Impact of applied biaxial stress on the piezoelectric, elastic, and dielectric properties of scandium aluminum nitride alloys determined by density functional perturbation theory

The effects of biaxial in-plane stress on the elastic, dielectric, and piezoelectric (PE) properties of c-axis textured thin film wurtzite phase scandium aluminum nitride (w-ScxAl1−xN) alloys have been calculated with density functional perturbation theory. The in-plane stress σR was kept below 1 GPa covering compressive and tensile values and applied to alloy supercells represented with special quasi-random structures. An increasingly tensile biaxial stress (σR > 0) produces higher displacement-response internal-strain coefficients for the constituent atoms of the alloy and the related PE properties are more sensitive to σR when the fraction x increases. A significant rise of the relative dielectric permittivity ϵr,33η and softening of the stiffness coefficient c33E are also reported with σR > 0. The effective thin film PE strain coefficient d33,f and coupling coefficient k33,f2 show a relative increase of 22% and 26%, respectively, at σR = 1 GPa and x = 0.438. Both tensile σR and x tend to decrease the c/a cell parameter ratio of the wurtzite structure with a significant impact on the PE coefficients. Based on the decomposition of the stiffness, dielectric, and PE coefficients as well as the structural data, it is suggested that tensile biaxial stress enhances the hexagonal character of w-ScxAl1−xN in a qualitatively similar manner as the scandium nitride fraction x does. The manufacture and PE characterization of a beneficially stressed thin film of w-ScxAl1−xN on a substrate of w-InyAl1−yN with adjusted x, y values are suggested to confirm the calculated values of d33,f.