# Effective Transition Rates for Epitaxial Growth Using Fast Modulation

### Martha A. Gallivan, David G. Goodwin, Richard M. Murray

*Physical Review B*, 70(4), Art No. 045409

Thin film deposition is an industrially-important process that is highly dependent on the process conditions. Most films are grown under constant conditions, but a few studies show that modified properties may be obtained with periodic inputs. However, assessing the effects of modulation experimentally becomes impractical with increasing material complexity. Here we consider periodic conditions in which the period is short relative to the time-scales of growth. We analyze a stochastic model of thin film growth, computing effective transition rates associated with rapid periodic process parameters. Combinations of effective rates may exist which are not attainable under steady conditions, potentially enabling new film properties. An algorithm is presented to construct the periodic input for a desired set of effective transition rates. These ideas are first illustrated by two simple examples using kinetic Monte Carlo simulations and are then compared to existing deposition techniques.

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submission: http://www.cds.caltech.edu/~murray/preprints/ggm01-cds.pdf