Vegard's law deviation in band gaps and bowing parameters of the wurtzite III-nitride ternary alloys

Abstract

The wurtzite Al_xGa_1-xN, In_xGa_1-xN, and Al_xIn_1-xN alloys are studied by numerical simulation based on first-principles calculations. For Al_xGa_1-xN the Vegard's law deviation parameter is 0.018 ± 0.001 Å for the a lattice constant and -0.036 ± 0.005 Å for the c lattice constant. For In_xGa_1-xN that is 0.047 ± 0.011 Å for the a lattice constant and -0.117 ± 0.026 Å for the c lattice constant. For Al_xIn_1-xN that is 0.063 ± 0.014 Å for the a lattice constant and -0.160 ± 0.015 Å for the c lattice constant The results indicate that the band gap bowing parameters obtained with the equilibrium lattice constant and with the lattice constants derived from the Vegard's law are 0.341 ± 0.035 eV and 0.351 ± 0.043 eV respectively for Al_xGa_1-xN, 1.782 ± 0.076 eV and 1.916 ± 0.068 eV respectively for In_xGa_1-xN, and 3.668 ± 0.147 eV and 3.457 ± 0.152 eV respectively for Al_xIn_1-xN.