Theory of Indirect Interband Tunneling in Semiconductors

Abstract

The theory of phonon-assisted tunneling by Keldysh and Kane is extended to incorporate the phonon interaction in a manner that is consistent with the requirements of crystal symmetry. Perturbation theory is used to evaluate the tunneling matrix element. The unperturbed wave functions are taken to be the approximate eigenstates of the pure crystal in a weak uniform field, as presented by Kane. The electron-phonon interaction is treated as the perturbation. Although the magnitude of the tunnel current agrees with experiment, the observed difference between the pressure coefficients of the transverse acoustical and the longitudinal acoustical phonon-assisted tunnel currents is not reproduced by the theory. It is concluded that Kane's "perfectly reflected" wave functions are not sufficiently good approximations for the calculation of phonon-assisted tunneling in germanium.