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 Ga x Al 1Ϫx N, In x Al 1Ϫx N and Ga x In 1Ϫx 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 on͒ 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 ͑1967͔͒. The calculations of the radiative recombination rates were performed in a wide range of temperature and alloy compositions.

The radiative recombination rates have been calculated for the first time in the wide band gap wurtzite semiconductors GaN, InN and AlN and their solid solutions Ga x Al 1-x N and In x Al 1-x N on the base of existing data on the energy band structure and optical absorption in these materials. We calculated the interband matrix elements for the direct optical transitions between the conductivity band and the valence one using the experimental photon energy dependence of the 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. The calculations of the radiative recombination rates were performed in the wide range of temperature and alloy compositions.

The radiative recombination rates have been calculated for the first time in the wide band gap wurtzite semiconductors GaN, InN and AIN and their solid solutions GaxAl1−xN and InxAl1−xN on the base of existing data on the energy band structure and optical absorption in these materials. We calculated the interband matrix elements for the direct optical transitions between the conductivity band and the valence one using the experimental photon energy dependence of the 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. The calculations of the radiative recombination rates were performed in the wide range of temperature and alloy compositions.

We calculated for the first time the interband radiative recombination rate R in the wide-gap semiconductors GaN, InN and AIN crystallizing in the hexagonal wurtzite structure, and in ternary InxGayAl1−x−yN alloys including also binary solid solutions GaxAl1−xN, InxAl1−xN and GaxIn1−xN. All our calculations were based on experimental data on energy band structures and optical absorption spectra of the nitride materials. The radiative recombination coefficient B defined according to the equation R = B np, n and p being the carrier densities, is higher in InN and lower in GaN, taking intermediate values in AlN. For example, B=(2.7, 0.4 and 0.15) × 10−10cm3/s for InN, AIN and GaN, correspondingly. The carrier lifetime in GaN equals 60ns at 300K and n=1 × 1017cm−3. The radiative recombination coefficient increases with the concentration of indium nitride in the ternary alloys.