By using two different isotropic elasticities for an epilayer and a semi-infinite substrate, plus appropriate boundary conditions at the hetero-interface, it was shown how to derive closed-form analytical expressions for the complete three-dimensional elastic field of an hexagonal network of misfit dislocations (possibly non-regular) as a function of the thickness of the epilayer. The boundary conditions were expressed as a set of 9 linear equations in 9 unknowns. In order to obtain some idea of the effects of inhomogeneities, in elastic constants or thickness, upon the elastic field of the bi-material, normal stresses and elastic dilatations were investigated numerically for three hetero-twin systems which were based upon (111)CoSi2/(111)Si. These systems differed in their elastic constants or thickness. Full bi-material solutions were compared with the results which were obtained when the elastic constants were taken to be those of Si throughout. In addition, two-dimensional cross-sections through the surface profiles of these hetero-systems were calculated for thicknesses varying from 2 to 12nm. It was shown that, for small thicknesses, the free surfaces exhibited pronounced bumps which were directly above dislocation lines and triple nodes.

Free Surface Relaxation of an Hexagonal Network of Misfit Dislocations. R.Bonnet: Philosophical Magazine A, 1996, 73[4], 1193-209