Band structure of ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ alloys and effects of pressure

${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ is a semiconductor alloy system with the remarkable property that the inclusion of only 2% nitrogen reduces the band gap by more than 30%. In order to help understand the physical origin of this extreme deviation from the typically observed nearly linear dependence of alloy properties on concentration, we have investigated the pressure dependence of the excited state energies using both experimental and theoretical methods. We report measurements of the low-temperature photoluminescence of the material for pressures between ambient and 110 kbar. We also describe a density-functional-theory-based approach to calculating the pressure dependence of low lying excitation energies for low-concentration alloys. The theoretically predicted pressure dependence of the band gap is in excellent agreement with the experimental data. Based on the results of our calculations, we suggest an explanation for the strongly nonlinear pressure dependence of the band gap that, surprisingly, does not involve a nitrogen impurity band.