fortunate enough to work with Dr. Tim Veal, Dr. Imran Mahboob, and Paul Jefferson. I would especially like to thank Tim for his guidance, encouragement and friendship. In retrospect, it was the excited conversations with Tim, Imran and Paul during our extended tea breaks that I enjoyed (and shall miss) the most. I would like to thank Rob Johnston for his technical help with the HREELS chamber, and Drs Danny Law and Graham Beamson for maintaining an excellent XPS facility at Daresbury. Drs Bill Schaff and Hai Lu are thanked for providing the InN samples from Cornell University, and Professor Yasushi Nanishi and Dr. Hiroyuki Naoi are also acknowledged for their high-quality samples from Ritsumeikan University. Bill is further thanked for continued interest in our group’s work. For their theoretical calculations and fruitful discussions, I would also like to thank Professor Friedhelm Bechstedt and Frank Fuchs. Thirdly, Chris has allowed me to proceed at my own pace throughout my Ph.D. and has encouraged me to publish and present my work. As a result of this approach, I have learnt valuable skills for the future, such as; writing papers; responding to referees’ reports; writing grant applications to facilities and research groups; and presenting my work at national and international conferences. I would like to thank Tim once again for his help in honing these skills. At this point I would like to thank my parents and my sisters for their love, friendship, encouragement and help. I would also like thank my friends and house-mate for putting up with me during the last two and a half years. Last but not least, I would like to thank my fiancée, Rebecca, for listening to me when I had work on my mind and for helping with the proof-checking of this thesis.

vii Declarations

I declare that this thesis contains an account of my research carried out in the Department of Physics at the University of Warwick between October 2003 and May 2006, under the supervision of Professor C. F. McConville. This research reported here has not been submitted, either wholly or in part, in this or any other academic institution for admission to a higher degree. The low-energy electron-diffraction (LEED) data from the InAs(100)-(4 2) and × InAs(110)-(1 1) surfaces, along with the high resolution electron energy-loss (HREEL) × spectra from the InAs(110)-(1 1) surface, reported in section 3.3 were taken by Dr. T. D. × Veal (University of Warwick). The HREEL spectra from the InAs(100)-(4 2) surface was × recorded by Dr. M. J. Lowe (University of Warwick). The X-ray photoemission spectra reported in section 4.4 were from measurements taken by Marc Walker (University of War- wick). The scanning electron microscopy in sections 3.2 and 5.4 was performed by Steve York and the atomic force microscopy mentioned in section 5.4 by Dr. N. R. Wilson (both, University of Warwick). The density functional theory calculations of InN in sections 5.5 and 6.4 were performed by Prof. Dr. F. Bechstedt, Frank Fuchs, and Prof. Dr. Furthmuller¨ (Friedrich-Schiller-Universität, Jena, Germany). The HREEL spectra in section 7.4 was measured by Dr. T. D. Veal and Dr. I. Mahboob (University of Warwick). The Hall measurements displayed in section 8.4 were from measurements made by Dr. W. J. Schaff and Dr. H. Lu (Cornell University, Ithaca, USA). The scanning tunnelling microscopy images and I-V spectra reported in section 9.4 were from measurements by Dr. M. H. Zareie and Dr. M. R. Philips (University of Technology, Sydney, Australia). All of the remaining data was obtained by the author. The data fitting, simulations, data analysis, and interpretation pertaining to these data was performed by the author.

Louis Frederick John Piper May 2006

viii Declaration ix

Several articles based on this research have been published.

L. F. J. Piper, T. D. Veal, C. F. McConville, H. Lu, and W. J. Schaff Origin of the n-type conductivity of InN: the role of positively-charged dislocations Appl. Phys. Lett., 88:252109, 2006. L. F. J. Piper, T. D. Veal, C. F. McConville, H. Lu, and W. J. Schaff Amphoteric defects and the origin of the high unintentional n-type conductivity of InN Phys. Stat. Sol. (c) 3:1841, 2006. L. F. J. Piper, T. D. Veal, M. J. Lowe, and C. F. McConville Electron depletion at InAs free surfaces: Doping induced acceptorlike gap states Phys. Rev. B, 73:19531, 2006. T. D. Veal, L. F. J. Piper, M. R. Phillips, M. H. Zareie, H. Lu, W. J. Schaff, and C. F. McConville

Scanning tunnelling spectroscopy of quantized electron accumulation at InxGa1−xN surfaces Phys. Stat. Sol. (a), 203:85, 2006. L. F. J. Piper, T. D. Veal, P. H. Jefferson, C. F. McConville, H. Lu, W. J. Schaff, F. Fuchs, J. Furthmuller,¨ and F. Bechstedt Valence band structure of InN from X-ray photoemission spectroscopy Phys. Rev. B, 72:245319, 2005. L. F. J. Piper, T. D. Veal, M. Walker, I. Mahboob, C. F. McConville, H. Lu, and W. J. Schaff Clean wurtzite InN surfaces prepared with atomic hydrogen J. Vac. Sci. Technol. A 23:617, 2005. L. F. J. Piper, T. D. Veal, I. Mahboob, C. F. McConville, H. Lu, and W. J. Schaff Temperature invariance of InN electron accumulation Phys. Rev. B 70:115333, 2004. T. D. Veal, L. F. J. Piper, I. Mahboob, H. Lu, W. J. Schaff, and C. F. McConville Electron accumulation at InN/AlN and InN/GaN interfaces Phys. Stat. Sol. (c) 2:2246, 2005. I. Mahboob, T. D. Veal, L. F. J. Piper, C. F. McConville, H. Lu, W. J. Schaff, J. Furthmuller,¨ and F. Bechstedt Origin of electron accumulation at wurtzite InN surfaces Phys. Rev. B 69:201307(R), 2004. T. D. Veal, I. Mahboob, L. F. J. Piper, C. F. McConville H. Lu, and W. J. Schaff Indium nitride: evidence of electron accumulation J. Vac. Sci. Technol. B, 22:2175, 2004. Declaration x

Additionally, the author has contributed to the following articles that have been published, are in press, or have been submitted.

T. D. Veal, L. F. J. Piper, C. F. McConville, and W. J. Schaff Inversion and accumulation layers at InN surfaces J. Cryst. Growth 288:268, 2006. T. D. Veal, L. F. J. Piper, P. H. Jefferson, C. F. McConville I. Mahboob, M. Hopkinson, M. Merrick, T. J. C. Hosea, and B. N. Murdin Photoluminescence spectroscopy of band gap reduction in dilute InNAs alloys Appl. Phys. Lett. 87:182114, 2005. T. D. Veal, L. F. J. Piper, S. Jollands, B. R. Bennett, P. H. Jefferson, P. A. Thomas, C. F. McConville, B. N. Murdin, L. Buckle, G. W. Smith, and T. Ashley Band gap reduction in GaNSb alloys due to the anion-mismatch Appl. Phys. Lett. 87:132101, 2005. T. D. Veal, I. Mahboob, L. F. J. Piper, T. Ashley, M. Hopkinson, and C. F. McConville Electron spectroscopy of dilute nitrides J. Phys.: Condens. Matter 16:S3201, 2004. T. D. Veal, I. Mahboob, L. F. J. Piper, C. F. McConville, and M. Hopkinson Core-level photoemission spectroscopy of nitrogen bonding in GaNAs alloys Appl. Phys. Lett. 85:1550, 2004. T. D. Veal, I. Mahboob, L. F. J. Piper, C. F. McConville, and M. Hopkinson Fuchs-Kliewer phonon excitations in GaNAs alloys J. Appl. Phys. 95:8466, 2004. P. H. Jefferson, L. F. J. Piper, T. D. Veal, C. F. McConville, B. R. Bennett, B. N. Murdin, L. Buckle, G. W. Smith, and T. Ashley

Band anti-crossing in GaNxSb1−x Appl. Phys. Lett., submitted, 2006. L. F. J. Piper, P. H. Jefferson, T. D. Veal, C. F. McConville, J. Zuńiga-P˜ érez, and V. Munoz-Sanjos˜ é Electronic structure of single-crystalline CdO(001) by X-ray photoemission spectroscopy Superlattices and Microstructures, submitted, 2006. Declaration xi

The author has presented work at the following national and international conferences, between 2003 and 2006.

Interfacial properties of ZnO and related materials (oral) European Materials Research Society (E-MRS) Spring Meeting, Nice, France. May 2006. † Indium nitride: a material for the future (poster) SET For Britain: Special Reception for Younger Physicists, Houses of Commons, London, UK. November 2005. InN explained within existing chemical trends (poster) E-MRS Fall Meeting, Warsaw, Poland. September 2005 . ‡ Valence band structure of InN from X-ray photoemission studies (oral) E-MRS Fall Meeting, Warsaw, Poland. September 2005 . ‡ Amphoteric defects and the origin of unintentional n-type conductivity of InN (oral) 6th International Conference on Nitride Semiconductors (ICNS-6), Bremen, Germany. August 2005. Extreme electron accumulation at InN surfaces for device purposes (oral) United Kingdom Nitrides Consortium (UKNC) meeting, Manchester, UK. January 2005. InN: Electron accumulation (poster) International Workshop on Nitride Semiconductors (IWNS), Pittsburgh, USA. July 2004. Temperature invariance of InN electron accumulation (poster), EMRS Spring Meeting, Strasbourg, France. May 2004.

I received the European Materials Research Society Young Scientists Award in ‘recognition of † the best paper presented during the E-MRS 2006 symposium’.

I received the European Materials Research Society and Polish Materials Science Society award ‡ in recognition of the best paper presented by a Ph.D. student at the E-MRS 2005 Fall Meeting. Abstract Recent advances in the growth of III-nitride compound semiconductors have resulted in high-quality InN becoming available. Following these improvements, native electron accumulation was directly observed at clean InN surfaces. For almost all other semiconductors an electron depletion layer is observed. As a result, InN presents an interesting material to study the physical properties which dictate the formation of the space-charge layer. Throughout this thesis, the location of the bulk Fermi level with respect to the branch- point energy (EB) - which corresponds to the cross-over from donor-like to acceptor-like surface states - is identified as an important parameter dictating the formation of the space-charge layer. This is highlighted in the first experimental chapter, where the surface of a conventional III-V compound, InAs, is studied. InAs is a narrow-gap (E 0.36 g ∼ eV) III-V compound semiconductor which exhibits native electron accumulation, allowing it to be considered as an analogue of the increasingly topical InN (E 0.64 eV). By g ∼ employing a combination of X-ray photoemission spectroscopy (XPS) and high-resolution electron energy-loss spectroscopy (HREELS), a depletion layer is observed at clean InAs surfaces when its bulk Fermi level lies above EB; the resultant upward band bending (due to negatively-charged acceptor-like surface states) ensures that the Fermi level is pinned close to EB at the surface. The remaining chapters of this thesis focus on InN. XPS and HREEL studies of clean InN(0001) reveal that the Fermi level is pinned above the conduction band minimum (CBM) at the surface. An accumulation layer is discussed in terms of the bulk Fermi level lying below the pinned surface Fermi level, with the downward band bending facilitated by positively-charged donor-like surface states. Density functional theory calculations - aided by the XPS studies of the valence band region of InN - confirm that EB lies above the CBM at the zone centre, in agreement with the location of the pinned surface Fermi level. Chemical trends suggest that the combination of the large, electropositive indium cation and small, highly electronegative nitrogen anion is responsible for the band edges lying extremely low with respect to EB at the zone centre. Other electronic properties of InN, such as the proclivity towards donor-like defects following ion bombardment, and the thickness dependence of the n-type conductivity of InN samples are also discussed in terms of the location of EB within this highly cation-anion mismatched compound.

xii Abbreviations

AAS Anion-on-cation Anti-Site defect ADM Amphoteric Defect Model AHC Atomic Hydrogen Cleaning BE Binding Energy CAICISS Co-Axial Impact Collision Ion Scattering Spectroscopy CAS Cation-on-anion Anti-Site defect CBM Conduction Band Minimum CV Capacitance-Voltage DFT Density Functional Theory EC Conduction Band Edge EV Valence Band Edge FWHM Full Width at Half Maximum HMC Highly Mismatched Compound HREELS High-Resolution Electron Energy-Loss Spectroscopy KE Kinetic Energy LDA Local Density Approximation LEED Low Energy Electron Diffraction IBA Ion Bombardment and Annealing MBE Molecular Beam Epitaxy MIGS Metal Induced Gap States MTFA Modified Thomas-Fermi Approximation RHEED Reflection High Energy Electron Diffraction SEM Scanning Electron Microscopy SIC Self-Interaction Correction SIMS Secondary Ion Mass Spectrometry

xiii Abbreviations and Common Symbols xiv

TOA Take-Oﬀ Angle UHV Ultra-High Vacuum UV Ultra-Violet UPS Ultra-violet Photoemission Spectroscopy VB-DOS Valence Band Density of States VBM Valence Band Maximum XPS X-ray Photoemission Spectroscopy XRD X-ray Diﬀraction

aB Bohr radius

α non-parabolicity parameter (1/Eg) β spatial dispersion coeﬃcient

γC plasmon-damping frequency

γp phonon damping parameter Γ centre of Brillouin zone d distance (thickness) δ deformation vibrational mode

∆SO spin-orbit splitting energy interval λ attenuation length of the photoelectrons

λT F Thomas-Fermi screening length ν stretching vibrational mode e electronic charge (1.6022 10 19 C) × − ² dielectric function ² permittivity of free space (8.854 10 12 N 1m 2C2) 0 × − − − ²(0) static dielectric constant ²( ) high frequency dielectric constant ∞ ξ eﬀective dielectric function E energy

Eb subband energy

EC (k) conduction band dispersion

EF Fermi energy Abbreviations and Common Symbols xv

EF S surface (or stabilised) Fermi level

Eg band gap at the Brillouin zone centre

E’g renormalised band gap

Ei incident electron energy E(k) energy band dispersion

Es scattered electron energy f(E) Fermi-Dirac distribution f(z) MTFA correction term g(E) density of states of the energy band ¯h Planck’s constant (1.0546 10 34Js) × − I current I(E) photoelectron ﬂux k wavevector K imaginary wavevector (k = iK) k Boltzmann’s constant (1.3807 10 23 JK 1) B × − − kF Fermi wave-vector L characteristic length of space-charge layer

mb∗ eﬀective mass of subband m electron rest mass (9.1095 10 31 kg) e × − mF electron mass at the Fermi level

m0∗ electron eﬀective mass at the CBM n free electron concentration

NA− density of acceptors 3D nbulk bulk 3D electron density + ND density of donors 2D nexcess residual charge of InN surface/interface 3D nHall Hall measured 3D electron density 3D nimp 3D electron density due to the donor impurities

nss surface state density N(ω) energy-loss spectrum Abbreviations and Common Symbols xvi

PCL(ω) classical-loss probability p eﬀective probing depth (also, electron momentum) q wavevector transfer (also, electron momentum) T absolute temperature

θi angle of incidence with respect to the surface normal µ electron mobility V potential (voltage)

Vbb band bending

vF Fermi velocity

V0 periodic (surface) potential ω frequency

ωF K Fuchs-Kliewer surface phonon frequency

ωP plasma frequency

ωSP surface plasmon frequency

ωT O transverse optical phonon frequency χ electron aﬃnity of the semiconductor

χM work function of metal

XM electronegativity of contact material ψ electron wavefunction

ΦSB Schottky barrier height

ΦSpec work function of the XPS spectrometer Υ photoelectron peak width z depth

z0 characteristic width of exponential well Chapter 1

Introduction

1.1 Motivation for the thesis

The development of semiconductor devices and related processes has always been inti- mately related to the progress made in fundamental studies of semiconductor surfaces and interfaces, due to the important role of the interface [1]. This has been best summarised by the 2000 Nobel Prize Laureate, Herbert Kroemer, who remarked in his Nobel Lecture: ‘Often, it may be said that the interface is the device’ [2]. For instance, the electronic properties of a Schottky diode (consisting of a metal-semiconductor interface) are characterized by the barrier height which is the energetic separation between the majority carrier’s band edge (for n-type material, this is the conduction band minimum) and the Fermi level, at the interface [3]. The formation of the Schottky barrier at metal-semiconductor contacts may be followed using surface-sensitive techniques, which monitor the evolution of the electronic properties of initially clean semiconductor surfaces at various stages of metal adatom deposition [3]. From these early studies, the phenomena referred to as ‘Fermi level pinning’ was reported; where, the Fermi level (and barrier height) at the interface became ﬁxed (or pinned) following increasing coverage. The pinning mechanism is attributed to ionized extrinsic adatom-induced gap states at the interface [3]. An important parameter dictating the Fermi level pinning mechanism at Schottky barrier heights was identiﬁed as the branch-point energy (EB) of the semiconductor, which corresponds to the cross-over between donor-like (positively-charged) and acceptor-like (negatively-charged) surface states [4, 5]. Fermi level pinning is also observed at clean semiconductor surfaces [e.g. Si(111) and III-V(100) surfaces], due to ionized intrinsic surface states [3]. From a fundamental view, interest is in whether EB plays a similarly important role in dictating the space-charge layers formed at semiconductor free surfaces and is the motivation for

1 1.1 Motivation for the thesis 2 this thesis. Here, the near-surface electronic properties of the topical III-nitride compound semiconductor, InN, have been investigated. Such fundamental studies of the near-surface of this material are still within their infancy. Earnest interest in the physical properties of InN only began in 2002, following the dramatic revision of its fundamental band gap [6, 7].

The band gap (Eg) is the defining property of a semiconductor; it represents the separation between the top of the valence band (filled states) and the bottom of the conduction band (empty states) in the solid. Early InN samples were either polycrystalline or thin films prepared by reactive radio-frequency nitrogen sputtering of indium targets [8]. Until 2002, the most quoted value of the band gap was 1.89 eV by Tansley and Foley obtained from sputtered films [9]. Improvements in its epitaxial growth, during the late 1990s, have resulted in single-crystalline InN thin films becoming available in the last few years [8]. In 2002, Davydov et al., reported E 0.9 eV from their absorption and photoluminescence g ∼ measurements on single-crystalline films [6]. Since then a consensus has been reached for the band gap of 0.7 eV [7, 10, 11, 12], with the most recent studies quoting a band ∼ gap of around 0.64 eV at room temperature [13, 14]. It is important to note that the topicality of the band gap revision has been met with some conflicting results. These are not discussed here, although the interested reader is referred to a concise review of the most recent developments regarding InN, following the European Materials Research Society (EMRS) Fall Meeting in 2005 [see Appendix A]. It was following the revision of the band gap of InN that interest in its near-surface electronic properties began. Hall measurements of a range of InN samples revealed an excess of electrons at the interface (with the buffer layer) and/or surface; meanwhile, capacitance-voltage profiling revealed an accumulation of electrons at the oxidized surface [15]. At the same time, X-ray photoemission studies of the barrier height at Ti-InN interfaces revealed that the Fermi level was pinned above the conduction band minimum (CBM) [16]. Both studies suggested an accumulation layer was present at InN surfaces. In 2004, the intrinsic electron accumulation was first directly measured at clean InN surfaces using surface-sensitive electron spectroscopy [17]. For almost all other semiconductors (except InAs [18]) the near-surface region is depleted of electrons, due to negatively-charged surface states [19, 20, 21]. It is this contrast with almost all other semiconductors which makes this novel material interesting for fundamental studies of the space-charge region. 1.2 Organisation of the thesis 3

The electron accumulation and the physical mechanisms involved are also important for future device applications involving InN, due to its extremely large sheet density. Mah- boob et al., revealed that the surface state density at clean InN surfaces was far larger than that at InAs surfaces (by at least an order of magnitude) [17]. Furthermore, increased understanding of the space-charge layer formed at InN surfaces will aid the characterization of its physical properties. This was evident in the work of Jones et al., where evidence for successful p-type doping of InN required the consideration of a thin n-type inversion layer at its surface [22].

1.2 Organisation of the thesis

In this thesis, the native electron accumulation layer formed at the InN surfaces - including its effects on the physical properties of this material - has been investigated. The proceeding sections of this chapter [Chapter 1 Introduction] begin by introducing the various models and approximations required to describe the electronic properties of semiconductors [section 1.3]. Fermi level pinning and the branch-point energy are next introduced in terms of previous studies of covalent and weakly ionic semiconductors interfaces (including free surfaces) [section 1.4]. The proceeding section thoroughly evaluates the method used in this thesis to calculate the space-charge profiles [section 1.5]. The introduction concludes by summarizing the key considerations - addressed in the previous sections - needed for studies of narrow gap semiconductor free surfaces [section 1.6]. The next chapter [Chapter 2 Experimental] describes the two primary surface-sensitive spectroscopies used in this research: X-ray photoemission spectroscopy (XPS) and high- resolution electron energy-loss spectroscopy (HREELS). The first experimental chapter [Chapter 3 Indium arsenide] of this thesis focuses on the near-surface region of InAs surfaces. This conventional, narrow-gap (E 0.36 eV) III-V compound semiconductor also g ∼ exhibits native electron accumulation [18]. As a result, InAs presents a suitable reference material to thoroughly validate the various models and approximations discussed in the introduction before focusing the attention on InN. The remaining chapters of this thesis focus on various aspects of InN, such as: the preparation of clean InN surfaces [Chapter 4 Indium nitride: surface preparation]; its valence band structure [Chapter 5 Indium nitride: valence band structure]; the origin of the electron accumulation [Chapter 6 Indium 1.3 Electronic properties of a semiconductor 4 nitride: origin of the electron accumulation]; the effects of low-energy ion bombardment on its near-surface region [Chapter 7 Indium nitride: Fermi level stabilisation by low energy ion bombardment]; the thickness-dependence of the Hall-measured carrier concentration [Chapter 8 Indium nitride: origin of the high unintentional n-type conductivity]; and the observation of quantized states within the potential well formed at the surface due to the downward band bending [Chapter 9 Indium nitride: electron tunnelling spectroscopy of quantized states]. The final chapter [Chapter 10 Epilogue] summarizes the key results and discusses the importance of the branch-point energy and its role in dictating many of InN’s electronic properties [section 10.1]. It concludes by considering this III-nitride compound in terms of the large size- and electronegativity-mismatch between the indium cation and nitrogen anion, comparing InN with other highly cation-anion mismatched compound semiconductors [section 10.2].

1.3 Electronic properties of a semiconductor

1.3.1 Deﬁnition of a semiconductor

For solids, the energy levels of an electron in a periodic potential are described by a family of energy bands, describing the allowed variation in energy of an electron at a particular level with wavevector. Such a description gives rise to the concept of the band structure of solids. The electronic properties of a solid are determined by the Fermi level of the solid.

The Fermi level (EF ), describes the maximum energy of the electrons of a solid at zero

Kelvin (i.e. all the energy bands are occupied below EF and are unoccupied above). For

ﬁnite temperatures, a distribution of ﬁlled and empty states around EF exist, as described by the Fermi-Dirac distribution [23]. Semiconductors are strictly insulators with a small enough fundamental band gap

(Eg) to allow the excitation of electrons into unoccupied higher energy bands at ﬁnite temperatures, such that they are insulators at very low temperatures (near absolute zero) but act as conductors at elevated temperatures (near room temperature). This behaviour is due to the non-vanishing probability that some electrons will be thermally excited from the valence band (highest occupied band) to the conduction band (lowest unoccupied

Eg/2kB T band). This probability varies as e− , with the conductivity rising rapidly with increasing temperature. This is in contrast to metals, where the conductivity falls as 1.3 Electronic properties of a semiconductor 5 the temperature is increased [23]. For most purposes, anything with a band gap less than 3 eV is considered to be a semiconductor, although some materials are classed as ∼ semiconductors with much larger band gaps e.g. AlN (E 6.2 eV). g ∼

1.3.2 Various semiconductors

The most common semiconductors are silicon and germanium, which are classed as group IV semiconductors and crystallize in the diamond lattice. Other semiconductors include, group III-V, II-VI and I-VII binary compounds (where the the numerals represent the group of the cation and anion from the periodic table). The alkali-halides (I-VII) are highly ionic while group IV elements are highly covalent. The group II-VI and III-V compounds are partially covalent (weakly ionic). All III-V compounds naturally form zincblende structures (similar to diamond but with two different elements), except for III-nitrides (AlN, GaN, and InN) which naturally form wurtzite structures. Continuous thermal agitation of pure semiconductor alloys results in the excitation of electrons into the conduction band, and the formation of positively-charged holes in the valence band. For such intrinsically-doped semiconductors, the number of electrons and holes are equal, and the Fermi level lies at the middle of the band gap [19]. The substi- tution of host semiconductor atoms with impurities (or doping) can result in a greater number of electrons (n-type material) or holes (p-type material), with the Fermi level of these extrinsically-doped semiconductors lying closer to the conduction band minimum or valence band maximum, respectively. To illustrate this further, consider a silicon atom (group IV element) being replaced by an arsenic atom (group V element), this results in an extra electron being donated which increases the n-type conductivity. In the same manner, doping with gallium (group III element) results in an electron being accepted and an increase in the p-type conductivity [19]. For the aforementioned cases, the dopant (e.g. arsenic) will effectively behave like a hydrogen atom embedded in Si due to the Coulombic screening. Hence, a donor can be described as an electron attracted to an equally positively-charged ‘nucleus’ with a mass much heavier than a proton so that it can be treated as infinite [24]. Meanwhile, an acceptor can be considered as a hole of positive charge attracted to an equally negatively-charged nucleus approximated by an infinite mass. These dopants are referred to as shallow dopants, whose solutions to the Schrödinger equation can be described within the effective-mass approximation [24]. The 1.3 Electronic properties of a semiconductor 6 energy levels of these shallow donors and acceptors lie closer to the conduction and valence band edges, respectively [19]. Other impurities can be used to dope a particular semiconductor, which cannot be described by the effective-mass approximation and are referred to as deep dopants [24]. Compared to the band gap, the separation between the dopant energy levels and the conduction (or valence) band is small. As a result, doping induced conduction generally dominates over thermally induced conduction, except at very large temperatures (far greater than 300 K). At high enough doping concentrations, the Fermi level moves into the conduction or valence band, resulting in a degenerately-doped semiconductor.

1.3.3 Band structure approximations

The electronic properties of a semiconductor are governed by the electrons at the Fermi level. For semiconductors, doping can alter the location of the Fermi level [see section 1.3.2]. Consequently, knowledge of the band structure about the Fermi level is required to understand the electronic properties of a particular semiconductor. In principle, solving the Schödinger equation for a particular crystal potential provides information of the energy band dispersion. Compound III-V semiconductors have either zincblende, also known as cubic (e.g. InAs), or wurtzite, occasionally referred to as hexagonal (e.g. InN) structures [25]. The zincblende and wurtzite crystal structures [and their reciprocal lattices] are displayed in figures 1.1 a) [b)] and 1.2 a) [b)], respectively. The basic arrangement of the atoms in the wurtzite structure is similar to the zincblende, since the atoms are arranged with tetrahe- dral symmetry for both (four nearest neighbours and twelve second nearest neighbours). The greatest difference between the two structures is the position of the third nearest neighbours. The similarity of their atomic arrangements means that the band structures for the two structures, for the same compound III-V, will be very similar. To highlight this further, figures 1.1 c) and 1.2 c) show the energy band diagrams (about the band gap) for GaAs (zincblende) and GaN (wurtzite), respectively. For zincblende materials, the lowest conduction band minima are found at the zone centre (Γ-point) and along the < 111 > (Γ L-point) and < 100 > (Γ X-point) → → directions. The valence band close to the fundamental band gap (at Γ) has three branches,

V1, V2 and V3. The maxima of V1 and V2 are almost the same energy and lie at the zone 1.3 Electronic properties of a semiconductor 7

a) b) c) ) V e (

y g r e n E

Figure 1.1: The zincblende a) crystal structure, b) reciprocal lattice [25], and c) calculated energy band dispersion of zincblende GaAs about the band gap at the zone centre (Γ), as reported by Cohen and Bergstresser [26].

centre. The maximum of V3 is separated from the other two by an energy interval ∆SO, referred to as the spin-orbit splitting [not observable in ﬁgure 1.1 c)]. The band structure of a wurtzite material is very similar to the zincblende. However, the conduction band minimum is located only at the Γ-point and the three valence band maxima are separated slightly from each other at the Γ-point (topmost three valence bands in ﬁgure 1.2). Each of these bands are split by spin-orbit interactions but the splitting is negligible, resulting in all three lying very close to each other [25]. The dispersion of the conduction and valence bands at a particular high symmetry point (e.g. the Γ-point) can be approximated by a Taylor expansion,

f(x) f(0) + Ax + Bx2 + Cx3 + . . . (1.1) '

Assuming that the conduction (or valence) band is isotropic close to the Γ-point, the functional form of the expression is then even. Therefore, the energy band dispersion with wavevector [E(k)] very close to the high symmetry point (i.e for small energies) can be approximated as

E(k) E(0) Bk2. (1.2) ' §

2 For our purposes it is convenient to define B as ¯h /2m0∗ where m0∗ is the effective mass at the band-edge (Γ-point for this case) which is usually different for electrons and holes. 1.3 Electronic properties of a semiconductor 8

a) b) c) ) V e (

y g r e n E

Figure 1.2: The wurtzite a) crystal structure, b) reciprocal lattice [25], and c) and calculated energy band diagram of wurtzite GaN about the band gap at the zone centre (Γ), as reported by Carrier and Wei [27].

