Simple theory of the optical absorption coefficient in nonparabolic semiconductors

A simple theory is developed of the optical absorption coefficient (OAC) in nonparabolic semiconductors on the basis of the three-band model of Kane, by considering the wave-vector (k⃗) dependence of the optical matrix element. It has been found that the OAC is proportional to [(ℏω)2−Eg2]1/2 (ℏω and Eg are the energy of the incident radiation and the bandgap, respectively) instead of [(ℏω)−Eg]1/2, the conventional form. It has been demonstrated, by taking n-InAs, n-InSb, Hg1−xCdxTe, and In1−xGaxAs1−yP1−y lattice matched to InP as examples, that the OAC increases with increasing photon energy and the value of the same coefficient in the three band model of Kane is greater than that in parabolic energy bands in all the cases. The well-known result for wide gap materials having parabolic energy bands has also been obtained from our generalized formulation under certain limiting condition.