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Title: Theoretical studies of epitaxial graphene formation on metal surfaces
Author: Posthuma De Boer, Joel
ISNI:       0000 0004 6348 1876
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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In this thesis we develop a set of phenomenological models that we apply to the problem of epitaxial growth of graphene on metal substrates. The high temperature and typically low flux conditions under which graphene growth occurs are such that state of the art techniques such as kinetic Monte Carlo (kMC) are extremely difficult to apply to study the growth processes. Rather we utilise simpler theories based on rate equations and also develop a technique based on the phase-field method of island front tracking. The latter method may be considered to be an addition to the class of techniques known as "island dynamics" models [1]. We use rate equations to study the nucleation and growth of graphene and to explore the dehydrogenation sequence of ethylene CH2CH2 on iridium. In the former study we develop a method for parameterising the parameters appearing in rate theories and apply the method to correct a previously reported rate theory to account for the exponential dependence of island density on temperature. In the former we find that kinetic models parameterised with ab-initio calculations are able to account for much of the dehydrogenation sequence observed experimentally. Reasons for discrepancies for the species observed at 300 K are discussed. We then present a detailed explanation of the phase-field simulations of epitaxial growth in the submonolayer regime. We demonstrate how the method is able to obtain agreement with KMC simulations of reversible and irreversible aggregation by reporting on the island size distributions and the scaling of island density with D/J in both regimes. Here D is the diffusion constant of adatoms on the substrate and J is the deposition rate. Discrepancies for the scaling of island density with D/J when temperature is varied is traced back to the dependence of phase field parameters on temperature. This conclusion is strengthened by the quality of the results obtained for phase-field simulations obtained for fixed temperature and varying flux, J. We also show how a simple variation of the algorithm allows us to obtain agreement with results obtained from KMC simulations in which nucleation rules for critical nuclei are explicitly incorporated and where detachment of adatoms from island boundaries are forbidden. Finally, we describe how such a phenomenological method may be used to describe qualitatively the growth of graphene on polycrystalline copper substrates. [1] R. E. Caflisch, M. F. Gyure, B. Merriman, S. J. Osher, C. Ratsch, D. D. Vvedensky, and J. J. Zinck. Island dynamics and the level set method for epitaxial growth. Appl. Math. Lett., 12(4):13 – 22, 1999.
Supervisor: Vvedensky, Dimitri Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral