Strain, dislocations, and critical dimensions of laterally small lattice-mismatched semiconductor layers

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Abstract
A rectangular strained epilayer with its length much larger than its height h and width 2l is considered. The energy change on introducing a 60° dislocation either parallel to the long dimension (longitudinal) or parallel to the short dimension (transverse) into the epilayer is calculated. The effects of free surfaces on the mismatch stress and on the dislocation energy are taken into account approximately. For a given misfit, there is a critical height and critical width such that if the dimensions of the layer exceed their critical values, introduction of a longitudinal misfit dislocation is energetically favored. However we show that a transverse dislocation always sets in before a longitudinal one and as a result, the critical thickness is almost equal to that for a film of infinite extent even when the width is very small. The results are found to be different from an earlier calculation [S. Luryi and E. Suhir, Appl. Phys. Lett. 49, 140 (1986)] and show that the relaxation caused by the free surfaces cannot explain the lower densities of dislocations observed experimentally in such structures.