Computational Methods for Problems in Material Science

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

This project concerns the development of efficient numerical methods for problems related to material science. The investigator studies computational issues concerning the numerical solution of continuum models for thin film growth. Many of these models include effects for surface diffusion, which is a nonlinear 4th order term. Consequently, these models are very stiff from a computational point of view. Because the surface diffusion term is nonlinear, it is difficult to use implicit methods. The investigator introduces a new semi-implicit level set method for solving motion by surface diffusion. He uses this new method to incorporate the effects of surface diffusion into models of polycrystalline thin films. He also develops a new approach for computing island dynamics, where the adatoms on the terraces are considered as a continuum field and the atoms on the edge of the island are treated discretely. This approach retains the potential advantage of continuum methods but at the same time preserves the discrete and stochastic effects present in island dynamics. The investigator includes effects of edge diffusion, surface tension, nucleation, and elasticity. An important computational aspect of this problem is the numerical solution of the diffusion equation in a complex domain. The investigator examines new methods for the efficient solution of this problem. Thin films occur in a large number of applications, from coatings on bearings to semi-conductor devices. In many cases these films are not single crystals but instead are polycrystalline and the quality of the film can depend on its texture. Films with good biaxial texture are close to being a single crystal and have applications in the manufacture of super-conducting tapes, for example. One important physical effect in determining the evolution of the texture is surface diffusion, but this is difficult to implement numerically and the investigator plans to develop a semi-implicit level set method to study the growth of polycrystalline thin films. The work here could help improve the fundamental understanding of these films. Another important process by which thin films are made is molecular beam epitaxy. The standard method for accurate simulation of this process is kinetic Monte Carlo. In many situations this method can be slow, and continuum models have the potential to greatly increase the speed of such computations. However, continuum models ignore discrete and stochastic effects. The investigator develops hybrid models that have good physical fidelity but offer considerable computational speed.