The Stability of a Dislocation Threading a Strained Layer on a Substrate

The continuum theory of elastic dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. The formation of strained epitaxial layers is of interest due to their special electronic or optical properties, and critical thickness is understood to be the smallest thickness at which interface dislocations con form “spontaneously.” The criterion invoked here is based on the work done by the layer stress in driving a threading dislocation to lay down a misfit dislocation along the layer-substrate interface, and it is applied in a way that leads to a result that is independent of the deflected shape of the threading dislocation. The general form of the dependence of critical layer thickness on mismatch strain is similar to that based on equilibrium dislocation analysis.