Epitaxial growth is a physical process where atoms are slowly deposited onto a substrate so that a crystal is grown, loosely speaking, one atomistic layer at a time. This is a fundamental scientific problem in which both nanoscale and macroscale effects are important. The resulting film morphology is determined by a complex interaction between thermodynamic and kinetic effects. In addition, epitaxial growth techniques have been used to create novel materials which contain quantum dots (nanometer sized collections of atoms embedded in a matrix of different species of atoms). The resulting material has unique electronic properties. For example, solid-state lasers have been made out of such materials. In addition, there is hope that such materials may be useful in quantum computing applications. Modeling the growth of such a material is still in its infancy.
The purpose of this proposal is to develop efficient algorithms for the simulation of epitaxial growth using a computer. The proposal will focus on atomistic models rather than continuous ones since they naturally include nanoscale physical effects such as nucleation and fluctuations. In particular, kinetic Monte Carlo models will be used, in which simple rules for atom motion are evolved in stochastic fashion. The proposal aims at devising efficient computational methods to simulate such models. Our computational strategy is based on coarse-graining both in time and space, taking special care to preserve physical fidelity. Preliminary results indicate that our algorithms are 5 to 10 times faster than the current state-of-the-art. It is felt that the numerical methods proposed here will allow model development to proceed at a much faster pace, thereby facilitating the design of new materials. The proposer plans to work closely with two experimental research groups in the Material Science and Engineering Departments at the University of Michigan.
