ONE-DIMENSIONAL MODEL OF THE MOBILITY OF SMALL EPITAXIAL ISLANDS .1. PARABOLIC SUBSTRATE POTENTIAL

A one-dimensional model of small epitaxial islands assuming a parabolic representation for the substrate potential is considered. General explicit solutions for the atom displacements and the potential energies of the chains as functions of the chain lengths and the number and location of the misfit dislocations are obtained. It is shown that the equilibrium chain configurations are stable. The activated states for the translation of the dislocations across one lattice parameter of the substrate are atoms-on-peaks configurations. The activation energies for reversible movement of the chains as a whole are calculated assuming the misfit dislocation slip mechanism proposed by Frenkel and Kontorova. It is shown that an observable mobility of small epitaxial islands is expected if the natural misfit is sufficiently greater than the critical misfit, when misfit dislocations can be introduced spontaneously at the free ends of the chains. Mobility is also expected for very small clusters whose sizes are comparable with the size at which the first misfit dislocation becomes energetically favoured. If the natural misfit is slightly greater than the critical misfit an occasional mobility of separate crystallites is expected. An azimuthal misorientation enhances the cluster mobility. An increase in the misfit leads to a reduction in the activation energies for surface diffusion of sufficiently long chains. For short chains the reverse dependence is observed. The shape of the barriers for surface diffusion is not symmetric if the chains are longer than the critical length, when a spontaneous introduction of misfit dislocations at the free ends becomes possible. © 1979.