# American Institute of Mathematical Sciences

March  2009, 11(2): 443-457. doi: 10.3934/dcdsb.2009.11.443

## The role of processing speed in determining step patterns during directional epitaxy

 1 Department of Mathematics, University of Tennessee, Knoxville, TN, 37996, United States 2 Department of Mathematics, University of Tennessee, 121 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996, United States

Received  January 2008 Revised  August 2008 Published  December 2008

We consider the growth of an epitaxial thin film on a continuously supplied substrate using both the Burton-Cabrara-Frank (BCF) mean-field model and kinetic Monte-Carlo (KMC) simulation. Of particular interest are effects due to the finite size of the deposition zone, which is modeled by imposing an up- and downwind adatom density equal to the adatom density on an infinite terrace in equilibrium with a step. For the BCF model, we find this scenario admits a steady-state pattern with a specific number of steps separated by alternating widths. The specific spacing between the steps depends sensitively on the processing speed and on whether the number of steps is odd or even, with the range of velocities admitting an odd number of steps typically much narrower. These predictions are only partially confirmed by KMC simulations, however, with particularly poor agreement for an odd number of steps. To investigate further, we consider alternative KMC simulations with the interactions between random walkers on the terraces neglected so as to conform more closely with the mean field model. The latter simulations also more readily allow one to disable the step detachment mechanism, in which case they agree well with the predictions of the BCF model.
Citation: Michael A. Saum, Tim Schulze. The role of processing speed in determining step patterns during directional epitaxy. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 443-457. doi: 10.3934/dcdsb.2009.11.443
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