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.