To a ﬁrst approximation, the conduction [EC (k)] band dispersion of a direct band gap semiconductor can be expressed by

2 2 Eg ¯h k EC (k) + , (1.3) ' 2 2m0∗ where m0∗, refers to the electron mass at the CBM. This parabolic approximation is only appropriate for describing the energy dispersion of a band when close to the reference point, with the energy in k-space far from this point varying non-parabolically. Additionally, the parabolic approximation is also only valid when interactions with other energy bands are neglected, such as for wide band gap materials (e.g. GaN: Eg = 3.4 eV at T = 300 K). As the band gap decreases, the interaction between the conduction and valence bands becomes increasingly signiﬁcant. This results in the energy dispersion being further modiﬁed. Therefore, the parabolic approximation is inappropriate for describing the energy band dispersion of narrow band gap materials (typically with Eg < 1 eV) and an alternative expression is required. One approach is to use the k p perturbation method to incorporate the interaction · between the conduction and valence bands, as described by Kane [28]. This method utilizes the periodic nature of the potential in the solid, which allows the properties of a particular point in the neighbourhood of a known point (i.e. the Γ-point) to be determined using perturbation theory. The k p interaction arises from substituting the Bloch function · 1.3 Electronic properties of a semiconductor 9 form of the electron wavefunction, given by

ik r ψn,k(r) = e · un,k(r) (1.4) into the one electron Sch¨odinger equation, such that

2 2 ¯h ik r ik r ∇ + V0(r) + VSO(r) e · un,k(r) = Ee · un,k(r) (1.5) Ã 2m0 ! where V0(r) is the periodic potential due to the crystal lattice and VSO(r) is the spin-orbit interaction, which yields

p2 ¯h ¯h2k2 + k p + + V (r) + V (r) u (r) = Eu (r) (1.6) 2m m 2m 0 SO nk nk · 0 0 · 0 ¸ where p = i¯h . The k p interaction between the conduction and valence bands is − ∇ · treated as a perturbation from the zone centre, and is described by an 8 8 interaction × matrix [28],

H˜ 0 H =   (1.7) 0 H˜    

Es 0 kP 0  0 E 1 ∆ √2 ∆ 0  ˜ p 3 SO 3 SO H =  −  (1.8)  √2   kP 3 ∆SO Ep 0     1   0 0 0 Ep + ∆SO   3    where E and E are the eigenvalues of (¯h2 2/2m) + V + V U = E U (here the s p { ∇ 0 SO} i i i complete set, Ui, forms the basis of the representation). The term P can be written in terms of Eg and m0∗ [25], as

1 1 P 2 = ¯h2 E /2. (1.9) m m g µ 0∗ − 0 ¶ Assuming a two-band approximation, where only one conduction and one valence band interact, and neglecting the spin orbit split oﬀ (Eg >> ∆SO), equation 1.8 can be further simpliﬁed to,

Es kP H =   . (1.10) kP Ep     1.3 Electronic properties of a semiconductor 10

By solving the Schr¨odinger equation, Hi,jψ = Eiψ, the energy dispersion can be expressed as

¯h2k2 E(1 + αE) = , (1.11) 2m0∗ where α = 1/Eg. Such a description is referred to as the α-approximation, where the non- parabolicity is governed by the band gap of the semiconductor. As the band gap increases, α 0 and the parabolic approximation is fully recovered. The eﬀects of including the → spin-orbit split-oﬀ can be achieved by suitably modifying the term α, without harming the elegance of equation 1.11. The conduction band dispersion can be derived by rearranging equation 1.11, such that

E E 2 ¯h2k2 E (k) = − g + g + E . (1.12) C 2 2 g 2m sµ ¶ 0∗ 1.3.4 Carrier statistics

Once the energy band dispersions of the semiconductor are known, it is possible to calculate the carrier statistics. This is ﬁrst achieved by evaluating the electron density of states [g(E)] of an energy band (e.g. the conduction band), given by

k2 dE 1 g(E) = C − . (1.13) π2 dk µ ¶ The product of the Fermi-Dirac distribution [f(E)] and g(E) of the conduction band is numerically integrated to determine the carrier (e.g. electron) concentration (n) using

n = ∞ f(E)g(E)dE. (1.14) Z0

The eﬀective mass dispersion [m∗(E)], can also be determined from the conduction band dispersion and is related by

1 2 dEC (k) − m∗(E) = ¯h k . (1.15) dk · ¸

Using equation 1.11, analytical expressions can be derived for both n and m∗(E). Once the variation in the parameters with energy is known, the transport properties can be evaluated by considering the parameters at the Fermi level. Note, in the parabolic approximation the effective mass is constant but when the effects of a non-parabolic conduction band the effective mass at the Fermi level can be significantly different from that at the band edge. 1.4 Semiconductor interfaces 11

1.4 Semiconductor interfaces

The Fermi level pinning mechanism (due to ionized adatom-induced gap states) has been identified as key to understanding the formation of Schottky barrier heights at metal- semiconductor interfaces [see section 1.1]. It was also noted that Fermi level pinning can occur at clean semiconductor surfaces (vacuum-semiconductor interfaces). Due to the progress of this field, it is necessary to introduce results from early metal-semiconductor studies before considering semiconductor free surfaces. Here, the studies by Schottky, Bardeen, and Kurtin et al. - which highlighted the importance of the Fermi level pinning mechanism at predominantly covalent semiconductors - are introduced first [section 1.4.1]. Next, adatom-induced gap states and the branch-point energy of a semiconductor are discussed in terms of results from studies of adatom/III-V(110) interfaces (following the improvements in vacuum technology in the mid 1970s) [section 1.4.2]. Finally, semiconductor free surfaces are concisely discussed in terms of the Fermi level pinning mechanism and ionized surface states [section 1.4.3].

1.4.1 Early studies of Schottky contacts

Schottky ﬁrst attempted to understand the properties of metal-semiconductor interfaces in 1931, in terms of the work function of the metal (χM ) and the electron aﬃnity of the semiconductor (χ) [29]. Such a description is known as the Schottky model where the

Schottky barrier height (ΦSB) is expressed simply as

Φ = χ χ. (1.16) SB M −

The Schottky barrier refers to the energetic distance between the Fermi level and the respective majority carrier band (e.g. the conduction band for n-type material). However, the model was in contrast with experimental results which revealed that the barrier height displayed little or no dependence on the metal used. In 1947, Bardeen proposed an alternative model to explain Schottky barrier heights, where the electronic structure of the semiconductor played an important role [30]. Localized states at the interface (within the forbidden gap region) act to ‘pin’ the Fermi level, thus explaining how the barrier height is relatively independent of the metal. The two models (Schottky and Bardeen) are depicted in ﬁgure 1.3. 1.4 Semiconductor interfaces 12

Figure 1.3: The a) Schottky and b) Bardeen models describing the bending of the conduction band (EC) and valence band (EV ) edges with respect to the Fermi level (EF ) at semiconductor- metal interface [21]. For the Schottky case, the Schottky barrier height (ΦSB) is determined by the work function of the metal (χM ) and electron aﬃnity of the semiconductor (χ). For the Bardeen model, the Fermi level is pinned by localized ‘gap’ states at the interface.

The greatest diﬀerence between the Schottky and Bardeen models is the phenomenon of Fermi level pinning (or stabilisation). Early studies by Kurtin et al., revealed a ‘fundamental transition in the electronic nature of solids’ corresponding to a cross-over between the two models [31]. To summarize, highly ionic materials (such as alkali-halides e.g. NaCl) can be described within the Schottky model, where the Schottky barrier height strongly depends on the electronegativity of the metal. Highly covalent materials (such as group IV elements) show little or no dependence with the deposited metal, and the Fermi level is stabilized (or pinned) at a particular energy. This work led to the concept of an S-parameter, deﬁned as

dΦ S = SB . (1.17) dXM where XM is the electronegativity of the contact material. 1.4 Semiconductor interfaces 13

Figure 1.4: The barrier energies (ΦBn), of various metals on n-type semiconductors plotted against electronegativity (XM ), as reported by Kurtin et al. [31]. For each material, the slope parameter (S) of the reference line is inversely proportional to the extent of the Fermi-level stabilisation at the semiconductor-metal interface. For Si (the most covalent), almost complete Fermi level stabilisation is observed; for SiO2 (the most ionic), the electronegativity of the adatom is signiﬁcant.

Figure 1.4 shows the variation in the S-parameter from strongly ionic to strongly covalent solids. The degree of Fermi level pinning can be expressed as S 0 for the Bardeen limit → and S > 2-3 for Schottky limit [32]. For intermediate materials (such as III-V compounds e.g. GaAs), Fermi level pinning does occur, but the electronegativity of the material has a secondary eﬀect.

1.4.2 Fermi level pinning

Equation 1.17 provides a useful but incomplete description of Schottky barrier formation [5]. For studying III-V materials, such as GaAs, the model is particularly unhelpful. It was only following the rapid progress in surface techniques [such as low-energy electron diﬀraction (LEED), EELS and XPS] made in the mid 1970s (for a review of the progress made during 1973-75 the interested reader is referred to the work of Philips [33] and references therein), that Schottky barrier formation studies became more abundant [34]. These studies investigated initially clean, well-cleaved, III-V(110) surfaces and monitored the evolution of the barrier height with adatom deposition [3]. The surface 1.4 Semiconductor interfaces 14

Figure 1.5: The position of the surface Fermi level (EF S) for Au, Cs, and O on GaSb, as reported by Spicer et al. [35]. Note that the ﬁnal pinning position is little dependent on the adatom and that is it reached with much less than a monolayer coverage.

Fermi level (EF S) was found to become pinned within the first monolayer of adatom coverage, with its position largely insensitive to type of metal (consistent with Kurtin et al. [31]) and the presence of impurities (such as oxygen and carbon) [35]. The pinning location was found to vary between materials; from close to the valence band (GaSb), the mid-gap (GaAs), and the conduction band (InP)[36, 37]. The pinning was also largely insensitive to doping (whether n- or p-type) and temperature [20]. The Fermi level pinning mechanism was described in terms of adatom-induced gap states [3]. Two alternative models were developed considering the physical origin of these gap states: the defect model [35] and the metal-induced gap states (MIGS) model [4]. The two models differed on the source of the interface states, originally proposed by Bardeen [30], responsible for the pinning. The first considered extrinsic defects incorporated during the interface formation. The second was based on the work originally by Heine [38] (later elaborated by Yndurain [39], Louie et al. [40] and by Tejedor et al. [41]), that localized states could exist within the ‘forbidden’ band gap and result in the Fermi level becoming pinned. The first model addressed the need to consider a ‘realistic’ interface. However, it could not explain the universal nature of the pinning. The second model was favoured by some, since it provided a universal parameter to describe the ultimate pinned Fermi level. The two models were neatly reconciled with the Physical Review Letters by Mönch 1.4 Semiconductor interfaces 15

Figure 1.6: The final Fermi level position (EF ) for a number of metals and oxygen on GaSb, GaAs, and InP (110) surfaces [35]. Note that there is little dependence on the chemical nature of the adatom. entitled ‘Role of Virtual Gap States and Defects in Metal-Semiconductor Contacts’ [42]. In this work, the metal-induced gap states (MIGS) were capable of describing the barrier heights at metal- and silicide-silicon contacts when either the defect density is low or the defects are completely charged. An important parameter was confirmed to be the branch- point energy (identified by Tersoff [4, 5]), with the electronegativity of the adatom playing a secondary role (dependent on the semiconductor’s high frequency dielectric constant). The branch-point energy is discussed further in two parts below. The first, in- troduces gap states and the importance of EB in dictating the character of these states [section 1.4.2.1]. The second, discusses amphoteric defects (formed by irradiation or at interfaces) and how their type is likewise dictated by EB [section 1.4.2.2]. 1.4 Semiconductor interfaces 16

1.4.2.1 Gap states and the branch-point energy

Surfaces represent the termination of a bulk crystal. Surface atoms have fewer nearest neighbours compared to the bulk atoms. Consequently, bonds are broken and the surface electronic properties are markedly different from the bulk. Even a truncated surface (an ideal surface termination) is largely different from that of the bulk. Generally, it is energetically favourable for the surface to relax or reconstruct further modifying the surface [21]. Intrinsic surface states arise naturally from the termination of the periodic crystal. The finite potential barrier at the surface (z = 0) means that electron wavefunctions can exponentially decay into the vacuum. Such a criterion requires the surface wavefunctions [ψ(z)] to vary with depth (z) in the form ψ(z) = Aeikz outside the solid. Considering the periodic nature of the crystal potential [equation 1.4] these states require imaginary wavevector components. Such a case is possible, provided that the surface states exist within the forbidden gap region (hence, the term gap states). These evanescent gap states can be shown to naturally arise from the Schödinger equation [20, 21, 43]. The solution to the two band Schrödinger equation [equation 1.10] for real and imaginary wavevectors is shown in figure 1.7 (as reported by Richard et al. [43]). Close to the band edge (k = 0) the energy dispersions are parabolic and become non-parabolic (linear) for large and real wavevectors. Solutions for imaginary wavevectors (such that k = iK) can exist provided that K E /2P , where P is given by equation 1.9. For real cases, additional boundary | | ≤ g conditions are imposed (due to the reconstruction) and surface states, and a continuum is not observed. Such localized surface states were independently confirmed experimentally by early photoemission studies of clean Si surfaces at Stanford (Wagner and Spicer) [44] and at IBM (Eastman and Grobman) [45] in 1972. At Schottky barriers, the Fermi level pinning mechanism results from the distribution of MIGS, combined with the requirement of charge neutrality. Unlike free surfaces, a continuum of MIGS exist within the band gap at metal-semiconductor interfaces (provided the defect density is sufficiently low), as depicted in figure 1.7. This has been experimentally confirmed at Fe-GaAs interfaces by First et al. [46]. Depending on their location within the band gap, MIGS will have either more conduction (acceptor) or valence (donor) band-like character [4, 20, 21]. The position at which MIGS have equal donor- and acceptor-like character corresponds to the branch-point energy (EB). For charge neu- 1.4 Semiconductor interfaces 17

Figure 1.7: The two-band model energy dispersion of the valence and conduction band, as reported by Richard et al. [43]. Within the band gap, states can exist with imaginary wavevectors and are referred to as evanescent states (or gap states).

trality, EF is pinned at EB at the interface, with slight energetic shifts associated with the electronegativity of the adatom [4, 42]. The spatially localized nature of the MIGS means that their character is derived from contributions from a substantial portion of the entire

Brillouin zone, not just the Γ-point band edges. Therefore, the position of EB corresponds to the middle of the indirect band gap, regardless of the energy of the Γ-point CBM or valence band maximum (VBM) [5]. This explains how the pinning positions vary between semiconductors, whilst remaining a universal phenomenon (as depicted in ﬁgure 1.6).

1.4.2.2 Amphoteric defects and the branch-point energy

A striking correlation between the Fermi level stabilisation in heavily electron irradiated semiconductors and the pinned Fermi level at Schottky barriers was ﬁrst reported by Walukiewicz [36]. His study revealed an agreement between the Fermi level stabilisation energy for electron irradiated semiconductors, the pinning level of Schottky barriers and the branch-point energy (or charge neutrality level) of covalent and weakly ionic semiconductors. For illustration, the Fermi level behaviour of GaAs was investigated [36]. Figure 1.8 displays the results, which show how the ultimate pinning level of GaAs is 1.4 Semiconductor interfaces 18

Figure 1.8: Comparison of the Fermi-level behaviour in (a) electron irradiated GaAs and (b) at Ti-GaAs interfaces for submonolayer Ti coverages, as reported by Walukiewicz [36].

independent of doping and method used (whether irradiation or metal deposition). For both the greatest metal coverage and irradiation dosage, the Fermi level agrees with 0.5 ∼ eV predicted for the location of EB [47, 48]. Therefore, a universal mechanism appears to be responsible. Since gap states cannot be considered for irradiated material this led to Walukiewicz ruling in favour of defects (in the form of amphoteric dangling bonds) at the surface being responsible for the pinning mechanism at Schottky barriers [36, 49]. However, it is important to note that the wavefunctions of the amphoteric dangling bonds will satisfy the Schr¨odinger equation and exponentially decay into the vacuum i.e. a gap state. The work by Walukiewicz highlighted the importance of the branch-point energy 1.4 Semiconductor interfaces 19 of a semiconductor, and led to the concept of the amphoteric defect model (ADM) [36,

50]. The position of EB corresponds to the energy level where the formation energies of the donor- and acceptor-like defects complexes are equal, according to the ADM [50].

From positron annihilation studies of GaAs: p-type material (bulk Fermi level < EB) formed anion vacancies and anion-on-cation antisite (AAS) defect complexes of donor- like character, and n-type material (bulk Fermi level > EB) created cation vacancies and cation-on-anion antisite (CAS) defect complexes of acceptor-like nature [36, 50]. With increasing irradiation the Fermi level of both types of material would stabilize at EB, driven by the formation of compensating amphoteric defects. After which, any further irradiation would not alter the position of the Fermi level.

Therefore, EB corresponds to a cross-over point with defect formations, in the same manner as for gap states. Depending on the position of the Fermi level with respect to EB, it is energetically favourable for defects and impurities to act as either donors or acceptors. By intentionally doping a semiconductor, such that the separation between the Fermi level and EB increases, the formation energy of the compensating donor or acceptor defect decreases. This mechanism is responsible for the observed doping limits of semiconductors [51]. Fermi level pinning and doping limits can then be understood by considering the branch-point energy to be the most energetically favourable state of the semiconductor.

1.4.3 Semiconductor free surfaces

For ideal semiconductor free surfaces, the Fermi level pinning is driven by a small number of ionized surface states [3, 4, 20, 21]. These surface (gap) states arise from the termination (or reconstruction) of the bulk crystal at the surface. Depending on their location, with respect to the band edges (over the entire complex band structure), these states will have either predominantly more conduction band (acceptor-like) or valence band (donor- like) character. Occupied donor-like surface states are neutral but become positively charged when unoccupied. The opposite is true for acceptor-like states, which are neutral if unoccupied and negatively charged if occupied [21]. The cross-over from primarily donor-like to acceptor-like character again corresponds to EB. For a free-surface where ionized surface states exist, charge-neutrality is satisﬁed once these states have been fully compensated by band bending. As a result, the Fermi level is found to be pinned close 1.5 Space-charge calculations of free surfaces 20

to EB. The nature of these states is debatable, although intrinsic defects (associated with the reconstruction) and extrinsic defects (introduced to the surface) are the likeliest candidates.

1.5 Space-charge calculations of free surfaces

In this section, the physics necessary to describe the space-charge layers formed at semiconductor free surfaces is introduced. Attention is focused on accumulation layer proﬁles where the non-parabolicity of the conduction band cannot be neglected (e.g. at InAs and InN free surfaces).

Figure 1.9: Schematic representations of the three types of space-space layers at semiconductor interfaces: electron depletion, inversion and accumulation. Figure taken from ref. [21].

At semiconductor free surfaces, where ionized surface states exist, charge neutrality is ensured by band bending due to the Fermi level being pinned at the surface. These ionized surface states are responsible for the near-surface space-charge layer formed (as depicted within ﬁgure 1.9). For n-type semiconductors, ionized donor-like (acceptor-like) surface states will result in downward (upward) band bending close to the surface and the formation of an electron accumulation (depletion) layer. Consequently, the space-charge layer can be considered to be a concentration of charge at the surface, which determines the distribution of carriers close to the surface. As a result, the space-charge potential [V (z)] can be described by the Poisson equation, given by

2 d V (z) e + 2 = NA− ND + n(z) + p(z) , (1.18) dz ²0²(0) − h i 1.5 Space-charge calculations of free surfaces 21

where ²0 and ²(0) refer to the permittivity of free space and static dielectric constant of + the semiconductor, respectively. The terms NA− and ND are the bulk acceptor and donor densities, respectively. These are assumed to be constant with no depth dependence, in comparison to the electron [n(z)] and hole [p(z)] depth-dependent densities reflecting the carrier profile. The distribution of carriers must also satisfy the Schödinger equation [equation 1.5]. Therefore, to calculate the near-surface profile of a semiconductor, it is necessary to self-consistently solve the Poisson and Schrödinger equations. This can be achieved by using a trial potential V (z) with an iterative method to obtain a single solution. The method is straight-forward when considering the parabolic approximation, where a constant effective mass is used. For non-parabolic descriptions where the effective mass is energy dependent, the Poisson-Schrödinger equation is no longer only defined by the potential. To highlight the energy dependence, by substituting equation 1.11 into equation 1.15, the effective mass at the Fermi level for a degenerately doped n-type narrow band gap semiconductor is given by

2EF mF∗ = m0∗ 1 + . (1.19) Ã Eg !

Full self-consistent Poisson-Schrödinger calculations, which include the full effects of non- parabolicity, have been solved [52, 53]. Such calculations require extensive computational algorithms. As with band structure calculations, suitable approximations can be made to describe the near-surface space-charge profiles of narrow band gap materials. One method involves solving the Poisson equation within the modified Thomas-Fermi approximation (MTFA) which allows the accumulation and depletion layer profiles to be described with an analytical approximation for the carrier density which takes into account the boundary condition for the wavefunction at the surface (ψ(z) 0 as z 0) [54, 55]. Poisson-MTFA → → calculations have been shown to yield results for both depletion and accumulation layers in good quantitative agreement with a full self-consistent theory by Ub¨ ensee et al. [55]. In addition, depletion, inversion and accumulation layer profiles are treated the same within the Poisson-MTFA framework, in contrast to full self-consistent calculations [55]. The electron density for a narrow band gap material, within the MTFA, is given by the following semi-classical expression [54],

1/2 3/2 E1/2 1 + E 1 + 2E f(z) 1 2m0∗ ∞ Eg Eg n(z) = 2 2 dE, (1.20) 2π ¯h 0 1 +³exp [β (E´ ³E V (´z))] µ ¶ Z − F − 1.5 Space-charge calculations of free surfaces 22

where β = 1/kBT and the MTFA correction term [f(z)] describes the decrease in the electron density at the surface (z = 0), given by

1/2 2z E 1/2 E f(z) = 1 sinc 1 + . (1.21)  L k T E  − µ B ¶ Ã g !   The term L refers to the characteristic length which describes the range of the inﬂuence the interface has on the eﬀective electron mass perpendicular to the interface [54]. This length can be determined from

¯h ∆x∆p, (1.22) ∼ where ∆p is change in the electron momentum. For a non-degenerate case, the momentum can be approximated by

p = 2m0∗kBT , (1.23) q which gives the thermal length as

¯h Lth = . (1.24) 2m0∗kBT

For degeneratep cases, this thermal approximation is no longer applicable. The general form of the momentum is required, given by

p = ¯hkF (1.25)

2 1/3 where kF is the Fermi wavevector (given by kF = (3π n) ), such that

1 L = . (1.26) kF

Referring back to 1.20, as z and f(z) 1 the classical solution is fully recovered → ∞ → [equation 1.14]. When describing the electron accumulation layer formed at narrow band gap semiconductor surfaces (such as InAs and InN), a triangular well approximation (for the downward band bending) can be used for V (z) to solve equation 1.20 [56]. However, such an abrupt description is unrealistic. For realistic solutions, a trial V (z) from the Poisson equation must initially be used to solve equation 1.20. An interval-bisection method is then required to converge on a single solution that satisﬁes the boundary conditions: V (z) → 1.6 Summary 23

0 and dV (z) 0 as z . The surface state density (n ) for the potential which is a dz → → ∞ SS solution of of the Poisson equation (within the stated boundary conditions), is then given by

²0ε(0) dV (z) nSS = . (1.27) e dz ¯z=0 ¯ ¯ Using this method, it is possible¯ to obtain quantitative agreement with full self-consistent Poisson-Schr¨odinger calculations. Figure 1.10 displays the Poisson-MTFA and full self- consistent calculations by Abe, Inaoka and Hasegawa [52, 57] using the same parameters for InAs. The full self-consistent calculations employed the local density approximation (with the two-band k p model to account for the non-parabolicity) of non-degenerately · doped n-type InAs. Agreement is observed between the two methods for a range of surface state densities and conﬁrms the suitability of the Poisson-MTFA for studying space-charge layers formed at InAs free surfaces. Furthermore, the similarity between InAs and InN means that the application of the Poisson-MTFA can also be extended to describing space- charge layers formed at InN free surfaces.

1.6 Summary

At the beginning of this chapter, InN was identified as a topical III-nitride semiconductor which shares many similarities with the more conventional III-V, InAs, including a narrow fundamental band gap (Eg < 1eV) and electron accumulation at the surface. The effects of the non-parabolic conduction band dispersion of narrow band gap semiconductors (such as InAs and InN) were shown to be significant when calculating their carrier statistics and electron accumulation layer profiles. The α-approximation (for calculating the conduction band dispersion) and the Poisson-MTFA (for calculating space-charge layers) models were introduced, which consider the non-parabolicity due to the close proximity of the valence bands and conduction band at the zone centre. These two models are used throughout this thesis when investigating the electronic properties of InAs and InN, and their free surfaces. When investigating semiconductor interfaces (such as free surfaces) the branch- point energy was discussed as an important parameter. It dictates many of the electronic properties of the semiconductor (e.g. type of surface states and the character of the amphoteric defects). As a result, this energy reference level is also considered throughout studies of the electronic properties of both InAs and InN. 1.6 Summary 24

Figure 1.10: A comparison between the full self-consistent Poisson-Schr¨odinger calculations (employing local-density-functional formalism) as reported by Abe, Inaoka and Hasegawa [52] (solid lines) and the Poisson-MTFA solutions (dotted lines) for non-degenerate n-type InAs (n = 1.3 1016 cm−3). The variation in the a) carrier-density depth-proﬁle [n(z)] of the accumulation × layer and b) potential well [V (z)] as a function of surface state (nSS) is shown for each method. Agreement is observed between the full self-consistent calculations and the Poisson-MTFA. Chapter 2

Experimental

2.1 Semiconductor surface spectroscopies

To investigate the free-surface electronic properties of semiconductors (such as InAs and InN), experiments must be performed within an ultra-high vacuum (UHV) chamber, in order to prepare and maintain the surface in a well-deﬁned condition. This requirement has been satisﬁed in this thesis by the use of X-ray photoemission spectroscopy (XPS) and high-resolution electron energy-loss spectroscopy (HREELS), and these were the primary techniques employed to investigate the near-surface electronic properties of InAs and InN. Here, these two surface-sensitive techniques are introduced.

2.2 Introduction to XPS

XPS is based upon the photoelectric eﬀect [58, 59] and was developed by Seigbahn et al., in the mid-1960s [60]. The process involves a beam of monochromatic X-rays irradiating the solid (the X-rays penetrate up to 1 µm within the solid) and a small solid angle of ∼ ejected photoelectrons being energy-analyzed. Their kinetic energy (KE) is given by

KE = hν BE Φ , (2.1) − − Spec where hν is the initial energy of the photons, BE is the binding energy seen by the photoelectron of the state (whether core or valence) and ΦSpec refers to the work function of the spectrometer. The BE of an emitted photoelectron is the diﬀerence between the energy of the (N 1)-electron ﬁnal state and the N-electron initial state [61]: −

BE = E(N 1) E(N). (2.2) − −

25 2.3 Features typical of an XPS spectrum 26

If one assumed no further rearrangement occurred following the emission of the photoelectron (i.e. treating the electrons as ‘frozen’), then the BE of the photoelectron is the orbital energy (Eorb):

BE E . (2.3) ∼ − orbs

Such an approximation is referred to as Koopmans theorem [62], and although strictly not valid for realistic scenarios is still useful when investigating the electronic structure of materials with XPS. For instance, the orbital energies of electrons vary between materials, the relationship between the orbital energy and binding energy [see equation 2.3] allows elements to be distinguished by their XPS spectrum. Following the emission of the photoelectron, the electrons within the solid rearrange themselves to respond to the creation of a hole, either by filling the hole with a higher orbital electron or by some other means to reduce the total energy of the ionized atom. Further corrections are required to consider the final-state relaxation energy. The interested reader is referred to ref. [63] for a more detailed introduction. Meanwhile, initial-state energy shifts can also be present, which reflect the change in the electronic environment due to the presence of an adsorbate e.g. oxygen. For binary compounds e.g. InAs, the host element indium maybe bonded to arsenic and or oxygen. A chemical shift is observed between the peaks associated with the In-As and In-O bonds; the shift reflects the difference in electronegativity between the species bonded to the indium [20]. Finally, all binding energies should ideally be referenced to the vacuum energy level, since this is the most relevant universal level for free electrons. However, binding energies are referred to the Fermi level in practice; the vacuum level requires accurate values for the work function and contact potentials for the particular set-up [63]. The Fermi level provides an intrinsic reference level, corresponding to, at least for metals, the weakest bonded electrons within the material.

2.3 Features typical of an XPS spectrum

Figure 2.1 displays a typical XPS spectra for InN prior to cleaning, using a monochromated

Al Kα source, displaying the following highlighted features: a series of core-levels peaks and valence-electron peaks above a step-like background. 2.3 Features typical of an XPS spectrum 27

Figure 2.1: The XPS spectrum of InN, prior to cleaning. The core-level peaks are identiﬁed as being due to photoelectrons from In and N orbitals. Additional peaks are observed, due to oxygen and carbon lying at the surface. The inset magniﬁes the valence band region (at very low binding energies). The valence band maximum (VBM) is extrapolated from the leading edge of the lowest-lying peak to the baseline. All binding energies are referenced to the Fermi level (zero eV).

2.3.1 Background

Equation 2.1 assumes an elastic photoemission process. Elastic processed are responsible for the series of discrete core-level peaks and the valence-band region. An inelastic photoemission process is when the photoelectron suﬀers an energy-change (usually an energy-loss) between the photoemission from the atom and the detector. Typically two types of background are present in a XPS spectrum due to the inelastic photoemission processes, a broad continuous distribution distribution (Bremsstrahlung radiation) and a ‘step-like’. For non-monochromated sources both are observed, with the Bremsstrahlung dominating at higher KE (lower BE) and the step-like background larger on the lower KE (higher BE) side of a signiﬁcant peak [64]. Standard X-ray sources are not monochromated and additional peaks, known as satellite peaks, can also be observed due to lower intensity lines (other than the principal Kα1,α2 principle line) [64]. Figure 2.1 displays the spectrum from a monochromated Al Kα source, therefore such satellite peaks and the 2.3 Features typical of an XPS spectrum 28

Table 2.1: The spin-orbit parameters.

Subshell j values Area ratio s 1/2 - p 1,2, 3/2 1:2 d 3/2, 5/2 2:3 f 5/2, 7/2 3:4

Bremsstrahlung background are both absent. Consequently, only the step-like background due to the inelastically scattered secondary electrons is discussed here. The background should be correctly subtracted or considered before evaluating the core and valence peaks. Various methods have been considered from the simplistic straight line interpolation, to the Shirley background [65] and the more advanced Tougaard background model [66]. An iterative integrated background subtraction, ﬁrst introduced by Shirley [65], has been employed throughout this thesis when studying an XPS spectrum. Although not as advanced as the Tougaard model, the Shirley method is considered to be adequate and can be easily incorporated into the curve-ﬁtting of the core-level peaks. For a detailed comparison between the various models for the background, the interested reader is referred to ref. [67].

2.3.2 Core-level peaks

Figure 2.1 highlights the O1s, In3d, N1s and In4d core-levels. The widths and intensities of the core-levels vary, while all non-s-levels are doublets e.g. In3d5/2,3/2, where the energy separation between the peaks (∆SO = 7.6 eV) is proportional to the spin-orbit coupling constant [64]. Note, the spin-orbit doublet peaks of the In4d (∆SO = 0.67 eV) are not resolved in figure 2.1. Table 2.1 summarizes the general spin-orbit parameters [64]. The full width at half maximum (FWHM) of a given photoelectron peak is determined by the lifetime of the core-hole convoluted with the instrumental resolution. The peak width (Υ) is related to the lifetime (τ) by Heisenberg’s Uncertainty Principle [61], by ¯h Υ . (2.4) ∼ τ Typically, Υ is larger for inner levels e.g. Υ(1s) > Υ(3d), since the lifetimes of inner electron orbitals is shorter than outer orbitals because inner core-levels can be rapidly filled 2.3 Features typical of an XPS spectrum 29 by outer core-level electrons. This Lorentzian core-level lineshape is then convoluted with the combined spread of the incident X-rays and the resolution of the analyzer. Typically, the contributions to the instrumental resolution have a Gaussian lineshape. Therefore, the resultant peaks, observed in figure 2.1, have a Voigt lineshape (a combination of a Gaussian and Lorentzian lineshape). Throughout this thesis, curve-fitting of the core- level peaks has been achieved by using a Shirley background with Voigt lineshapes with spin-orbit parameters as shown in 2.1 with FWHM of typically 1 eV or better. ∼ The core-level peak intensities of the core-level peaks reflect the concentration of the element within the material. However, XPS is surface-sensitive due to the attenuation length of the photoelectrons within the solid. For a homogeneous solid, the intensity of a particular photoelectron flux [I(E)] will be given by

d/λ I(E) = I0(E)e− (2.5) where the terms I0(E), d and λ refer to the initial intensity of photoelectron flux, the distance within the solid the photoelectrons have travelled and the attenuation length of the photoelectrons. After a distance of 3λ the flux has reduced by 95% of its initial intensity. For electron energies in the range of 50-200 eV, the attenuation length is typically less than 10A˚ [63]. The variation in relative intensities of the photoelectron peaks with angle, can distinguish which elements are located closer to the surface. By varying the emission angle [with respect to the surface plane] (θi), as depicted in figure 2.2, photoelectrons travelling the same distance within the solid (d) will now originate from a distance (d0) from the surface [where d0 = d sin(θi)]. Therefore, equation 2.5 becomes

0 d /λ sin(θi) I(E) = I0(E)e− , (2.6) reducing to equation 2.5 for normal incidence (θi = 90◦).

