Effect of Band Nonparabolicity on the Inter Band Tunneling in Semiconductors

A simple yet generalized theory is developed to study inter band tunneling property of narrow band gap III–V compound semiconductors. The band structures of these low band gap semiconductors with sufficiently separated split-off valance band are usually described by the three energy band model of Kane, so this has been adopted here for the analysis of interband tunneling property in the case of InAs, InSb, and In_1-xGa_xAs_yP_1-y lattice matched to InP as representative direct band gap semiconductors having varied split-off valence band compared to their bulk state band gap energy. It has been found that the magnitude of tunneling rate from heavy hole decreases with increasing band nonparabolicity and the impact is more significant at high electric field in the three-band model of Kane than those with simple parabolic energy band approximations reflecting the direct influence of energy band parameters on inter band tunneling transitions. With proper consideration of band nonparabolicity, the results of the analysis of tunneling rate of these narrow gap materials show significant deviations from the results when simple parabolic band approximation is considered. The exact physical basis of the sources of deviation in the nonparabolic case from the corresponding parabolic band approximations is discussed in association to band coupling effect, transverse energy dependence, and the interplay between them. Moreover, under certain limiting conditions, our results reduce to the well-known results of parabolic band approximation and thus providing an indirect test to the accuracy of our generalized formulations.