It was noted that epitaxial systems with semi-coherent hetero-interfaces sometimes contained complex bi-periodic networks of misfit dislocations. Analytical solutions for the elastic fields of threefold-symmetry structures could be derived in the form of Fourier series, in which explicit constants took account of the detailed geometry of the misfit dislocation pattern. In principle, any complex planar pattern could be so treated. The material was considered to be elastically heterogeneous, with each medium having its own isotropic elastic constants. As an application of the theory, the InAs/GaAs(111)A system was treated in detail for an InAs epitaxial layer thickness of 1.3nm. The dislocation network consisted of edge misfit dislocations which were arranged in a regular hexagonal-based pattern; with each alternating node being dissociated into a faulted triangle. Three different networks could be produced; according to the extent of dissociation. These were a honeycomb network (no dissociation) which was formed of misfit dislocations with Burgers vectors of ½<110>, a partially dissociated network with b = ½<110> and b = 1/6<112>, and a faulted triangular network with only b = 1/6<112>. For each of these networks, a computer-generated grey-scale topograph of the free surface was generated. It was shown in particular that, directly above each dissociated node, the increase in elevation was equal to 0.122nm when the network passed from the first to the second of the above configurations.

Topographic Effect of the Misfit Dislocation Dissociation in Threefold Symmetry Epitaxial Systems. R.Bonnet: Philosophical Magazine A, 1999, 79[8], 1909-22