Piezoelectricity of ordered (ScxGa1-xN) alloys from first principles

First-principles calculations are performed to compute the e(33) piezoelectric coefficients of GaN, ScN and (ScxGa1-xN) alloys exhibiting an alternation of hexagonal GaN, with hexagonal ScN along the c-axis. For Sc compositions larger than 50%, each atom has nearly five nearest neighbors (i.e., the ground state exhibits a phase that is five-fold coordinated). On the other hand, Sc-deficient (Sc, Ga) N alloys adopt a ground-state that is four-fold coordinated). The magnitude of e(33) in the Sc-deficient ideally ordered (Sc0.25Ga0.75N) is found to be larger than the magnitude of the corresponding e(33) coefficients resulting from the compositional weighted average over the hexagonal (h-ScN) and the wurtzite (w-GaN) parent compounds. On the other hand, the e(33) coefficients of the Sc-rich ordered (Sc0.75Ga0.25N) is found to be negligibly small. In addition, e(33) piezoelectric coefficients in ordered (Sc0.5Ga0.5N) exhibit quite large magnitudes, due to the nonpolar to polar transition occurs at Sc composition x = 0.5, and thus can bridge the corresponding coefficients of (Ga, In) N and ferroelectric alloys. The microscopic origins for this huge enhancement in the piezoelectric behavior in Sc-low and Sc-intermediate alloys and the role of each atom are revealed and discussed.