2.3.3 Valence bands

Shirley showed that the XPS valence band spectrum of gold could be directly compared with the valence band density of states from band structure calculations [65]. Around the same time, similar studies of Ge, GaAs and ZnSe revealed that agreement between the experimental valence band spectrum and the pseudopotential density of states [68]. 2.3 Features typical of an XPS spectrum 30

Figure 2.2: A schematic representation of the change in the eﬀective depth (d0) of the escaping photoelectrons with change in angle (θ). For both cases, the photoelectrons travel the same distance (d) within the material to escape, yet correspond to diﬀerent depths within the solid.

The location of the 3d states was found to aﬀect the agreement between the experimental theoretical results; for ZnSe the Zn3d states lie within the valence band (unlike the Ge3d and Ga3d for the other semiconductors) and more elaborate calculations were considered to be necessary to provide further agreement between experiment and theory for ZnSe. A more detailed study by Ley et al., on a wider range of III-V and II-VI semiconductors, revealed that high energy photoemission spectroscopy i.e. XPS could be used to deduce the total valence band density of states of the material, with less ambiguity than from using either ultraviolet photoemission spectroscopy (UPS) or optical measurements [69]. By comparing a range of III-V and II-VI materials, a generalized valence band photoelectron spectrum for the binary semiconductors was deduced [69]. Figure 2.3 displays this valence band structure; three peaks PI , PII and PIII in increasing binding energy are always observed. Peaks PII and PIII are separated by the ionicity gap (EIII - EII or EIII

- EI provided PI is resolvable from PII ), which generally widens when proceeding from

III-V to II-VI compounds i.e. with increasingly ionic compounds. Peak PI is the broadest and can sometimes exhibit resolvable ﬁne structure. Figure 2.4 displays an example of the comparison between the experimental valence band spectrum (background subtracted) from XPS of GaP and the valence band density of 2.4 Introduction to HREELS 31

Figure 2.3: The typical valence band spectrum of a zincblende semiconductor displaying three distinct peaks, as reported by Ley et al. [69].

states calculated from the band structure of GaP. Agreement between the XPS spectrum and theoretical density of states is observed once a 0.7 eV - 0.8 eV FWHM Gaussian broadening is included [69].

2.4 Introduction to HREELS

In contrast to XPS, incident mono-energetic electrons are used in HREELS to study the surface; the inelastic scattered electrons are then energy-analyzed [33]. Figure 2.5 displays a schematic of the scattering occurring in HREELS, where the incident angle is equal to the electron scattering angle. A specular geometry (usually 45◦) is employed since this favours scattering associated with the interaction between low-energy incident electron (Ei < 100 eV) and long-range dipole fields originating from the sample [21]. Other scattering mechanisms do occur, such as impact scattering where slow electrons interact directly with the local atomic potential of the surface atoms. Such scattering results in large scattering angles, unlike the small deviations from the elastic scattering angle due to inelastic scattering associated with the long-range dipole fields. Examples of long-range dipole fields are oscillating dipole fields at the surface which may originate from from 2.4 Introduction to HREELS 32

Figure 2.4: The comparison between the XPS valence band spectrum of GaP (top) and the calculated valence band density of states (with [ρ0(E)] and without [ρ(E)] instrumental broadening), as reported by Ley et al. [69]. The energy band dispersion of GaP (bottom) used to calculate the density of states is also shown.

collective excitations from the surface lattice (phonon) or carriers (plasmon), or from the dynamic dipole ﬁeld moments of vibrating adsorbed atoms or molecules [21]. Figure 2.6 displays typical spectra obtained from an InN surface before and after cleaning. The large zero energy-loss peak corresponds to the dominant elastic scattering at the surface. The majority of electrons are elastically scattered resulting in the intense peak at zero-loss energy observed in both spectra. The full width at half maximum of the elastic peak (typically the FWHM is 4 - 15 meV) results from the instrumental broadening introduced by the monochromator and analyser used, and deﬁnes the instrumental resolution of the spectrometer. Before cleaning, vibrational modes associated with contaminants (e.g. the In-O stretching mode) are observed in the energy-loss spectrum. However, following cleaning the surface optical phonon mode and the surface conduction-band electron plasmon mode are instead observed. 2.4 Introduction to HREELS 33

Monochromator Analyser

v|| z v⊥

φa φb

θ θ x

ε1(q,ω) d1

ε2(q,ω) d2

ε3(q,ω) d3

Figure 2.5: A schematic representation of a HREELS experiment, illustrating the specular geometry employed and the electron trajectory from the electron monochromator to the energy analyser. The solid is represented by a layer model; each layer is described by its thickness (di) and dielectric function (²i). The ﬁgure is based on the original ﬁgure used by Lambin et al. [70].

HREELS provides a non-invasive method of obtaining depth-dependent electronic information of the near-surface region of a solid. The dipole ﬁelds associated with surface plasmon excitations exponentially decay into the vacuum in the form, exp( q z), where − k q is the wavevector transfer parallel to the surface and z is the depth of the excitation. k 1 Therefore, the ﬁelds decay with a characteristic length p q− . For a particular surface ≡ k plasmon energy (¯hωSP ) the following expression can be derived

2¯h2 √E p i . (2.7) ≈ s m0∗ Ã¯hωSP sinθi ! where the terms Ei and θi refer to the incident electron energy and angle, respectively [21]. By increasing the incident electron energy, information can be gleaned from deeper within the material (up to 1000 A˚ depending on the excitation energy and incident electron 2.4 Introduction to HREELS 34

Figure 2.6: Typical HREELS spectra, for the same incident electron energy, of InN [72]. A large peak at zero energy loss is observed for both spectra, corresponding to elastic scattering. Additional peaks are due to inelastic scattering involving interactions between the incoming electrons and collective excitations. Before cleaning, these energy-loss peaks are associated with vibrational modes of the surface contaminants. After cleaning, peaks due to interactions between the phonon and conduction band electron plasmon excitations are prominent.

energy [71]). The surface plasmon frequency is related to the carrier concentration by

ne2 ωSP = . (2.8) s²0(²( ) + 1)m∗ ∞ F Equation 2.8 is strictly valid for homogenous semi-infinite solids only, as it ignores band bending, spatial dispersion and plasmon damping. However, by measuring the energy-loss of the surface plasmon as a function of incident energy, a qualitative description of the free-carrier profile in the near-surface region is obtained. For a quantitative description, the dielectric theory of inelastic scattering is necessary where the dielectric properties of the solid are described by its complex dielectric function [²(ω) = ²1 + i²2] because of the long-range nature of the scattering potential [21]. According to Fermi, the bulk energy- 1 loss spectrum [N(ω)] of fast electrons is determined by Im ²(0−,ω) , where ²(q, ω) is the ³ ´ 2.5 Semi-classical dielectric theory 35 complex dielectric function of the solid and ¯hω and ¯hq refer to energy and momentum lost by the incident electron, respectively [33]. For solid/vacuum interfaces, the surface 1 energy-loss spectrum is instead considered and is described by Im 1+²−(0,ω) . In this thesis, semi-classical dielectric theory has been used to obtain a quantitativ³ e free-carrier´ profile to simulate the HREEL spectra.

2.5 Semi-classical dielectric theory

Dielectric theory is used to describe the inelastic scattering of electrons as a result of long- range dipole-fields originating from collective excitations (such as phonons and plasmons) within the solid. The approach was first applied by Fermi, when he successfully described the bulk scattering of high-energy electrons [73]. For low-energy electrons (typically < 100 eV) surface scattering dominates, however the same approach can be used with suitable modifications [21]. Although other scattering mechanisms other than by long-range dipole- fields (e.g. impact scattering of slow electrons) do exist, by choosing a specular geometry, long-range dipole-field scattering is favoured [21]. A semi-classical approach is considered in this work; a classical description is used to evaluate the classical loss spectrum, which describes the likelihood of electrons losing a particular amount of energy due to interactions with the surface excitations at zero temperature; meanwhile, multiple-scattering energy losses and gains for an arbitrary temperature are accounted for by a thermodynamic average of boson-like surface excitations (viewed as quantum-mechanical harmonic oscillators driven by the Coulomb force exerted by the probing electron travelling along its classical trajectory) [70].

2.5.1 Program outline of HREELS of multilayers

In this work, the program HREELS of multilayers by Ph. Lambin, J. -P. Vigneron and A. A. Lucas is used to simulate the experimental HREEL spectra [70]. In this program, the single-event inelastic scattering is first classically described by evaluating the work done (W ) by the polarization field [E(r(t), t)] of the solid on the electron (responsible for the polarization field) along its classical trajectory [with a velocity, ve(t)], given by [74]

W = e ∞ v (t) E(r(t), t)dt, (2.9) − e · Z−∞ 2.5 Semi-classical dielectric theory 36

From equation 2.9 the classical-loss probability [Pcl(ω)] is determined by

∞ W = ¯hωPcl(ω)dω. (2.10) Z0 Next, multiple-scattering events are considered at non-zero temperature. The characteristic function [F (τ)] of the energy-loss probability [P (ω)] i.e. its Fourier transform, is described as [70]:

F (τ) ∞ P (ω) exp( iτω)dω ≡ − Z0 ∞ ¯hω0 ∞ = exp coth P (ω0) 1 cos(ω0τ) dω0 i P (ω0) sin(ω0τ)dω0 − 2k T cl − − cl ½ Z0 µ B ¶ Z0 ¾ £ ¤ Finally, comparison with experimental energy-loss spectra is obtained by convoluting P (ω) with a model of the instrumental resolution function [R(ω)]:

1 P (ω) = ∞ ∆(τ)F (τ) exp(iωτ)dτ, (2.11) 2π Z−∞ where ∆(τ) is the Fourier transform of R(ω) [70].

2.5.2 Evaluating the classical-loss probability for HREELS

The classical-loss probability describes the single-event scattering of the electrons by long- range dipole ﬁelds. From equation 2.11, the form of the classical-loss probability determines the overall energy-loss spectra observed experimentally. By analytically evaluating

Pcl(ω) the physical principles of the inelastic scattering can be better understood.

Lambin et al., evaluated the Pcl(ω) for fast electrons travelling along an unperturbed classical trajectory, given by [74]

r(t) = tv + tv , (2.12) k ⊥ such that v and v describe the electron velocity parallel to the surface and perpendicular k ⊥ to the surface, respectively. In this approximation the eﬀects of the image charge forces and ﬁnite penetration of the electrons are neglected, as discussed by Lucas et al., [75]. Figure 2.5 depicts the specular geometry used in HREELS. The solid is treated as a series of dielectric layers [²i(q , ω)] with thickness (di), and each dielectric layer is homogeneous. k 2.5 Semi-classical dielectric theory 37

After much algebra, Lambin et al., described Pcl(ω) in terms of an effective dielectric function at the surface [ξ(q , z = 0, ω) ξ0(q , ω)], such that [74] k ≡ k 2 3 4e q v 1 2 P (¯hω, q ) = k ⊥ Im d q (2.13) cl 2 2 2 2 − k π ¯h v D [(ω q v ) + (q v )] (ξ0(q , ω) + 1) k ⊥ Z Z − k · k k ⊥ k kinematic factor surface loss fn | {z } | {z } where the surface effective dielectric function (for a multilayer model as depicted in figure 2.5) is expressed as a continued fraction, given by

2 b1 ξ0(q , ω) = a1 2 , (2.14) k − b2 a1 + a2 − a2+... such that ai = ²i(ω)/tanh(q di) and bi = ²i(ω)/sinh(q di) [70, 74]. k k Equation 2.13 is only valid provided that the analyzer is centered around the spec- ularly reﬂected electron beam [70], a depicted in ﬁgure 2.5. Providing that ξ0(q , ω) does k not depend upon the polar angle the 2D q integration can be reduced to a 1D integra- k tion [71]. This integrand reduction is used for zincblende semiconductors (e.g. InAs).

Anisotropic materials, such as wurtzite Al2O3, have diﬀerent infrared properties parallel and perpendicular to the c-axis and cannot be considered in the same manner as isotropic materials [75]. However, the integrand reduction is valid for weakly anisotropic material

(e.g. GaN and InN), if a mean isotropic dielectric function is used: ²mean = √² ² [76]. ⊥ k The integrand of equation 2.13 is separated into two distinct parts: the ‘kinematic factor’ and the ‘surface-loss function’. The electron trajectory is described by the kinematic factor and provides no information about the solid. The surface-loss function relates the substrate dielectric response to the energy-loss probability. For instance, the polarization ﬁeld in the vacuum vanishes unless [74]:

ξ0(q , ω) = 1, (2.15) k − solving equation 2.15 yields the dispersion of the surface eigenmodes.

2.5.3 Dielectric functions and collective excitations

When simulating the HREEL spectra, a layer model is used to describe the solid (ﬁgure

2.5). All of the diﬀerent dielectric functions ²i(q , ω) consist of contributions from the k 2.5 Semi-classical dielectric theory 38 lattice and free carriers, such that a particular dielectric function [²(q , ω)] can be expressed k as

²(q , ω) = ²L(ω) + ²e(q , ω) (2.16) k k where ²L(ω) describes the lattice term and is wavevector independent. For surface optical phonons

[²(0) ²( )]ω2 ² (ω) = ²( ) + − ∞ T O , (2.17) L ∞ ω2 ω2 iγ ω T O − − P the terms ωT O and γP are the transverse optical phonon frequency and phonon damping parameter, respectively. Assuming a single-layer model approximation, a prominent phonon energy-loss feature is observed when ²L(ω) = -1, in absence of phonon damping

(γP = 0), such that

²(0) + 1 1/2 ω = ω . (2.18) F K T O ²( ) + 1 · ∞ ¸

The term ωF K is the energy-loss frequency for the Fuchs-Kliewer surface optical modes, observed in HREELS from compound semiconductors. Their existence was theoretically predicted in 1965 by Fuchs and Kliewer [77] and they were experimentally detected by Ibach at ZnO surfaces using HREELS [78]. The second part of equation 2.16 only describes the free electrons. In this study, only strongly n-type InAs and InN are investigated using HREELS. Therefore, the free hole contribution is neglected when simulating the data. Here, the hydrodynamic model is used, given by

ω2 ² (q, ω) = ²( ) 1 p , (2.19) e ∞ − ω (ω + iγ ) β2q2 Ã C − ! where the terms γC and β refer to the plasmon-damping frequency and spatial dispersion, respectively. Equation 2.19 is characterized by the plasma frequency (ωP ), such that

ne2 ω = . (2.20) P ²( )² m ∞ 0 F∗ The hydrodynamic model is favoured over the more simplistic Drude model suggested by Lambin et al. [70] and the more sophisticated microscopic models such as the Lindhard random-phase approximation model [79]. The Drude model lacks a spatial dispersion 2.6 InN samples 39 contribution, whilst the macroscopic hydrodynamic model can be suitably modiﬁed to agree with the more sophisticated Boltzmann model with the Mermin correction [23] within certain limits [80]. Assuming q, γ 0, equation 2.19 can be approximated by C → 2 2 2 ωp β q ²e(q, ω) ²( ) 1 1 + , (2.21) ≈ ∞ " − ω (ω + iγC ) Ã ω (ω + iγC )!# which has the same form, for weak spatial dispersion, as the Boltzmann-Mermin dielectric model, providing

3 β2 = v2 , (2.22) 5 F for the high frequency limit (ω >> γC ) [80]. The term vF refers to the Fermi velocity. For non-degenerately doped cases equation 2.22 is replaced with

3k T β2 = B . (2.23) m0∗

Assuming once again a simplistic single-layer approximation a prominent surface plasmon energy-loss feature is observed when

²( ) ω2 = ∞ ω2 + β2q2. (2.24) SP ²( ) + 1 P ∞ Noting that the characteristic probing depth is inversely related to the wavevector transfer parallel to the surface and referring to equation 2.7, the surface plasmon frequency will shift towards higher frequencies as the incident electron energy decreases.

2.5.4 HREEL simulations and Poisson-MTFA

Near-surface space-charge profiles were obtained by simulating the HREEL spectra using layer profiles. Each layer characterized by a thickness, plasma frequency (i.e. a carrier concentration) and damping parameters. The same layer profile is used to simulate the spectra for a range of incident energies. A solution is obtained when the corresponding Poisson-MTFA calculation [see section 1.5] describes the HREEL layer profile.

2.6 InN samples

The InN samples referred to throughout this thesis were grown at Cornell University, USA under the direct supervision of Dr. Hai Lu and Dr. William Schaﬀ [81, 82, 83]. Thin 2.6 InN samples 40

InN(0001) films (50 nm to 10000 nm) were grown by molecular beam epitaxy (MBE) using thermal evaporation sources of In, Ga and Al, within a 3-inch substrate capable Varian GEN II growth chamber. Nitrogen was supplied from low purity nitrogen boil- off and passed through three stages of particle and oxygen/moisture removal. An RF plasma source was used to generate the active and atomic nitrogen. Sapphire substrates were initially exposed to the 500W RF plasma source for 45 minutes at 200◦C in order to change the sapphire surface into one with some AlN surface structure. Afterwards, the wafer temperature was increased to 750◦C for the AlN buffer layer growth. For some samples, a GaN buffer layer was also used. For these cases the AlN buffer layer was 10 nm thick and the GaN layer was grown at 750◦C. Details of the buffer layer thickness for individual InN films are stated in each chapter. The InN layers were grown at 450◦C, with RF plasma powers of 250-400W and nitrogen flow rates of 0.5 to 1 standard cubic centimetres per minute. Detailed transmission electron microscopy, X-ray diffraction and optical characterization have been performed on InN samples grown under the same optimized growth conditions as those stated above [84]. It was reported that these samples were stoichiometric, with a single-crystalline wurtzite structure, and dislocation densities not exceeding mid- 10 2 10 cm− . Meanwhile, optical absorption and photoluminescence spectroscopy of these samples confirmed that the band gap of InN is 0.70 0.05 eV. § In wurtzite InN crystals, the [0001] and [0001]¯ directions are different. In-polarity is defined as the direction along the c-axis that the single bond of the indium atom is normal to and directed towards the surface [85]. The convention used to describe the polarity of wurtzite InN is illustrated in figure 2.7. Note that polarity is a bulk property, it does not refer to the surface termination [85]. For instance, N-polarity GaN(0001¯) can be terminated by a monolayer of gallium [86]. Although a range of experimental techniques are employed to study the polarity of wurtzite GaN, the two most favoured are reflection high energy electron diffraction (RHEED) measurements of the surface reconstruction as a function of temperature [87], and chemical etching using alkaline solutions (e.g. KOH) combined with scanning electron microscopy (SEM) [88, 89]. Due to the lack of reports on RHEED reconstructions of InN surfaces, chemical etching studies have been the major method of determining the polarity of InN. Note that such studies do not directly determine the bulk polarity of the crystal but rather the surface termination. 2.6 InN samples 41

Figure 2.7: Ball and stick schematic, illustrating the In-polarity [0001] and N-polarity [0001¯] directions of wurtzite InN [91]. The large dark grey balls represent In atoms and small light grey balls represent N atoms.

The InN films grown under the above stated conditions at Cornell University are considered to be predominately In-polarity. Evidence is based upon wet etching experiments of InN samples grown under different conditions. InN grown at 500◦C with InN buffer layers etched by KOH solution were identified has being N-polarity from SEM studies [90]. In the same study, InN grown at 450◦C with GaN buffer layers (similar to those grown at Cornell University) were In-polarity. Additional evidence for predominately In-polarity is from co-axial impact collision ion scattering spectroscopy (CAICISS) measurements and XPS studies at the University of Warwick. CAICISS studies of InN grown at 450◦C with a GaN buffer layer reported to be predominantly In-polarity from initial simulations [91]. Meanwhile, In-polarity (R693) and N-polarity (R941) InN were grown under the supervision of Professor Yasushi Nanishi and Dr. Hiroyuki Naoi at Ritsumeikan University, Japan. Their polarities were confirmed by chemical etching with KOH solution followed by SEM [92]. XPS studies of their valence band regions revealed that the valence peak intensities of In-polarity R693 agreed with all the valence band XPS spectra of the Cornell-grown InN samples studied in this thesis. Meanwhile, the valence band intensity ratios were significantly different for N-polarity R941. Although more studies are required to determine the origin of this difference (thought to be due to different reconstructions associated with the opposite terminations), it is worth noting that the Cornell-grown InN samples exhibit characteristics similar to In-polarity grown elsewhere. 2.7 Atomic hydrogen sources 42

2.7 Atomic hydrogen sources

Low-energy (typical < 1eV) atomic hydrogen used for preparing clean InAs and InN surfaces was generated using a TC50 thermal gas cracker from Oxford Applied Research (OAR), UK [93]. Unlike other thermal crackers which employ a very hot ( 2500 C) ∼ ◦ tungsten filament at high powers ( 400W) and typically have low efficiency ( 3-6 %), ∼ ∼ the OAR TC50 can operate at low temperatures (< 1000 ◦C) and low powers (< 60W) with cracking efficiency of up to 70 %. During hydrogen exposure, the chamber pressure was 2 10 5 mbar and the power was set at 55 W. All atomic hydrogen exposures are × − 6 reported in Langmuir (L), defined as 1 L = 10− torr s exposure (where 1 torr = 1.3332 mbar). Note, this unit was preferred due to its convenience when repeating the surface preparation in either of the separate XPS and HREELS chambers. Note, all temperatures referring the surface preparation are given in degrees Celsius (◦C), while all temperatures referring to electronic properties are given in Kelvin (K). Chapter 3

Indium arsenide

3.1 Surface preparation of indium arsenide

3.1.1 Introduction

Before employing high-resolution electron energy-loss spectroscopy (HREELS) to investigate the native, near-surface space-charge layer formed at semiconductor free surfaces, it is necessary to prepare contaminant free, undamaged, well-ordered surfaces: otherwise the vibrational modes associated with hydrocarbons and native oxides will dwarf the surface vibrational excitations (i.e. phonons and plasmons) [21]. The ideal method of characterization is to employ an in-situ HREELS system that is connected to the growth chamber, eﬀectively allowing the surface to be investigated. Noguchi et al., investigated both the As-terminated and In-terminated surfaces of native InAs(100) grown by molecular beam epitaxy (MBE) with in-situ HREELS [18]. Intrinsic electron accumulation, due to the presence of ionized donor-like surface states, was found to exist at both terminations. Sim- ulations of the HREEL spectra (performed within the HREELS of multilayers programme proposed by Lambin, Vigneron and Lucas [74] [see section 2.5.1]) aided their space-charge calculations. These calculations revealed a higher ionized surface state density for the As-rich (2 4) reconstruction than for the In-rich (4 2) reconstruction [18]. × × When such extensive facilities are unavailable, various methods of in-situ surface preparation are routinely used, such as cleaving, high temperature annealing, As- decapping, and low-energy ion bombardment and annealing (IBA). Traditionally, the non-polar (110) surfaces of III-V materials were prepared by in-situ cleaving [21]. For perfectly cleaved InAs(110) surfaces, the In- and As-derived dangling bonds relax and lie above and below the conduction band minimum (CBM) and valence band maximum (VBM), respectively [52]. Consequently, no ionized surface states exist within the band

43 3.1 Surface preparation of indium arsenide 44 gap, and provided the materials is non-degenerately doped, no band bending is observed (i.e. flat bands). However, this is rarely achieved for InAs, and electron accumulation has been reported when a minute amount of defects are introduced to the surface [94], or after the adsorption of hydrogen on the surface [95]. Due to the difficulty associated with cleaving combined with it being only applicable for the cleavage plane (110): decapping and low-energy IBA are generally preferred. Although these methods are capable of producing clean semiconductor surfaces, for InAs they can alter the electronic properties. For instance, Hall measurements of the surface conductivity of InAs have revealed that donor- like defects are introduced by Ar ion bombardment [96, 97]. The formation of donor-like defects is energetically favourable for InAs, due to the branch-point energy (or ultimate Fermi stabilization level) lying above the CBM [36]. Meanwhile, the high temperature annealing required for As-decapping (typically 625 - 725 K [98]), may also result in the formation of amphoteric defects. A recent study of InAs(100)-(4 2)/c(8 2) surfaces prepared by both As- × × decapping and IBA by Aureli et al. reported that both techniques produced high-quality LEED patterns [99]. It was reported that the two methods did not alter the electronic structure. However, the sequence of bulk and surface states displayed in the angle-resolved ultra-violet photoemission spectra of the two surfaces were strikingly different (consistent with electronic damage being introduced during the IBA). Such damage would result in the bulk Fermi level changing, which would be problematic for studies of the native electronic properties. Therefore, in order to obtain clean damage-free InAs surfaces by ex-situ means, the use of small doses of low energy (typically < 1 eV) atomic hydrogen irradiation combined by low temperature annealing has been favoured here. Such atomic hydrogen cleaning (AHC) has previously been used to successfully prepare a whole host of III-V surfaces [100]. During the AHC, surface oxides and other contaminants are removed by chemical reaction and subsequent desorption of the reaction products. The main advantage of this process lies in the fact that no structural damage due to sputtering occurs, although the exact H∗ dosage and annealing temperature varies slightly depending on material. Previous HREELS studies of InAs prepared by AHC have produced results which agree with in-situ HREEL studies of MBE-grown InAs by Noguchi et al. [101]. Here, XPS has been used to investigate the preparation of InAs surfaces by AHC. Following AHC, a contaminant-free, In-terminated InAs surface was observed, which is consistent 3.1 Surface preparation of indium arsenide 45

with the H∗ dosage and annealing temperature used. Furthermore, studies of the valence band spectrum following the AHC consistent with an In-terminated InAs(100)-(4 2) re- × construction.

3.1.2 Experimental details

The samples investigated were n-type InAs(100) (S-doped n = 2 1017 cm 3), supplied × − by Wafer Technology, UK. The hydrogen clean was performed in an ultra-high vacuum (UHV) preparation chamber connected to the main chamber of the X-ray photoemission 3 spectrometer. The clean consisted of a 16 kL (1 kL = 10− Torr s) dose of hydrogen at

275◦C, using an Oxford Applied Research thermal gas cracker with a cracking eﬃciency of 50%, followed by a further 1 hour anneal at 275 C. The as loaded and atomic hydrogen ∼ ◦ cleaned InAs(100) surfaces were investigated by XPS performed using a Scienta ESCA 300 spectrometer at the National Centre for Electron Spectroscopy and Surface Analysis, Daresbury Laboratory, UK. This incorporates a rotating anode Al-Kα x-ray source (hν = 1486.6 eV), X-ray monochromator and 300 mm mean radius spherical-sector electron energy analyser and parallel electron detection system. The analyser was operated with 0.8 mm slits and at a pass energy of 150 eV, with a eﬀective instrumental resolution of 0.45 eV. Finally, the Fermi level was calibrated to an Ag reference sample.

3.1.3 Core-level spectra

The O1s, C1s, As3d and In3d core-level photoelectron spectra before and after AHC were investigated for 30◦ and 90◦ take-off angles (TOA) with respect to the sample’s surface. All photoemission spectra were curve fitted with a Shirley background with the core-levels decomposed into Voigt line-shapes ( 25 % Lorentzian and 75 % Gaussian) [section 2.3.2]. ∼ ∼ For each spectrum, the full width at half maximum (FWHM) of each core-level line-shape was constant. In figure 3.1, a single peak at 285.3 eV - associated with the adventitious hydrocarbon - was required to fit the 90◦ TOA C1s spectrum. Meanwhile, four peaks were required to fit the as-loaded O1s spectrum displayed in figure 3.1, with binding energies of 530.9 eV, 531.7 eV, 532.6 eV and 533.3 eV. These peaks are attributed to the following: adventitious oxygen, In2O3, As2O3 and As2O5. The spin-orbit doublet (∆SO = 7.6 eV) of the In3d spectrum prior to AHC, displayed in figure 3.1, required two components to fit 3.1 Surface preparation of indium arsenide 46

Figure 3.1: The normalised XPS spectra of InAs, prior to AHC (dots). The In3d and As3d core- level regions are displayed, along with C1s and O1s regions. Each spectrum has been curve-fitted (thick lines) by a combination of Voigt functions (representing the different bonds) with a Shirley background (thin lines); details of the fit are given in the main text.

the data. The first In3d5/2 component lies at 444.5 eV and is associated with the InAs. The lower intensity second In3d component, shifted by 1 eV lying at 445.5 eV, is 5/2 ∼ attributed to the In2O3. The increasing binding energy of the peaks reflects the increasing electronegativity of the species bonded to the indium. Three spin-orbit doublets (∆SO = 0.67 eV) were required to fit the as-loaded spectrum of the As3d region shown in figure 3.1.

The three components of the spectrum are associated with the InAs, As2O3 and As2O5 bonds, such that As3d5/2 (InAs), As3d5/2 (As2O3) and As3d5/2 (As2O5) lie at 40.9 eV, 43.3 eV and 45.6 eV, respectively. Once again, the increasing binding energy of the peaks correspond to the chemical shift reflecting the increasing electronegativity of the species bonded to (and therefore the local environment of) the arsenic. The oxide components are absent following the AHC in the As3d and In3d spectra, shown in figure 3.2. Also absent are the intense peaks associated with contaminants in the C1s and O1s spectra. A small peak is distinguishable in the C1s spectrum in figure 3.2, but is considered to be a consequence of the relatively low annealing temperature used during the anneal (compared to 625 - 725 K used for As-capped InAs [98]) combined 3.1 Surface preparation of indium arsenide 47

Figure 3.2: The normalised XPS spectra of InAs, following AHC (dots). The In3d and As3d core-level regions are displayed, along with C1s and O1s regions. The intensity of the Cit1s and O1s has been reduced to the background noise level. The In3d and As3d regions are curve-ﬁtted (thick lines) by a single spin-orbit doublet (due to the In-As bond) and a Shirley background (thin lines).

with the comparatively poor base pressure at NCESS (base pressure typically 5 10 8 × − mbar in the preparation chamber). Note, when employing AHC for HREELS studies at Warwick the base pressure is typically better than 1 10 9 mbar. × − The III-V ratio was determined by the area of the In3d5/2 and As3d5/2 peaks normalised by their atomic sensitivity factors: 13.32 and 1.82, respectively. The angular dependence of the clean surface In/As ratio revealed an In-rich termination, with the In/As ratio increasing from 1.92 at a TOA = 90◦ to 2.31 at a TOA = 30◦. This is consistent with previous AHC studies of InAs(100) surfaces, where the As-stabilised InAs(100)-(2 4) × surface is achieved with a maximum annealing temperature of 473 K. Further increasing the annealing temperature results in an In-terminated InAs(100)-(4 2) surface [101]. ×

3.1.4 Valence band spectrum

XPS is particularly useful for investigating the bulk valence-band structure of III-V semiconductors [see section 2.3.3]. Furthermore, the surface Fermi level can be determined by 3.1 Surface preparation of indium arsenide 48

Figure 3.3: The normalised XPS spectrum of the In4d semi-core level and valence band region (dots). The In4d peak has been curve-fitted (thick line) by the sum of a Voigt function representing the spin-orbit doublet (corresponding to the In-As) and a Shirley background (thin lines). The inset displays the magnified valence band region. Three peaks are identified (labelled III, II, and I) and two extra features (S2 and S3) consistent with photoemission studies of III-Vs [69] and indium-rich InAs [103]. The valence band maximum was extrapolated from the leading edge of peak I to the baseline, and was found to be 0.48 0.05 eV below the Fermi level (zero eV). § extrapolating the VBM from the leading edge of the lowest binding energy valence band peak. This method is valid for XPS spectra obtained with monochromated X-rays, as used here [69]. To date, reports on the position of the surface Fermi level of the In-rich InAs(100)-(4 2) surface have been conflicting. For instance, HREEL studies by Noguchi × et al. reported an electron accumulation profile at InAs(100)-(4 2) surfaces prepared × in-situ by MBE, with a surface state density of n = 5 1011 cm 2 [18]. This would SS × − correspond to a surface Fermi level 0.46 eV above the VBM ( 0.1 eV above the CBM). ∼ ∼ However, other work by UPS ruled out the existence of electron accumulation on MBE- prepared InAs(100)-(4 2) surfaces, with the surface Fermi level lying close to the CBM × [102, 103]. Whilst for surfaces prepared by IBA the surface Fermi level was reported to be pinned 0.6 eV above the VBM [103]. Figure 3.3 displays the low binding energy region of the spectrum of the In- terminated InAs(100) surface, after AHC at a TOA = 90◦. The In4d semi-core level 3.1 Surface preparation of indium arsenide 49

Figure 3.4: The SEM image of the InAs surface following the AHC. A flat surface is observed with small amounts of In droplets ( 25 nm in diameter). ∼ was curve-fitted with a Voigt line-shape (as mentioned previously for the core-levels) with a FWHM = 0.6 eV. A single spin-orbit doublet (∆SO = 0.85 eV) [corresponding to the InAs] was necessary to obtain agreement with the spectrum. The inset shows the magnified low binding energy region of the valence-band peaks. Three valence band peaks are observed (labelled III, II and I), reflecting the VB-DOS of the valence bands [see section 2.3.3] [69]. The binding energies of the three peaks agree with the experimental band structure dispersion plots along the Γ-X direction by Hakansson et al. determined by angle-resolved UPS [103]. Two additional features (labelled S2 and S3) are also noticeable, which correspond to surface states arising from the dimer bonds and back-bonds of the surface reconstruction, repectively [103]. Surface states due to the As dangling bonds (occupied and therefore neutral) have also been shown to lie 1 eV below the VBM using ∼ angle-resolved UPS, but cannot be resolved here. For Ga-rich GaN, the presence of large formations of metallic gallium droplets results in a feature being observed close to the Fermi level, associated with the convolution of the valence band spectrum of the semiconductor with the density of states of the metallic droplets [104]. Large formations of indium droplets on the InAs surface due to the AHC have been ruled out by the lack of such a feature at the Fermi level associated with metallic indium density of states in the inset of figure 3.3. This is further supported by scanning electron microscopy (SEM) of the surface (after the AHC), where only small formations of indium droplets were observed. It is thought that these droplets were not sufficient enough to contribute to the XPS spectrum. The SEM image is shown in figure 3.4 3.2 Space-charge profiles of indium arsenide 50

In the inset of ﬁgure 3.3, the VBM was extrapolated from the leading edge of the valence-band peak I to the base line and gave 0.48 0.05 eV below the surface Fermi level, § in agreement with other photoemission studies of the InAs(100)-(4 2)-c(8 2) surface × × by Pandova et al. [105]. Therefore, the pinned surface Fermi level lies 0.12 eV above the ∼ CBM, in agreement with the ﬁndings of Noguchi et al. [18]. It will be shown [section 3.3] from HREEL studies, that the InAs(100)-(4 2) surface exhibits electron accumulation, in × agreement with the results of Noguchi et al. [18].

