The rate of radiative recombination in the nitride semiconductors and alloys

The radiative recombination rates of free carriers and lifetimes of free excitons have been calculated in the wide band gap semiconductors GaN, InN, and AlN of the hexagonal wurtzite structure, and in their solid solutions ${\mathrm{Ga}}_x{\mathrm{Al}}_{\text{1−x}}\mathrm{N},$ ${\mathrm{In}}_x{\mathrm{Al}}_{\text{1−x}}\mathrm{N}$ and ${\mathrm{Ga}}_x{\mathrm{In}}_{\text{1−x}}\mathrm{N}$ on the base of existing data on the energy band structure and optical absorption in these materials. We determined the interband matrix elements for the direct optical transitions between the conduction and valence bands, using the experimental photon energy dependence of absorption coefficient near the band edge. In our calculations we assumed that the material parameters of the solid solutions (the interband matrix element, carrier effective masses, and so on) could be obtained by a linear interpolation between their values in the alloy components. The temperature dependence of the energy gap was taken in the form proposed by Varshni [Physica 34, 149 (1967)]. The calculations of the radiative recombination rates were performed in a wide range of temperature and alloy compositions.