Modeling and experiments on epitaxially grown multilayers with implications to critical thickness

Abstract

In this study, using the equations for static equilibrium and Hooke’s law for isotropic materials under a plane stress condition, the elastic fields associated with each layer have been calculated. A model has been developed to calculate the elastic fields in multilayers grown epitaxially on a planar substrate. The strain partitioning in this model reduces to the limiting case of a two-layer structure that is available in the literature. We have chosen a particular system (SiGe) and calculated strain energy density for any number (N) of layers of graded Ge (SixGe1−x) on silicon. The model was compared with experiment for graded SiGe grown over a planar silicon substrate. The results revealed qualitative agreement between the calculated strain energy density and the experimentally observed dislocation density in the layers. The effect of the choice of a strain partitioning model on the calculation of a film/epilayer critical thickness is demonstrated.