Logarithmic approximation for the energy band in nonparabolic semiconductors

We propose a semi-empirical logarithmic approximation to the conduction band of small gap semiconductors. This approximation enables us to obtain analytical expressions for the intrinsic absorption coefficient and free electron density, and these expressions are valid for a large temperature range. We show that the exponential variation of the absorption coefficient, as observed by Chu et al. [J. H. Chu et al., J. Appl. Phys. 71, 3955 (1991)] in Hg_1-xCd_xTe, can be fitted very well for any temperature using only a few parameters whereas the analytical expression for free electron density is useful in optical and transport simulations.