Continuum Theory of Epitaxial Crystal Growth. I

Abstract

We present various continuum limits to describe epitaxial thin film growth. We consider a hierarchy of models which can take into account the diffusion of terrace adatoms, attachment and detachment of edge adatoms, vapor phase diffusion and the effect of multiple species. The starting point is the Burton–Cabrera–Frank type step flow model. We have obtained partial differential equations in the form of a coupled system of diffusion equation for the adatom density and a Hamilton–Jacobi equation for the film height function. This is supplemented with appropriate boundary conditions at the continuum level to describe the growth at the peaks and valleys on the film. The results here can be used in a macroscopic description of thin film growth.