A rectangular strained epilayer, with a length much greater than its height or width, was considered. The energy change which occurred upon introducing a 60º dislocation either parallel to the long dimension (longitudinal) or parallel to the short dimension (transverse) was calculated. The effects of free surfaces upon the mismatch stress and upon the dislocation energy were taken into account approximately. For a given misfit, there was a critical height and critical width such that - if the dimensions of the layer exceeded the critical values - the introduction of a longitudinal misfit dislocation was energetically favored. However, a transverse dislocation always appeared before a longitudinal one and, as a result, the critical thickness was almost equal to that for a film of infinite extent; even when the width was very small. The results were found to be different to those of earlier calculations, and showed that the relaxation which was caused by the free surfaces could not explain the lower densities of dislocations which were observed experimentally in such structures.

Strain, Dislocations, and Critical Dimensions of Laterally Small Lattice-Mismatched Semiconductor Layers. A.Atkinson, S.C.Jain, A.H.Harker: Journal of Applied Physics, 1995, 77[5], 1907-13