Critical thickness for GaN thin film on AlN substrate

The critical thickness is the smallest thickness of a uniformly strained thin layer on a substrate for which it becomes energetically possible for a misfit dislocation to form spontaneously at the interface between the layer and the substrate. The critical thickness can be calculated by different criterions. The most used criterions assume that both the thin layer and the substrate isotropic with the same elastic properties. Recently a new criterion was developed to describe the formation of a misfit dislocation buried at a distance h below the free surface, assuming different elastic constants of the thin film and the substrate with hexagonal symmetry. We compared the results of this criterion for an Al
_1-x
Ga
_x
N film on an AlN substrate with the result obtained by the isotropic criterions. After this, we calculated the critical thickness for the Al
_1-x
Ga
_x
N on an AlN substrate for different temperatures.