Electronic Structure and Spontaneous Polarization in Sc_xAl_yGa_1-x-yN Alloys Lattice-Matched to GaN: A First-Principles Study

We performed first-principles calculations of the spontaneous polarization and electronic band structures in Sc_xAl_yGa_1-x-yN alloys assuming their growth on freestanding GaN. We found an apparent deviation from the Vegard's law of the lattice constants of the Sc_xAl_yGa_1-x-yN alloys lattice-matched to GaN. It was supposed that this deviation comes from the different bonding properties of IIIB and IIIA nitrides, resulting in different crystal structures, such as hexagonal and wurtzite structures. As was reported in our previous report on Y_xAl_yGa_1-x-yN [K. Shimada et al.: J. Appl. Phys. 110 (2011) 074114], we also found that in Sc_xAl_yGa_1-x-yN alloys, the superlattice-like structure of Sc atoms reduced the magnitude of spontaneous polarization [K. Shimada et al.: Semicond. Sci. Technol. 27 (2012) 105014]. The magnitude of the spontaneous polarization of Sc_xAl_yGa_1-x-yN is larger than that of Y_xAl_yGa_1-x-yN in a wide mole fraction range of Ga. We found the nonlinearity and dependence of the atomic arrangement of Sc in the alloys. The band-gap energies at Γ have the same characteristics as the spontaneous polarization. The band-gap energies of Sc_xAl_yGa_1-x-yN are also larger than those of Y_xAl_yGa_1-x-yN in the wide mole fraction range of Ga. The band structures of Sc_xAl_yGa_1-x-yN have a direct gap at Γ and form a flat band around the valence band top originating from the hybridization of the Sc 3d and N 2p electrons.