Exact closed-form solutions were derived for the stresses that were due to periodic arrays of dislocations, and polygonal inclusions of infinite length, in a generally anisotropic half-space. These solutions permitted the analysis of the stability of a range of strained semiconductor structures. Critical thickness calculations were performed for non-buried strained layers and for buried strained layers and quantum wire arrays in the GeSi/Si system. In the case of strained layers (buried or unburied), these results were in agreement with experiment. The results for quantum wires suggested that, when buried, they might be able to support - without any loss of coherency - up to 7 times the lattice mismatch that could be accommodated by a strained layer of comparable thickness. A comparison of these results with those which were obtained by 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 in the case of non-buried strained layers. A stability criterion was presented which was based upon modelling the dislocation distribution as being periodic and by considering the driving force which acted upon a threading segment that was gliding through the periodic distribution. A closed-form solution, for this driving force, was presented which took full account of the effects of anisotropy. 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. Unlike approaches which incorporated only the mean stress 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 that was due to lattice mismatch.

T.J.Gosling: Philosophical Magazine A, 1996, 73[1], 11-45