3.1.5 Conclusion

XPS studies of the core-level peaks of InAs has revealed a contaminant-free surface with an In-rich termination following the AHC cycle. The positions of the valence band peaks and surface states are in agreement with previous photoemission studies of the valence band region of In-rich InAs(100)-(4 2) surface. An In-rich (100)-(4 2) surface is consistent × × with the temperature used during the AHC and the In/As ratio determined as a function of angle. Finally, the pinned surface Fermi level determined by extrapolating the leading edge of the lowest binding energy valence band peak was found to be 0.48 0.05 eV. §

3.2 Space-charge proﬁles of indium arsenide

3.2.1 Introduction

Indium arsenide is unique amongst zincblende III-V semiconductors, since an electron accumulation layer is observed (instead of an electron depletion layer which is almost always observed) [18, 102, 106]. The first direct investigation of the quantized electron accumulation was with InAs-oxide-Pb tunnel junctions by Tsui, following earlier evidence of its existence by transport measurements [106]. Electron accumulation at free surfaces of InAs(100) was first observed with HREELS by Noguchi et al. who reported a reconstruction dependence with the ionized donor-like surface state density larger for the As-rich (2 4) reconstruction (n = 1 1012 cm 2) than for the In-rich (4 2) reconstruction × SS ∼ × − × (n = 5 1011 cm 2) [18]. The electron accumulation at InAs surfaces is due to SS ∼ × − evanescent, donor-like, surface states pinning the Fermi level above the CBM, resulting in the downward band bending [18, 20]. A flat band layer profile (i.e. no band bending) is observed at clean, well-cleaved non-polar InAs(110) surfaces, due to its surface exhibiting 3.3 Experimental details 51 the same relaxation as GaAs(110) [52, 107]. However, electron accumulation is observed when either a small number of defects are introduced to [94], or hydrogen is adsorbed on [95] the surface of weakly doped n-type non-polar InAs. To date, electron depletion has never been observed at InAs free surfaces.

The location of the branch-point energy (EB) has been discussed as important in determining the pinned Fermi level at semiconductor interfaces (including free surfaces), since it corresponds to cross-over from donor-like and acceptor-like surface states [see section 1.4]. Here, HREELS has been employed to investigate the near-surface space-charge proﬁles of InAs free surfaces in order to highlight the importance of the location of the bulk

Fermi level with respect to EB. HREEL studies of weakly degenerate n-type InAs(100)- (4 2) free surfaces revealed an accumulation layer proﬁle consistent with previous studies × [18, 101]. This is in stark contrast with highly-degenerate n-type InAs(110)-(1 1) free × surfaces, where a depletion layer was observed. Although the presence of a depletion layer is initially surprising, it can be understood in terms of the bulk Fermi level lying above EB. In fact, the two diﬀerent space-charge regions observed here are consistent with the bulk

Fermi level lying below (accumulation) and above (depletion) EB; from comparisons with other III-V semiconductors the origin and nature of the surface (or gap) states responsible for the Fermi level pinning mechanism at InAs free surfaces are speculated.

3.3 Experimental details

In this work two sets of InAs samples supplied by Wafertech, UK were investigated, n-type InAs(100) (S-doped, n 2 1017 cm 3) and InAs(110) samples (S-doped, n 5 1018 ∼ × − ∼ × 3 cm− ). Following insertion into the HREELS chamber, the preparation of the InAs(100) samples was achieved by AHC which has been shown to successfully prepare clean InAs surfaces [see section 3.2]. The InAs(100) samples were prepared using a two stage method involving a 5 kL dose of H∗ at 125◦C followed by a further 20 kL dose of H∗ at 200◦C to produce a clean As-rich (2 4) reconstruction. Following the cleaning, the surface was × dosed with sulphur using an electrochemical cell for investigating the sulphur-induced electron accumulation (reported elsewhere [101]). The sulphur was fully desorbed after annealing at 400 C and produced an In-rich (4 2) reconstruction, as shown by the LEED ◦ × pattern in ﬁgure 3.5 a). 3.4 HREEL spectra 52

Figure 3.5: The LEED patterns following cleaning cycles of the a) InAs(100)-(4 2) b) InAs(110)- (1 1) reconstructed surfaces recorded at incident electron energies of 57.7 eV and× 49.0 eV, respec- tiv×ely.

The surface preparation of the InAs(110) samples involved initially cleaning the sample at 60◦C with 15 kL dose of H∗ followed by a further 15 kL dose of H∗ at 300◦C and a final anneal at 350 C for 10 minutes. Sharp (1 1) LEED patterns, indicating well- ◦ × ordered surfaces, were observed after cleaning as shown in figure 3.5 b). The removal of atmospheric contaminants for both sets of samples was confirmed using HREELS, by the absence of vibrational modes associated with adsorbed hydrocarbons and native oxides. The adsorption of hydrogen is known to result in the formation of an accumulation layer at InAs(110) surfaces [95]. After the AHC, the HREEL spectra contained no In-H (205 meV) or As-H (260 meV) vibrational modes [108], indicating that any hydrogen adsorbed during the AHC was completely desorbed by the annealing.

3.4 HREEL spectra

The energy loss of the conduction band electron plasmon is related to the carrier concentration [see section 2.4]. The dispersion of the plasmon peak as the kinetic energy of the incident electron is varied indicates the from of the electron density profile close to the surface. The plasmon peak energy will generally shift towards higher (lower) energies with increasing probing energy for depletion (accumulation) layers. However, the situation is 3.4 HREEL spectra 53 further complicated by spatial dispersion, which shifts the plasmon peak to higher energies with decreasing probing depth [see section 2.5.3]. Also, the plasmon and phonon can interact if they lie in close proximity energetically, resulting in the formation of a coupled mode, known as a plasmaron. Figure 3.6 a) displays the HREEL spectra recorded from the InAs(100)-(4 2) × surface, for a range of incident energies. Here, the proximity of the Fuchs-Kliewer phonon frequency (29 meV) [77] to the conduction band plasmon frequency has resulted in the formation of a plasmaron. The presence of the plasmaron requires semi-classical dielectric theory simulations of the spectra in order to investigate the near-surface profile. The spectra obtained from the InAs(110)-(1 1) surface are shown in figure 3.6 b). Here the × Fuchs-Kliewer phonon and plasmon peaks are clearly distinguished and are not coupled. In this case, the plasmon peak lies at a greater energy-loss position, reflecting the higher carrier concentration of this sample compared to the InAs(100)-(4 2). The lack of a clear × plasmon peak shift with increasing probing energy could correspond to the opposing shifts due to a depletion layer profile and spatial dispersion cancelling each other out. The corresponding dielectric theory simulations of the HREEL spectra, for each incident energy, are shown in figures 3.6 a) and b). The HREEL simulations were calculated using a wavevector dependent dielectric function [see section 2.5], as described by Lambin et al. [70, 74]. In this model, the solid at the surface is approximated by a few thin layers on top of a bulk layer. Each layer is described by its own individual dielectric function and thickness. An effective dielectric function is then calculated from the layer contributions and is then used to simulate the spectra. Two unique layer profiles were used to simulate all of the spectra shown in figures 3.6 a) and b). For the InAs(100)-(4 2) surface, a 40 A˚ dead layer, followed by two further × layers above a bulk layer were required. The larger plasmon energies required in the second and third layers compared to the bulk layer is consistent with the accumulation of charge near the surface. The dead layer was required to account for the quantized nature of the electron wavefunctions, resulting from the potential barrier formed at the surface, which suppresses the carrier concentration close to the surface [18]. An accumulation layer profile is immediately ruled out for the InAs(110)-(1 1) surface since a two-layer profile × was required consisting of of 40 A˚ layer of zero plasmon frequency and a bulk layer. 3.5 Analysis 54

Figure 3.6: The HREEL spectra (points) from the clean a) InAs(100)-(4 2) surface and b) InAs(110)-(1 1) surface, for a range of probing energies are shown, vertically× oﬀset. The corresponding semi-classical× dielectric simulations (lines), for each incident energy, are also shown.

3.5 Analysis

The HREEL layer profiles used in the semi-classical dielectric simulations were translated from plasma frequencies into carrier concentrations. The narrow band gap of InAs (0.356 meV at 300 K) means the non-parabolicity of the conduction band needs to be considered in any calculation. Here, the α-approximation model was used to describe the conduction band dispersion [25], using the parameters cited in the recent review of III-V parameters by Vurgaftman et al. [109]. The two translated HREEL layer profiles, used to simulate the spectra of the two surfaces, are shown in figures 3.7 and 3.8. To complicate the situation further, conduction band renormalisation effects due to 3.5 Analysis 55 electron-electron and electron-ionized impurity interactions (previously studied in highly n-type Si and Ge [110]) cannot be neglected when investigating the highly-degenerate n- type InAs(110)-(1 1) surface, due to the high bulk carrier concentration of the material. × Such effects have been shown to be significant in degenerately doped n-type InN [111], a material similar to InAs with a non-parabolic conduction band and intrinsic electron accumulation [17]. The resultant band gap shrinkage, due to the conduction band renormalisation, has been fully incorporated into the α-approximation used to calculate the non-parabolic conduction band dispersion. The band gap shrinkage has been described by conduction band shift due to electron-electron interactions (∆Ee e), such that − 2 2 2e kF e kT F 4 kF ∆Ee e = − 1 arctan , (3.1) − π²(0) 2²(0) π k − · − µ T F ¶¸ 1/2 where, kT F = (2/√π)(kF /aB) is the Thomas-Fermi screening wave vector such that ˚ aB = 0.53²(0)(m0/mF∗ ) is the Bohr radius measured in A, and an electron-impurity related conduction band shift (∆Ee i), given by − 4πe2n ∆Ee i = − , (3.2) − ²(0)aBkT F as reported by Wu et al. for describing InN [111]. To validate these calculations, the Hall measurements of InAs samples irradiated by high-energy protons by Brudny˘i et al. were referred to [112]. Their work revealed that the carrier concentration stabilised at n = 2.6 1018 cm 3. The stabilised carrier con- × − centration, corresponds to the bulk Fermi level lying at EB [36]. Any further irradiation results in the formation of compensating amphoteric defects that ensure that the Fermi level remains stabilised at EB, as described by the amphoteric defect model [50] [section

1.4.2.2]. The positions of the band edges with respect to EB (or Fermi stabilisation level) have been shown to be important for understanding the electronic properties of a semiconductor [51]. For InAs, EB lies 0.500 eV above the VBM from real-space Green function methods and empirical tight-binding calculations [47, 48]. The high-energy irradiation stabilised carrier concentration of n = 2.6 1018 cm 3 reported by Brudny˘i et al. [112], × − corresponds to a Fermi level of 0.198 eV above the CBM with a renormalised band gap of 0.301 eV, in our calculations. Therefore, the calculated Fermi level of 0.499 eV above the VBM from the Hall measurements is in excellent agreement with the 0.500 eV expected. Incorporating the effects of non-parabolicity in calculating space-charge profiles has been shown to be necessary for InAs [52]. Here, realistic smooth charge-profiles were 3.5 Analysis 56

Figure 3.7: The translated histogram HREEL layer proﬁle (dashed line) and corresponding smooth Poisson-MTFA solutions (solid line) for the InAs(100)-(4 2) surface. When the bulk × Fermi level lies below the branch-point energy (EB), an electron accumulation layer proﬁle is observed. The inset plots the resultant downward band bending of the valence band maximum (VBM), conduction band minimum (CBM) and EB, with respect to the Fermi level (EF ).

calculated by solving the Poisson equation within the modified Thomas Fermi approximation (MTFA) [see section 1.5]. The MTFA correction reduces the carrier concentration to zero at the surface and describes the interference between the incoming electron waves and those reflected at the surface potential barrier [54]. This allows the non-parabolicity to be incorporated straightforwardly compared to the complications associated with appropriately modifying the Schrödinger equation. Such an approach has previously proved successful in describing the accumulation profiles of both InAs [101] and InN [113]. The corresponding Poisson-MTFA solutions for the two translated HREEL layer profiles are shown in figures 3.7 and 3.8, for the lowly- and highly-degenerate n-type InAs samples, respectively.

3.5.1 InAs(100)-(4 2) × In figure 3.7 an accumulation layer profile is observed with a downward band bending of 0.110 eV, pinning the Fermi level at 0.481 eV above the VBM, facilitated by a donor-like surface state density of 5.83 1011 cm 2 in agreement with previous studies [18]. The × − 3.5 Analysis 57 inset plots the corresponding band bending as a function of depth; the Fermi level tends towards EB at the surface. The Poisson-MTFA used to solve the space-charge region has a characteristic length term (L), which corresponds to the minimum space for a particle determined by ∆z∆p ¯h, where ∆z = L and ∆p is the change in momentum of the ∼ particle [114]. This length corresponds to the radius of the bulk plasmon i.e. the de Broglie wavelength [115]. The bulk carrier concentration of the InAs(100)-(4 2) corresponds to × a Fermi level 0.015 eV above the CBM. In the calculations, L = 1/kF [where kF is the 2 1/3 Fermi wavevector and is given by kF = (3π n) ] has been appropriately used as required for a degenerate semiconductor. For this carrier concentration, L = 57 A˚ and corresponds well to the distance between zero electron density at the surface to the peak of electron accumulation, as shown in figure 3.7. The amount of band bending required within the Poisson-MTFA of the InAs(100)-(4 2) corresponds to a pinned Fermi level of 0.481 eV × above the VBM at the surface. This result agrees with the 0.48 0.05 eV obtained § from XPS studies of AHC-prepared In-rich InAs(100)-(4 2) surfaces reported above [see × section 3.2]

3.5.2 InAs(110)-(1 1) × Figure 3.8 displays the translated HREEL layer profile required to simulate the HREEL spectra, consisting of a 40 A˚ thick layer of zero plasma frequency. The Poisson-MTFA solution for the depletion layer (assuming the Fermi level tends to EB at the surface) is presented in figure 3.8. For further comparison with the HREEL layer profile, the Poisson-MFTA solution for the flat band case (i.e. an ionized surface state density of zero) is also shown in figure 3.8; the calculated electron density profile is consistent with the description by Appelbaum and Baraff [116]. Although both the dead layer and depletion region describe the reduction of the electron concentration close to the surface, they are distinguishable as shown by Ritz and Luth¨ [117]. For flat band and accumulation profiles, the dead layer corresponds to a region of uncompensated donors localised at the surface [116]. The dead layer is typically found to be roughly L/2 for HREEL layer simulations of accumulation (as seen in figure 3.7) and flat band space-charge regions. For n = 4.8 1018 cm 3 the bulk Fermi level is 0.263 eV above the CBM, which yields L = 19.2 A˚ × − for n = 4.8 1018 cm 3 with a dead layer width of 10 A.˚ Here, a 40 A˚ layer of zero × − ∼ plasma frequency is required to simulate the spectra, which is far larger than the 10 ∼ 3.5 Analysis 58

Figure 3.8: The translated histogram HREEL layer profile (dashed line) and corresponding smooth Poisson-MTFA solutions for a flat band scenario (solid gray line) and a depletion layer case (solid black line) for InAs(110)-(1 1) surface are shown. A depletion layer is considered to × best represent the HREEL layer profile, consistent with the bulk Fermi level (EF ) lying above the branch-point energy (EB). Close to the surface (z 10 A)˚ a feature associated with construc- tive interference between the electron wavefunctions∼is observed for both calculations. The inset plots the resultant upward band bending of the valence band maximum (VBM), conduction band minimum (CBM) and EB with respect to EF .

A˚ necessary to approximate the flat band profile (as shown in figure 3.8). Instead, the HREEL layer profile represents the two-layer description of the depletion layer solution (refer to figure 3.8). For a degenerate semiconductor it is necessary to use a Thomas-Fermi screening length (λT F ) rather than thermal screening length for the depletion layer [118]. For n = 4.8 1018 cm 3, λ = 48 A˚ and agrees with 40 A˚ required by the HREEL × − T F layer profile to simulate the spectra. Therefore, a depletion layer profile rather than a flat band case is concluded to be present at the highly degenerate n-type InAs(110)-(1 1) × surface prepared by AHC. The inset of figure 3.8 displays the corresponding 0.050 eV upward band bending, driven by the 1.04 1011 cm 2 acceptor-like surface states, for the × − Poisson-MTFA depletion layer solution. The upward band bending results in the Fermi 3.6 Discussion 59

level being pinned at 0.502 eV above the VBM i.e. close to EB.

3.6 Discussion

At semiconductor free surfaces, the Fermi level pinning mechanism is driven by a small number of ionized surface states, referred to as gap states [3, 20]. Such states arise from the termination of the bulk crystal at the surface and merely describe the spatially localised surface wavefunctions; these wavefunctions satisfy the Schrödinger equation with the requirement that they exponentially decay into the vacuum [20, 21]. For instance, dangling bonds associated with a particular reconstruction represent an example of a gap state. The evanescent nature of these states is satisfied provided that their wavevectors are complex and therefore the surface states are restricted to ‘forbidden’ band gap regions. The spatially localised nature of the surface states means that their character is derived from contributions over a substantial portion of the Brillouin zone, whilst the Γ-point provides little in comparison [5]. States will have either predominantly valence or conduction band character corresponding to donor- and acceptor-like states, respectively. The cross-over from donor- to acceptor-like states is referred to as EB, which lies close to the middle of the average or dielectric gap at the mean-value point [5, 47]. Charge neutrality is satisfied when all donor-like states are occupied and all acceptor-like states are empty, and occurs ideally when the Fermi level lies at EB. However, the large screening lengths of these surface states combined with their discrete rather than continuous nature means that the Fermi level pinning can occur away from EB [4].

The location of the bulk Fermi level with respect to EB chieﬂy determines the space-charge proﬁle observed. The location of EB can be estimated using 1 E [EC + EV ], (3.3) B ≈ 2 where 1 EV = EV ∆ , (3.4) − 3 SO and EC is the indirect conduction band edge (minimum), EV is the valence band edge

(maximum) and ∆SO is the spin-orbit splitting [5]. Typically, EB < Eg/2 for most semiconductors, as shown in ﬁgure 3.9. GaAs, the archetypal compound semiconductor, provides an excellent example of the role EB plays in the formation of the space-charge layer; 3.6 Discussion 60

n-type GaAs always has a bulk Fermi level above EB and so, if any occupied acceptor-like states exist, upward band bending will occur with charge neutrality achieved once the ultimate band bending is compensated by the remaining negatively-charged acceptor-like surface states. A depletion layer is then formed at the surface with the pinned surface

Fermi level lying close to EB, which for GaAs lies close to the mid-gap position. When a depletion layer is not observed with n-type GaAs free surfaces, then ﬂat bands occur i.e. there is no band bending due to the absence of ionized surface states. Such a situation occurs if the bulk Fermi level lies at EB so that no ionized states exist or for perfectly cleaved non-polar (110) surfaces. For all compound semiconductors, the anion and cation dangling bonds have valence and conduction band character, respectively. The non-polar surface, if perfectly cleaved, relaxes such that all of the anion and cation dangling bonds lie below the VBM and above the CBM, respectively [107]; provided that the Fermi level lies within the band gap i.e. non-degenerate, then all of the states are neutral. However, if any imperfections exist or if the bulk Fermi level lies such that it does ionize a gap state, then a space-charge layer will form to maintain overall charge neutrality.

The location of EB high above the CBM for InAs - as shown in ﬁgure 3.9 - generally results in the formation of an accumulation layer, due to the bulk Fermi level lying below

EB. Charge neutrality is achieved when the surface Fermi level is pinned close to EB, with the ultimate amount of downward band bending being compensated by the remaining unoccupied donor-like surface states. However, if the bulk Fermi level of InAs lies above

EB, then the situation is the same as for n-type GaAs and a depletion layer is expected.

It is important to note that the position of EB is not unusually high for InAs, rather the Γ-point CBM is extremely low. In fact, there is evidence that the position of EB is universal for all covalent and weakly ionic semiconductors, lying approximately 4.9 eV below the vacuum level [119, 120]. Instead, chemical trends reveal that the CBM is particularly sensitive to the cation; by changing the cation from Al Ga In, the → → Γ-point minimum decreases, as shown in figure 3.9 [5]. From this rule alone, the same phenomenon should also occur for InSb. However, the VBM is affected most by the spin- orbit splitting. Antimonides have the greatest spin-orbit splitting and this results in the Γ-point maximum lying higher than for arsenides (see figure 3.9) [5]. This is the reason why EB lies close to the VBM for InSb, whilst for InAs it lies above the CBM. As previously explained, the high-energy proton irradiated InAs stabilised carrier 3.6 Discussion 61

Figure 3.9: The band line-up of AlAs, GaAs, InAs and InSb referenced to the calculated positions of the branch-point energy (EB) (solid thin line) [5, 47] using band parameters from the III-V review by Vurgaftman et al. [109]. Also shown is the midgap (Eg/2) position of each of the semiconductors (dotted thin line). The change in the cation from Al Ga In acts to push the conduction band minimum (CBM) downwards, whilst as the spin-orbit→splitting→ increases from As to Sb the valence band maximum (VBM) is pushed upwards. InAs (highlighted) represents an extreme point in the band line-up since its CBM lies below EB and its low location is responsible for free surface electron accumulation and proclivity to n-type conductivity.

concentration corresponds to the bulk Fermi level lying at EB; the carrier concentration of n = 2.6 1018 cm 3 reported by Brudny˘i et al., [112] means that the InAs(100)- × − (4 2) (n = 1.73 1017 cm 3) and the InAs(110)-(1 1) (n = 4.8 1018 cm 3) samples × × − × × − investigated here have bulk Fermi levels below and above EB, respectively. Accumulation (see ﬁgure 3.7) and depletion (see ﬁgure 3.8) layers are observed when the bulk Fermi level lies below and above EB, respectively. Furthermore, in both cases the band bending can be explained in terms of the Fermi level tending towards EB at the surface.

This work highlights the importance of both the location of EB and the bulk Fermi level when investigating the near-surface electronic properties of a semiconductor. Within the context of these results, it is possible to speculate on the physical origin of the surface states responsible for the universal nature of the Fermi level pinning mechanism at free surfaces. Although adatom-induced surface states cannot not be ruled out - due to the presence of possible adatoms (e.g. oxygen and hydrogen) below our detection limit - the 3.6 Discussion 62 surface states are likely to be associated with states intrinsic to the semiconductor e.g. defects. The remarkable agreement between studies of InAs grown by molecular beam epitaxy, characterized in-situ with HREELS by Noguchi et al. [18] and the InAs(100)-(4 2) × case reported here supports this claim. Also, defects are consistent with the presence of a space-charge layer observed at heavily-doped n-type InAs(110)-(1 1) reported here; per- × fectly cleaved III-V(110)-(1 1) surfaces exhibit flat bands, yet space-charge formation oc- × curs following the introduction of defects [94]. Furthermore, studies of adsorbate-induced surface states at InAs(110)-(1 1) surfaces revealed that non-degenerately doped p- and × n-type (such that EF < EB) surfaces produced inversion and accumulation layers, respectively; following continued exposure of chlorine and oxygen, the Fermi level became pinned at 0.52 eV above the VBM for both cases, suggesting that the physical origin of the adsorbate-induced surface state is the same and must be related to defects which are not adsorbate specific [121]. The remainder of this section focuses on the striking correlation between Fermi level pinning in heavily irradiated semiconductors and at metal-semiconductor interfaces reported by Walukiewicz [36], within the context of these findings here of the Fermi-level dependence of the type of surface state (whether acceptor- or donor-like). It is known that the formation energies of the donor-like (acceptor-like) defect complexes decrease as the bulk Fermi level increases (decreases) with respect to EB, according to the amphoteric defect model [50]. These amphoteric defects, when localised at the surface, are considered to be the gap states responsible for the Fermi level pinning, such that if the Fermi level lies above (below) EB, the creation of acceptor- (donor-) like defect complexes at the surface becomes energetically favourable. To highlight this, the positron annihilation studies of

GaAs are referred to, in which p-type material (bulk Fermi level < EB) formed anion vacancies and anion on cation antisite (AAS) defect complexes of donor-like character; and n-type material (bulk Fermi level > EB) created cation vacancies and cation on anion antisite (CAS) defect complexes of acceptor-like nature [36, 50]. Antisite defects have previously been considered as the surface state responsible for the pinning mechanism, from comparisons of experimental results and tight-binding calculations [122]. In other studies, the CAS defect, with largely conduction band character, is considered to be the acceptor-like surface state responsible for pinning the Fermi level at most n-type III-V surfaces [123]. Such a situation requires that some of the CAS defects 3.7 Conclusion 63 are occupied in order to be negatively charged, otherwise they would be neutral [20]. For most III-Vs this appears plausible, except for n-type InAs where donor-like surface states are generally observed. Olsson et al. suggested that the source of the donor-like surface states was CAS defects [102], as suggested by P¨otz and Ferry [123]. However, these states would only ever be either neutral or negatively charged. Instead, the donor-like surface states are attributed to unoccupied dangling bonds of the AAS defect, with largely valence band character, which would be positively charged. The downward band bending is then facilitated by the transfer of electrons to the conduction band from a small number of ionized antisite defects (typically of the order of 1012 cm 2). By analogy, it is likely ∼ − that the occupied CAS and unoccupied AAS are the acceptor-like and donor-like surface states responsible for the Fermi level pinning, respectively, with the location of the bulk

Fermi level with respect to EB determining the likelihood of each type of defect at the surface.

3.7 Conclusion

The Fermi level pinning mechanism at semiconductor free surfaces is discussed in terms of the position the bulk Fermi level with respect to EB. From HREEL studies of InAs, an electron depletion and accumulation layer were observed when the bulk Fermi level was above and below EB, respectively. Depending on the location of the bulk Fermi level, amphoteric defects are incorporated into the reconstruction, which if ionized facilitate the band bending that results in the surface Fermi level becoming pinned close to EB. Occupied CAS and unoccupied AAS defects at the surface are considered to be the ionized surface states responsible for the depletion and accumulation layer proﬁles, respectively. Chapter 4

Indium nitride: surface preparation

4.1 Introduction

The preparation of clean, well-ordered and stoichiometric surfaces of III-V semiconductors is crucial for studying their surface and near-surface properties. Ideally, surface characterization is undertaken in a vacuum chamber connected to the epitaxial growth facility. However, when such facilities are unavailable, various in-situ preparation methods, such as high temperature annealing and low energy ion bombardment and annealing (IBA), are routinely used. Preparation of clean InN surfaces using these techniques is difficult for two reasons. The first is the fact that the oxide desorption temperature exceeds the low dissociation temperature of InN (approximately 550◦C) [100, 124]. As a result, cleaning by annealing is restricted to low temperatures in order to prevent In-enrichment, and is therefore largely ineffective. The second reason is associated with the extremely low conduction band minimum (CBM) at the Γ-point of InN [125] [Chapter 6]. The location of the Γ-point CBM, below the Fermi level stabilisation energy, favours the existence of donor impurities and formation of donor-like defects [119]. A similar situation exists for InAs [36]. The standard method of in-situ cleaning of III-V surfaces, using cycles of low energy IBA, has been shown to result in severe structural damage and the introduction of donor-like defects for InAs surfaces [126]. Therefore, IBA is also unsuitable for InN. Indeed, recent studies of InN surface preparation have shown that Ar+ IBA results in In-enrichment due to preferential sputtering [127]. Whilst this effect can be minimised by optimised sputtering conditions (grazing incidence and low ion energy) it cannot be completely eradicated. Further investigation of the electronic effects of IBA on InN surfaces is required [Chapter 7]. In this Chapter, the use of low energy (typically < 1 eV) atomic hydrogen irra-

64 4.2 Experimental details 65 diation to produce clean InN surfaces is reported. A whole host of III-V surfaces have previously been successfully prepared by atomic hydrogen cleaning (AHC) [100]. During AHC, surface oxides and other contaminants are removed by chemical reaction and subsequent desorption of the reaction products. The main advantage of this process lies in the fact that a signiﬁcantly lower annealing temperature is required to remove the surface contaminants, although the exact H∗ dosage and annealing temperature varies slightly depending on material. For InN, as mentioned previously, this fact is especially important to ensure clean, well-ordered, atomically ﬂat, stoichiometric InN surfaces with limited N desorption. An earlier attempt to clean InN surfaces by AHC was undertaken by Ohashi et al

[100]. In their work they produced promising results, which indicated that H∗ irradiation is effective in reducing native oxides using a thermal cracker with a H H conversion 2 → ∗ efficiency of 1.5 %. Here, clean, well-ordered, stoichiometric InN surfaces have been ∼ prepared using AHC, as confirmed by a combination of X-ray photoemission spectroscopy (XPS), low electron energy diffraction (LEED) and high-resolution electron energy-loss spectroscopy (HREELS).

