Computed epitaxial monolayer structures: II. Two-dimensional model: Equilibrium monolayer structures in the case of rectangular interfacial symmetry

Abstract

A computational procedure dealing with a one-dimensional epitaxial monolayer model was developed in part I. In this part it is extended and applied to the two-dimensional case, allowing for misfit along two perpendicular interfacial directions. The model employed differs slightly from that used by van der Merwe in that the overgrowth film is simulated by a plane of atoms linked to each other by elastic springs. This allows for an exact determination of the equilibrium boundary conditions. The results show (i) that the rectangular boundary edge is slightly deformed, lateral contractions occurring where the misfit dislocations intersect the boundary edge, (ii) that the dependence of stable structures on misfit is in good agreement with the analytical results of van der Merwe, (iii) that misfit dislocations are introduced alternately at the mutually perpendicular edges of a system having quadratic symmetry, (iv) that a segmented dependence of lowest energy on crystal size is obtained, one segment for each additional dislocation, (v) that a saw-toothed dependence of average strain on crystal size, in qualitative agreement with the experimental work of Vincent, results and (vi) that a fine structure in the energy curves results from discrete adatom peripheral growth.