Strain partitioning in coherent compliant heterostructures

Abstract

A self-consistent set of equations describing strain partitioning in planar bilayers is developed using a typical definition of strain, the assumption of a coherent interface and a mechanical equilibrium criterion. This approach eliminates the need for the concepts of lattice mismatch and compatibility of deformation, leading to a general solution for the strains and in-plane lattice parameter in bilayer structures. Using the strain equations, the strain energies in the system are calculated as a function of the epilayer to substrate thickness ratio. It was found that for a given substrate thickness, the epilayer strain energy contains a maximum at a layer thickness ratio of ∼1. The peak epilayer strain energy is only ∼25% of the maximum possible in the system. A criterion based on energy considerations is proposed for determining whether to use the epilayer or substrate dislocation formation energy when calculating the epilayer critical thickness. This criterion is applied to the GexSi1−x/Si(100) material system and is manifested by a kink in the critical thickness versus substrate thickness curves. The kink is interpreted as a boundary identifying whether a threading dislocation will most favorably be injected into the substrate or epilayer when the critical thickness is exceeded.