4.2 Experimental details

The InN layer investigated was unintentionally n-type doped. Details of the molecular beam epitaxial growth can be found elsewhere [82]. Single field Hall measurement indicated an average conduction electron density, n = 1.83 1018 cm 3 and an average × − 2 1 1 mobility of µ = 1200 cm V− s− . The polarity of the InN film was determined by co-axial impact collision ion scattering spectroscopy to be approximately 75 % In-polarity and 25 % N-polarity at the surface [91]. The XPS spectra were recorded in an ultra-high vacuum (UHV) chamber using a dual anode Mg Kα x-ray source (Vacuum Generators, UK) with a 100 mm concentric hemispherical electron energy analyser (VSW, UK). A range of take-off angles (TOA) referenced to the surface of the sample, from 90◦ to 15◦, were used. All of the binding energies were calibrated with respect to the adventitious hydrocarbon C 1s peak at 284.6 eV [128]. The HREEL spectra were obtained in a separate UHV chamber. The HREEL spectrometer (VSW Ltd., UK) consists of a fixed monochromator and rotatable analyser; 4.3 XPS spectra 66

both were of the 180◦ hemispherical deﬂector type, with a four-element entrance- and exit-lens system. The instrumental resolution was typically 12 meV full width at half maximum (FWHM) in the elastic peak. The HREELS experiments were performed using a specular scattering geometry with an incident and scattered polar angle of 45◦. Finally, both chambers were equipped with a retractable LEED optics (Omicron, Germany). An Oxford Applied Research thermal gas cracker, with a cracking eﬃciency of ∼ 50% was used to prepare the InN surface. In both UHV chambers the AHC consisted of a 8 kL dose of hydrogen, followed by a further 8 kL at 175◦C. Afterwards it was annealed at 300◦C for 2 hours before being left to cool to room temperature.

4.3 XPS spectra

The 45◦ TOA core-level spectra of the C1s and O1s photoelectrons prior to and after AHC are shown in figure 4.1. It can be seen that prior to the clean, both the C1s and O1s spectra show strong signals. The X-ray photoemission spectra were curve-fitted using a Shirley background and decomposing the core-level signals into Voigt line-shapes (25 % Lorentizian and 75 % Gaussian) of equal FWHM (1.6 eV) [see section 2.3.2]. A single peak at 284.6 eV describes the C1s signal. For the O1s spectra prior to AHC, two peaks are necessary to reproduce the data, with a more intense peak at 530.3 eV and a slightly less intense peak at 532.0 eV. The former is assigned to the In2O3 contribution, and the latter is assigned to adventitious oxygen. After AHC, both the C1s and O1s signals in figure 4.1 reduce to the background noise level. Although there is an indication that a C1s peak remains after cleaning, it will be mentioned later that AHC is able to produce surfaces with contamination levels < 0.1 % of a monolayer.

In figure 4.2, the corresponding 45◦ TOA In3d and N1s core-level spectra prior to and after AHC are shown. The XPS spectra are also curve-fitted using the same method as previously described for the C1s and O1s spectra. Before and after AHC, the N1s spectrum is fitted by a single peak at 397.0 eV corresponding to the In-N bond [129]. The intensity at high binding energies (> 400 eV) in the N1s spectra in figure 4.2 is due to the shoulder from the Ta4d peak at 406 eV [128], resulting from the Ta foil clips used 5/2 ∼ to mount the sample. There is the possibility that the small C1s peak after AHC may be associated with adventitious carbon from the Ta foil clips. 4.3 XPS spectra 67

Figure 4.1: The 45◦ TOA C1s and O1s core-level spectra (circles) recorded prior to and after AHC. For the prior to AHC spectra, for both the C1s and O1s, the corresponding fits (thick lines) are shown. The decomposed background and peak contributions of each fit (thin lines) are also shown vertically offset for all spectra.

The spin orbit doublet (7.6 eV) of the prior to AHC In3d spectrum in figure 4.2 consists of two components, in contrast to the N 1s spectrum. The first In3d5/2 component is located at 443.7 eV, corresponding to the In-N bond. The second In3d5/2 component shifted by 1 eV at 444.7 eV in figure 4.2 is attributed to In O . This 1 eV shift is ∼ 2 3 consistent with previous photoelectron spectroscopy results for InP [130]. Other features are due to the α3 and α4 satellite energies of the spin orbit In3d and In2O3 doublets from the Mg Kα source [128]. The In2O3 contributions to the spin orbit In3d doublet are absent after AHC (as shown in figure 4.2). The In/N ratio is 2.8 0.7, as determined § from the In3d5/2 and N1s Voigt line-shapes in the after AHC spectra (figure 4.2), with the appropriate atomic sensitivity factors. Finally, LEED revealed a (1 1) surface periodicity × after cleaning, which is shown in the inset of figure 4.4. 4.4 Angular dependence 68

Figure 4.2: The 45◦ TOA In3d and N1s core-level spectra (circles) recorded prior to and after AHC. For each spectrum the corresponding curve fit is also shown (thick lines). The decomposition of each fit into background and peak components (thin lines) is also shown vertically offset for all spectra. Also highlighted in the In3d spectra is the the spin orbit In2O3 (solid lines) and In3d (dashed lines) doublets and their corresponding satellite peaks (dashed lines). After AHC the spin orbit In2O3 doublet is absent.

4.4 Angular dependence

The angular dependence of the In/N intensity ratio is plotted in the inset of ﬁgure 4.3.

Also shown in figure 4.3 are the In3d and N1s core-level spectra after cleaning, at both 90◦ and 30◦ TOA. By decreasing the angle, the escape depth of the photoelectrons is reduced. As a result, the smallest TOA spectra have the greatest surface sensitivity. By reducing the effective probing depth the counts are reduced, as seen in both the In3d and N1s spectra. However, the N1s intensity is found to decrease by a greater amount relative to the In3d signal. This is highlighted further in the inset of figure 4.3, with the increase in the In/N ratio with decreasing angle. Therefore, the surface region is found to be In-rich. In order to further interpret the variation in the In/N intensity ratio with angle, model computations were performed by summing the In and N intensity contributions from each atomic layer, using the standard expression I = I exp( d/λ sin θ ), where, I 0 − i 4.4 Angular dependence 69

Figure 4.3: The In3d and N1s core-level spectra after AHC, at both 90◦ and 30◦ TOA. The In/N intensity ratio determined from XPS against angle is plotted in the inset. Also included in the inset is the calculated variation in the In/N photoelectron intensity ratio with angle, assuming an In-adlayer model analogous with GaN 0001 -(1 1) surfaces. { } ×

is the attenuated XPS intensity from an atomic layer of depth (d), for a TOA (θi). I0 refers to the intensity from the layer if un-attenuated and λ is the inelastic mean free path of the photoelectrons within the sample [see section 2.3.2]. Mean free path lengths of 12.28 A˚ for the In3d5/2 photoelectrons and 11.41 A˚ for the N1s photoelectrons are used in the modelling [131]. For a bulk-truncated In-terminated, In-polarity, stoichiometric wurtzite crystal, the expected In/N ratio is 1.1 at 45◦. This is significantly smaller than the experimental ratio of In/N = 2.8 0.7. However, comparisons with GaN provide § a better interpretation of the In/N ratio. In-rich conditions are used during growth in order to achieve high quality InN [132], suggesting that the InN surfaces are stabilised by In atoms in analogy with GaN grown under Ga-rich conditions [133]. It is believed that this Ga adlayer formation at GaN surfaces results from the large size difference between Ga and N, resulting in naturally occurring Ga-rich surface reconstructions [133]. A similar situation should also occur for InN but to a larger degree, because of the larger size mismatch between In and N. Auger electron spectroscopy measurements on GaN 4.5 HREELS 70 have revealed a 2-3 monolayer (ML) Ga-adlayer for Ga-polarity (0001) ‘pseudo’ (1 1) × surfaces and a 1 ML Ga-adlayer for N-polarity (0001¯)-(1 1) surfaces [133]. For Ga- × polarity, a laterally contracted (1 1) Ga-bilayer has been calculated from first principles × for GaN(0001) [86]. It is reasonable to assume that a similar termination is one of the energetically favourable (1 1) reconstructions that can naturally exist at InN surfaces. × Considering a similar adlayer situation for 75 % In-polarity and 25 % N-polarity, In- terminated, bulk stoichiometric, wurtzite InN, the In/N intensity ratio was calculated and is plotted in the inset of figure 4.3. It is in agreement with In/N intensity ratio determined by XPS, within error limits.

4.5 HREELS

HREELS provides further indication that AHC produces clean, well-ordered InN surfaces. The technique is especially sensitive to adsorbate vibrational modes associated with surface contaminants (to 0.1 % of a monolayer [134]), which interact with the probing electrons. The HREEL spectrum recorded prior to AHC in figure 4.4(a) shows several strong vibrational modes associated with atmospheric contaminants. These were confirmed as adsorbate vibrational modes since their peak intensity decreased as the probing energy 1/2 (E) increased by the factor E− [135]. The band between 80 and 120 meV is attributed to oxide vibrational modes, in this case the stretching mode ν(In-O) [126]. The peaks at 170 meV and 360 meV are associated with the hydrocarbon deformation mode ∼ ∼ δ(C-H) and the hydrocarbon stretching mode ν(C-H), respectively [126]. After AHC, the FWHM of the elastic peak is reduced from 39 meV to 12 meV, as seen in figure 4.4(b). This FWHM of 12 meV is consistent with the nominal spectrometer resolution for the settings used. The adsorbate vibrational modes are no longer present in figure 4.4(b) indicating, as previously mentioned, that AHC produces contaminant free surfaces. The removal of the vibrational modes results in the appearance of the Fuchs-Kliewer phonon peak at 66 meV and a conduction electron plasmon peak at 250 meV. The clean ∼ ∼ surface HREEL spectrum in figure 4.4(b) was simulated using semi-classical dielectric theory, details of which can be found elsewhere [see section 2.5]. The simulation considers only the interaction between the probing electrons and the excitations arising from the conduction electrons and lattice vibrations. Only HREEL spectra from clean well-ordered 4.6 Conclusion 71

Figure 4.4: The HREEL spectra (points) for a probing energy of 15 eV are shown (a) prior to and (b) after AHC. Surface contaminant vibrational modes are present in (a), whilst these contaminant modes are absent after AHC (b). The clean surface spectrum in (b) is simulated by semi-classical dielectric theory (line). The inset shows the (1 1) LEED pattern recorded after cleaning, using an electron energy of 164 eV. ×

InN surfaces can be successfully simulated.

4.6 Conclusion

It has been shown that an AHC process is able to overcome the problems associated with the low dissociation temperature and particularly low Γ-point CBM, to prepare clean, well-ordered surfaces of bulk stoichiometric InN. This was conﬁrmed by a combination of XPS, HREELS and LEED. Analysis of the XPS revealed angle dependent In/N intensity ratios consistent with calculations of mixed polarity InN with In-adlayers. The removal of atmospheric contaminant vibrational modes in the HREEL spectra further veriﬁed a clean and well-ordered InN surface. Chapter 5

Indium nitride: valence band structure

5.1 Introduction

Previous photoemission studies of high-quality InN have only focused on the core-levels and the surface Fermi level [16, 72, 127, 136, 138]. There has been a distinct lack of studies of the valence band structure of InN, due to both the poor quality of early InN samples and the difficulty of appropriately preparing surfaces for photoemission studies. The advent of reproducible growth of single-crystalline InN [83, 137] in 2002, combined with the ability to prepare clean InN surfaces by use of atomic hydrogen cleaning (AHC) [see Chapter 4] in 2005 [72], has meant that it is now possible to investigate the valence band structure of InN. In this work, the valence band XPS spectra from high-quality, single-crystalline InN(0001) surfaces prepared by AHC are investigated. The experimental results are compared with theoretical calculations of the VB-DOS. Theoretical calculations of InN suffer from the effects of the shallow In4d semi-core electrons [139]. Typically, density functional theory (DFT) calculations within the local density approximation (LDA) result in negative band gap values, due to severe overestimation of the amount of pd-repulsion arising from the proximity of the In4d electrons to the valence band [140, 141]. This can be overcome by incorporating the true amount of pd-repulsion into self-interaction corrections (SIC) [140, 141]. Using the separation determined experimentally between the In4d semi-core electrons and the valence band maximum (VBM) the true amount of pd-repulsion was estimated. Agreement between the valence band spectra of the InN and the resulting theoretical VB-DOS was observed.

72 5.2 Experimental details 73

5.2 Experimental details

The XPS experiments were performed within a conventional ultrahigh-vacuum (UHV) chamber using a Scienta ESCA300 spectrometer at the National Centre for Electron Spec- troscopy and Surface analysis (NCESS), Daresbury Laboratory, UK. The Al-Kα X-ray source (hν = 1486.6 eV) was monochromated, and the instrumental resolution was 0.45 eV. The Fermi level position (zero of the binding energy scale) was calibrated using the Fermi edge of a Ag reference sample. An unintentionally n-type doped 18 nm thick InN(0001) sample (GS1409) was grown by gas-source molecular beam epitaxy, on top of a 220 nm GaN buffer layer. A further 10 nm AlN layer was grown between the buffer layer and c-plane sapphire substrate. Details of the optimised growth conditions used are reported elsewhere [81]. For reference purposes, a second 350 nm thick InN sample (GS1469), with the same buffer layer and substrate structure, was also used in this study. The samples were unintentionally doped n-type. Hall measurements revealed electron concentrations of n = 1.83 1018 cm 3 and × − 3.8 1019 cm 3 with mobilities of µ = 950 cm2V 1s 1 and 160 cm2V 1s 1 for GS1469 × − − − − − and GS1409, respectively. The high quality of the InN samples grown under the same optimized growth conditions as GS1409 and GS1469 has been confirmed by careful and extensive structural characterization, which revealed that the samples were stoichiometric and single-crystalline [84]. The InN surface was prepared by AHC, which has previously been shown [see Chapter 4], by a combination core-level XPS and high-resolution electron energy-loss- spectroscopy, to successfully produce clean, well-ordered InN surfaces [72]. The AHC employed here was performed in a separate preparation chamber connected to the XPS analysis chamber. For GS1409, the atomic hydrogen clean consisted of three cycles of hydrogen irradiation followed by short, low temperature (< 300 ◦C) anneals in order to ensure no significant In-enrichment. Core-level XPS was used between cleaning cycles to 3 monitor the contamination levels. The first cycle consisted of a 2.7 kL (1 kL = 10− torr s) dose of thermally cracked hydrogen (H∗) at 225.5◦C followed by a further 0.5 hour anneal at 190 ◦C. XPS revealed strong O1s and C1s signals. The second cycle involved a 3.6 kL dose of H∗ at 190 ◦C, with no anneal. The O1s and C1s signals were reduced but still remained. A final 4.5kL dose of H∗ was performed at 200 ◦C, followed by a 0.5 hour anneal 5.3 Experimental results 74

at 270 ◦C. The O1s and C1s core-level spectra revealed a small amount of adventitious carbon remained, while the oxygen signal was reduced to the background noise level. This sub-monolayer level of contamination was deemed acceptable for XPS studies of the valence band. In XPS, photoelectrons from deeper within the sample contribute to the valence band spectra compared to ultraviolet photoemission, allowing surfaces with up to sub-monolayer amounts of contamination to be investigated [69]. Currently, only sample preparation by AHC has been capable of reducing the contamination to this level without causing severe structural and electronic damage [72].

The second InN sample (GS1469) was prepared with a longer H∗ dose and higher temperature anneal than for GS1409. A single 16 kL dose of H∗ at 275 ◦C, followed by a further 1 hour anneal at 275 ◦C was used to prepare the surface of GS1469. For this case, the AHC resulted in the formation of In droplets and was used in this study for comparison purposes, to verify the lack of In droplets produced by the preparation of GS1409.

5.3 Experimental results

Figure 5.1 displays the XPS spectra of the In4d semi-core level of the a) untreated and b) AHC prepared InN surface of GS1409. The spectra were curve fitted using Voigt functions of equal full width at half maxima (FWHM) with a spin-orbit splitting of 0.80 eV. Three components were required to fit the In4d semi-core level presented in the untreated spectrum. The In4d peaks were found to have binding energies of 16.9 0.1 eV, 17.4 5/2 § 0.1 eV and 18.5 0.1 eV. These were assigned as being due to the In-In, In-N and § § In-O bonds, respectively. Their assignment reflects the increasing electronegativity of the species bonded to the indium resulting in increasing binding energies. Following the optimized AHC cycle used to prepare GS1409, the In4d (In-O) bond was absent, as seen in figure 5.1 b). This is consistent with the O1s core-level signal reducing to the background noise level and confirms the assignment. Previous XPS studies of metallic InN by Pollak et al., reported the In4d5/2 (In-In) bond having a binding energy of 16.74 eV [143]. This is similar to a binding energy of 16.9 0.1 eV reported here for § the In4d5/2 (In-In) bond in InN, further confirming the assignment. Finally, the signal intensity of the In4d (In-N) bond was found to increase following the AHC cycle, consistent with the removal of the attenuating oxide overlayer. 5.3 Experimental results 75

Figure 5.1: The a) untreated and b) after AHC In4d semi-core level spectra of the InN sample, GS1409, (dots), with the corresponding curve-fits (thick lines). The background and peak components (thin lines) of the fits are also shown. Three components were required to fit the as-loaded In4d level, corresponding to In-O, In-N and In-In bonds. After AHC, the In-O bond is absent and the In-N bond has an increased signal. A feature at 15 eV in both spectra is from the N2s orbital. The insets show the magnified valence band region∼ for both the as loaded and after AHC spectra. The valence band maximum, after AHC, was extrapolated from the leading edge of the valence peak PI . Also shown for comparison is the valence band spectrum of GS1469 after AHC (grey triangles) using the same intensity scale. The extra peak (highlighted by the grey arrow) close to zero binding energy in the valence band spectrum of GS1469 indicates metallic In droplet formation.

Figure 5.1 b) shows that the In4d (In-In) remained following the optimized AHC cycle used to prepare the surface of GS1409. The bond may be due to either the formation of In droplets following the clean or the existence of an In-adlayer reconstruction. Ga- adlayers have been shown to naturally exist at Ga- and N-polarity GaN surfaces [133, 86]. The adlayer results from the large size difference between the cation and anion making such a reconstruction energetically favourable [133]. Since a larger size mismatch between the cation and anion is present in InN, an In-adlayer reconstruction should also exist. Further work is required to investigate the InN surface. However, a combination of XPS, scanning electron microscopy (SEM) and atomic force microscopy (AFM) has been employed to 5.3 Experimental results 76 rule out metallic In droplet formation at the surface of GS1409 due to the AHC cycle used. The inset of figure 5.1 b) displays the valence band regions of GS1409 and GS1469 following their respective AHC cycles. The greatest difference between the two spectra is an extra peak lying close to zero binding energy (between 2 and 0 eV) observed in the valence band spectra of GS1469. This distinct peak resembles the same feature found in the valence band spectra of Ga-rich GaN samples studied by XPS [104]. Such a peak reflects the metallic density of states superimposed onto the valence band spectra and has previously been observed with GaN suffering from the presence of Ga-droplets and was absent for Ga droplet-free surfaces [104]. By analogy with GaN, the extra peak in the valence band spectra of GS1469 following the harsh AHC cycle (compared to the valence band spectra of GS1409 prepared by the optimized AHC cycle) is considered to be due to small amounts of metallic In droplets formed at the surface. The absence of such a peak in the valence band spectra of GS1409, indicates the lack of metallic In droplet formation following the optimized AHC cycle. A combination of SEM and AFM was employed to further investigate the effect of the surface preparation. Figure 5.2 a) displays a featureless SEM image of the surface of GS1409 following its AHC cycle. AFM confirmed the flat nature of the surface with a rms roughness of 2.0 nm. No evidence of metallic In droplets was observed for GS1409 prepared by the optimized AHC cycle, consistent with the XPS results. In fact, the optimized AHC cycle used here for GS1409 was superior to established AHC cycles used to prepare clean InAs surfaces [see section 3.2.4]. A network of metallic In droplets was instead observed on the surface of GS1469 following the harsh AHC cycle, as seen in figure 5.2 b). These XPS, AFM and SEM results confirm that a clean, flat and metallic In droplet-free surface was achieved for GS1409 following the optimized AHC cycle. Therefore the In4d (In-In) bond observed in the XPS spectra of figure 5.1 b) is considered to be due to the presence of an In-adlayer rather than In droplets. An In-adlayer has previously been suggested from core-level XPS studies [72] [see section 4.5] and growth studies [144] of InN. The position of the VBM on the binding energy scale was extrapolated from the leading edge of the valence band peak [PI in the inset of figure 5.1 b)] of GS1409 after AHC and was found to be 1.4 0.1 eV. The position of the VBM of InN is consistent § with the reported downward band bending observed at n-type InN surfaces due to the 5.3 Experimental results 77

(a) (b)

Figure 5.2: The SEM images of a) GS1409 and b) GS1469 after AHC cycles for the same 1µm scale. For GS1409, a ﬂat and featureless surface is observed in contrast to the large In droplets on the surface of GS1469. intrinsic electron accumulation, resulting in the Fermi level being pinned at up to 1.6 ∼ eV above the VBM at the surface [17, 125, 136]. This is explained further elsewhere [see Appendix B], in terms of the exponential form of the XPS signal combined with the short screening lengths of the degenerately doped n-type InN samples. The separation between the In4d (In-N) (17.4 0.1 eV) bond and VBM (1.4 5/2 § § 0.1 eV) was found to be 16.0 0.1 eV in this study, in contrast to the experimental value § of 14.9 eV which has previously been used for the In4d-VBM separation [140], based on the work by Guo et al. [145]. In the work of Guo et al., the InN sample was prepared by high- energy (4 keV) Ar+ sputtering. As mentioned earlier, this results in severe structural and electronic damage to the material. Furthermore, no evidence was shown of the removal of oxide components in the In core-levels in their work [145]. An oxide component may still exist in the In4d semi-core level, which would dramatically aﬀect the determination of the In4d-VBM separation. In contrast, the oxide component has been successfully removed in our study. Finally, Guo et al. used 40 eV synchrotron radiation UPS for investigating the total valence band density of states [145], rather than the preferable XPS (for the aforementioned reasons) used in this study. 5.4 Comparisons with theoretical calculations 78

5.4 Comparisons with theoretical calculations

The wurtzite InN band structure was calculated elsewhere by Prof. Dr. Friedhelm Bechst- edt, Mr. Frank Fuchs, and Prof. Dr. Jurgen¨ Furthmuller¨ (Friedrich-Schiller-Universität, Jena, Germany). The calculation was performed within the framework of DFT-LDA and many-body perturbation theory, using the GW approximation for the self-energy; the terms G and W refer to the dressed Green’s Function and the dynamically screened Coulomb interaction in the first term in an expansion of the self-energy operator, respectively [146]. A plane-wave expansion of the eigenfunctions and non-normconserving pseudopotentials was implemented in the Vienna Ab initio Simulation Package (VASP) [147, 148]. The In4d electrons were treated as valence electrons (dval) to guarantee that the correct structural properties are obtained, as described elsewhere [140, 141]. However, such calculations result in a negative band gap energy [Eg(dval) = -0.19 eV] from the small overlap of the conduction and valence bands at the Γ-point. Therefore, pseudopotentials were used instead, which account for the self-interaction corrections of the 4d electrons in the underlaying atomic calculations but freeze the In4d electrons in the core. On top of the DFT-LDA eigenvalues, obtained in this fashion, GW corrections were applied. Using perturbation arguments, the fraction of 16.0/13.5 was used to obtain the true percentage contribution of the pd-repulsion (as mentioned in ref. [140]), where 16.0 and 13.5 refer to the experimental and DFT-LDA values of the In4d5/2(In-N)-VBM separation. This yielded a band gap value of 0.86 0.2 eV, in contrast to an earlier value of 0.81 eV 0.2 § § eV [140]. This agrees with a band gap value of 0.85 0.1 eV for InN recently predicted by § Carrier and Wei using an alternative semiempirical method to correct for the DFT band gap problem [27]. Therefore, a consensus is emerging amongst the theoretical calculations of InN, as with the experimental results. Furthermore, the revised value of 0.86 0.2 eV § agrees within uncertainty limits with 0.69 eV at 0 K for InN from temperature dependent photoluminescence measurements [149]. Figure 5.3 a) displays the XPS valence band spectra with the Shirley background removed. The DFT-LDA-SIC calculated valence band structure, using the revised experimental In4d5/2(In-N)-VBM separation, is shown in figure 5.3 b). The resultant calculated VB-DOS from the DFT-LDA-SIC is plotted with the XPS spectra, figure 5.3 a), with and without the 0.45 eV broadening to reflect the experimental resolution of the analyzer. A 5.4 Comparisons with theoretical calculations 79

Figure 5.3: The a) XPS valence band spectra, with the Shirley background subtracted, is plotted (dots), and the b) DFT-LDA-SIC calculated valence band structure using the revised pd-repulsion. The resultant calculated valence band density of states, VB-DOS, is shown in a) without (thin line) and with (thick line) 0.45 eV broadening (scaled to match the intensity of the x-ray photoemission spectrum). The broadened VB-DOS is horizontally oﬀset by 1.4 eV for comparison with the XPS spectra.

shift of 1.4 eV was used in the broadened VB-DOS. The theoretical calculations are ∼ performed with a Fermi level lying at the VBM. However, the intrinsic electron accumulation results in the Fermi level being pinned at up to 1.6 eV above the VBM at the surface [16, 17, 125, 136]. Therefore, the calculated VB-DOS (with broadening) has been horizontally offset by 1.4 eV to agree with the experimental location of the VBM in the XPS spectra. This horizontal shift is used so that better comparison between the XPS spectra and the calculated VB-DOS can be made. The 1.4 eV shift has not been incorporated into the theoretical calculations. Agreement between the calculated VB-DOS (with broadening) and the XPS spectra is then observed. The slight difference between the calculated and experimental intensities is attributed to contributions from the In-adlayer termination discussed earlier. DFT-LDA calculations of the surface band structure of InN with different terminations are necessary to investigate this further. 5.5 Conclusions 80

5.5 Conclusions

XPS has been used to investigate the valence band structure and In4d semi-core level of InN, prepared by an optimized AHC cycle. A combination of XPS, AFM and SEM conﬁrmed that the InN surface prepared by the optimized AHC cycle was clean, ﬂat and free of metallic In droplets. Evidence of the presence of an In-adlayer reconstruction was also observed. From the XPS spectra the In4d5/2 semi-core level due to the In-N bond was found to lie 16.0 0.1 eV above the VBM. Theoretical calculations of the VB-DOS from § the resultant DFT-LDA-SIC band structure calculation were performed, which incorporated the revised In4d5/2(In-N)-VBM separation in self-interaction corrections. Agreement between the XPS valence band spectra and theoretical VB-DOS was observed, once the instrumental broadening and downward band bending were considered. Chapter 6

Indium nitride: origin of the electron accumulation

6.1 Introduction

Recent improvements in the epitaxial growth of InN have resulted in significant improvements its epitaxial quality [83, 137, 150]. Consensus has now been reached that the band gap of this high quality InN is about 0.6 - 0.8 eV [6, 7, 151], rather than the previously accepted value of 1.9 eV [9]. In fact, optical measurements of samples with some of the ∼ lowest carrier concentrations have reported band gaps of 0.6 - 0.65 eV [10, 13]. As a result, III-nitride-based semiconductors can now be made to encompass a broader wavelength, from infrared of InN to the ultraviolet of AlN [152]. In order to fully realize the potential of InN low dimensional devices it is necessary to understand the influence of the surface and interface properties. Previous evidence suggesting the presence of electron accumulation at the surface of InN has included: measurements of the sheet electron density as a function of InN film thickness, which revealed an excess of electrons; capacitance-voltage profiles of InN surfaces that displayed a reduction in electron density with increasing depth; and Ohmic behaviour of current-voltage curves of Hg, Ni, Al, and Ti metal layers on InN [15]. Recent photoemission results from both Ti deposited on Ar-sputtered InN samples [16], and clean InN samples prepared by atomic hydrogen cleaning (AHC) [136, 153] have indicated that the surface Fermi level is pinned high above the conduction band minimum (CBM). Recently, high-resolution electron energy loss spectroscopy (HREELS) has been employed to quantify the space-charge region formed at clean AHC-prepared InN, and confirmed that electron accumulation is an intrinsic property of InN surfaces [17]. Here, the origin of the electron accumulation is discussed in terms of the calculated ab initio bulk band structure of InN. This work is separated into two distinct parts, followed by a discussion of the findings. In the first part, HREELS is employed to experi-

81 6.2 Experimental studies of clean InN surfaces 82 mentally quantify the accumulation layer present at clean (0001) surfaces of degenerately doped n-type InN. In the second part, the bulk band structure of wurtzite InN is calculated using density functional theory (DFT) within the local density approximation (LDA) with self-interaction corrections (SIC) [see section 5.5]. In the discussion, comparisons are made between the carrier proﬁle determined from the HREEL spectra and the theoretical calculations, which conﬁrm that the electron accumulation observed at clean n-type InN surfaces is due to its CBM lying extremely low with respect to the branch-point energy

(EB). As a result of the bulk Fermi level lying below EB, ionized donor-like surface states can exist which are responsible for pinning the Fermi level close to EB at the surface. The physical origin of these surface states is thought to be defects associated with the particular surface reconstruction. From chemical trends of III-V semiconductors, the combination of both the indium cation and nitrogen anion is considered to be responsible for the energetically low band edges of InN with respect to EB.

6.2 Experimental studies of clean InN surfaces

6.2.1 Experimental details

Experiments were undertaken using a conventional ultra-high vacuum chamber equipped with low-energy electron diffraction (LEED) and HREELS (VSW Ltd., UK). Surface preparation was carried out using TC50 thermal cracker (Oxford Applied Research, UK). InN(0001) thin films were grown to a thickness of 200 nm by migration enhanced gas source molecular beam epitaxy on top of a 200 nm GaN buffer layer. A further 20 nm AlN layer was grown between the buffer layer and the c-plane sapphire substrate. The InN layer was unintentionally n-type doped. Details of the growth can be found elsewhere [82]. Single field Hall measurement indicated an average conduction electron density, n = 1.83 1018 cm 3 and an average mobility of µ = 1200 cm2V 1s 1. × − − − Following insertion into the HREELS chamber, InN surface preparation was achieved in situ by AHC in order to remove the atmospheric contaminants. Clean, damage-free InN(0001)-(1 1) surfaces have been successfully prepared with AHC [see Chapter 4], as × confirmed by a range of techniques including X-ray photoemission spectroscopy, low-energy electron diffraction (LEED), HREELS, scanning electron microscopy and atomic force microscopy [17, 72, 153]. The sample was initially cleaned at room temperature for 8 kL of 6.2 Experimental studies of clean InN surfaces 83

H2 and then heated to 175◦C for a further 8 kL of H2. Afterwards the sample was annealed for 1 hour at 300 C. The InN(0001) sample produced a (1 1) LEED pattern after ◦ × cleaning, indicating a well ordered surface. The removal of atmospheric contaminants was conﬁrmed by HREELS, due to the absence of vibrational modes associated with adsorbed hydrocarbons and native oxides.

