Piezoelectric Coefficients of Complex Semiconductor Alloys from First-Principles: The Case ofGa1−xInxN

A first-principles-derived scheme is developed to compute the piezoelectric coefficients $e_{ij}$ of semiconductor alloys. This method is applied to study the effect of atomic arrangement and composition on $e_{33}$ in wurtzite ${\text{Ga}}_{1-x}{\text{In}}_x\text{N}$. Results obtained by this method for ordered structures are in good agreement with direct first-principles calculations. We predict that atomic ordering can have a large effect on piezoelectricity and that $e_{33}$ of disordered materials is nearly linear with composition. Microscopic origins for these features are revealed.