ELASTIC AND PLASTIC RELAXATION IN SLIGHTLY UNDULATED MISFITTING EPITAXIAL LAYERS - A QUANTITATIVE APPROACH BY 3-DIMENSIONAL FINITE-ELEMENT CALCULATIONS

We quantitatively calculate with three-dimensional finite elements the elastic relaxation by surface undulations (consisting of a two-dimens ional periodic array of troughs and ridges) of growing heteroepitaxial layers on a low misfitting substrate. Our calculations can generally be applied and are use Si0.97Ge0.03 on Si as an example. The geometric al shapes of the undulations that are introduced into the three-dimens ional finite element models are obtained from transmission electron mi croscopy and atomic force microscopy. Our calculations show that ridge s are correlated with a relaxation of the lattice towards the bulk lat tice constant (of SiGe), whereas the troughs represent regions of incr eased strain. The lattice distortion in the SiGe layer is transformed into distortions with opposite sign in the substrate below the interfa ce (i.e. for SiGe/Si: tensile strains at the ridges in the layer are t ransformed into compressional strain in the substrate below the ridges ). The calculations show that it is the free relaxation of the ridges, which makes the elastic relaxation, whereas the substrate does not co ntribute to elastic strain relaxation. The plastic relaxation starts i n the troughs by dislocation nucleation and glide, due to the enhanced shear stresses there. We discuss the pertaining mechanisms with due c onsideration of the actual layer geometry and strain distribution. Esp ecially, we quantify shear stresses in the substrate, that drive misfi t dislocations from the (chemical) interface into the substrate as fre quently observed.