Critical thickness during two-dimensional and three-dimensional epitaxial growth in semiconductor heterostructures

Abstract

Abstract The homogeneous nucleation of misfit dislocations in two-dimensional and three-dimensional epitaxial structures on rigid substrates was analyzed. It is shown that nucleation and growth of a dislocation in the epilayer involves an activation energy barrier. We propose that this activation energy barrier can be overcome from the residual coherent strain energy in the film. A critical thickness of the epilayer is defined at which a dislocation is nucleated. The activation energy and the coherent strain energy were determined for several different configurations of 60° glide and 90° climb dislocations. The discrepancies that are associated with different formulations are pointed out. Specific numerical calculations were performed for dislocation nucleation in the GaAs/Si system. The results are given in terms of the various energy contributions responsible for nucleation of misfit dislocations, and the critical thickness of the epilayer is evaluated. The critical thickness of the epilayer under the two-dimensional and three-dimensional growth conditions are compared and the results described in terms of the mechanisms of dislocation nucleation.