Piezoelectric tensor of AlN calculated by the Berry phase approach implemented in Quantum ESPRESSO
The proper piezoelectric tensor of AlN was determined using the changes of the Berry phases in response to axial and shear strains in the linear regime. Phases arose from the variation of the wavevector of the Bloch states. Calculations were done in the Quantum ESPRESSO software package using Vanderbilt's formulation of the proper piezoelectric tensor. The maximum longitudinal piezoelectric modulus |eij|max coefficient of 1.461 C/m2 was found when both the change in the Berry phase and strain were along the c-axis.