Elastic stress fields caused by a dislocation in Ge x Si1−x /Si film-substrate system

The elastic stress fields caused by a dislocation in Ge_xSi_(1-x) epitaxial layer on Si substrate are investigated in this work. Based on the previous results in an anisotropic bimaterial system,the image method is further developed to determine the stress field of a dislocation in the film-substrate system under coupled condition. The film-substrate system is firstly transformed into a bimaterial system by distributing image dislocation densities on the position of the free surface. Then,the unknown image dislocation densities are solved by using boundary conditions,i.e.,traction free conditions on the free surface. Numerical simulation focuses on the Ge0.1Si0.9/Si film-substrate system. The effects of layer thickness,position of the dislocation and crystallographic orientation on the stress fields are discussed. Results reveal that both the stresses σxx,σxz at the free surface and the stress σxy,σyy,σyz on the interface are influenced by the layer thickness,but the former is stronger. In contrast to the weak dependence of stress field on the crystallographic orientation the stress field was strongly affected by dislocation position. The stress fields both in the film-substrate system and bimaterial system are plotted.