## Kinetic Monte Carlo for Strained Epitaxial Growth

#### Peter SmerekaUniversity of Michigan

We present weakly-off-lattice and off-lattice kinetic Monte Carlo models for strained epitaxial growth. Both formulations are based on the observation that near equilibrium, the chemical potential is the thermodynamic driving force for film evolution. For each surface atom we calculate the change in energy, DE, if that atom was to be removed from the system. Since the ensemble average of exp(DE/kT) is exp(P/kT) where P is the chemical potential, it is thermodynamically consistent to take K exp(DE/kT) as a hopping rate. A hopping event moves an atom to nearby local minimum and the system is relaxed after each hop. Kinetic Monte Carlo is used to evolve the system. For the weakly off-lattice system, the energy is taken from a bonding counting, ball and spring model whereas in the off-lattice case an intermolecular potential is used. The weakly-off-lattice case has been implemented in 2+1 dimensions whereas off-lattice case has been implemented
in 1+1 dimensions with a Lenard-Jones potential. Both approaches are able to simulate Stranski-Krastanov growth, however the off-lattice case captures the formation of edge dislocations, interstitials, and vacancies. This is joint work with Henry Boateng and Tim Schulze.

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