Simulation of Epitaxial Growth by Means of Density Functional Theory, Kinetic Monte Carlo, and Phase Field Methods

Numerical calculations for epitaxial growth span a wide range of scales and methods. In this chapter different methods on atomic and on microscale will be introduced. Starting from their basic concepts, some examples will be given to highlight their capabilities and limitations. In particular, density functional theory (DFT) calculations will be presented as the choice of ab initio methods for solid-state problems. To capture the kinetics, the kinetic Monte Carlo (KMC) method will be introduced and applied to problems like transition from layer-by-layer growth to island growth. A step toward a continuum description of the epitaxial growth is the use of a phase field method, which is an efficient numerical tool to solve the equations introduced by Burton, Carbrera, and Frank. Also, the rather new method of phase field crystal (PFC) will be discussed in the framework of epitaxial processes.