Theory for rotation and translation of islands on a substrate

Abstract

A theory is developed for rotation and translation of islands deposited on a substrate by assuming the harmonic potentials for both an island and the substrate themselves and a Gaussian type potential between them. The probability density that the island takes a set of values for the rotational and translational coordinates on the substrate surface is obtained by calculating the partition function in which integration is performed over all the other variables. The integration over the vibrational coordinates results in a set of effective parameters for the interaction potential, which differ from the original ones by few percent in typical cases. The integration over the rotational and translational coordinates other than those on the surface results in a pre-exponential factor, which affects the relative probability within one order of magnitude in typical cases.