Heteroepitaxy on compliant substrates: relaxation of misfit stress at low critical film thickness

In spite of outstanding experimental success in reducing the density of threading dislocations (TDs) within thin films grown heteroepitaxially on using a compliant substrate instead of a conventional bulk substrate, theories of strain relief on compliant substrates are often based on inadequate theorems like the elastic strain-partitioning and the free-slipping hypothesis. Instead, the present paper modifies the well accepted dislocation model of Matthews by supposing that the misfit dislocations (MDs) relax or dissipate owing to the presence of a weak layer in compliant substrates. This relaxation reduces the drag force on the TDs and therefore the critical film thickness as estimated in a quantitative way. The consequences include less interaction and multiplication of the dislocations, reduced TD density, more homogeneous film structure, and lower final equilibrium strain.