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Bulk and Transfer Doping of Diamond A First-Principles Study on BULK AND TRANSFER DOPING OF DIAMOND Stephen John Sque Original submission: November 1, 2005 Examination: December 19, 2005 This version: April 1, 2007 Submitted by Stephen John Sque, to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Physics, November 2005. This thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledge- ment. I certify that all material in this thesis which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University. — Stephen Sque i Abstract Presented herein are the results of theoretical investigations addressing current issues in the doping of diamond. The work has been conducted using first-principles calculations based on density-functional theory under the local-density approximation. Particular emphasis is placed upon two currently problematic aspects of doping diamond: the lack of a suitable shallow donor impurity for n-type doping of the bulk, and the need for a sta- ble adsorbate material for p-type doping of the diamond surface (transfer doping). Since the latter clearly requires an understanding of the properties of the various diamond sur- faces, the effects of atomic geometry and surface termination on the electronic structure of the technologically important diamond surfaces have also been investigated. This study reproduces the experimentally well-known properties of nitrogen and phos- phorus defects in diamond, and proceeds to predict that arsenic and antimony will be shallower donors than phosphorus, which is at present the most successful n-type dopant. However, the practicality of doping with these larger species may be hindered by the dif- ficulty of incorporating their atoms into the diamond lattice, and by their high likelihood of becoming compensated by forming complexes with vacancies or hydrogen. Mean- while, the controversial sulphur defect is found to be a deep donor, while the recent experimental observations of shallow-donor behaviour in deuterated, boron-doped dia- mond samples are not explained by any of the boron-hydrogen complexes modelled in this study. Finally, the N–Si4 shallow-donor candidate has been critically investigated. The effects of hydrogen and oxygen termination on the diamond surface are investigated in detail, and both the structural and electronic properties are shown to agree well with experimental observations. An important distinction is made between bulk- and surface- related electronic properties, and the influence of surface states on band bending and electron emission is discussed. Regarding p-type transfer doping of diamond, this study finds that buckminsterfullerene (C60) can effect an electron transfer from hydrogen-terminated diamond, when present in the form of one or more closely packed monolayers on the surface. This work also reports the prediction that the greater electron affinities of fluorinated fullerenes (such as C60F36) will enhance the effect, to such an extent that individual molecules may extract electrons from a diamond substrate — a finding that has been borne out in recent experiments. ii Acknowledgements First and foremost, I am indebted to Prof. Bob Jones for allowing me to study in his research group, and for being an excellent supervisor over the last three years. His en- thusiasm, generosity, and methods of seeking progress are legendary, and deservedly so. I also thank Bob for very kindly helping me to obtain a new position as a Post-Doctoral Research Assistant in his group. Grants from the U.K. Engineering and Physical Sciences Research Council (EPSRC) have made both my Ph.D. and Post-Doc. possible in the first place, and I am thankful to the board members, despite their anonymity. I must thank the many colleagues that I have worked with in this fast-changing research group, for making the environment in Exeter an enjoyable and productive one. While the members of the AIMpro family that I have worked alongside are now too numerous to detail, I am especially grateful to James Adey and Thomas Eberlein for using their `se- niority' to help guide me through. I am also grateful to Derek Palmer and G.P. Srivastava for their interest and help, which often provided an alternative look at a problem. The team in Newcastle deserve a special mention for their work on the AIMpro code, es- pecially Patrick Briddon for his excellent development and maintenance of the program, for which a newer version always seems to be available. Jon Goss deserves special recog- nition too, for his deft handling of my many naïve questions regarding aspects of the code and condensed-matter physics in general. Elsewhere, I am very grateful to Sven Öberg for