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We present a computational approach for the determination of the equilibrium misfit dislocation density and strain in a semiconductor heterostructure with an arbitrary compositional profile. We demonstrate that there is good agreement between our computed results and known analytical solutions for heterostructures containing a single linearly graded layer or a single uniform composition layer. We have calculated the dislocation density and strain profiles in Si1−xGex/Si(001), InxGa1−xAs/GaAs(001), and ZnSySe1−y/GaAs(001) heterostructures, each containing a uniform composition layer (uniform layer) on a linearly graded buffer layer (graded layer). The density of misfit dislocations in the graded layer is inversely proportional to its grading coefficient and is unchanged by the presence of the uniform layer, but the dislocated thickness increases with the uniform layer thickness. If the uniform layer is sufficiently thick, misfit dislocations will exist throughout the graded layer, but additional misfit dislocations are not produced in the uniform layer. The biaxial strain in the uniform layer is inversely proportional to its thickness and is unchanged by the graded layer. We have also calculated the equilibrium configuration in a convex, exponentially graded Si1−xGex/Si(001) layer, for which the misfit dislocation density is tapered with distance from the interface. Other nonlinear grading profiles offer opportunities to tailor the misfit dislocation density and strain profile.

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