A first-principles-derived method for computing the piezoelectric coefficients of complex semiconductor Sc1−xGaxN alloys

We use direct first-principles techniques and Keating's semiempirical valence force field (VFF) approach to develop a first-principles-derived method to calculate the piezoelectric coefficients eij of semiconductor heterostructures and alloys. This technique is applied to study the effect of the atomic arrangement and composition on e33 piezoelectric coefficients of hexagonal ordered and disordered Sc1−xGaxN alloys. Our results on ordered structures are in excellent agreement with local density approximation (LDA) first-principles calculations. Our results reveal that atomic ordering can have a large effect on piezoelectricity and that e33 of ordered and disordered Sc1−xGaxN alloys as a function of Ga concentration can be fitted into a fourth-order and a fifth-order polynomial, respectively. Results of this work are predicted to have a large impact on improving the quality of Sc1−xGaxN alloys and heterostructures grown on ScN substrates. The microscopic origins for these effects are discussed and explained in detail.