Modeling of Crystal Growth Processes

This chapter provides an overview of the current practice of modeling melt and solution crystal growth processes. The continuum transport equations describing these systems are reviewed, numerical solution strategies are outlined, and the special modeling challenges posed by the crystal growth are discussed. At a microscopic scale of tens of nanometers or less, ab initio molecular dynamics (MD) methods are employed to study the atomic behavior of crystallization. Molecular dynamics methods based on classical potentials are able to compute for much larger ensembles and longer time scales. To simulate even larger length scales and longer time scales, the kinetic Monte Carlo (KMC) method can be applied to many systems. On a macroscopic scale of tens of microns and larger, the continuum methods can be applied to describe the physical phenomena. There are various phenomena associated with the crystal growth that can occur on a "meso-scale", comprising hundreds of nanometer to tens of microns and occurring over long time scales. In the case of bulk crystal growth, modeling directly connects the processing conditions to the outcomes. Since bulk crystals are usually incorporated into the electronic, optical, or optoelectronic devices, the outcome is measured in terms of the crystal properties relevant to these devices.