An equilibrium theory approach was presented, for the study of strain relaxation in hetero-epitaxial semiconductor structures, which took account of surface relaxation effects and elastic interactions between straight misfit dislocations. The free-surface boundary conditions were satisfied by placing an image dislocation outside of the crystal so that its stress field cancelled that of the real interface misfit dislocation at the surface. The effect of the Airy stress function which removed the fictitious shear and normal stresses at the surface was considered. This image method constituted an equilibrium theory which correctly predicted the experimentally observed values of critical strained layer thickness, and completely described elastic and plastic strain relief and work hardening in lattice-mismatched SiGe epilayers. It was shown that the elastic coherency stress of the strained material was affected by a large surface relaxation stress. This was essential for the experimental determination of the Ge content, of extremely thin films, as a function of the tetragonal distortion of the cubic lattice cells. The equilibrium theory was also used to define the degree of strain relaxation, and to predict the residual strain following the thermal relaxation of metastable SiGe/Si heterostructures.

A.Fischer, H.Kühne, M.Eichler, F.Holländer, H.Richter: Physical Review B, 1996, 54[12], 8761-8