Theoretical Modeling of Epitaxial Graphene Growth on the Ir(111) Surface (eBook)

Supervisor’s Foreword 6
Abstract 8
Parts of this thesis have been published in the following journal articlesGrowth of epitaxial graphene: Theory and experiment, H. Tetlow, J. Posthuma de Boer, I.J. Ford, D.D. Vvedensky, J. Coraux, L. Kantorovich, Physics Reports, 542 (2014) 195–295.Ethylene decomposition on Ir(111): Initial path to graphene formation, Holly Tetlow, Joel Posthuma de Boer, Ian J. Ford, Dimitri D. Vvedensky, Davide Curcio, Luca Omiciuolo, Silvano Lizzit, Alessandro Baraldi, and Lev Kantorovich, Physical Chemistry Chemical Physics 18 (2016) 27897–27909.A free energy study of carbon clusters on Ir(111): Precursors to graphene growth, H. Tetlow, I. J. Ford, and L. Kantorovich, Journal of Chemical Physics 146 (2017) 044702.Hydrocarbon decomposition kinetics from first principles H. Tetlow, L. Kantorovich, In Progress. 9
Acknowledgements 10
Contents 12
1 Review of Epitaxial Graphene Growth 15
1.1 Epitaxial Graphene Growth 15
1.1.1 Experimental Techniques 16
1.2 The Graphene Growth Process 19
1.2.1 Producing a Carbon Source 19
1.2.2 Forming Carbon Clusters 28
1.2.3 Graphene Formation on Ir(111) 34
1.2.4 Graphene Substrate Interaction 37
1.2.5 Removing Defects 39
References 47
2 Theoretical Modelling Methods 50
2.1 Density Functional Theory 50
2.1.1 Formalism 50
2.1.2 The Exchange-Correlation Functional 52
2.1.3 Van der Waals Forces in DFT 53
2.2 Basis-Sets 55
2.2.1 K-Point Sampling 57
2.3 Pseudopotentials 58
2.4 The Nudged Elastic Band Method 59
2.4.1 Climbing Image NEB 60
2.5 Lattice Dynamics 61
2.5.1 Vibrational Free Energy 63
2.6 Core Level Binding Energies 64
2.7 Kinetics 64
2.7.1 Transition State Theory 65
2.7.2 Rate Equations 67
2.7.3 Kinetic Monte Carlo 68
2.7.4 Lattice-Based kMC 70
2.8 Molecular Dynamics 70
2.8.1 Canonical Ensemble: NVT 71
2.8.2 Langevin Thermostat 73
2.9 Ir(111) Surface Parameterisation 74
2.9.1 Bulk Lattice Constant 75
2.9.2 Ir(111) Surface 76
2.9.3 Plane Wave Cutoff Energy 77
References 78
3 Producing a Source of Carbon: Hydrocarbon Decomposition 80
3.1 Theoretical Method Outline 80
3.2 Decomposition Reaction Scheme 81
3.3 Hydrocarbon Species 82
3.4 Hydrogen 83
3.5 Photoemission Experiments 85
3.5.1 Binding Energy Calculations 86
3.5.2 Interpretation of XPS Data 87
3.6 Reaction Energy Barriers 89
3.7 Rate Equations 92
3.8 Conclusions 97
References 98
4 Hydrocarbon Decomposition: Kinetic Monte Carlo Algorithm 99
4.1 Method 99
4.2 Surface Lattice Grid 101
4.3 Hydrocarbon Species 102
4.4 Reactions 104
4.4.1 Hydrogenation and Dehydrogenation Reactions 105
4.4.2 H2 Desorption Reaction 106
4.4.3 C-C Breaking and C-C Recombination Reactions 107
4.4.4 Isomerisation Reactions 110
4.4.5 Diffusion 111
4.4.6 Product Species Fitting 112
4.5 Time Step Calculation 113
4.6 kMC Efficiency 114
4.7 Conclusions 116
5 Thermal Decomposition in Graphene Growth: Kinetic Monte Carlo Results 117
5.1 Temperature Ramping Programmed Growth 118
5.1.1 kMC Results 118
5.1.2 Comparison with Experimental Results 120
5.1.3 Energy Barrier Tuning 122
5.1.4 Comparison with Rate Equations 125
5.2 Fixed Temperature Programmed Growth (kMC) 126
5.3 Ethylene Decomposition on Pt(111) 128
5.3.1 Energy Barriers 129
5.3.2 kMC Results 130
5.4 Chemical Vapour Deposition 131
5.4.1 Ethylene 132
5.4.2 Methane 133
5.5 Conclusions 135
References 137
6 Beginnings of Growth: Carbon Cluster Nucleation 138
6.1 Classical Nucleation Theory 138
6.1.1 Derivation of ??(N) 139
6.2 Carbon Clusters 142
6.2.1 Rotational Multiplicity 142
6.3 Zero-Temperature Formation Energy 143
6.4 Temperature Dependence of the Work of Formation 145
6.5 Vibrational Free Energy Dependence on Cluster Type 147
6.6 Cluster Isomerisation During Growth 148
6.7 Conclusions 150
References 152
7 Removing Defects: Healing Single Vacancy Defects 153
7.1 Theoretical Method Outline 153
7.2 Single Vacancy Defects 154
7.3 Langevin Thermostat 154
7.3.1 Computation of Phonon DOS 155
7.3.2 Choice of the Damping Parameter 157
7.4 Molecular Dynamics Simulations of Defect Healing 158
7.4.1 System Configuration 158
7.4.2 Initialisation 158
7.4.3 Ethylene Molecule Deposition 159
7.4.4 Ethylene Molecule Starting Position 159
7.4.5 Simulation Results 162
7.4.6 Conclusions from the MD Simulations 166
7.4.7 Final States 167
7.5 NEB Healing of the Single Vacancy Defect 168
7.6 Conclusions 169
References 170
8 Final Remarks 171
8.1 Conclusions 171
8.2 Limitations and Further Work 174
References 176
Appendix A Hydrocarbon Decomposition 177
A.1 Lowest Energy Hydrocarbon Geometries 177
A.1.1 NEB Reaction Profiles 178
A.1.2 Core Level Binding Energy Calculations 182
A.1.3 Convergence of Energy Barriers with Number of Layers 182
A.1.4 H2 Desorption 184
A.1.5 Pre-exponential Factors 184
A.1.6 Vibrational Frequency Calculations and Coverage Effects 185
A.1.7 Rate Equations 186
Appendix B Carbon Clusters and Their Formation Energy at T=0 189
Reference 192