Elastic constants and critical thicknesses of ScGaN and ScAlN

Elastic constants of hexagonal ScxGa1−xN and ScxAl1−xN up to x = 0.375 were calculated using a stress-strain approach. C11, C33, C44, and C66 decreased while C12 and C13 increased slightly with increasing x. The biaxial 0001 Poisson ratios increased from 0.21 for GaN to 0.38 for Sc0.375Ga0.625 N and from 0.22 for AlN to 0.40 for Sc0.375Al0.625N, due to greater u values, in-plane bond lengths and bond ionicities. Subsequently, critical thicknesses for stress relaxation were calculated for ScxAl1−xN/AlN, ScxGa1−xN/GaN, and ScxAl1−xN/GaN heterostructures using an energy balance model. These range from 2 nm for Sc0.375Al0.625N/AlN and Sc0.375Ga0.625N/GaN to infinity for lattice-matched Sc0.18Al0.82N/GaN.