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We demonstrate an x-ray rocking curve method which allows detection of an asymmetry in the dislocation densities in an heteroepitaxial (001) zinc blende semiconductor layer. These dislocations exist on two types of slip systems with their misfit dislocation line segments oriented along either a [1−10] direction (type A) or a [110] direction (type B). An imbalance in the densities of dislocations on these slip systems produces an observable azimuthal variation in the rocking curve width for symmetric x-ray reflections. An approximate quantitative model allows the estimation of the dislocation densities on the two types of slip systems.

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.

We have calculated the equilibrium strain and misfit dislocation density profiles for heteroepitaxial Si1−xGex/Si (001) with convex exponential grading of composition. A graded layer of this type exhibits two regions free from misfit dislocations, one near the interface of thickness y1 and another near the free surface of thickness h−yd, where h is the layer thickness. The intermediate region contains an exponentially tapered density of misfit dislocations. We report approximate analytical models for the strain and dislocation density profile in exponentially graded Si1−xGex/Si (001) which may be used to calculate the effective stress and rate of lattice relaxation. The results of this work are readily extended to other semiconductor material systems and may be applied to the design of exponentially graded buffer layers for metamorphic device structures including transistors and light emitting diodes.