Multiscale modelling of heteroepitaxial thin films
Multiscale models are developed to investigate the evolution of heteroepitaxial thin films at high temperatures via surface diffusion. Continuum models for the kinetics and thermodynamics of these systems are derived from atomistic potentials in chapter 2. A modified Lennard-Jones potential is used to introduce a coordination dependence and model the effects of surface stress. Novel hybrid atomistic-continuum models are developed in chapter 3 to investigate the static elastic field around a surface step due to the discontinuity in surface stress. They have atomic scale resolution around the defect to capture the non-linear response in highly deformed areas. Far away from the discontinuity, classical linear elasticity is used. An analytic force dipole model and the more general finite element method are chosen to represent the continuum. The kinetics of surface evolution are then investigated using a fully atomistic off-lattice Kinetic Monte Carlo (KMC) model. This allows the atoms on the surface of an atomistic lattice statics simulation to evolve via diffusive events, and readily incorporates the non-linear effects of strain on the thermodynamics and kinetics of the system. The flattening process of a rough (sinusoidal) surface is considered in chapter 4. The results are then compared with a derivative microscopic step flow model in chapter 5, which is extended to consider asymmetric step kinetics. The parameters in the step flow model are obtained from the interatomic potentials and are used to determine estimates of the macroscopic surface mobilities. The evolution of strained surfaces is investigated in chapter 6 using the off-lattice KMC model. The surface is found to be stable below a certain strain magnitude, in contradiction of the predictions of conventional theories. A new theory based on a discontinuous (cusped) surface energy orientation function is proposed and found to explain the simulation results.