Modeling, Simulation and Analysis of Epitaxial Film Growth

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DMS Award AbstractAward #: 0103825PI: Schulze, TimothyInstitution: University of Tennessee, KnoxvilleProgram: Applied MathProgram Manager: Catherine MavriplisTitle: Modeling, Simulation and Analysis of Epitaxial Film GrowthThis proposal concerns the growth of epitaxial films. The simulation technique and coarse-grained model discussed in this proposal are based on kinetic Monte-Carlo (KMC) simulations, which are an established method of simulating crystal growth on an atom-by-atom basis. While believed to be faithful to the micro-scale physics, KMC simulations are extremely slow and there is a recognized need for models appropriate for larger length and time scales. The first of the two approaches discussed in this proposal is a new simulation technique referred to as an Atomistic Difference Scheme. In this method, one assumes that the distribution of atoms on the surface of the film is in near equilibrium and can be computed by time-stepping difference equations derived directly from the KMC transition probabilities. The topography of the crystal, on the other hand, is assumed to evolve on a slower time-scale and is computed on a discrete basis that conserves mass. The second approach seeks a homogenized, continuum version of this micro-scale model. The continuum model takes the form of partial differential equations that describe the system's evolution on macroscopic length and time scales. A final component of this investigation considers the application of these two methods to a continuous processing configuration where substrate (a tape) is continuously passed through a deposition zone. The continuously moving contact-line and its stability are of particular interest.Epitaxial films are of vital technological importance in the semi-conductor industry. As applications for high-temperature super-conductors (HTSC) develop, epitaxial films hold still further promise, with extensive efforts under way to produce HTSC wires and tapes that have enormous current-carrying capacities. At the same time, the film growth process is a burgeoning source of inspiration for applied mathematicians, requiring a wide range of mathematical techniques and simulation tools to explore the behavior of these systems over an enormous range of length scales. In particular, the research undertaken in this proposal seeks to enhance our ability understand and control the nano-scale structure of materials, placing a special emphasis on linking atomic-scale models with traditional modeling approaches.Date: June 22, 2001