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We show that for a mismatched heteroepitaxial layer with linear compositional grading, the first misfit dislocations will be introduced at a finite distance yC from the substrate interface. This is of practical as well as fundamental importance; it alters the value of the critical layer thickness for lattice relaxation and it moves the misfit dislocations away from the interface, where contaminants and defects may cause dislocation pinning or mobility reduction. We have calculated the position of the initial misfit dislocations yC for linearly graded Si1-xGex/Si(001) heteroepitaxial layers with lattice mismatch given by f=Cfy, where Cf is the grading coefficient and y is the distance from the interface. The distance of the first misfit dislocations from the interface yC decreases with increasing grading coefficient but can exceed 40 nm in layers with shallow grading (|Cf|<12 cm-1). For the range of grading coefficients investigated, yC varies from 6% to 11% of the critical layer thickness. Based on the model presented here it is possible to choose the grading coefficient to achieve the desired separation of the misfit dislocations from the substrate interface. [ABSTRACT FROM AUTHOR]

The equilibrium strain and misfit dislocation density profiles for heteroepitaxial [Si.sub.1-x][Ge.sub.x]/Si(001) with convex exponential grading of composition. Appropriate analytical models are described for the strain and dislocation density profile in exponentially graded [Si.sub.1-x][Ge.sub.x]/Si(001) that is used for calculating the effective stress and rate of lattice relaxation.

A computational approach is described for determining the equilibrium misfit dislocation density and strain in a semiconductor heterostructure with an arbitrary compositional profile. The density of misfit dislocations in the graded layer is inversely proportional to its grading coefficient and is unchanged in the presence of the uniform layer and the biaxial strain in the uniform layer is inversely proportional to its thickness and is unchanged by the graded layer.