First-principles study of spontaneous polarization and band gap bowing in Sc _xAl _yGa _{1 x y}N alloys lattice-matched to GaN

First-principles calculations are carried out to estimate the spontaneous polarization and the band gap bowing in the Sc _xAl _yGa _{1 x y}N alloys lattice-matched to GaN based on the density functional theory together with a pseudopotential plane-wave method. The results indicate nonlinear behavior of the spontaneous polarization and the band gap energies in the Sc _xAl _yGa _{1 x y}N alloys similar to that in Y _xAl _yGa _{1 x y}N (Shimada et al 2011 J. Appl. Phys. 110 074114). The band gap energies and the magnitude of the spontaneous polarization of Sc _xAl _yGa _{1 x y}N is larger than that of Y _xAl _yGa _{1 x y}N in a wide range of the mole fraction of Ga. We find that the atomic configuration of Sc affects the magnitude of the polarization in Sc _xAl _yGa _{1 x y}N. Another finding is the apparent deviation from Vegard's law of the lattice constants of the Sc _xAl _yGa _{1 x y}N alloys lattice-matched to GaN.