Modeling and simulation of heteroepitaxial growth

The objective of this work is to construct a model for simulation and study of strained Heteroepitaxial growth and use the same to study the nature of the surface instability in the system. This is done with the intent of studying the intermixing and its effects, on the surface instability and the critical thickness of island formation. A solid on solid kinetic Monte Carlo approach is adopted in order to model the discrete stochastic effects. The model uses simple surface atom hops to capture surface diffusion effectively. The hopping rates are modeled based on the energetics of the system. The energetics of the system are in turn modeled by bond counting (surface energy) and a ball and spring network (elastic energy). An efficient numerical method for the elastic computations is constructed. This approach involves the local estimation of the change in elastic energies using the Expanding Box method and upon failure the global evaluation using the Multigrid Fourier method. An efficient algorithm for evolution of the system based on a reduced rejection kinetic Monte Carlo is presented. In this method the hopping rates are replaced by computationally inexpensive upper bounds with a rejection step to compensate for the overestimate. The continuum limit of this model is shown to be equivalent to a classical phenomenological continuum model. Using this relation the existence of the Asaro-Tiller-Grinfeld instability in the model is discussed. The limitations of the continuum theory and the need for the discrete stochastic approach is addressed. Finally the kinetic Monte Carlo model is used to study the role of intermixing in the surface instability. Significant intermixing of the film with the substrate due to kinetic roughening of the film and hence the dilution of the film, is observed. This dilution is found to have a stabilizing role in the surface instability, leading to a retarded onset of island formation. The dependence of critical thickness on the composition of the film and the temperature is found to be consistent with experiments. The effect of surface segregation on the critical thickness is also discussed.