Temperature dependence of the carrier lifetime in narrow-gap Cd$_x$Hg$_{1-x}$Te solid solutions: Radiative recombination

The probability of the radiative recombination of carriers in narrow-gap semiconductors is analyzed for the example of Cd$_x$Hg$_{1-x}$Te solid solutions. Expressions are derived for the imaginary part of the dielectric permittivity in terms of the three-band Kane’s model with consideration for the nonparabolic dependence of the carrier energy on the wave vector. It is shown that taking into account this nonparabolicity of the energy spectrum of carriers modifies the dependence of the imaginary part of the dielectric permittivity on frequency. Expressions for the probability of radiative recombination, derived in terms of the simple parabolic model and Kane’s model with and without the nonparabolicity effect taken into account, are compared. It is shown that the contributions to recombination from electron transitions to heavy- and light-hole bands are close and the contribution from light holes cannot be neglected when calculating the radiative-recombination probability.