Isotropic and Anisotropic Elasticity Studies of Mismatch Dislocations, Critical Thickness and Work Hardening in Epilayers

Abstract

The critical thickness of an epilayer on a substrate with different elastic constants is investigated by isotropic and anisotropic elasticity treatments using both superposition and Fourier transformation. A closed formula determining the critical thickness is derived from either isotropic or anisotropic elasticity study. It is easier to form a mismatch dislocation in the interface if the substrate is softer than the epilayer, and consequently the critical thickness is smaller. The dislocation-dislocation interaction yields work hardening during generating a fresh dislocation if preexisting dislocations are in the interface. The harder the epilayer is than the substrate, the more work hardening occurs. Grading composition of the epilayer changes the mismatch stress field and makes dislocation emission more difficulty. As a result, the aspect ratio of threading dislocation density to mismatch dislocation density is lower in a compositionally-graded epilayer than that in a compositionally-uniform epilayer.