We calculate the radiative, Auger, and the Shockley-Read-Hall recombination rates with Fermi-Dirac statistics and accurate band structures to explain the measured temperature dependence and doping dependence of minority carrier lifetimes in three n-and one p-type sample. We show that a trap state tracking the conduction band edge with very small activation energy can explain the lifetimes in the n-doped samples considered here. Similarly, for moderately p-doped HgCdTe alloy, a trap level at 75 meV is needed to explain the observed lifetimes. In either case, movement of Fermi level with respect to the trap level explains the temperature dependence of the lifetimes.