Analysis of epitaxial morphology evolution due to stress and diffusion

Abstract

In this paper, a new phase-field model based on diffusion interface is put forward to describe the epitaxial growth including island nucleation, growth, and ripening. Thermodynamics and kinetics play an important role in epitaxial morphology evolution. This model includes combined effects of the following processes, such as elastic field, surface energy, deposition, diffusion, desorption, and energy barrier etc. We use the classical BCF model to describe the atomic diffusion and nucleation processes, and use a new free energy function, including elastic strain energy, to obtain a phase-field equation that can describe the growth of dynamic multi-island by variation method. This model can effectively simulates the complex morphology in epitaxial growth. The nonlinear coupled equations can be solved by finite difference scheme. Numerical result shows that this model can reproduce the real multilayer epitaxial growth structure, and the simulation results are consistent with the experimental results. At the same time we also simulate the complex growth stress with morphology evolution. Results show that, accompanied with the epitaxial growth, a complex stress distribution is produced, and the stress reaches a local maximum on the boundaries of the island, which is consistent with the experimental results. Most importantly, the stress significantly affects the atomic diffusion process. While the stress exists, the epitaxial structure will change faster. These results can make a significance effect on the research of physical mechanism in epitaxial growth.