6.2.2 HREEL Spectra

Examples of normalised HREEL spectra recorded from a clean InN(0001) surface at 295 K and 565 K at two different probing energies, along with semi-classical dielectric theory simulations is shown in figure 6.1. Two distinct features are observed in the HREEL spectra. The first loss feature at 66 meV is assigned to Fuchs-Kliewer surface phonon ∼ excitations [77]. The second loss feature at 200 to 250 meV results from conduction ∼ band electron plasmon excitations. Both the 295 K and 565 K data sets show a decrease in plasmon peak energy with increasing probing energy. The plasmon peak dispersion for a larger set of probing energies shows the same trend at both temperatures, as shown in figure 6.2. The higher probing energies correspond to deeper probing depths. The variation in probing depths arises from the long-ranged electric fields associated with surface excitations. The field exponentially decays from the excitation into the vacuum in the form, exp(-q z), where q is the wavevector transfer parallel to the surface and z is the depth k k of the excitation. By varying the kinetic energy of the probing electron, the inverse of the wave-vector transfer parallel is changed thus enabling the probing depth to be varied [18, 71, 154]. In this case a maximum probing depth of 200 A˚ is achieved. Figures 6.1 and 6.2 can then be understood in terms of a higher plasma frequency nearer the surface for both temperatures, thus indicating the existence of electron accumulation near the surface. HREELS simulations are calculated using a wavevector dependent dielectric function [70, 74] [see section 2.5]. A five layer model was used to simulate the HREEL spectra recorded at each temperature. The individual layer properties are summarised in table 6.1 for both temperatures and show slight differences between the two models. Plasma dead layers of 3 A˚ and 3.8 A˚ were required for 295 K and 565 K, respectively. In order to simulate HREEL spectra from surfaces exhibiting electron accumulation, a dead layer is 6.2 Experimental studies of clean InN surfaces 84

Figure 6.1: Specular HREEL spectra recorded at 295 K and 565 K from an atomic hydrogen cleaned InN(0001)-(1 1) surface with incident electron energies of 15 and 45 eV (points) and the corresponding semi-classical× dielectric theory simulations (solid lines).

required to account for the quantized nature of the electron wavefunctions. This reﬂects the potential barrier formed at the surface resulting in a boundary condition on all the wavefunctions, which suppresses the carrier concentration near the surface [18, 155]. The carrier concentration tends to zero over a length approximately equal to the average de Broglie wavelength of all the electron wavefunctions [see section 3.6]. Three further layers of enhanced plasma frequency were needed to reproduce the plasmon tail at high loss energy. Finally, a bulk layer with a plasma frequency of 192 meV (for both temperatures) reproduced the plasmon peak position.

6.2.3 Space-charge calculations

In order to interpret the HREELS simulations for both temperatures, it is necessary to calculate the semiconductor statistics, that is the plasma frequency and electron eﬀective mass at the Fermi level as a function of the electron concentration. The two main parameters required to calculate the conduction band dispersion are the band-edge eﬀective mass (m0∗) and band gap (Eg). The band gap of InN has been recently revised from the previously accepted value 6.2 Experimental studies of clean InN surfaces 85

Figure 6.2: The surface plasmon peak (ωsp) energy dispersion curves for both 295 K (solid line) and 565 K (dotted line). The plasmon peak positions were obtained from the HREEL spectra recorded from atomic hydrogen cleaned InN(0001)-(1 1) surface. × of 1.89 eV [9] to the now accepted value of around 0.7 eV [10, 156, 157]. The revision in the band gap has been attributed to improvements in the quality of InN growth. Earlier growths of InN may have suffered from oxygen incorporation. Optical measurements have shown that the absorption edge blue shifts with increased oxygen incoporation, in some cases up to 2 - 3 eV [158]. Additionally, the high carrier concentrations of most of the ∼ InN grown so far, has inhibited the quantification of the fundamental band gap, due to the Moss-Burstein effect [159, 160], which increases the energy of the optical transitions. At the same time, band renormalisation shrinks the band gap, which further complicates the situation. In this work, the value reported by Wu et al. was used, with the Eg(T = 0K) = 0.69 eV and the Varshni parameters, γ = 0.41 meV/K and β = 454 K [13] . This gives intrinsic band gap values of 0.642 eV at 295 K and 0.561 eV at 565 K. The highly degenerate nature of the InN thin films grown so far has meant that there is still uncertainty over the value of m0∗. Previous measurements of the effective mass (m∗) for heavily doped n-type hexagonal InN by Kasic et al., estimated an isotropically averaged m0∗ = 0.14m0 from a combination of ellipsometry data analysis and Hall 6.2 Experimental studies of clean InN surfaces 86

Table 6.1: The plasma frequency proﬁle used in the dielectric theory simulations of the HREEL spectra for both 295 K and 565 K.

Layer 1 2 3 4 5 T = 295 K d (A)˚ 3 0.5 3.5 0.5 8.0 1 25 2 § § § § ∞ ω (meV) 0 446 10 328 2.5 248 1.5 192 1 p § § § § T = 565 K d (A)˚ 3.8 0.5 6.0 0.5 8.0 1 25 2 § § § § ∞ ω (meV) 0 415 10 328 2.5 254 1.5 192 1 p § § § §

∗ Table 6.2: The band-edge eﬀective mass (m0) for each temperature considered, based on the ∗ empirical relationship with the band gap (Eg): m 0.07 Eg for III-V materials. 0 ∼ Temperature (K) 0 295 565 Eg (eV) 0.690 0.642 0.561 m0∗ (m0) 0.0480 0.0446 0.0390

measurements [161]. Improvements in the crystalline quality of the material grown has resulted in a shift towards lower values of m0∗ being observed, with Wu et al. extrapolating their infrared reflection and Hall results to obtain an effective mass of 0.07m0 at the bottom of the conduction band [111]. Recently, an effective mass of 0.042m0 for InN samples with n = 7 1017 cm 3 has been obtained [162]. In this work, m = 0.048m at × − 0∗ 0 T = 0 K is used, based on the empirical relationship for semiconductors of m 0.07 E , 0∗ ∼ g as shown in figure 6.3 [163]. The effective mass used for each temperature, along with the corresponding band gap, is shown in table 6.2. The α-approximation model has been used to calculate the non-parabolic dispersion of the conduction band [see section 1.3.3]. This model was modified for application in the high Fermi level regime because of the huge unintentional n-type doping. As mentioned previously, at these high carrier concentrations there are two competing effects; Moss- Burstein and conduction-band renormalisation. The Moss-Burstein effect refers to the shift towards larger optical transitions, as a result of band filling. The conduction-band renormalisation arises from electron-electron and electron-impurity interactions [111]. These interactions result in the shrinkage of the band gap, with a red shift of 0.15 eV per ∼ decade of change of the carrier concentration beyond 1019 cm 3 being reported [111]. ∼ − The α-approximation model was modified to account for band gap renormalisation [see 6.2 Experimental studies of clean InN surfaces 87

Figure 6.3: The plot of the band-edge eﬀective mass as a function of zero temperature band gap [Eg(T = 0K)] for a range of III-V materials (triangles), based on the values provided by Vurgaftman et al [109]. The revised value for the eﬀective mass is included (square).

section 3.6], and therefore all subsequent references are to the renormalised band gap (Eg0 ) rather than the intrinsic band gap. The resulting conduction band dispersion relation enabled the calculation of the semiconductor statistics [see section 1.3.4]. The calculated statistics are plotted in figure 6.4, and were used to translate the HREELS simulations into layer profiles of the space- charge region for the two temperatures. Figure 6.4 shows only a small difference between 295 K and 565 K. Realistic smooth charge profiles were calculated by solving the Poisson equation within the modified Thomas-Fermi approximation (MTFA) [54]. This allows non-parabolicty to be incorporated in a straight forward manner compared to the complications associated with modifying the Schrödinger equation to include non-parabolicity [see section 1.5]. In the Poisson-MTFA method, the carrier concentration as a function of depth [n(z)], depends on the local Fermi level which is determined by the bulk Fermi level and the value of the potential [V (z)], which, in turn, is given by the solution to the Poisson equation [101]. The MTFA accounts for the quantized nature of the electron wave-function, whereby the 6.2 Experimental studies of clean InN surfaces 88

Figure 6.4: The plot of the semiconductor statistics, that is the variation in the plasma frequency ∗ (ωp), effective mass at the Fermi level (mF ), and carrier concentration n, as a function of Fermi level (EF ), calculated using the α-approximation model modified for the high Fermi level regime, for both 295 K (solid lines) and 565 K (dotted lines). Both plots show little variation between ∗ the two temperatures. Finally, the band-edge effective mass, m0, is highlighted and refers to the ∗ ∗ effective mass at EF = 0 eV. The values m0 = 0.0446 m0 for 295 K and m0 = 0.0390 m0 for 565 K were used for the calculations. surface potential barrier reduces the carrier concentration to zero at the surface. The smooth charge profiles, which match the HREELS simulation layer profiles the closest are shown in figure 6.5 for both temperatures. The calculations reveal the surface state density and surface Fermi level are constant for the two temperatures, with n 2.4 1013 cm 2 and E 1.55 eV, respectively. The surface Fermi level can be SS ∼ × − F S ∼ seen more clearly in figure 6.6. Figure 6.6 plots the Fermi level, CBM(z), and VBM(z), with respect to the VBM in the bulk, as a function of depth, for both temperatures. The surface Fermi level can be seen to be temperature invariant.

6.2.4 Discussion

Surface electron accumulation was found to be present at both temperatures, as shown in ﬁgure 6.5. The carrier proﬁles of the near surface region reveal a temperature invariant accumulation. The surface Fermi level with respect to the valence band maximum and 6.2 Experimental studies of clean InN surfaces 89

Figure 6.5: The HREELS simulation layer proﬁles (solid lines) for 295 and 565 K, along with their carrier-proﬁles (dashed lines) calculated by solving the Poisson equation within the MTFA. The corresponding bulk Fermi level [EF (bulk)], surface Fermi level (EF S), band bending [Vbb], renor- 0 malised band gap (Eg), and surface state density (nSS), for each temperature are also included.

surface state density calculated from the Poisson equation within the MTFA was found to be independent of temperature, yielding E 1.55 0.10 eV and n 2.4 ( 0.2) F S ∼ § SS ∼ § × 13 2 10 cm− , respectively. These results are similar to previous measurements of the surface Fermi level [17] and surface state density [15, 17, 164]. The temperature invariance of the near surface region can be attributed to the small temperature dependence of the band gap. For narrow-gap semiconductors the non- parabolicity of the conduction band determines many of the electronic properties, such as effective mass and density of states. By increasing the temperature, the band gap reduces and as a result the interaction between the conduction band and valence band increases. The increased interaction modifies the conduction band curvature and the electronic properties change as a consequence. For InN the change in the electronic properties with respect to temperature is small as highlighted in figure 6.4. This can be attributed to the small reduction in the band gap with temperature compared to other narrow-gap semiconductors. For instance the band gap of InN decreases by 19 % as the temperature is increased from 0 to 565 K [13], whereas for GaSb, which has a similar band gap, a 6.2 Experimental studies of clean InN surfaces 90

Figure 6.6: The energy plot, that is the variation in the Fermi level (EF ), conduction band minimum (CBM), and valence band maximum (VBM), with respect to the VBM at the bulk, as a function of depth (z) for both 295 K (solid lines) and 565 K (dotted lines), calculated by solving the Poisson equation within the MTFA. The bulk VBM refers to the VBM where there is no band bending is occurring i.e. z 90 A.˚ The surface Fermi level (EF S) is defined as the difference ≥ between the EF and VBM at z = 0 A,˚ which was found to be 1.55 eV for both temperatures. ∼ decrease of 28 % occurs for the same change in temperature [109]. The slightly broader HREELS simulation profile and corresponding Poisson-MTFA solution for 565 K compared to 295 K, observed in figure 6.5, is a consequence of a longer electron screening length. The charge profile width is determined by the screening length of the plasma formed by the conduction electrons. For degenerate semiconductors the electron screening length is described by,

π 1/3 a λ2 = B∗ (6.1) T F 6 1/3 µ ¶ 4n where λT F is the Thomas-Fermi screening length of the electron gas, and a0∗ is the eﬀective

Bohr radius, given by aB∗ = ²(0)(aB/mF∗ ) with ²(0) the static dielectric constant, a0 the Bohr radius and mF∗ the effective mass at the Fermi level [165]. By varying the temperature, the screening length varies as a consequence of the change in the electron effective mass. For 565 K the screening length is calculated to be 22.1 A˚ compared to 21.6 A˚ for 295 K, resulting in a slightly broader HREELS simulation layer profile being 6.3 Ab initio calculations of the electronic structure of InN 91 required to simulate the high temperature spectra observed in figure 6.5. The maximum carrier concentration for the HREELS simulation layer profile is smaller for the higher temperature in figure 6.5. The carrier profile of the near surface region is determined by the surface state density, bulk carrier concentration and the screening length of the electron gas. Since the surface state density and bulk carrier concentration are temperature invariant the amount of accumulated charge to ensure charge neutrality is also temperature invariant. In order to compensate for the longer screening length at 565 K, the maximum accumulation in the carrier profiles for 565 K (for both the HREELS simulation layer profile and Poisson-MTFA solution) is lower than for 295 K, as shown in figure 6.5.

6.3 Ab initio calculations of the electronic structure of InN

Amongst the III-V family of semiconductors, InAs and InN are the only materials to exhibit intrinsic electron accumulation at clean n-type surfaces. For InAs, the electron accumulation results from its bulk band structure. More precisely, at room temperature the CBM of InAs lies 0.14 eV below EB [5]. The location of EB deﬁnes the cross-over from mainly conduction band derived (acceptor-like) states to mainly valence band derived (donor-like surface states), and lies at the centre of the band gap (in one dimension) across the entire Brillouin zone [4]. When the Fermi level lies at EB at the surface, all donor-like surface states are occupied and neutral, and all acceptor-like surface states are unoccupied and neutral. In reality, this scenario is rarely observed. Instead, charge neutrality is achieved by the valence and conduction bands bending to generate the space- charge layer required to neutralise the charge due to the ionized surface states. As a result, the surface Fermi level is pinned close to EB, with the charge associated with the band bending fully compensating the remaining ionized surface states (whether unoccupied donor-like states or occupied acceptor-like states). Recently, electron accumulation and depletion layer proﬁles have been demonstrated at n-type InAs surfaces, when the bulk

Fermi level lies below and above EB, respectively [see section 3.3]; these results highlight the importance of the bulk band structure (i.e. the location of band-edges with respect to

EB) for understanding the space-charge layer. Likewise, the space-charge proﬁles obtained in the previous section are expected to be a consequence of the bulk band structure of 6.3 Ab initio calculations of the electronic structure of InN 92

Figure 6.7: The DFT-LDA-SIC calculated bulk band structure of wurtzite InN. The branch-point energy (EB) is shown to be located in the conduction band at the Γ-point.

InN. Here, ab initio calculations of the bulk band structure of InN are reported along with the location of EB with respect to its band edges. The bulk band structure of InN, calculated using DFT within the LDA, is presented in ﬁgure 6.7. The true percentage contribution of the pd-repulsion for DFT-LDA (with self- interaction corrections) calculations of InN has been determined from X-ray photoemission studies of the In4d semi-core level and valence band region [153], and has been employed in this calculation [see section 5.5]. This yielded a band gap of E = 0.86 0.2 eV, which g § agrees within the error limits of 0.69 eV at 0 K obtained from temperature-dependent photoluminescence measurements [149]. The calculated bulk electronic structure can be used to determine the location of the EB with regard to the band edges of InN. The location of EB (with respect to the VBM at the Γ-point) is given by [5] [see section 3.7]

1 E [EC + EV ], (6.2) B ≈ 2 and EC is the indirect conduction band edge (minimum) [for InN, it is the A-point and lies 3.8 eV above the VBM], and EV is the valence band edge (maximum) corrected to account 6.4 Origin of the electron accumulation 93 for the spin-orbit splitting [for wurtzite InN the spin-orbit splitting is negligible, and therefore EV is considered to be the VBM]. Using this convention, the branch-point energy of InN is found to lie 1.9 eV above the VBM at the Γ-point, as depicted within ﬁgure ∼ 6.7. In the next section, comparisons are made between the experimentally determined surface Fermi level and the calculated branch-point energy.

6.4 Origin of the electron accumulation

In section 6.3, the surface Fermi level of InN was found to be pinned 1.55 eV above ∼ the VBM by 2.44 1013 cm 2 donor-like surface states, from space-charge calculations × − of the HREEL layer proﬁles. Meanwhile, ab initio bulk band structure calculations have revealed that E lies 1.9 eV above the VBM. These results are consistent with the B ∼ electron accumulation layer formed at n-type InN surfaces being due to its bulk band structure. For instance, the downward band bending of the accumulation layer - due to the bulk Fermi level lying below EB - results in the surface Fermi level being pinned 1.55 eV above the VBM by 2.44 1013 cm 2 ionized donor-like surface states; these states are × − unoccupied (and therefore positively-charged) since they lie above the surface Fermi level

(1.55 eV) whilst below EB (1.9 eV).

6.4.1 Chemical trends of III-V semiconductors

The location of the Fermi level with respect to EB has been shown to be an important parameter for the Fermi level pinning and resultant space-charge proﬁle. Figure 6.8 displays the band line-up of a range of III-V semiconductors. Certain chemical trends become apparent. As the cation changes from Al Ga In the CBM decreases with respect → → to EB; meanwhile, by decreasing the spin-orbit splitting by changing the anion from Sb (∆ = 810 meV [109]) to N (∆ 5 meV [166]) the VBM decreases with respect to SO SO ∼ EB [5]. As a result, InN can be considered as being at the extrema of the chemical trends, with the In and N resulting in the band-edges lying extremely low with respect to EB.

6.4.2 Surface state density of InN

The surface state density of the electron accumulation at InN surfaces is far larger than that observed at InAs surfaces. For example, an ionized donor-like surface state density 6.4 Origin of the electron accumulation 94

Figure 6.8: The band line-up of a range III-V semiconductors references to the branch-point energy (EB) - from empirical tight binding calculations [47], using the band parameters (at T = 0 K) from the III-V review by Vurgaftman et al. [109]. The location of EB with respect to the band edges of InN are directly taken from the DFT-LDA-SIC calculations.

of n 5 1011 cm 2 is present at InAs(100)-(4 2) surfaces [18, 101] [see section 3.3]. SS ∼ × − × The larger electron accumulation present at InN surfaces is attributed to the band edges lying far lower with respect to EB for InN than for InAs, as shown in ﬁgure 6.8. As a result, for moderately degenerately-doped n-type InN far greater band bending is required for the surface Fermi level to approach EB, than for similarly doped InAs samples. This increased band bending requires a larger ionized surface state density to achieve charge neutrality.

6.4.3 Physical nature of the surface states

Further studies - employing a wider range of surface-sensitive techniques in conjunction with surface band structure calculations - are required to determine the physical nature of the surface states responsible for pinning the Fermi level at InN(0001) surfaces, although the likeliest candidate is defects localized at the surface. The Fermi level pinning at most III-V free surfaces is considered to be due to antisite defects at the surface, based on comparisons of theoretical and experimental studies [122, 123]. Moreover, recent 6.4 Origin of the electron accumulation 95

HREEL studies of InAs have revealed that the type of surface state (whether donor-like or acceptor-like) was dependent upon the bulk Fermi level; consequently, occupied cation-on- anion antisite defects and unoccupied anion-on-cation antisite defects at the surface were considered to be the ionized surface states responsible for the depletion and accumulation layer proﬁles, respectively [see section 3.3]. For InN surfaces, antisite defects have been shown to be energetically unfavourable for InN (and other III-Ns) [167, 168] - due to the small lattice constant and large size-mismatch between the constituent atoms [169] - and are unlikely to be the surface state responsible for the pinning mechanism. Instead, defect vacancies at the surface are considered to be responsible for pinning the Fermi level at surfaces of InN(0001). DFT calculations have revealed that positively charged nitrogen vacancies are increasingly energetically favourable within InN for Fermi levels below 1.9 eV (i.e. EB) [167, 168] and are therefore considered to be the donor-like surface states responsible for the accumulation layer (if unoccupied and localised at the surface). Indeed, native defects (such as nitrogen vacancies) have also been considered by Walukiewicz et al. as being responsible for the electron accumulation at InN surfaces [170].

6.4.4 Conclusion

Electron accumulation occurs at n-type InN surfaces because of its bulk band structure. The indium cation and nitrogen anion are responsible for the conduction and valence band edges of InN lying far below EB, respectively. Consequently, even for degenerately n-type doped InN, the bulk Fermi level lies below EB and ionized donor-like surface states exist. To ensure charge neutrality, the surface Fermi level is pinned above the conduction band minimum close to EB; the unoccupied, ionized, donor-like surface states (lying below EB yet above the pinned Fermi level) are compensated by the charge due to the resultant downward band bending. Chapter 7

Indium nitride: Fermi level stabilisation by low energy ion bombardment

7.1 Introduction

The extreme electron accumulation at InN surfaces [15, 17] is interesting for potential future device applications. The electron accumulation can be understood in terms of the location of the branch-point energy (EB), with respect to the band edges of InN [see section 6.5]. This also explains the high proclivity of InN towards high n-type conductivity. High- energy irradiation studies of GaAs, revealed that the bulk Fermi level (EF ) and carrier concentration are stabilised when EF is at EB [50]. The irradiation results in the formation of amphoteric defects, whose nature (whether donor- or acceptor-like) depends upon the location of EF with respect to EB [see section 1.4.2.2]. At EB, the formation energies of both types of defect are equal and any further introduction of amphoteric defects by irradiation results in compensating defects ensuring that EF remains at EB. Recently, this mechanism was found to also occur in III-Ns, with the carrier concentration of InN stabilising at n 4 - 5 1020 cm 3 [170]. Such a highly degenerate n-type carrier ∼ × − concentration is consistent with E lying 1 eV above the CBM for InN. Here, it is B ∼ reported that the carrier concentration of InN dramatically increases close to the surface following low energy (< 500 eV) ion bombardment and annealing (IBA). Instead of the expected electron accumulation layer for the near surface of InN, a damage-induced donor- like defect-proﬁle is observed; a stabilized carrier concentration of n 5 1020 cm 3 close ∼ × − to the surface is reported, in agreement with the high-energy irradiation studies of InN.

96 7.2 Experimental details 97

7.2 Experimental details

Experiments were undertaken in a conventional ultra-high vacuum chamber equipped with both low energy electron diffraction (LEED) and HREELS (VSW Ltd., UK). 500 nm thick InN(0001) films, grown by gas-source molecular beam epitaxy on top of a 200 nm GaN buffer layer with a 200 nm AlN layer between the buffer layer and the sapphire substrate, were investigated. Details of the growth conditions used can be found elsewhere [81]. Sin- gle field Hall measurements after the growth revealed an ‘average’ electron concentration of n = 1.0 1018 cm 3. The surface was prepared with a cycle of low energy (400 eV) ion × − bombardment with nitrogen ions, consisting of a dose of 4.75 1015 ions cm 2 set at a 45 × − ◦ sputter angle. Following the ion bombardment, the sample was annealed for a 2.5 hours at 295 C. After cooling, a (1 1) reconstruction was observed with LEED. The removal of ◦ × surface contaminants was confirmed by the absence of vibrational modes associated with hydrocarbons and native oxides in the HREELS spectra after the surface preparation [see section 4.6].

7.3 Results

Figure 7.1 plots the normalised HREEL spectra, for a range of probing energies, recorded from the IBA prepared InN surface. A shoulder at 66 meV is observed, which is ∼ assigned to the Fuchs-Kliewer surface-phonon excitation [113]. A broad low intensity peak is observed at 450 meV and is assigned as the plasmon peak. Comparisons with ∼ other HREELS studies of clean, damage-free InN, prepared by atomic hydrogen cleaning (AHC), reveal that the plasmon peak observed here for IBA-InN, is far larger than that previously observed for AHC-InN ( 200-250 meV) [see section 6.3.2]. The plasmon ∼ frequency is related to the carrier concentration. Therefore, the larger peak plasmon frequencies observed here for the IBA prepared InN surface, compared to AHC prepared InN surface, reﬂect a higher carrier concentration closer to the surface. This is in spite of the fact that the ‘average’ Hall carrier concentrations of the IBA prepared and AHC prepared InN samples were similar (n = 1.0 1018 cm 3 compared to n = 1.8 1018 × − × 3 cm− ). By changing the kinetic energy of the incoming electrons the eﬀective probing depth can be varied. Higher probing energies correspond to deeper probing depths. Therefore, 7.3 Results 98

Figure 7.1: The HREEL spectra (points) of InN prepared by IBA for a range of probing energies, from 15 eV to 45 eV, vertically oﬀset. The spectra are normalised with respect to their elastic peaks. The corresponding dielectric simulations (lines), for each spectrum, are also included. Note, the arrow is to illustrate the lack of plasmon peak dispersion with incident energy.

an increase in peak plasma frequency with decreasing probing energy would correspond to an increase in electrons closer to the surface, as expected for an accumulation layer profile [17, 113]. However, for the IBA prepared InN surface, there is no plasmon peak dispersion. Instead, the peak plasma position remains roughly constant with increasing probing energy indicating a relatively flat, high carrier concentration profile near to the surface. This suggests that an accumulation layer profile is no longer present. HREELS simulations were calculated using semiclassical dielectric theory [70] with a wave-vector dependent dielectric function. The corresponding HREEL simulations calculated, for each incident energy, are shown in figure 7.1. In this model, the sample is approximated by three thin layer on top of a bulk layer. Each layer is described by its own individual dielectric function and thickness. An effective dielectric function is then calculated from the layer contributions and is used to simulate the spectra. A unique four layer model was used to simulate all of the spectra shown in figure 7.1. 7.4 Analysis 99

Figure 7.2: a) the translated layer profile used to simulate all of the IBA HREEL spectra (thick solid line); also shown are two Poisson-MTFA calculations (thin solid lines) for two different bulk carrier concentrations, i) n = 4.5 1019 cm−3 and ii) n = 1.0 1018 cm−3, respectively. The stabilised carrier concentration of InN× from high-energy, irradiation× studies is also shown for comparison (dotted line) [170]. b) the translated AHC HREEL layer profile and corresponding Poisson- MTFA solution are shown, as reported elsewhere [see section 6.3.3].

7.4 Analysis

The unique HREEL layer profile was translated from plasmon frequencies into carrier concentrations. The non-parabolicity of the conduction band and band renormalisation effects were considered during the translation [see section 6.3.3], accounting for the narrow band gap of InN and high carrier concentrations present in this sample, respectively. The translated IBA HREEL layer profile is displayed in figure 7.2 a). The profile describes the variation in the electron density close to the surface determined from the HREEL spectra. To investigate the electronic profile further, space-charge calculations were performed. The calculations were performed by solving the Poisson equation within the modified Thomas Fermi approximation (MTFA), which accounts for the non-parabolicity of the conduction band [54, 125]. Figure 7.2 b) displays the HREEL layer profile and corresponding Poisson-MTFA calculation for a damage-free AHC prepared InN surface at room temperature [see section 7.4 Analysis 100

6.3.3]. The Fermi level was pinned at 1.58 eV above VBM in the calculations. Agreement between the experimentally determined HREEL layer profile and the Poisson-MTFA calculation is observed. The variation in the carrier concentration close to the surface, in figure 7.2 b), can be described by the presence of ionised donor-like surface states at the surface giving rise to an accumulation layer profile [17, 113, 125]. For the IBA-prepared InN surface, no agreement between the HREEL layer profile and Poisson-MTFA calculations could be achieved. To highlight this, two different ‘bulk-like’ doping levels, i) n = 4.5 1019 cm 3 and ii) n = 1 1018 cm 3, were used for × − × − the Poisson-MTFA calculations. The two values reflect the carrier concentration at 150 A˚ deduced from the translated HREEL layer profile and the ‘averaged’ Hall determined carrier concentration, respectively. The pinned Fermi level was set to 1.58 eV, to agree with the observed pinning level of InN(0001)-(1 1) [113]. Both Poisson-MTFA profiles are × displayed in figure 7.2 a) against the IBA HREEL layer profile. The calculated Poisson- MTFA profiles are different for the two bulk carrier concentrations, reflecting a change in the screening length; for degenerate semiconductors, as the bulk electron density increases the Thomas-Fermi screening length decreases as seen in figure 7.2 a). No agreement between any Poisson-MFTA calculation and the IBA HREEL layer profile could be achieved, since the the screening length is far too small at such high carrier concentrations to agree with the broad IBA HREEL layer profile observed in figure 7.2 a). Prior to the IBA, an accumulation layer similar to that depicted by the Poisson- MTFA in figure 7.2 b) would have existed. However, after the IBA, a damage-induced donor-like defect profile was formed and is responsible for the variation in carrier concentration close to the surface. Unlike for the AHC-prepared surfaces, the IBA has resulted in the formation of donor-like defects close to the surface (due to the band structure of InN), which saturate the carrier concentration and lead to the absence of charged surface states. In fact, the Fermi level in the near surface region has stabilised at EB (at 1.9 eV above the VBM [see section 6.4]); in figure 7.2 the HREEL layer profile close to the surface reveals a stabilised carrier concentration of n 4 - 5 1020 cm 3, in agreement with the ∼ × − high energy irradiation studies of InN [170]. 7.5 Conclusion 101

7.5 Conclusion

Low energy IBA has resulted in the formation of donor-like defects close to the surface of InN. In fact, the Fermi level has stabilised the carrier concentration at EB close to the surface. Our work highlights how easily damage can dramatically increase the n- type conductivity of InN. The IBA has resulted in a damage-induced, donor-like, defect- proﬁle accounting for the variation in carrier concentration with depth. The lack of an accumulation layer proﬁle (expected for InN surfaces [see section 6.5]) can be understood in terms of the lack of ionised surface states due to the Fermi level lying at EB at the surface. This is in contrast to AHC-prepared surfaces, where an accumulation layer is present with the surface Fermi level lying slightly below EB. Chapter 8

Indium nitride: origin of the high unintentional n-type conductivity

8.1 Introduction

As-grown InN always exhibits n-type conductivity, with unintentional free-electron con- 21 3 centrations as high as 10 cm− [8]. Many theoretical and experimental studies have focussed on determining the major reason for the unintentional n-type conductivity of InN [8]. However, no consensus has yet been reached. The traditional candidates fall into two categories: donor impurities and donor-type native defects. The impurities most commonly suggested as the primary cause of InN’s n-type conductivity are oxygen [167] and hydrogen [171]. Amongst native defects, the nitrogen vacancy (VN ) has been found from theoretical calculations to be a donor [167] and has also been suggested as the major reason for the high n-type conductivity [8]. Self-interstitials and anti-site defects are energetically unfavourable in InN due to the small lattice constant and the large-size mismatch between the cations and anions, respectively [167, 169]. More recently, surface electron accumulation has emerged as another factor contributing to the n-type conductivity in InN [15, 17]. The purpose of this Chapter is to investigate the relative importance of these three contributions to the n-type conductivity of InN. To this end, calculations of the film thickness-dependence of the free-electron concentration in InN are compared with Hall measurements of high-quality InN films grown by molecular-beam epitaxy (MBE). The observed dramatic reduction in carrier concentration with increasing film thickness is successfully modelled by considering a homogeneous background of donor impurities, a constant surface sheet density due to electron accumulation, and positively-charged VN along dislocations whose density declines exponentially away from the InN/buffer layer

102 8.2 Experimental Details 103

Figure 8.1: The free-electron density (n) as a function of thickness for a range of InN films (dots). Two calculated free-electron density versus film thickness curves are also shown. The first (thin 3D dashed line) includes a uniform background free-electron density from impurity donors of nimp = 2 17 −3 13 −2 10 cm and a constant two-dimensional surface sheet density of nSS = 2.5 10 cm . The second× is the same but with the addition of free-electrons from positively-charged ×dislocations (thick solid line). The inset is a schematic representation of the inhomogeneous electron distribution in an InN film. Three regions are identified: (a) where the surface electron accumulation layer is the major contribution to n, (b) a bulk layer where the electron density is mainly due to the background donor density from impurities and (c) an interface region dominated by the contribution from the positively-charged nitrogen vacancies along dislocations.

interface.

