Ab initio study of temperature-dependent piezoelectric and electronic properties of thermally stable GaPO₄

Gallium-phosphate (GaPO₄) is one of the ultra-high thermally stable piezoelectric materials with a high critical temperature of 1206 K. Here, first principles calculations with quasi-harmonic approximation are performed to study thermal and other physical properties of α-GaPO₄. For the electronic structure, we focus on the electron-phonon interaction and lattice expansion effects on the temperature-dependent band gap, which plays a significant role in zero-point renormalization. Significantly, the large piezoelectric constants e₁₁ primarily comes from intrinsic sensitivity of Ga and O sites to axial strain, while P atoms contribute little, which remains true in other quartz-like type APO₄ (A = B, Al, In). Our work provides an insight into the temperature-dependent electronic and piezoelectric properties of α-GaPO₄ and motivates its applications in a high temperature environment.