Electronic Transport in Graded-Band-Gap Semiconductors

After briefly reviewing the theory of abrupt semiconductor heterojunctions, we consider a semiconductor whose composition gradually changes from that of a small-band-gap material at one end to that of a large-band-gap material at the other. From general theoretical aspects of the energy-level structure of nonuniform semiconductors, we clarify the sense in which the system has a graded band gap. In order to separate the effect of the graded band gap on electronic charge transport from the effect of the electric field originating from space charges, we consider a graded-band-gap semiconductor which is doped inhomogeneously with donors and acceptors so that there is no space charge. Electronic transport is analyzed by a novel method which is based on intraband transitions between eigenstates of the complete Hamiltonian. In addition to the normal diffusion term, another term is obtained which is linear in the gradient of the band edge for each type of carrier. In previous work this term was ascribed to a “quasifield”; we show that it originates from asymmetric diffusion. The transport equations for both types of carriers are presented.