Pressure dependence of energy band gaps for Al_xGa_{1 - x}N, In_xGa_{1 - x}N and In_xAl_{1 - x}N

Using a first-principles method, we study the effect of pressure on the band gap energy of wurtzite Al_xGa_{1 - x}N, In_xGa_{1 - x}N, and In_xAl_{1 - x}N. Starting with the binaries, GaN, InN and AlN, the direct band gap is found to increase linearly with pressure but becomes indirect for AlN at 13.88 GPa. The direct band gap pressure coefficients are 31.8 meV GPa^-1 for GaN, 18.8 meV GPa^-1 for InN and 40.5 meV GPa^-1 for AlN, which are in good agreement with other calculations. For the ternary alloys, the fundamental band gaps energy are direct and increase rapidly with pressure. The pressure coefficients vary in the range of 31.9-34.5 meV GPa^-1 for Al_xGa_{1 - x}N, 19.8-24.8 meV GPa^-1 for In_xGa_{1 - x}N and 16.7-20.7 meV GPa^-1 for In_xAl_{1 - x}N; they depend on alloy composition with a strong deviation from linearity. The band gap bowing of InGaN increases linearly with pressure, but those of AlGaN and InAlN strongly decrease when the AlN band gap becomes indirect.