Initial misfit dislocations in a graded heteroepitaxial layer

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