Defect interactions on solid surfaces

Abstract

A unified approach to the calculation of the elastic interaction between defects on a surface that describe, for example, steps, islands, and stress domains is presented. This is accomplished by determining the spatial dependence of the elastic displacement fields generated by the idealized point and line forces representing these defects and applying a power counting argument. This argument is then extended to determine the dependence of the interaction energy of two such elastic defects on their separation. In order to apply this analysis to a spatially extended surface defect we develop a multipole expansion of the displacement field that can be used to easily classify the force distribution of this defect in terms of its moments and, hence, determine the dependence of defect-defect interaction energies on separation. As a specific example, we calculate the elastic interaction between two separated circular islands on the surface of an elastic half-space and interpret the results in terms of power counting arguments.