Modeling the Elastic Fields in Epitaxially Grown Multilayers

Abstract

AbstractA model was developed to calculate the elastic fields, including strain energy density, in multilayers grown epitaxially on a planar substrate. This model works well for compliant and non-compliant substrates. In particular we illustrate the model for four layer heterostructure and apply it for graded Ge (SixGe1−x) grown on a planar silicon substrate. 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 were calculated. The strain partitioning in this model reduces to the limiting case of a two- layer structure available in the literature. As it turns out here, strain partitioning is a function of the bulk unstrained lattice parameters, elastic constants and thicknesses of the layers. The model was qualitatively verified by comparing the strain energy density with the dislocation density away from a relatively thick substrate. This model helps shed some light on the factors important in achieving defect free multilayers for optoelectronic devices.