Geometrical theory of critical thickness and relaxation in strained-layer growth

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Abstract
In the growth of pseudomorphic strained layers, the critical thickness is the thickness up to which relaxation does not occur and beyond which relaxation occurs by plastic deformation of the layer. Previous theories have concentrated on the strain energy and kinetics of dislocation formation. We present a purely geometrical argument which predicts critical thicknesses and also predicts how relaxation progresses with increasing thickness. We find that the critical thickness, in monolayers, is approximately the reciprocal of the strain. Some relaxation occurs abruptly at critical thickness, and further relaxation is hyperbolic with thickness. The model can also handle multilayer structures. If all the layers have the same sign of strain, the model predicts that relaxation will occur at the lowest interface. These results are found to be in good agreement with experimental observations of dislocations in epitaxial structures of InGaAs grown on GaAs.