performing many of my calculations on his powerful Swedish supercomputers, and for apparently working at very strange hours to ensure that my results were ready in time for tricky deadlines. Chris Ewels is also thanked for his (sometimes literally) animated help regarding all things nano. On a more personal level, I gratefully thank my family for supporting me throughout all of my academic endeavours (and for paying for some of them too). Finally, I offer my heartfelt thanks to Susy for being a devoted and wonderful companion for the bulk of my time in Exeter. iii List of Publications First author Structure, electronics, and interaction of hydrogen and oxygen on diamond surfaces • S. J. Sque, R. Jones, and P. R. Briddon Physical Review B 73 (8), 085313 (February 2006) Hydrogenation and oxygenation of the (100) diamond surface and the consequences for • transfer doping S. J. Sque, R. Jones, and P. R. Briddon Physica Status Solidi (A) 202 (11), 2091–2097 (August 2005) First-principles study of C and C F as transfer dopants for p-type diamond • 60 60 36 S. J. Sque, R. Jones, J. P. Goss, P. R. Briddon, and S. Öberg Journal of Physics: Condensed Matter 17 (2), L21–L26 (January 2005) Shallow donors in diamond: chalcogens, pnictogens, and their hydrogen complexes • S. J. Sque, R. Jones, J. P. Goss, and P. R. Briddon Physical Review Letters 92 (1), 017402 (January 2004) Shallow donors in diamond: pnictogen and chalcogen hydrogen defects • S. J. Sque, R. Jones, J. P. Goss, and P. R. Briddon Physica B: Condensed Matter 340–342, 80–83 (December 2003) Co-author Vacancy-impurity complexes and limitations for implantation doping of diamond • J. P. Goss, P. R. Briddon, M. J. Rayson, S. J. Sque, and R. Jones Physical Review B 72 (3), 035214 (July 2005) Quantum mechanical modeling of the structure and doping properties of defects in diamond • J. P. Goss, P. R. Briddon, R. Sachdeva, R. Jones, and S. J. Sque Proceedings of the 27th International Conference on the Physics of Semiconductors, Flagstaff, Arizona, USA, 26–30 July 2004 AIP Conference Proceedings 772 (1), 91–94 (June 2005) iv Donor and acceptor states in diamond • J. P. Goss, P. R. Briddon, R. Jones, and S. Sque Diamond and Related Materials 13 (4–8), 684–690 (April–August 2004) Boron-hydrogen complexes in diamond • J. P. Goss, P. R. Briddon, S. J. Sque, and R. Jones Physical Review B 69 (16), 165215 (April 2004) The vacancy-nitrogen-hydrogen complex in diamond: a potential deep centre in chemical • vapour deposited material J. P. Goss, P. R. Briddon, R. Jones, and S. Sque Journal of Physics: Condensed Matter 15 (39), S2903–S2911 (October 2003) Unpublished Transfer doping of diamond: the use of C and C F to effect p-type surface conductivity • 60 60 36 S. J. Sque, R. Jones, S. Öberg, and P. R. Briddon Physica B: Condensed Matter, in press (March 2006) Transfer doping of diamond: Buckminsterfullerene on hydrogenated, hydroxylated, and • oxygenated diamond surfaces S. J. Sque, R. Jones, S. Öberg, and P. R. Briddon submitted to Journal of Materials Science: Materials in Electronics (October 2005) Contents 1 Introduction 1 1.1 Carbon as diamond . 1 1.1.1 Fundamental properties . 1 1.1.2 Crystal structure . 3 1.1.3 Impurities . 4 1.1.4 Classification of diamond . 5 1.1.5 Synthesis of diamond . 6 1.2 Applications of diamond . 8 1.2.1 Diamond as a semiconductor material . 8 1.3 Aims of this investigation . 12 2 Theoretical Method 13 2.1 The many-body problem . 13 2.2 Born-Oppenheimer approximation . 14 2.3 Variational principle . 16 2.4 Hartree-Fock method . 17 2.5 Density-Functional Theory . 20 2.5.1 Kohn-Sham equations . 21 2.5.2 The exchange-correlation functional . 22 2.6 Pseudopotentials . 23 2.7 The AIMpro implementation of DFT . 25 2.7.1 Supercell AIMpro . 25 2.7.2 Sampling of the Brillouin zone . 26 2.7.3 Basis functions . 27 2.7.4 Basis functions in reciprocal space . 28 2.8 Calculation of observables . 29 2.8.1 Atomic geometry . 29 2.8.2 Formation energies . 32 v CONTENTS vi 2.8.3 Complex binding energies . 33 2.8.4 Donor and acceptor levels . 34 2.9 Electronic state characterisation . 38 2.9.1 Mulliken bond population analysis . 38 2.9.2 Wavefunction visualisation . 38 2.10 Convergence criteria . 39 2.11 Modelling surfaces . 40 2.11.1 Convergence criteria . 40 2.11.2 Electron affinity, ionisation potential, and work function . 41 2.12 Chapter summary . 44 3 Experimental 45 3.1 Introduction . 45 3.2 Studying bulk defects . 46 3.2.1 Electron spin/paramagnetic resonance (ESR, EPR) . 46 3.2.2 Infrared (IR) spectroscopy . 49 3.2.3 Photoluminescence (PL) . 54 3.3 Investigating surfaces . 58 3.3.1 Electron diffraction studies . 58 3.3.2 Scanning-probe microscopies .
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