Spontaneous polarization and band gap bowing in Y_xAl _yGa_1-x-yN alloys lattice-matched to GaN

First-principles calculations are carried out to estimate the spontaneous polarization and the energy band gap bowing in Y_xAl _yGa_1-x-yN alloys lattice-matched to GaN. The ground state properties of alloys are computed by using the pseudopotential-planewave method in conjunction with generalized gradient approximation to density functional theory. We find nonlinear behavior of the spontaneous polarization and the band gap energies in Y _xAl_yGa_1-x-yN alloys and the values depend on the atomic geometry in the unit cell, especially on that of yttrium.