List of Figures

2.1 The supercell method of modelling an infinite solid
2.2 A schematic diagram of two methods for finding reaction paths.
2.3 A schematic representation of a pseudopotential
2.4 The error in band energy for the atom at the centre of a cluster for different cluster sizes
2.5 The density matrix between atoms in a cluster for C, Si and Ti
3.1 Error in binding energy for diamond
3.2 Error in binding energy for Si in the diamond structure
3.3 Error in vacancy formation energy for diamond
3.4 Error in vacancy formation energy for Si in the diamond structure
3.5 The z force on an atom in the unreconstructed Si(001) surface
3.6 Time taken for a given accuracy for the different O(N) methods for the diamond vacancy
3.7 Error in vacancy formation energy for hcp titanium
3.8 Time taken for a given accuracy for the different methods for a vacancy in hcp titanium
3.9 The energy for a fictitious reaction, SiH₄ + SiH₃ SiH₃ + SiH₄, used for fitting
3.10 The scaling for a fictitious tetrahedral Bi cell
3.11 The density of states for a fictitious diamond Bi cell
3.12 The scaling for a fictitious tetrahedral zincblende SiBi cell
3.13 The density of states for a fictitious zincblende SiBi cell
4.1 An STM image of the Si(001) surface
4.2 A schematic diagram of the Si(001) surface
4.3 STM images of the Si(001) surface at different bias voltages
4.4 A schematic picture of the three structures for the 1DV
4.5 Simulated STM images for the 1DV
4.6 Local densities of states for a 1DV
4.7 A simple LCAO picture of bonding to explain the 1DV enhancement
4.8 A schematic picture of steps on the Si(001) surface
4.9 Step energies for B-type steps
4.10 Step energies for A-type steps
4.11 An STM image of steps on the Si(001) surface
4.12 Simulated STM images for the clean rebonded step
4.13 Simulated STM images for the clean unbonded step
4.14 Simulated STM images for the hydrogenated rebonded step
4.15 Kinked A-type and B-type steps
4.16 Convergence of kinking energy for a B-type rebonded step
4.17 Energies for a kink in a B-type step of different depths
4.18 Probability of separation of kinks
5.1 How bismuth adsorbs on Si(001)
5.2 An STM image showing the long straight lines of Bi
5.3 A detailed STM image of the Bi line
5.4 Possible structures for the Bi line
5.5 LDOS for the proposed Bi line structure
5.6 Proposed schemes for formation of the Bi lines
5.7 The schematic appearance of the c(4x4) structure formed by Si
5.8 An STM image of the c(4x4) structure formed by Bi
5.9 Structures for the Bi c(4x4) structure
6.1 STM images of stationary hydrogen
6.2 STM images of slowly moving hydrogen
6.3 STM image of rapidly moving hydrogen
6.4 The experimental graph for hydrogen diffusion
6.5 The hydrogen diffusion barrier from LDA and GGA
6.6 The hydrogen diffusion barrier from TB
6.7 Si-H-Si distances as hydrogen diffuses
6.8 STM images showing paired hydrogen diffusion
6.9 The diffusion barrier for paired hydrogen diffusing separately from TB
6.10 The diffusion barrier for paired hydrogen diffusing concertedly from TB
6.11 The diffusion barrier for a hydrogen atom diffusing down a B-type step from TB
6.12 The diffusion barrier for a hydrogen atom diffusing away from a 1DV from TB
7.1 STM images showing the fragments formed from disilane adsorption
7.2 A schematic diagram of SiH₂ bonding sites
7.3 Position and charge for the on-dimer structure
7.4 Position and charge for the intra-row structure
7.5 Position and charge for a clean surface dimer
7.6 Charge densities for dimer ends
7.7 The energy surface for diffusion of an SiH₂ group
7.8 A schematic of monohydride dimer formation
7.9 The energy for monohydride dimer formation
7.10 Positions for the rotating, dehydrogenated dimer
7.11 The energy for a clean dimer rotating over the trench from LDA and GGA
7.12 A bond forming during rotation of an ad-dimer
7.13 Positions for the rotating, hydrogenated dimer
7.14 The energy for a hydrogenated dimer rotating over the trench from LDA
7.15 The energy for a possible mechanism for dehydrogenation of a monohydride dimer
7.16 The energy surface for dimer diffusion
7.17 The probability for a dimer to reform after a given time
7.18 The probability for a dimer to reform a certain distance away from its start point
7.19 STM image of squares
7.20 Filled and empty states STM images of a square
7.21 High and low bias STM images of a square
7.22 The square structure and appearance in STM
7.23 Formation and decomposition for the square
7.24 The energy to form a square and to form a TR from a square, from TB
7.25 The energy to form a string of three dimers from a square and a dimer
7.26 The entire pathway for Si(001) growth from adsorbed fragments to dimer strings
7.27 Convergence of APB energy with separation
7.28 A schematic diagram of all the APB structures modelled
7.29 STM images of an APB
7.30 Energy for adsorbing dimers onto a string on an APB and the clean surface
7.31 The structure of an even-numbered length string and an odd-numbered length string on an APB
8.1 An STM image of germanium hut clusters

Firstly, my supervisors Andrew Briggs and David Pettifor, who have allowed me the freedom to pursue what I found interesting, while being happy to provide advice, guidance and help wherever needed. I have greatly enjoyed my time working with them. I would also like to thank my new employer, Mike Gillan, for allowing me to work on my thesis as well as on CONQUEST, and for his insights into the subject.

It is often the case that while the supervisors provide overall guidance and ideas, post docs give a more detailed level of help. I have been extremely fortunate in working closely with two post docs in particular: Chris Goringe and Andrew Horsfield. They have both helped me enormously over the last three years, while being very patient with my incessant questions. Chris has helped me more with the systems I have modelled, while Andrew has taught me more about the methods I have used, but there has also been a great deal of overlap.

As well as theoretical work, this thesis revolves around experiments, and those experimentalists I have worked with deserve thanks for their patience and enthusiasm. First and foremost of these is James Owen, whose thesis should be consulted for details of any of the experiments mentioned herein. Our collaboration has proved fruitful, and our friendship has enriched my time in Oxford. Other people in the lab with whom I have worked closely include Ilan Goldfarb, Kazushi Miki and Holger Nörenberg.

The Materials Modelling Laboratory is a superb environment in which to work, and there are many people there who have helped me at one time or another. Neil Long performs wonders in maintaining the computers, and has been very helpful and supportive during the writing of this thesis. Other people who have helped me include Alex Bratkovsky, Mike Fearn, Hideaki Fujitani and Tony Paxton.

Many friends have contributed to keeping me and Erica sane and happy during this time, and I should like to thank Mike and Hester, Steve and Heather, John and Claire, Chris and Su; as well as these friends around the country, there have been many friends in the lab and around Oxford who have contributed to the profits of the Royal Oak with us: James, Catherine, Adam, Adrian, Chris, Paul, Rob, James and Joanna.

Finally I would like to acknowledge my family: my grandmother, for her love and friendship over many years, for teaching me the piano and sharing the Blüthner; my father, for showing me how to do physics properly, and for willing help during the writing of this thesis; and Erica, whose love and support has made all this possible.