Modeling and simulation of faceted thin film crystal growth

The control of crystal shape is one of the keys to the fine tuning of mechanical, electrical, and optical properties of many thin film materials. Realistic three-dimensional crystal growth morphology prediction is hindered by the difficulties in obtaining the full set of strong anisotropic physical-chemical quantities and the complexities of many competing growth mechanisms. To bypass these difficulties, we focus on the intrinsic factors controlling crystal growth morphologies. First, we identify the symmetry group of crystal growth shape and the interface stiffness tensor. As a byproduct, we propose an efficient thermal fluctuation simulation method to determine the interface stiffness tensor. Then, we identify the essential differences between equilibrium and nonequilibrium crystal growth. Next, we demonstrate that, beyond a critical length scale, the kinetic growth morphology is controlled by shape-independent growth velocities. This leads to our focus on the v-plot (i.e., polar plot of velocity versus surface orientations) model. Meanwhile, based on graph theory and growth processes classification, we develop a systematic approach to determine the full set of dimensionless numbers representing the competitions between growth processes. Then, a systematic approach is proposed to determine the v-plot. Next, a level set method tailored for selective area growth (SAG) is developed. The application of the v-plot and level set simulation methods to GaN grown by SAG is able to capture all of the major features of growth morphologies observed in a diverse set of experiments. Furthermore, the simulations correctly predict the stability of fast growing surfaces against perturbations and unveil the intrinsic imperfect nature of crystal merging. Based on the simulation result, a simple residual mismatch strain model is proposed to deduce that smaller aspect ratio (window width to island height) is preferred to produce lower angle grain boundaries on merging and higher quality crystals. Finally, the effects of non-surface energies on equilibrium crystal shape are studied. The major conclusion is that although the non-surface energies modify the Wulff shape, they only distort the Wulff shape and do not create or remove orientations. This conclusion greatly reduces the efforts to solve the variational problem associated with energy minimization.