8.2 Experimental Details

InN films were grown on sapphire substrates by molecular beam epitaxy (MBE) [81, 84]. The optimised growth method that results in the highest quality epitaxial InN films, with the lowest electron concentrations, highest mobilities and lowest dislocation densities, uses an AlN nucleation layer and a GaN buffer layer deposited prior to InN growth. 8.3 Results 104

8.3 Results

Figure 8.1 displays the variation in the free-electron concentration as a function of film thickness for a set of InN samples that were all grown under similar conditions. The electron density decreases by two orders of magnitude (n low 1019 cm 3 to low 1017 ∼ − 3 cm− ) as the film thickness is increased by almost four orders of magnitude (50 nm to 12000 nm). The respective Hall electron mobility (not shown) steadily increases by at least one order of magnitude (µ 100 cm2V 1s 1 to 2000 cm2V 1s 1) for the same ∼ − − ∼ − − change in film thickness. Any explanation of the origin of the n-type conductivity in InN films must quantitatively account for this Hall data.

8.4 Discussion

Donor impurities (e.g. O and H) are the first possibility to consider to explain this film thickness-dependence of the free-electron density in InN. This is because theoretical calculations have shown that the energy required for impurities to become donors is lower than the formation energy of native defect donors [167]. High background impurity doping could be the major reason for the high n-type conductivity observed in some InN films when very high impurity densities are present. However, if InN films are grown without impurities being incorporated in significant concentrations, impurity-derived donors cannot be the main source of unintentional n-type doping. Indeed, secondary ion mass spectrometry (SIMS) of high-quality MBE-grown InN indicates that the concentration of impurities (O and H) is too low to fully account for all of the measured free-electron densities [172]. Furthermore, irrespective of the absolute concentrations of impurities (which can be difficult to reliably quantify by SIMS), SIMS results show that the impurity densities do not follow the trend of film thickness-dependence exhibited by the free-electron concentration in figure 8.1. This suggests that impurities are not the major cause of n-type conductivity in high-quality MBE-grown InN. The second phenomenon to consider to explain the film thickness-dependence of InN’s free-electron density is the native surface electron accumulation. Since this contributes a constant two-dimensional (2D) sheet free-electron density at the surface of each InN film irrespective of the film’s thickness, it immediately offers one qualitative explanation of the film thickness-dependence of the three-dimensional (3D) free-electron 8.4 Discussion 105

3D concentration. In order to obtain the experimental 3D free-electron densities (nHall) plotted in figure 8.1, the sheet density obtained from the Hall measurement is divided by the film thickness. For an electron accumulation layer, this means that, as the film thickness is increased, the fixed surface sheet density is numerically averaged over a greater depth, reducing the apparent 3D electron density. It must be emphasised that this does not in any way suggest that the charge associated with the electron accumulation is physically distributed through the film; it is localized within a few nm of the surface [17]. While surface electron accumulation gives the correct trend with film thickness, its contribution to the free-electron density must be quantitatively evaluated against the experimental data in figure 8.1. Taking a constant surface sheet density of nSS = 2.5 1013 cm 2, in agreement with previous studies of InN surfaces [15, 17], gives a value × − for n3D of 2.5 1016 cm 3 for a 10000 nm-thick film. This is more than an order of Hall × − magnitude lower than the experimental value for this thickness (3.5 1017 cm 3) shown × − in figure 8.1. This suggests that electron accumulation alone cannot fully account for the measured free-electron densities and that a low background concentration of donor impurities also contributes. Indeed, variable magnetic field Hall measurements of a thick InN film (7500 nm), analysed by multiple carrier fitting and quantitative mobility spectrum analysis, indicated that the true bulk free-electron density (below the accumulation layer and far from the InN/buffer layer interface) is 2 1017 cm 3 [173]. Therefore, any ∼ × − thickness-dependence of the electron density must be superimposed on a uniform background of electrons from donor impurities. Therefore, for an InN film of thickness (d), the 3D Hall-measured total sheet density, (nHalld), has been calculated as the sum of the sheet 3D density arising from a uniform background of donor impurities (nimpd) and the surface sheet density resulting from the electron accumulation layer

3D 3D nHalld = nimpd + nSS. (8.1)

The Hall-derived 3D electron density is then given by dividing equation 8.1 through by d:

n n3D = n3D + SS , (8.2) Hall imp d where n3D = 2 1017 cm 3 and n = 2.5 1013 cm 2. The calculated electron density imp × − SS × − variation with ﬁlm thickness according to this model is shown in ﬁgure 8.1 (dashed line). 8.4 Discussion 106

For this case, the calculated electron density is significantly lower than that observed for all film thicknesses. This indicates that an additional film thickness-dependent phenomenon is required to completely reproduce the experimental data. The remaining possibility is a film thickness-dependent contribution from donor defects. The obvious candidate is defects associated with dislocations, whose origin is the large lattice mismatch between the epi- layer and the buffer layer. The dislocation density in InN is assumed to vary in a similar manner to GaN, since structurally these two materials are alike. In GaN, the dislocation density exponentially decays with increasing distance from the buffer layer with the form:

log10x D(x) = A(10− ), (8.3) where D(x) represents the dislocation density at a distance x from the buffer layer interface, and A is a constant [174]. This variation is due to the annihilation and fusion of the dislocations with increasing growth [175]. The few transmission electron microscopy (TEM) studies of InN films performed so far support this assumption. For instance, dislocation densities in InN of 5 1020 cm 2 [171] and 2 1020 cm 2 [175] have been measured × − × − at 450 nm and 760 nm away from the interface, respectively. Additionally, a very recent cross-sectional TEM study of the dislocation density in InN indicates an exponential decay with increasing distance from the interface [176]. Figure 8.2 displays the dislocation density variation with distance from the interface for GaN for direct comparison with the TEM studies of InN. To a first approximation, the variation in the dislocation density of the InN with increasing distance from the interface can be considered to be described by equation 8.3. To account for the charge associated with the dislocations, a term can be added to equation 8.2, such that

n2D C d n3D = n3D + SS + D(x)dx, (8.4) Hall imp d d Z0 2 where D(x) represents the exponential variation of the dislocation density (in cm− ) with distance from the interface (for d > 50 nm), as given by equation 8.3. The total sheet density of electrons from donor VN along dislocations in a ﬁlm of thickness d is determined by integrating the exponentially varying dislocation density over the entire ﬁlm thickness 8.4 Discussion 107

Figure 8.2: The variation of the dislocation density of GaN with increasing distance from the buﬀer layer interface, as reported by Jasinski and Liliental-Weber [174]. Also shown are reports of the dislocation density of InN from TEM studies by Look et al. [171], Lu et al. [175], and Lebedev et al. [176]. For both GaN and InN, an exponential decay is observed.

and multiplying by the charge contribution per unit length of each dislocation, C). The contributions from each depth are summed to determine the total contribution to the free-electron density from dislocations. Using the same quantities for the background and electron accumulation terms as before, a charge contribution of one electron every two nanometres along each dislocation is sufficient to reproduce the experimental variation of electron density with InN film thickness, as shown in figure 8.1 (solid line). This one electron every two nanometres along each dislocation equates to a local free-electron density from dislocations of 1 1017 cm 3 at the distance from the interface where the × − dislocation density is 2 1010 cm 2. × − For this model to be plausible, the donor character of nitrogen vacancies in n-type InN must be explained. In n-type GaN, threading dislocations contribute to the unintentional doping [177] as a result of acceptor-type gallium vacancies (VGa− ) forming along the dislocation core [178]. Studies of the effects of dislocations on the carrier mobility in GaN have indicated that approximately two acceptors per nanometre exist along the dislocation line [45]. A previous InN study considered negatively-charged acceptor dislocations 8.4 Discussion 108

Figure 8.3: The calculated energetic positions of the Γ-point conduction band minimum (CBM) and valence band maximum (VBM) of AlN, GaN and InN with respect to the branch-point energy (EB) (dashed line) [47]. The mid-gap energy at the Γ-point is also shown (thin dotted line). The bulk Fermi levels for n-type GaN (EF 1) and n-type InN (EF 2) are also shown, above and below EB, respectively. The inset schematically shows the variation of the formation energies with Fermi + − level of VN and VIII for III-nitrides (after ref. [168]). The cross-over between the two types of defects corresponds well to the location of EB.

by analogy with GaN [171]. However, in view of the revision of the band gap since this work, positively-charged donor nitrogen vacancies along dislocations are now considered to be energetically favourable for n-type InN. Theoretical calculations of III-nitrides have revealed similarities between InN and

GaN [168]. Group III vacancies (VIII ) become increasingly favourable as the Fermi level + is increased with respect to the valence band maximum (VBM). Conversely, VN become increasingly energetically favourable with decreasing Fermi level, as shown in the inset of ﬁgure 8.3. The cross-over between the two types of defects corresponds well to the position of the branch-point energy (EB): for example, the VBM lies 2.4 eV below EB for GaN [47] in agreement with the cross-over energy reported for GaN [168]). As described by the amphoteric defect model [50], movement of the Fermi level away from EB, lowers the formation energy of the type of defect required to move the Fermi level back towards EB. Figure 8.3 shows the location of the Γ-point band-extrema of III-nitrides with respect to the location of EB. For n-type GaN, the bulk Fermi level generally lies above EB. 8.5 Conclusion 109

Compensating VGa− become increasingly energetically favourable as the n-type conductivity is increased. However, even for highly degenerate n-type InN, the bulk Fermi level lies far + below EB and so VN are instead energetically favourable.

8.5 Conclusion

The variation of the Hall-measured electron concentration with increasing InN film thickness has been successfully modelled by a constant background electron density (due to + donor impurities), a fixed surface sheet density and the free-electrons from VN along the dislocations. Therefore, impurities, native defects and electron accumulation all play a significant role in producing the n-type conductivity of as-grown InN. The existence of + VN , donor impurities and surface electron accumulation in n-type InN is due to the CBM lying far below EB. In this sense, the band structure of InN is the major reason for its n-type conductivity. Chapter 9

Indium nitride: electron tunnelling spectroscopy of quantized states

9.1 Introduction

One of the most striking features of InN is the native electron accumulation present at the surface due to its bulk band structure [see Chapter 6]. High resolution electron energy loss spectroscopy (HREELS) studies of n-type InN surfaces have revealed that a strong screening electric field is associated with extreme downward band bending at the surface [17]. Such a strong electric field is expected to result in the quantization of the electron accumulation layer in the direction perpendicular to the surface. The band bending at the surface creates a potential (or quantum) well in which quantized energy levels (or subbands) exist. The observed excess of electrons at InN surfaces [15, 17] is due to these occupied quantized states. Here, electron tunnelling spectroscopy has been employed to investigate quantized states at a range of InN surfaces with different doping levels.

9.1.1 Electron tunnelling spectroscopy

Electron tunnelling spectroscopy involves a tunnel junction between two conducting electrodes separated by a thin insulating layer. The current (I) through the junction is measured as a function of applied voltage (V) at energies (eV) above and below the Fermi level of the electrodes. In this sense, tunnelling can be considered to be an ultra-low energy form of electron spectrometry, since I-V - and normalised conductance [(dI/dV)/(I/V)] - curves characteristics contain information about the electronic properties of the electrodes [179]. As a result this technique is especially suited for investigating the spatially-localized, two- dimensional, quantized states (or subbands) at space-charge induced accumulation layers. Indeed the ﬁrst direct observation of quantized levels within an accumulation layer was

110 9.1 Introduction 111 obtained by Tsui using planar electron tunneling spectroscopy at the InAs-oxide interface at a temperature of 4 K [180, 181]. This result followed the pioneering work by BenDaniel and Duke a few years earlier, where features in the tunnelling conductance of Al-oxide-Bi junctions were tentatively considered to be due to tunnelling via localized states associated with the accumulation layer at the metal-semimetal interface [182]. Since then, electron subbands have been resolved in scanning tunnelling microscopy (STM)-acquired tunnelling spectra by Feenstra et al., [183]. In their work, InAs/GaSb superlattices cleaved in vacuum were studied in cross-section, which allowed the subband energies in the InAs quantum well to be determined. In vacuo scanning tunnelling spectroscopy (STS) has also been used to investigate both Landau levels in tip-induced electron accumulation at InAs(110) surfaces in an applied magnetic field [184] and the quantized states formed at the surface of ZnO by low-energy H ion implantation [185]. Here, the tunnelling junction formed at the InN-oxide-tip interface - similar to the junction employed by BenDaniel and Duke [182], and Tusi [180, 181] - is displayed schematically in figure 9.1. The unintentionally doped n-type InN sample exhibits a bulk Fermi level above the conduction band minimum (CBM). The downward band bending at the InN surface is shown, which is due to the surface Fermi level being pinned high above the CBM. Between the InN and STM tip is InN’s native oxide. This oxide layer acts as the thin insulating layer (or tunnelling barrier). Two quantized states are also shown within the potential well formed by the downward band bending of at the InN-oxide interface. The tunnelling current measured is dependent upon the applied bias of the STM tip. For the set-up displayed in figure 9.1, when no bias voltage is applied the potential difference between the Fermi levels of the sample and STM tip is taken up entirely by the oxide [181]. Note, for in vacuo STS studies the tip and clean sample are placed in contact before the experiment resulting in their Fermi levels being aligned at zero bias voltage [184]. For the case when an accumulation layer is present as depicted in figure 9.1, when a small positive voltage is applied to the STM tip - such that the Fermi level of the tip lies far below the Fermi level of the sample and the CBM at the surface - electrons from the tip can tunnel through the oxide layer into unoccupied states in the conduction band. However, this positive current (from sample to tip) is low due to the low probability associated with this tunnelling. A slight increase in the positive current occurs when the Fermi level of the tip reaches the CBM of the sample at the surface. As the applied positive 9.1 Introduction 112

n-InN I Pt-Ir tip - E 1.5 e F EF

) 1.0

V o e (

x ∆U

g i r 0.5 e d n

E e

0.0

-0.5 200 150 10 0 50 0 Distance from surface (Å)

Figure 9.1: An energy diagram schematic of the tunnel junction formed by the STM tip, the oxide layer and the InN surface. The Fermi levels of the InN and the tip are shown as dotted lines. The band bending at the InN surface is shown with the Fermi level pinned high above the CBM at the surface. The InN sample is degenerately doped n-type with the bulk Fermi level lying above the CBM. ∆U represents the applied bias and I is the tunnelling current (which, by convention, is opposite to the direction of the electrons). In the InN, the dark grey shading signiﬁes both the occupied valence band states and the occupied bulk conduction band states below the Fermi level. The white region is the band gap. The light grey region indicates empty conduction band states. The horizontal lines above the CBM in the surface potential well represent the two subband minima. In the STM tip, the Fermi level divides the occupied (dark grey) and empty states (light grey).

voltage is increased further - such that it approaches the Fermi level of the sample at the surface - the probability of the tunnelling (of electrons from the STM tip tunnelling to unoccupied conduction band states) dramatically increases resulting in a rapid increase in the positive current. A similar rapid increase in the negative tunnelling current (due to electrons tunnelling from the sample into STM tip) is expected when the applied negative bias voltage corresponds to the Fermi level of the tip lying at the valence band maximum (VBM) of the sample. Superimposed upon this tunnelling spectra - between the CBM and Fermi level of the sample - additional features associated with the subbands in the surface potential well may be observed. Therefore, the I-V curve of the tunnelling junction yields electronic information regarding the VBM, the band gap (Eg), the pinned Fermi level of the InN-oxide interface, and the energies of the subbands within the potential well. 9.1 Introduction 113

Note, for a depletion case (not depicted here) large negative and positive current onsets are observed at the VBM and CBM, respectively. Furthermore, no quantized states are observed.

9.1.2 Calculations of surface-bound quantized states

Ideally, full self-consistent Poisson-Schrödinger calculations would be preferred to investigate the quantized states within the potential well formed at InN surfaces. Unfortunately, these calculations do not yet exist for InN and are beyond the scope of this study. Instead, various approximations are required to calculate the energies of the subbands at InN surfaces. Here, the two approximations needed - the Poisson-MTFA and the exponential well approximation - are discussed. It will be shown that application of the Poisson-MTFA and exponential well for InAs, results in remarkable agreement with the full self-consistent calculations. Like InN, InAs has a narrow band gap and can exhibit electron accumulation at its surface when degenerately doped n-type (if n < 2.6 1018 cm 3). In this sense, × − InAs is a suitable candidate for fully testing the validity of applying these approximations for studying the quantized electron accumulation at InN surfaces. The potential well formed by the downward band bending at InAs (and InN) surfaces is first solved by employing the Poisson-MTFA; the resultant potential well is then approximated by an exponential form in order to calculate the subband energies, with the non-parabolicity of the conduction band included by an additional iterative process. The Poisson-MTFA method is capable of producing space-charge profiles in agreement with local-density-approximation calculations (which include the full effects of the non- parabolic conduction band dispersion) reported by Abe, Inaoka and Hasegawa [52] [see section 1.5]. The surface potential well obtained by solving the Poisson-MTFA method is approximated by an exponential form (with a least squares-fit), and is parameterized by a surface potential (V0) and a characteristic length (z0), such that

V (z) = V exp( z/z ) (9.1) − 0 − 0 and

V (0) . (9.2) → ∞

The one dimension independent Schr¨odinger equation with this potential can be solved 9.1 Introduction 114

analytically for a parabolic band [180]. The energies of the quantized levels (Eb) are given by

¯h2p2 Eb = 2 , (9.3) 8mb∗z0 where the p values are determined by the Bessel-function relation

Jp(q) = 0, (9.4) and

2 1/2 8mb∗V0z0 q = 2 . (9.5) " ¯h #

The non-parabolicity of the conduction band is then accounted for by including the energy- dependence of the eﬀective mass of the subband (mb∗), according to

2Eb mb∗ = m0∗ 1 + . (9.6) Ã Eg !

The band-edge effective mass (m0∗) is initially used to obtain a subband energy, which is then used in turn to modify the values of q and p, resulting in a revised value of Eb. The iterative process is repeated until self-consistent values of Eb and mb∗ are obtained. Full self-consistent solutions to the Poisson and Schrödinger equations for degenerately doped n-InAs have previously been obtained by Zhang, Slinkman and Doezema [53]. Figure 9.2 displays the subband energies and potential well at InAs surfaces - with a fixed free carrier density of 1.8 1017 cm 3 - as a function of surface state density, × − using both the method employing the Poisson-MTFA and exponential well (referred to as the exponential well approximation method) and full self-consistent method. Remarkable agreement is observed between the two methods regarding the evolution of the subband energies with increasing surface state density. The validity of exponential well approximation for describing quantized accumulation layers is further supported by figure 9.3. Agreement between the energy versus wavevector dispersion of the subbands calculated using both methods, at a fixed carrier concentration (n = 1.8 1017 cm 3) and donor-like surface state density (n = 0.7 × − SS × 12 2 10 cm− ). For these surface-bound electrons, the parabolic dispersion relation

¯h2k2 E = (9.7) 2mb∗ 9.1 Introduction 115

0 E2 a) E1

E0 -100 ) V e m (

g E

r 2

e b) E1 n

E -200 E0

V0 V0

-300 0 10 20 30 11 -2 nSS (10 cm )

Figure 9.2: a) The calculated subband energies (at k = 0) and potential [V(0)] at the InAs surface as a function of total surface-electron concentration of n = 1.8 1017 cm−3, using the exponential well approximation of the Poisson-MTFA solution. b) The inset× displays the calculated subband energies and potential as reported by Zhang et al. [53].

is valid for describing the energy dispersion. The eﬀective mass of each state varies due to the inclusion of non-parabolic conduction band: states lying deeper in the well have larger eﬀective masses. This variation is best explained by considering the two-dimensional density of states of each subband and their contribution to the total accumulated carrier density. The two-dimensional density of states [gb(E)], for a particular subband is given by

mb∗ gb(E) = (9.8) ¯h2π2

Referring back to the evolution of the subbands calculated by Abe, Inaoka and Hasegawa [52]: an increased donor-like surface state density corresponds to a deeper potential well with lower lying subband energies; these lower lying subbands have larger eﬀective masses (and therefore a larger density of states) which in turn correspond to larger contributions to the accumulated carrier density required to compensate for the larger donor-like surface 9.2 Experimental details 116

2 1/3 k = (3π n) 80 F b)

E ) 40 F V e m

( j=1

g r e

n j=0 E 0

-40 0 1 2 wavevector, k (106 cm-1)

Figure 9.3: a) The calculated dispersion relation E versus k of InAs, for n = 1.8 1017 cm−3 12 −2 × when the ﬁrst subband is bound and occupied (nSS = 0.7 10 cm ), reported by Zhang et al. [53]. b) The subband energy dispersion calculated using the× exponential well approximation of the Poisson-MTFA solution, for the same carrier density and surface state density.

state density.

9.2 Experimental details

The high quality InN films used in this study were grown by molecular beam epitaxy on (0001) orientation GaN/AlN/sapphire structures as described elsewhere [81, 84]. InN films with thicknesses of 2000, 650 and 350 nm have been investigated with single-field Hall measured carrier concentrations of 6 1017 (GS1804), 2.5 1018 (GS2019) and 6 × × × 18 3 2 1 1 10 cm− (GS1454) and Hall mobilities of 1400, 1050 and 550 cm V− s− , respectively. These represent ‘average’ values of the carrier concentration and mobility due to the extreme electron accumulation, donor-like impurities, and positively-charged threading dislocations [see Chapter 8]. Electron tunnelling spectra were collected from InN samples using freshly-cut Pt- 9.3 Experimental results 117

Ir tips (0.2 nm) with a Digital Instruments Multimode Nanoscope IIIa scanning probe microscope at room temperature. Previous electron tunnelling measurements of InAs have usually been taken at low-temperatures to optimize the spectral resolution (e.g. k T 1 meV at 10 K). However, InN (0.6 - 0.7 eV) has a far larger band gap than InAs B ∼ (0.356 eV) and as a result it is possible to resolve the spectral features of InN at room temperature. The tunnelling spectroscopy was performed with the STM tip in contact with the oxide, in air and at room temperature, with the feedback loop switched oﬀ. The I-V curves collected were the average of six successive voltage sweeps, with all six being within measurement error. This averaging enhances the signal-to-noise ratio.

9.3 Experimental results

Figure 9.4 displays the STM images of the three InN samples. The height scale of the topographic images changes from 2 nm for the thickest film (GS1804) to 10 nm for thinnest (GS1454). This improvement in surface morphology with increasing film thickness is consistent with the improved transport properties of the samples, as determined by the Hall measurements. This correlation between the transport properties and film thickness is a consequence of the dislocations within the InN films acting as donor-type defects [see Chapter 8]. Since these dislocations originate from the InN/buffer layer interface, as the film thickness is increased, the influence of the dislocations diminishes and the crystal quality and transport properties improve, as reflected by the STM images (figure 9.4) and the Hall measurements. The tunnelling I-V and (dI/dV)/(I/V) spectra of the three InN samples are shown in figure 9.5. Similar I-V curves were obtained from a large number of different locations in all three samples. These data indicate that the I-V results are not spatially localized over the sample’s surface, and the tunnelling current onsets do not vary across each sample. Since the density of states in the valence band of the InN sample increases below the VBM, a rapid increase in both the negative tunnelling current and normalised conductance intensity determines the VBM for each film (as highlighted in figure 9.5). A slight increase in the positive current is observed for three samples 0.6 V from the VBM, consistent ∼ with the Fermi level of the tip lying at the CBM of the sample (as indicated in figure 9.5. This width is consistent with E 0.64 eV at room temperature determined by optical g ∼ 9.3 Experimental results 118

(i) (ii)

(iii)

Figure 9.4: Topographic STM images of three InN ﬁlms with thicknesses (i) 2000 nm (GS1804), (ii) 650 nm (GS2019) and (iii) 300 nm (GS1454). The height scales of the images are 2, 5, 10 nm, respectively; with the surface morphology improving with increasing ﬁlm thickness.

absorption, photoluminescence and photoreflectance measurements [13]. A rapid increase in the positive tunnelling current and normalised conductance intensity is then observed for all three samples at 1.3 0.05 V from the VBM (shown in figure 9.5). This onset § is consistent with the Fermi level of the STM tip lying at the surface Fermi level (1.4 eV) of the oxidized InN samples [see Appendix B]. This value is lower than the reported 1.5 - 1.6 eV previously reported from HREEL studies of clean InN samples [17, 113] [see Chapter 6]. This is due to the charge transfer between the InN and native oxide layer affecting the ultimate Fermi pinning level and is discussed further elsewhere [see Appendix B]. Finally, distinct features are observed in the spectra of all three samples (shown in figure 9.5) between the onset of the CBM and pinned Fermi level of the InN-oxide surface. The energetic locations of these features vary between the samples. The variation in their energetic positions with doping levels of the InN samples will be shown to be consistent with quantized levels within their different potential wells (due to the different doping 9.4 Analysis 119

8 (

2 d I / ) 6 d A 0 V n

E ) (

1 /

( I E 4

0 I /

-2 V

2 ) -4 4 0 E

8 ( 2 d ) I / d A 6 V n E

( 0 E 1 ) 0 I /

4 ( I /

-2 V

2 ) -4 4 0 E

8 ( 2 d I ) / d

A 6 V n

( 0 )

/ I

E E ( 0 1 4 I / -2 V

2 ) -4 0 -0.5 0.0 0.5 1.0 1.5 sample voltage (V)

Figure 9.5: From top to bottom: the I-V curves (dashed lines) and normalised conductance (solid lines) of samples with Hall measured carrier concentrations of 6 1017 cm−3 (black), 2.5 1018 cm−3 (red) and 6 1018 cm−3 (blue). From left to right: the dark×region corresponds to occupied× valence bands; the×white region corresponds to the band gap; the light grey region corresponds to above the CBM at the surface, but below the Fermi level; and the medium grey region corresponds to above the Fermi level. The Fermi level is taken to be 1.3 V above the VBM for each spectrum corresponding roughly to the pinned surface Fermi level of the InN-oxide surface (1.4 eV). The downward arrows display the calculated subband energies (using the method outlined in the text) with respect to the pinned Fermi level for each surface.

levels) rather than defects associated with the material.

9.4 Analysis

In this section, the Poisson-MTFA and exponential well approximation calculations of the InN samples (GS1804, GS2019, and GS1454) are reported. For each sample, the Fermi level is assumed to be pinned 1.4 eV above the VBM at the InN-oxide surface [see 3D Appendix B]. The bulk carrier concentrations (nbulk) have been determined from the Hall 3D measured values (nHall) by the following equation

n2D n3D = n3D excess , (9.9) bulk Hall − d 9.4 Analysis 120

3D Table 9.1: The corrected bulk carrier concentration (nbulk), corresponding bulk Fermi level (EF ), 0 renormalised band gap (Eg), downward band bending (VBB) - ensuring the Fermi level is pinned 1.4 eV above the VBM at the oxidized surface - of each InN sample. Also shown is the corresponding surface state density (nSS), for each sample.

3D 3 2 sample nbulk (cm− ) EF (meV) Eg0 (meV) VBB (meV) nSS (cm− ) GS1804 4.75 1017 32 604 764 1.08 1013 × × GS2019 2.11 1018 112 589 689 1.28 1013 × × GS1454 5.28 1018 206 575 619 1.30 1013 × ×

Table 9.2: A summary of the surface potential (V0) and characteristic length (z0), of the exponential well approximation used to describe the space-charge region of each InN sample. Also included are the calculated subband energies - with respect to the Fermi level pinned at the surface - (Eb), for each InN sample.

sample V0 (meV) z0 (A)˚ E1 (eV) E0 (eV) GS1804 734 39 57 247 GS2019 663 31 115 290 GS1454 589 27 206 334

2D where nexcess refers to the residual charge from thickness-dependent Hall studies by Lu et al. [15]. This accounts for inhomogeneous electron distribution within these thin films [see Chapter 8 and Appendix C]. The bulk Fermi level (corresponding to the bulk carrier concentration) has been calculated using the α-approximation for the non-parabolic conduction band [see section 1.3.3]. The intrinsic band gap and band-edge effective mass of InN used in the calculations are Eg = 0.627 eV and m0∗ = 0.045 m0, respectively [see Appendix C]. The effects of the degenerate n-type doping (especially important for GS1454) have been considered by a non-parabolic conduction band with the effects of the band gap shrinkage, as described elsewhere [see Appendix C]. Table 9.1 displays, for each sample, the bulk Fermi level (corresponding to the bulk carrier concentration), the renormalised band gap for that carrier concentration (due to the band gap shrinkage), and downward band bending (ensuring the Fermi level is pinned at 1.4 eV above the VBM) used to calculate - within the Poisson-MTFA - the potential well formed at their surface. Also shown within table 9.1 is the calculated surface sheet density for each sample. All three space-charge profiles have been described by an exponential form (equation 9.1) using a least-squares fit. The surface potential and characteristic length for each 9.4 Analysis 121

Figure 9.6: The band bending of the conduction band minimum (CBM) and valence band maximum (VBM) (solid lines) of GS2019 as a function of depth (z), calculated within the Poisson- MTFA. The Fermi level (EF ), is shown to be pinned 1.4 eV above the VBM at the InN-oxide surface. The inset displays the total accumulated carrier concentration as a function of depth. The potential well formed at the surface by the band bending of the CBM has been described by an exponential from [V (z) = V0exp( z/z0)] by a least-squares ﬁt. The calculated subband − − energies (E0) and (E1), are shown withn the exponential well.

profile is reported in table 9.2. The calculated subband energies (using the exponential well approximation) for each exponential well are reported in table 9.1. For illustrative purposes, figure 9.6 displays the conduction and valence band bending near the InN-oxide surface of GS2019 calculated within the Poisson-MTFA. The potential well formed by the conduction band has been approximated by an exponential well, which was used to calculate the subband energies shown within the potential well. Referring to figure 9.5, the calculated subband energies (with respect to the pinned Fermi level) reported in table 9.2 for each sample are displayed as downward arrows. For samples GS1804 and GS2019, these arrows coincide with dips in the normalised conductance. The closer proximity of the subbands to each other for GS1454 combined with the resolution of the electron tunnelling spectroscopy accounts for the lack of such distinct features in its spectrum. The agreement between the calculated subband energies and the features in the electron tunnelling spectra of these InN samples confirm the presence of quantized states within the accumulation layer at InN-oxide surfaces. 9.5 Conclusion 122

9.5 Conclusion Tunnelling spectroscopy has been used to investigate the native electron accumulation layer at the the surface of n-type InN. The tunnelling spectra all exhibit a zero tunnelling plateau of 0.6 V corresponding to the band gap of InN. For all three spectra, a separation ∼ of 1.3 V is observed between the rapid negative current onset at the VBM and positive current onset at the pinned Fermi level. Additional features in all three spectra were observed between the CBM and pinned surface Fermi level. Subband calculations using a method employing the Poisson-MTFA and exponential well approximation (which was shown to reproduce self-consistent calculations of degenerate n-InAs surfaces) revealed that these features coincided with the quantized states lying within the potential well formed by accumulation layer for the InN-oxide surface. Chapter 10

Epilogue

10.1 Importance of the branch-point energy

The location of the branch-point energy (EB) of III-V semiconductors (e.g. InAs) has been identiﬁed as an important parameter for understanding the formation of the space- charge layer. In this sense, InN has been shown to behave no diﬀerently. The location of EB determines many of the physical properties of a semiconductor, due to it being energetically favourable for the Fermi level of a III-V semiconductor to lie close to EB at interfaces (including free-surfaces) and following high-energy irradiation [4, 36, 47]. The extreme electron accumulation and strong proclivity towards n-type conductivity of InN is neatly understood in terms of the conduction band minimum (CBM) lying far below EB. As a result, it is energetically favourable (at interfaces and following irradiation) for the

Fermi level to lie above the CBM i.e. close to EB. Here, the location of EB with respect to the band edges of InN is discussed in terms of the indium and nitrogen.

