A one-dimensional model for the mobility of small epitaxial islands II: Sinusoidal potential

Abstract

A one-dimensional model of finite epitaxial islands assuming a sinusoidal representation of the substrate potential field is considered. The equilibrium solutions, both stable and unstable, are obtained numerically. The activation energies for surface diffusion of entities composed of chains of atoms connected by springs are calculated as a function of the misfit, chain length (island size) and the energy parameters assuming that plastic deformations in solids can be explained by the dislocation slip mechanism suggested by Frenkel and Kontorova. It is found that the activation energies oscillate around a nearly constant value which is lower than that for a single atom if the natural misfit is greater than the critical misfit, above which misfit dislocations can be spontaneously introduced at the free ends. In the opposite case the activation energies increase monotically with the chain length after reaching a minimum value which is connected with the appearance of the first dislocation as a lowest energy state. It is concluded that an observable mobility is only to be expected in the first case. In the second case mobility can only be expected for very small clusters. The critical misfit is calculated as a function of the energy parameters and it is found that it deviates considerably from that estimated by Frank and van der Merwe who considered a continuum sinusoidal model only for very deep potential troughs and small elastic moduli of the overgrowth.