Rotation and Translation of Islands in the Growth of Heteroepitaxial Films

A simple yet realistic model is introduced for the description of islands of epitaxial overgrowth on a substrate surface. The model is employed to examine the potential energy surface for both rotation and translation of the islands as a whole. It is shown that one or more overwhelmingly easy directions of orientation exist, and that islands which manage to be rotated out of these easy directions can both rotate and translate with activation energies of the order of magnitude of the activation energy for surface diffusion of isolated atoms. The results provide semiquantitative support for Bassett's observation via the electron microscope that large islands of overgrowth (∼1000 atoms) seem to both rotate and translate. Considerations of surface nucleation indicate that although nucleation rate depends on orientation, subsequent growth of islands does not. A growth law independent of orientation is then derived. It is also shown semiquantitatively that under typical experimental conditions for slow deposition, nucleation occurs but once—islands initially formed grow, while their number remains constant. This result is also consistent with several observations. The process by means of which misoriented islands anneal by rotational diffusion into the easy orientation, while they simultaneously grow, is analyzed. A formula is developed which indicates that under certain conditions, islands of overgrowth become ``stuck'' in misoriented positions before they coalesce. The conditions effecting this phenomenon are discussed. General comments and observations are made concerning the initial origin of misoriented nuclei, and means are suggested for adjusting conditions so as to permit misorientation to anneal before coalescence. Typical densities of dislocations introduced by misorientation are estimated. Crucial experiments are suggested for examining the hypothesis of this paper.