For almost all other III-Vs, EB lies within the band gap (Eg) of the semiconductor;

InAs and InN are diﬀerent, for them EB lies above the CBM at the zone centre. For both materials, the indium cation is responsible for the CBM lying low at the Γ-point compared to the rest of the conduction band (and more importantly EB) [5] [see section 6.5.1]. The situation is far more dramatic for InN, due to the the negligible spin-orbit splitting in wurtzite III-Ns (∆SO(InN) = 5 meV [186]). The spin-orbit splitting (due to the anion) pushes the mostly anion-derived valence band maximum (VBM) at the Γ-point upwards at the zone centre with respect to EB [5]. This is most noticeable for InSb, where the large spin-orbit splitting (∆SO(InSb) = 810 meV [109]) results in the VBM lying close to EB [5]. The small spin-orbit splitting of wurtzite InN results in the VBM lying extremely low with respect to EB compared to other indium-based III-Vs. Therefore, from comparisons

123 10.2 Indium nitride: a highly mismatched compound 124 with other III-V semiconductors: it is the combination of both the indium and nitrogen that is considered to be responsible for the low lying CBM and VBM, respectively [see section 6.5.1]. The mismatch between the large, (relatively) electropositive indium cation and the small, highly electronegative nitrogen anion of InN is discussed further in the next section, along with comparisons with other similar compounds which have large mismatches between their atoms.

10.2 Indium nitride: a highly mismatched compound

In last few years, a new class of material has recently been recognized: highly mismatched compounds (HMCs). Intrinsic to these materials is the large size- and electronegativity- mismatch between the constituent atoms. For example, dilute nitride alloys (e.g. GaNxAs1 x) − - where metallic and electropositive anions are replaced by highly electronegative nitrogen atoms - form part of the HMC family [187]. In this case, the large mismatch is responsible for the dramatic band gap reduction observed in III-N-V alloys [188] (and II-O-VI alloys [189]), as depicted in figure 10.1. The ionic semiconductors InN, ZnO and CdO, all have a large size- and electronegativity -mismatch between the cation and anion, and also form part of the HMC family. This result of the mismatch for these materials is most evident in their violation of the common cation rule [119, 191]. This rule holds that for semiconductors with the same cation (or anion), the band gap at the Γ-point increases as the period of the anion (or cation) decreases [191]. This rule is true for Al- and Ga-based III-V compounds. However, InN(E 0.7 eV) has a smaller band gap than InP (E = 1.46 eV) breaking this rule for g ∼ g the In-based III-Vs. Wei et al. attributed this violation to the combined effects of the very low N2s orbital energy (lowering the CBM) and the small deformation potential of ionic InN [191]. The small deformation potential is a result of the large difference of the In5s and N2s orbital energies; the large pd-repulsion between the shallow-core In4d and p-like valence band states [see Chapter 5]; and, the large bond length of InN (compared to AlN and GaN) [191]. In a similar manner, the mismatch between the zinc and cadmium cations and the oxygen anion is also responsible for ZnO and CdO violating the common-cation rule. These highly cation-anion mismatched compounds share many similar properties. 10.2 Indium nitride: a highly mismatched compound 125

Figure 10.1: The band gap variation of several III-V semiconductors as a function of the lattice constant, as reported by Veal et al. [190]. A small amount of band bowing is exhibited by both conventional mixed cation and mixed anion III-V ternary alloys (e.g. GaxIn1−xAs and InAsxSb1−x). By contrast III-Nx-V1−x alloys undergo enormous band gap bowing. For 0 x 0.1 the dilute nitride gaps (solid lines) have been calculated, the remaining compositions (dashed≤ ≤ lines) are merely schematic extrapolations to illustrate the possible extent of the band gap bowing.

All three materials have a strong proclivity towards unintentionally high n-type conductivity. This is highlighted by: 1) p-type ZnO only being realized in 2002 [192]; 2) the mounting evidence of p-type InN only in the last year [22, 193]; and 3) the lack of any- 18 3 thing but heavily-doped n-type CdO (lowest values typically low 10 cm− ) [194]. Another property is the location of EB with respect to their band edges. This is illustrated by: the observed electron accumulation at InN [17] and more recently ZnO [195] surfaces (studies of the near-surface region of CdO are currently lacking but are now increasingly interesting following the improvements in the crystalline quality of this material in last few years [196, 197, 198]). These shared properties are consistent in terms of their band edges lying low with respect to EB, due to the mismatch between the cation and anion. Figure 10.2 depicts the location of the band edges of InN [section 6.4], ZnO [199], and CdO - along with the archetypal compound semiconductor GaAs [5, 47]- with respect to EB. It shows that the mid-gap energy lies far below EB for all three HMCs, unlike for GaAs. Note, the exact location of EB for CdO still remains uncertain. The unintentionally high n-type 10.2 Indium nitride: a highly mismatched compound 126

1.0 Highly mismatched EC 0.5 co mp o u n ds Eg/2 0.0 E ) B V e

( -0.5 EV y g

r -1.0

e n

E -1.5

-2.0

-2.5

-3.0 GaAs InN CdO ZnO

Figure 10.2: The Γ-point conduction (EC) and valence (EV ) band edges of InN, CdO and ZnO, with respect to the branch-point energy (EB). These highly mismatched compounds are characterized by their low-lying band edges with respect to EB. These materials are in contrast with the archetypal compound semiconductor, GaAs, which has its Γ-point mid-band gap point (Eg/2) lying close to EB.

conductivity of CdO indicates that the conduction band edge lies close to EB. Indeed, this is consistent with X-ray photoemission studies of CdO, which reported a Fermi level to VBM separation of 1.5 eV at the surface [200] suggesting that the conduction band ∼ edge might lie below EB (assuming an indirect band gap of 1.09 eV [201]). To conclude, InN is best considered as a highly cation-anion mismatched compound. The size- and electronegativity-mismatch between the heavy indium and small, highly electronegative nitrogen, results in the conduction and valence band edges lying extremely low. So low in fact, its Γ-point CBM lies below EB. Therefore, the strong proclivity towards n-type conductivity and native electron accumulation of InN can neatly be understood as it being energetically favourable for the Fermi level lying close to EB (following irradiation and at interfaces), just as for other III-V semiconductors. Appendix A

EMRS Fall meeting 2005: the current status of InN

The European Materials Research Society (EMRS) 2005 Fall meeting in Warsaw, Poland, dedicated an entire symposium to indium nitride. In the last few years the number of studies of InN has increased dramatically. This is partly due to the realisation of reproducible, high-quality, single-crystalline material by molecular-beam epitaxy and the revision of the fundamental band gap of InN to 0.7 eV [6, 7]. The pace of this field has resulted in ∼ some conflicting results from various groups. The EMRS symposium provided an excellent opportunity to discuss the various results. This report is designed to provide a concise review of the current status of InN following this symposium to the general semiconductor audience. One of the most controversial reports regarding InN so far has been the work of Shubina (Ioffe Physico-Technical Institute, Russia) et al., where Mie resonances due to the scattering or absorption of light in InN-containing metallic indium clusters was presented as being responsible for ‘erroneous’ analysis of the band gap of InN [202]. Prior to the conference, the work was heavily criticised in a comment to Physical Review Letters by F. Bechstedt, J. Furthmuller¨ (Friedrich-Schiller-Universität, Germany), O. Ambacher and R. Goldhahn (Technische Universität Ilmenau, Germany) [203]. They found that after repeating the simulations reported in [202], agreement between the theory and absorption spectrum for 2% metallic indium could only be made when the onset of the absorption edge of InN was 0.9 eV [203] and not 1.4 eV as reported in ref. [202]. The onset at 0.9 eV agrees well with the expected absorption onset for InN with a band gap of 0.7 eV and a carrier concentration of 2 1019 cm 3 (as reported for the sample considered in ref. [202]) × − due to Moss-Burstein shift [111]. Furthermore, co-authors of ref. [202] have since reported that ‘conclusions on the projected band gap of pure InN from studies of such composite samples (ref. [202]) are therefore unreliable’ [204], thus supporting Bechstedt et al [203]. After Shubina’s presentation in Warsaw, she had to concede that an optical transition of

127 128

0.9 eV was most likely following persistent questions from both Bechstedt and Goldhahn. It appears that the meeting in Warsaw has finally resolved this controversy; the reported band gap of InN has not been ‘erroneous in tens of papers’ as reported in ref [202] and the fundamental band gap of InN is now considered to be 0.6-0.65 eV. Recently valence electron energy-loss spectroscopy (VEELS) has been employed to investigate InN [205], where a strong peak at 1.9 eV was found and the band gap was considered to be 1.7 eV. At the 6th International Conference on Nitride Semiconductors (ICNS-6) in Bremen the previous week to the EMRS, Specht (University of California Berkeley, USA) reported that the band gap of not only InN but also InGaN alloys was incorrectly determined from a whole host of optical techniques. At Warsaw, the same presentation was given. Veal (Warwick University, UK) and Walukiewicz (Lawerence Berkeley National Laboratory, USA) argued that for InN the sample preparation by ion milling and the transmission electron spectroscopy itself had created donor-like defects stabilizing the Fermi level at 1.9 eV for InN. It is known that donor-like defects are en- ∼ ergetically favourable for InN as described by the amphoteric defect model and confirmed by irradiation studies of InN [170]. Goldhahn had earlier reported his work on the dielectric function of InN and InGaN alloys from spectroscopic ellipsometry studies. Excellent agreement between the dielectric function and parameter-free ab-initio density functional theory (DFT) calculations by Bechstedt was also reported, confirming that InN is indeed a narrow band gap material. Goldhahn presented his own analysis of the VEELS presented by Specht during the rump session. Using his dielectric function results he determined 1 the loss-function Im ²−(ω) and obtained agreement between the loss function and the ³ ¯ ¯´ VEEL spectra. From ¯his analysis¯ he ruled out the assignment of 1.7 eV as the band gap ¯ ¯ of InN, in agreement with Veal and Walukiewicz. Arguments were presented by Butcher (Macquarie University, Australia) over the extent of the Moss-Burstein shift at Warsaw. However, in his presentation sputtered material was compared with single-crystalline epitaxially grown InN. It should be noted that only cautious comparisons between the two should be made, since the measured real and imaginary absorption coefficients of sputtered and epitaxially grown material have been shown to be very different over a large energy range [206]. Only single-crystalline epitaxially grown InN was concluded to represent bulk-like wurtzite InN from comparisons with first principle calculations [206]. Furthermore, Walukiewicz reported how the absorption 129

17 3 edge of low doped (low 10 cm− ), single-crystalline epitaxially grown InN samples dramatically increased from 0.6 eV to 1.6 eV following high energy 4He+ irradiation. ∼ ∼ Simulations of the spectra revealed how the Fermi level in these samples dramatically increased giving rise to a strong Moss-Burstein shift in the absorption edge. These results were completely consistent with previous reports of the Moss-Burstein shift [111] and high energy irradiation studies of nitrides [170]. It is important to note that within the InN community there does still remain some debate over the fundamental band gap of InN, even after the resolution of the Mie resonances, VEELS and Moss-Burstein work. This is regarding whether the band gap is 0.60 eV or 0.64 eV at room temperature for non-degenerately doped InN. Photoluminescence experiments combined with simulations of the data by both Klochikhin (St. Petersburg Nuclear Physics Institute, Russia) [207] and Valcheva (Sofia University, Bulgaria) provided some of the strongest evidence for a fundamental band gap of 0.60 - 0.64 eV at room temperature. It was following improvements in the epitaxial growth of InN and the reduction of the unintentional n-type conductivity of InN, that evidence of an electron accumulation layer at InN surfaces was first observed [15]. Soon afterwards, studies on clean, damage-free n-type InN surfaces using high-resolution electron-energy-loss-spectroscopy [17] combined with theoretical band structure calculations [125] revealed that the electron accumulation was an intrinsic property of the material. For most III-V semiconductors an electron depletion layer is typically observed at n-type material. Consequently, there was some uncertainty within the InN community over whether the electron accumulation was indeed an intrinsic property of the material. A consensus has now been reached regarding the electron accumulation following the Warsaw Meeting. At ICNS-6 in Bremen the previous week, the electron accumulation was confirmed to be an intrinsic property of InN from theoretical calculations by Segrev and Van de Walle (University of California Santa Barbara, USA). This is due to InN exhibiting an extremely low Γ-point conduction band minimum (CBM) resulting in the Fermi level at the surface being pinned high above the CBM, in agreement with earlier studies [17, 125]. In Warsaw, further evidence was presented. The first was capacitance-voltage profiles of a range of InGaN samples showing the variation from accumulation (InN) to depletion (GaN) profiles as a function of com- position by Walukiewicz. The second was direct evidence of quantized subbands in the 130 accumulation layers for a range of In-rich InGaN alloys samples using electron tunnelling spectroscopy presented by Veal [208]. Excellent agreement between the energetic location of subbands from the tunnelling spectra and space-charge calculations was also shown. Discussions followed in the rump session over how the electron accumulation could be passivated or even exploited. The electron accumulation arises from the physical properties of the material i.e. the extremely low Γ-point CBM of InN with respect to the rest of the conduction band and will always exist at InN surfaces. Perfectly cleaved (1120)¯ surfaces in vacuo were briefly considered as a possible exception, where flat bands are expected as discussed by Segrev. However, such applications have limited use for device purposes. Instead, it was emphasized that the electron accumulation could be exploited: for instance, as a promising tera-Hertz emitter [209]. After the band gap and the native electron accumulation, the accurate determination of the energetic location of the In4d electrons is considered to be one of the most important measurements for further understanding InN. Bechstedt illustrated in his presentation in Warsaw how band structure calculations of InN using DFT within the local density approximation (LDA) results in an overlap of the conduction and valence bands around the Γ-point, giving rise to negative band gaps due to extremely shallow In4d electrons interacting with the valence bands [140]. Pseudo-potentials accounting for the self-interaction corrections of the In4d electrons can be used to avoid this [140]. Such corrections require the accurate determination experimentally of the In4d electrons with respect to the valence band maximum (VBM). Cobet (Technischen Universität Berlin, Germany) also reported how ellipsometry measurements of the conduction band require accurate determination of the In4d electrons to investigate In4d-In5p transitions. X-ray photoemission spectroscopy (XPS) is the obvious technique for accurately determining this feature. However, the surface preparation of InN is non-trivial; so far only atomic hydrogen cleaning (AHC) has been successful in producing contaminant-free, well ordered surfaces suitable for XPS studies of the In4d semi-core level and valence band [72]. XPS studies of InN prepared by low energy AHC presented by Piper (Warwick University, UK) reported clean, indium droplet-free, InN surfaces. The In4d electrons due to the In-N bond were found to lie 16.0 0.1 eV above the VBM. Evidence was also presented for an § indium bi-layer reconstruction. Such a reconstruction had been shown to be possible by Segrev the previous week at ICNS-6, Bremen. Piper also reported agreement between the 131 valence band spectra from XPS and the valence band density of states from DFT-LDA (including corrections considering the location of the In4d level) calculations performed by Bechstedt [153]. Finally, Piper received the European Materials Research Society and Polish Materials Science Society award in recognition of the best paper presented by a PhD student at the EMRS 2005 Fall meeting. Appendix B

Fermi level pinning at oxidized InN surfaces

To date, the majority of studies of the Fermi level pinning have been in vacuo studies of clean InN surfaces. Here, the effects of the pinned Fermi level at oxidized InN surfaces have been investigated using a combination of X-ray photoemission spectroscopy (XPS) measurements and Poisson-MTFA calculations of both clean and oxidized InN surfaces. The XPS experiments were performed within a conventional ultra-high vacuum chamber using a Scienta ESCA300 spectrometer at the National Centre for Electron Spec- troscopy and Surface analysis (NCESS), Daresbury Laboratory, UK. The Al-Kα x-ray source (hν = 1486.6 eV) was monochromated, and the resultant instrumental resolution was 0.45 eV. The Fermi level position (zero of the binding energy scale) was calibrated using the Fermi edge of a Ag reference sample. The 18 nm thick InN(0001) sample was grown by gas-source molecular beam epitaxy, on top of a 220 nm GaN buffer layer. A further 10 nm AlN layer was grown between the buffer layer and c-plane sapphire substrate. Details of the growth conditions used are reported elsewhere [81]. The as-loaded InN has been used for studying the oxidized surface. The clean InN surface was prepared by atomic hydrogen cleaning (AHC), which has previously been shown, by a combination core-level XPS and HREELS, to successfully produce clean, well- ordered InN surfaces [72]. The AHC was performed in a separate preparation chamber connected to the XPS analysis chamber, using the AHC method reported elsewhere [see section 5.3]. Scanning electron microscopy following the clean confirmed the lack of metallic In droplets following the cleaning cycle; meanwhile, the root-mean-square roughness was found to be 2 nm by atomic force microscopy [153]. Figure B.1 displays the In4d semi-core level of the a) oxidized and b) AHC prepared InN surface. The spectra were curve fitted using Voigt functions of equal full width at half maxima. Three components were required to fit the spectrum from the oxidized surface, which were attributed to the In-In (16.9 eV), In-N (17.4 eV) and In-O (18.5 eV)

132 133

Figure B.1: The a) oxidized and b) after AHC In4d semi-core level spectra of the InN sample (dots), with the corresponding curve-fits (thick lines). The background and peak components (thin lines) of the fits are also shown. Three components were required to fit the as-loaded In4d level, corresponding to In-O, In-N and In-In bonds. After AHC, the In-O bond is absent and the In-N bond has an increased signal. A feature at 15 eV in both spectra is from the N2s orbital. The insets show the magnified valence band-edge∼region for both spectra. The VBM was found, by extrapolation to baseline (shown), to lie 1.20 0.10 eV below the Fermi level (0 eV) for the oxidized spectra, whilst lying 1.40 0.10 eV belo§w following the AHC. § bonds, respectively. This assignment reflects the increasing electronegativity of the species bonded to In resulting in greater binding energy. The In-O component was absent after the AHC cycles, confirming a clean, oxygen-free surface. The presence of the In-In bond contribution in the In4d spectra for (both oxidized and clean surface) is believed to be due to an In-adlayer termination and not In droplets [72, 153] and references therein. The valence band maximum (VBM) was extrapolated from the leading edge of the lowest binding energy valence band peak to the baseline for each spectrum, as shown in the insets of figure B.1. The VBM of the oxidized and clean InN surfaces were found to lie 1.20 § 0.10 eV and 1.40 0.10 eV below the Fermi level, respectively. § The exponential form of the photoemission intensity (due to the attenuation length of the photoelectrons) combined with the short screening lengths of the degenerately-doped n-type InN sample, means that VBM to Fermi level separation determined by the XPS is 134

Figure B.2: The Poisson-MTFA calculations of the near-surface region of degenerately-doped n-InN, assuming a pinned surface Fermi level of 1.6 eV (black line) and 1.4 eV (grey line) corresponding to the clean and oxidized surface, respectively. The distance from the surface, D = 0.7 nm, refers to the eﬀective depth corresponding to the VBM to Fermi level separation determined by XPS.

an average over a finite depth from the surface. To illustrate this, figure B.2 displays the Poisson-MTFA calculations of the clean and oxidized InN near-surface regions, assuming similar room temperature bulk band properties as reported elsewhere [see section 6.6.3]. The Fermi level was assumed to lie 1.6 eV above the VBM at the clean InN surface, with 2.15 1013 cm 2 ionized donor-like surface states. After a depth z = D (D = 0.7 nm) - as × − depicted in figure B.2 - the Fermi level lies 1.38 eV above the VBM in agreement with 1.40 0.1 eV from the XPS of the clean InN surface. Since the VBM to Fermi level separation § determined by XPS is an average over a finite depth from the surface, the distance z = D is considered to be the effective depth (to a first approximation). If a pinned Fermi level of 1.4 eV is used (with 1.4 1013 cm 3 ionized donor-like surface states) at z = D, the × − Fermi level lies 1.23 eV in agreement with 1.20 0.10 eV from the XPS of the oxidized § InN surface. Therefore, the surface Fermi level of the oxidized InN is 1.4 eV. 135

Figure B.3: The schematic space-charge proﬁles for an electron a) depletion and b) accumulation layer at degenerate n-type clean semiconductors (thick dashed lines) with respect to the Fermi level (thin solid line). The band bending is also shown when an electronegative (electropositive) adatom e.g F (Cs) is deposited onto the surface (thick solid lines) as a function of depth within the material (z = 0 corresponds to the surface). When electronegative adatoms are deposited upon a clean semiconductor with a depletion layer (accumulation layer) proﬁle more (less) upward (downward) band bending is observed (arrow).

The reduced band bending at oxidized InN surfaces (due to the lower pinned Fermi level) can be explained in terms of the charge transfer between the semiconductor and oxygen adatoms. For predominantly-covalent semiconductors (such as III-Vs) there is a weak dependence of the Schottky barrier height (defined as the pinned Fermi level with respect to majority carrier band edge) with the electronegativity of the adatom [3, 5, 31]. When adatoms are deposited on a clean surface, charge transfer between the adatoms and the semiconductor modifies the ionized surface state density, resulting in charge neutrality being satisfied at a different pinned Fermi level, compared to the clean surface. Figure B.3 depicts the band bending at clean, degenerately doped n-type semiconductors for a) a depletion and b) an accumulation case; also shown is the band bending for each case when highly electronegative and electropositive adatoms are deposited. For a depletion layer, typically present at n-type III-V surfaces, the Schottky barrier height increases as the electronegativity increases, as depicted in figure B.3 a). When 136 sub-monolayer to monolayer amounts of highly electronegative adatoms (e.g. fluorine or oxygen) are deposited onto the surface, charge transfer from the conduction band to the adatoms at the surface increases the amount of occupied, negatively-charged, acceptor- like surface states. Therefore, more band bending is required to achieve charge-neutrality compared to the clean surface. Less band bending is required to achieve charge neutrality when highly electropositive adatoms (e.g. caesium) are deposited. For accumulation regions (such as at n-InN surfaces) negative Schottky barrier heights are considered, since the pinned Fermi level lies above the conduction band edge. Using the same arguments as previously, when highly electronegative adatoms (e.g. fluorine or oxygen) are deposited, charge transfer from the conduction band to the adatoms at the surface will decrease the amount of unoccupied, positively-charged, donor-like surface states. Therefore, less downward band bending is required to achieve charge-neutrality, compared to the clean surface, as depicted in figure B.3 b). In the same manner, highly electropositive adatoms should increase the amount of band bending required for charge- neutrality, compared to clean surfaces. To summarise, a distinct difference between the VBM (with respect to the Fermi level) determined by XPS is observed for the clean (1.40 eV 0.10 eV) and the oxidized § (1.20 eV 0.10 eV) InN surfaces. This can be explained by the concept of a charge transfer § between the semiconductor and the highly electronegative oxygen adatoms, reducing the band bending required to achieve overall charge-neutrality at the oxidized surface. This is illustrated by Poisson-MTFA calculations of the near-surface regions of the oxidized and clean surfaces, which reveal pinned surface Fermi levels of 1.4 eV and 1.6 eV, respectively. The reduced band bending of the oxidized surface is due the charge transfer (from the semiconductor to the oxygen adatoms) reducing the amount of ionized donor-like surface states: from n = 2.14 1013 cm 2 from clean case to n = 1.42 1013 cm 2 for SS × − SS × − oxidized case. This is consistent with previous studies of InN, which have shown lower surface state densities at oxidized InN surfaces (n = 2.2 1013 cm 2 [210]) compared SS × − to the clean surfaces (n = 2.5 1013 cm 2 [17]). SS × − Appendix C

Eﬀects of the inhomogeneous electron distribution of InN

The inhomogeneous electron distribution of InN films [173] due to the contributions from the ionized donor-like surface states, donor-like impurities and positively-charged threading dislocations [see Chapter 8] means that Hall measurements only provide an ‘average’ bulk carrier concentration. Here, a method is presented to estimate the bulk Fermi level of InN thin films. The method has been employed to calculate the shift in the absorption edge of various InN samples with different degenerate n-type conductivities (known as the Moss-Burstein shift). The Moss-Burstein shift of InN samples was first investigated by the pioneering work of Wu et al. in 2002 [111]. In their study, the effects of the non-parabolic conduction band [due to the narrow band gap of InN (E 0.64)] and band gap shrinkage g ∼ [due to the degenerate n-type conductivity] were considered. Since then, the observation of extreme electron accumulation at InN surfaces [15, 17] has meant that the effects of the inhomogeneous electron distribution should also be included when investigating the Moss-Burstein shift of the absorption edge of InN thin films. It has been shown that for an InN film of thickness d, the Hall measured 3D electron 3D 3D density (nHall) is the sum of the 3D density due to the donor impurities (nimp); the 2D surface sheet density due to the donor-like surface states (nSS); and, the charge density associated with the dislocation density in the film, such that n2D C d n3D = n3D + SS + D(x)dx, (C.1) Hall imp d d Z0 where D(x) is the exponential decay of the dislocation density as a function of distance x from the buffer layer interface, and C is the charge contribution of each dislocation per unit length [see chapter 8]. To a first approximation, the ‘bulk’ carrier concentration 3D responsible for the space-charge (nbulk), shall be considered to be related to the Hall measured carrier concentration, by n2D n3D = n3D excess , (C.2) bulk Hall − d

137 138

Figure C.1: The calculated absorption edge (line) as a function of electron concentration. Also included are the experimental results from Wu et al. [111] and Kasic et al. [204, 211], along with their corresponding corrected 3D bulk carrier concentrations.

2D where nexcess refers to the residual charge from thickness-dependent Hall studies by Lu et al. [15]. This is under the assumption that the inhomogeneous carrier concentration due to the three contributions can be treated as a ‘bulk’ carrier concentration with excess interfacial contributions. In order to prove the validity of equation C.2, comparisons have been made with optical absorption spectroscopy measurements. Figure C.1 displays the Moss-Burstein shift [159, 160] of the absorption edge of various InN samples as a function of carrier concentration. All of the InN samples shown in figure C.1 were chosen since their film thickness and type of buffer layer are known. Kasic et al., reported the thickness and type of buffer layer for each sample [211]. The corresponding absorption edges, for each sample, were determined by the extrapolation of absorption coefficient squared, reported elsewhere [204]. Sample GS1250 reported by Wu et al., has a thickness of 120 nm and was grown on an AlN buffer layer [111]. The corresponding corrected carrier concentrations (equation C.2) for each sample are also shown in figure C.1. For degenerate doping levels, the fundamental absorption onset (edge) corresponds to vertical transitions between the valence bands and the bulk Fermi level. For this case, 139 the calculated absorption edge is considered to be the energetic separation between the valence band maximum (VBM) and ‘bulk’ Fermi level (EF ) [corresponding the Fermi level for bulk carrier concentration determined by equation C.2]. The VBM is used since the dispersion of the valence bands are treated as flat compared to the conduction band dispersion. The lack of studies of p-type material has meant that the hole effective masses are still unknown, but calculations have predicted a heavy hole band-edge effective mass of 2.56 m0 [212] which support this flat valence band approximation. Here, the α-approximation [see section 1.3.3] has been used to calculate the conduction band dispersion as a function of wavevector [EC (k)], in order to account for the non-parabolic conduction band, given by

2 2 EC ¯h k EC 1 + = , (C.3) Ã Eg ! 2m0∗ where the band gap (Eg) and band-edge effective mass (m0∗) are the only parameters required. Room temperature photoluminescence measurements on 7.5 µm thick InN samples grown by molecular beam epitaxy with free electron densities of 3.5 1017 cm 3 (n3D × − bulk = 3.1 1017 cm 3) and mobilities of 2050 cm2V 1s 1 (determined from single-field Hall × − − − measurements) exhibit a peak at 0.64 eV [13]. The PL peak of non-degenerately (or ∼ 1 even moderately degenerately doped) semiconductors corresponds to the Eg + 2 kT [215]; this makes the band gap of InN 0.627 eV at room temperature. The band-edge effective mass of a semiconductor is related to the band gap of the semiconductor by the empirical rule, m 0.07 E [163]. Therefore, a band-edge effective 0∗ ∼ g mass of 0.045 m0∗ has conservatively been chosen here. This is in good agreement with recent infrared magneto-optic generalized ellipsometry (IRMOGE) measurements of 1.5 µm thick InN samples with a free electron density of 1.8 1017 cm 3 which gave effective × − masses in the perpendicular and parallel direction of m∗ = 0.047 m0 and m∗ = 0.039 m0, ⊥ k respectively [213]. Therefore, the isotropically averaged density of states effective mass 2 1/3 17 3 mD∗ = [(m∗ ) m∗] = 0.044 m0 at n = 1.8 10 cm− in good agreement with 0.045 ⊥ k × m0 considered here. Note, IRMOGE dispenses with single-field Hall measurements and the technique is able to separately determine both the electron density and corresponding effective mass (either in the perpendicular or parallel direction to the c-axis). At degenerate doping levels, band gap shrinkage occurs due to Coulomb interactions among the free electrons themselves (electron-electron) and their interactions with 140 the ionized impurity centres (electron-impurities). The conduction band is modified from the unperturbed band energy by the self-energy associated with the electron-electron and electron-impurities scattering when free electrons are added [110]. For the degenerate levels involved with InN, Wu et al., highlighted the need to consider these effects when investigating the Moss-Burstein shift of InN [111]. Here, the band gap shrinkage (∆Eg) is assumed to result solely from the conduction band being modified by the Hartree-Fock self energy [110], such that

2e2k ∆E = F , (C.4) g − ²(0)π where ²(0) is the static dielectric constant and the Fermi wavevector is given by kF = (3n2π)1/3 where n is the carrier concentration. Here, the isotropically averaged static dielectric constant has been determined by combining the high frequency dielectric constant, ²( ), with information on the relationship between ²(0) and ²( ) from high-resolution ∞ ∞ electron-energy-loss spectroscopy (HREELS). The observed Fuchs-Kliewer surface optical phonon frequency (ωF K ) is related to the transverse optical phonon frequency (ωT O) and the dielectric constants by ω2 = ω2 [²(0) + 1] / [²( ) + 1]. The Fuchs-Kliewer phonon F K T O ∞ frequency observed by HREELS is 66 meV [17, 113, 125] and ωT O is 56 meV [214]. While it is recognized that ²( ) values of 5.8 [216] and 8.4 [9] have been reported, the recently ∞ obtained experimental value for ²( ) of 6.7 [19] is preferred as it is similar to the theo- ∞ retical value of 7.16 [140]. Using this high frequency dielectric constant of 6.7 with the stated ωF K and ωT O values, gives a static dielectric constant of 9.7. For each carrier concentration, the corresponding Fermi wavevector was used to determine the amount of band gap shrinkage; then the renormalised band gap (Eg0 = Eg

+ ∆Eg) was incorporated into the α-approximation to determine EF . The absorption edge was then considered to be the sum of the renormalised band gap and Fermi level. Figure C.1 displays the calculated Moss-Burstein shift for InN using this method. Agreement is observed between the calculated variation in the absorption edge with carrier concentration and the experimental results corrected by equation C.2. This supports the validity of equation C.2 for correcting the Hall measurements to account for the inhomogeneous electron distribution. Bibliography

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