Piezoelectricity of ordered (Sc<Subscript>x</Subscript>Ga<Subscript>1-x</Subscript>N) alloys from first principles

First-principles calculations are performed to compute the e<Subscript>33</Subscript> piezoelectric coefficients of GaN, ScN and (Sc<Subscript>x</Subscript>Ga<Subscript>1-x</Subscript>N) 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<Subscript>33</Subscript> in the Sc-deficient ideally ordered (Sc<Subscript>0.25</Subscript>Ga<Subscript>0.75</Subscript>N) is found to be larger than the magnitude of the corresponding e<Subscript>33</Subscript> 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<Subscript>33</Subscript> coefficients of the Sc-rich ordered (Sc<Subscript>0.75</Subscript>Ga<Subscript>0.25</Subscript>N) is found to be negligibly small. In addition, e<Subscript>33</Subscript> piezoelectric coefficients in ordered (Sc<Subscript>0.5</Subscript>Ga<Subscript>0.5</Subscript>N) 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006