Exact closed-form solutions were derived for the stresses due to periodic arrays of dislocations, and arbitrarily polygonal inclusions of infinite length, in a generally anisotropic half-space. These solutions permitted analysis of the stability of a range of strained semiconductor structures. Critical thickness calculations were performed for unburied strained-layers and for buried strained-layers and quantum-wire arrays in the GeSi/Si system. For strained-layers (buried or unburied), these were in agreement with experiment. The results for quantum-wires suggested that, once buried, they might be able to support - without loss of coherency - up to seven times the lattice mismatch that could be accommodated by a strained-layer of comparable thickness. A comparison of these results with those obtained using the isotropic approximation showed that, for the GeSi system, the effect of anisotropy was to increase the predicted critical thickness by more than 30%. Dislocation formation above the critical thickness was studied for unburied strained layers. A stability criterion was presented which was based upon modelling the dislocation distribution as being periodic and by considering the driving force on a threading segment gliding through the periodic distribution. A closed-form solution for this driving force was presented which took the effects of anisotropy fully into account. The configuration was defined to be stable when there was no path of positive driving force for the threading segment through the periodic distribution. The stability criterion yielded results, for the equilibrium dislocation density, that were in reasonable agreement with experiment. This contrasted with approaches that incorporated only the mean stress which was due to the background dislocation distribution. The present approach predicted that, for a given layer thickness, the equilibrium residual strain should depend upon the initial strain due to the lattice mismatch.

The Stresses due to Arrays of Inclusions and Dislocations of Infinite Length in an Anisotropic Half Space - Application to Strained Semiconductor Structures. T.J.Gosling: Philosophical Magazine A, 1996, 73[1], 11-45