Dislocations and strain relief in reverse-graded semiconductor layers

We have calculated the equilibrium misfit dislocation density and strain profiles in reverse-graded heteroepitaxial layers, using Si1−xGex/Si (0 0 1) as a model material system. In these structures there is a finite lattice mismatch at the substrate interface and the composition is graded linearly in such a way that the lattice mismatch decreases with distance from this interface. Reverse-graded layers exhibit two distinct behaviors which may be referred to as unkinked and kinked. In the unkinked reverse-graded layer the misfit dislocations are confined to a thin region near the substrate interface, the residual strain is a linear function of distance from the interface and the strain exhibits a sign reversal within the layer. Kinked reverse-graded layers exhibit a kink in the strain versus distance characteristic, and this kinked region contains a nearly constant density of misfit dislocations. We have developed models for the behavior of both types of reverse-graded layers, and we show that these models provide accurate predictions for Si1−xGex/Si (0 0 1) reverse-graded layers