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A Dissertation Entitled a Theoretical Study of Bulk and Surface Diffusion A Dissertation entitled A Theoretical Study of Bulk and Surface Diffusion Processes for Semiconductor Materials Using First Principles Calculations by Jason L. Roehl Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics Dr. Sanjay V. Khare, Committee Chair Dr. Jacques G. Amar, Committee Member Dr. Terry Bigioni, Committee Member Dr. Robert Deck, Committee Member Dr. Randall Ellingson, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo May 2014 Copyright 2014, Jason L. Roehl This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of A Theoretical Study of Bulk and Surface Diffusion Processes for Semiconductor Materials Using First Principles Calculations by Jason L. Roehl Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics The University of Toledo May 2014 Diffusion of point defects on crystalline surfaces and in their bulk is an important and ubiquitous phenomenon affecting film quality, electronic properties and device functionality. A complete understanding of these diffusion processes enables one to predict and then control those processes. Such understanding includes knowledge of the structural, energetic and electronic properties of these native and non-native point defect diffusion processes. Direct experimental observation of the phenomenon is difficult and microscopic theories of diffusion mechanisms and pathways abound. Thus, knowing the nature of diffusion processes, of specific point defects in given materials, has been a challenging task for analytical theory as well as experiment. The recent advances in computing technology have been a catalyst for the rise of a third mode of investigation. The advent of tremendous computing power, break- throughs in algorithmic development in computational applications of electronic den- sity functional theory now enables direct computation of the diffusion process. This thesis demonstrates such a method applied to several different examples of point de- fect diffusion on the (001) surface of gallium arsenide (GaAs) and the bulk of cadmium telluride (CdTe) and cadmium sulfide (CdS). All results presented in this work are ab initio, total-energy pseudopotential cal- culations within the local density approximation to density-functional theory. Single iii particle wavefunctions were expanded in a plane-wave basis and reciprocal space k- point sampling was achieved by MonkhorstPack generated k-point grids. Both surface and bulk computations employed a supercell approach using periodic boundary con- ditions. Ga adatom adsorption and diffusion processes were studied on two reconstruc- tions of the GaAs(001) surface including the c(4×4) and c(4×4)-heterodimer surface reconstructions. On the GaAs(001)-c(4×4) surface reconstruction, two distinct sets of minima and transition sites were discovered for a Ga adatom relaxing from heights of 3 and 0.5 A˚ from the surface. These two sets show significant differences in the interaction of the Ga adatom with surface As dimers and an electronic signature of the differences in this interaction was identified. The energetic barriers to diffusion were computed between various adsorption sites. On the GaAs(001)-c(4×4)-heterodimer reconstruction, structural and bonding features of the surface were examined including a comparison with the c(4×4) re- construction. Minimum energy sites (MES) on the c(4×4)-heterodimer surface were located by mapping the potential energy surface for a Ga adatom. Barriers for dif- fusion of a Ga adatom between the neighboring MES were calculated by using top hopping- and exchange-diffusion mechanisms. Signature differences between elec- tronic structures of top hopping- and exchange-diffusion mechanisms were studied for relevant atoms. A higher diffusion barrier was observed for the exchange mechanism compared to top hopping. Diffusion profiles for native, adatom and vacancy, and non-native interstitial adatoms were investigated along the open [1 1 0] channel in bulk zinc-blende CdTe. This includes native Cd and S and non-native Cu, Ag, Au, Mo, P, Sb, O, S, and Cl. High symmetry Wyckoff positions were found to be the global minimum energy location for Cd, Ag, Mo, O and Cl interstitials. Adatoms of Cu, Au, P, Sb, S show an asymmetric shape of the energy diffusion barrier with two structurally equivalent iv minima and two energetically distinct maxima in the pathway. Adatoms of Mo, Ag and Cd interstitial and vacancy, show a symmetric diffusion barrier with two struc- turally unique minima and a maximum. Adatoms of O, Cl, and Te interstitial and vacancy, show a symmetric diffusion barrier with a unique maximum and minimum. Diffusion for Cu, Au, Te and S