Predicted elastic constants and critical layer thicknesses for cubic phase AlN, GaN, and InN on β-SiC

Elastic constants for zinc-blende AlN, GaN, and InN have been estimated from the elastic constants of the wurtzite phase. This has been accomplished by recognizing that the crystal structures of the wurtzite and zinc-blende phases are related by a simple rotation. This rotation was then applied to the elastic constants and a least-squares fit is used to match the results. Using the zinc-blende elastic constants the critical thickness of the nitrides on β-SiC substrates was calculated. The critical thickness of a single overlayer of AlN was calculated to be 14.1 nm, and for GaN the critical thickness was found to be 0.7 nm. In the elastic continuum model used there was no solution for the critical thickness of InN.