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Monte Carlo Simulation of Epitaxial Growth

J.L. Blue, ACMD

We are modeling crystal growth by two commonly used methods, Molecular Beam Epitaxial Growth and Chemical Vapor Deposition. In both methods, atoms impinge on a crystalline substrate, are adsorbed, and are then can move around on the surface.

We are doing a Monte Carlo method to do the simulation. The key to rapid simulation is a search method we have developed to pick the right random item from a non-ordered list. A straight-forward method is , where N is the total number of items in the list. The formerly standard method was ; our method is . Last year Blue, Beichl, and Sullivan produced a method which is . This year I developed a method which is for most problems of interest. (If there are only L different probabilities or rates in the N items, the time is .)

Our first efforts use a simple model of the physics involved; this year I expect to simulate a real growth process, the deposition of chromium on an iron substrate, in collaboration with the Physics Laboratory.