interstitials proceeds along the [1 1 0] channel in a near straight line path. Diffusion for Cd, Ag, O and Cl proceeds along two nearly straight line paths along [1 1 1] and [1 1 -1]. Diffusion for Mo, P and Sb is along the [1 1 0] channel deviating slightly from the straight line paths along [1 1 1] and [1 1 -1]. The diffusion barriers range from a low of 0.10 eV for a Ag interstitial to a high of 1.83 eV for a Cd vacancy. The barriers for Cu, Ag, Te, Cl and S are in agreement with the available experimental data. The symmetric or asymmetric nature of the diffusion path as well as the bond length and atomic coordination at the energetic extrema positions were found to influence the size of the diffusion energy barrier. In addition there exist electronic signatures in the local density of states for the bond breaking, difference in the hybridization and energy of occupied states between the global minimum and global maximum energy positions. Diffusion profiles for native Cd and S, adatom and vacancy, and non-native in- terstitial adatoms of Te, Cu and Cl were investigated in bulk wurtzite CdS. The interstitial diffusion paths considered in this work were chosen parallel to c-axis as it represents the path encountered by defects diffusing from the CdTe layer. Because of the lattice mismatch between zinc-blende CdTe and hexagonal wurtzite CdS, the c-axis in CdS is normal to the CdTe interface. The global minimum and maximum energy positions in the bulk unit cell vary for different diffusing species. This results in a significant variation, in the bonding configurations and associated strain ener- gies of different extrema positions along the diffusion paths for various defects. The diffusion barriers range from a low of 0.42 eV for an S interstitial to a high of 2.18 eV for a S vacancy. The computed 0.66 eV barrier for a Cu interstitial is in good v agreement with experimental values in the range of 0.58 - 0.96 eV reported in the literature. There exists an electronic signature in the local density of states for the s- and d-states of the Cu interstitial at the global maximum and global minimum energy position. The work presented in this thesis is an investigation into diffusion processes for semiconductor bulk and surfaces. The work provides information about these pro- cesses at a level of control unavailable experimentally giving an elaborate description into physical and electronic properties associated with diffusion at its most basic level. Not only does this work provide information about GaAs, CdTe and CdS, it is intended to contribute to a foundation of knowledge that can be extended to other systems to expand our overall understanding into the diffusion process. vi For you, Mom and Dad. Thank you. Acknowledgments To begin, I would like to thank my research advisor, Prof. Sanjay V. Khare. Not only for his guidance throughout my research and the knowledge he has shared with me during our many informative talks but also for his support and encouragement when it was needed most. Next, I would like to thank my committee members - Prof. Jacques G. Amar, Prof. Terry Bigioni, Prof. Robert Deck and Prof. Randall Ellingson for all of their suggestions and time while serving on my committee. Thank you to all of my professors for sharing their knowledge and helping me to better understand and appreciate the world around us. Thank you to all of the current and former members of Dr. Khare's research group for their help when I started and their support and friendship throughout. Thank you to all the faculty, past and present, of the Department of Physics and Astronomy for their help and support during my time as a graduate student. A special thanks to Dr. Richard Irving for his computer system support and for taking the time for the many invaluable conversations regarding all that is computing and life. And finally I would like to thank God, my family and loved ones for all of their love, support, patience and understanding. It is because of you that all of this has been possible. viii Contents Abstract iii Acknowledgments viii Contents ix List of Tables xiii List of Figures xiv List of Abbreviations xvii 1 Introduction 1 1.1 Thesis outline . 1 2 Materials 3 2.1 GaAs . 3 2.1.1 Structure . 4 2.1.2 GaAs(001)-c(4×4) Surface Reconstruction . 4 2.1.3 GaAs(001)-c(4×4)-hd Surface Reconstruction . 4 2.2 CdTe . 6 2.2.1 Structure . 8 2.3 CdS . 9 2.3.1 Structure . 11 ix 3 Diffusion 13 3.1 Overview . 13 3.2 Surface Diffusion Mechanisms . 13 3.2.1 Top Hopping Diffusion . 14 3.2.2 Exchange Diffusion . 15 3.3 Bulk Diffusion Mechanisms . 17 3.3.1 Interstitial Diffusion . 17 3.3.2 Bulk Exchange Diffusion . 18 3.3.3 Vacancy Diffusion . 19 3.4 Describing Diffusion .
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