A model was derived for strain relaxation in linear compositionally-graded epitaxial layers. The equilibrium dynamics of misfit dislocation generation were applied to each compositional segment of the graded layers throughout the film thickness. A local relaxation thickness for compositionally graded layers was calculated as a function of the film thickness. The calculated critical thickness agreed well with the depth of the dislocation-free region which was observed at the top of graded layers, for various grading rates. By analyzing the model, the origin of dislocation structures and minimal threading dislocation densities in compositionally graded layers was explained. The compositional grading produced a large equilibrium dislocation spacing, as compared with that of highly mismatched conventional stepwise growth. This permitted misfit dislocations to glide freely, without dislocation-dislocation interaction. At successive local relaxation thicknesses, lateral dislocations piled up horizontally via continuous dislocation generation and expansion.

Strain Relaxation in Compositionally Graded Epitaxial Layers. S.D.Kim, S.M.Lord, J.S.Harris: Journal of Vacuum Science and Technology B, 1996, 14[2], 642-6