Resonant tunneling of holes in the multiband effective-mass approximation

Abstract

General expressions for the current density and the group velocity under the Luttinger-Kohn multiband effective-mass approximation are presented. The resonant tunneling of holes through a semiconductor double barrier using the transfer-matrix technique is then studied. Strong mixing of the light hole (LH) and the heavy hole (HH) at nonzero in-plane k vectors is shown clearly in the transmissivity diagrams. Splitting of the resonant-tunneling peaks by an applied electric field due to the removal of the Kramers degeneracy is demonstrated numerically. The total tunneling current is calculated by integrating over all the incident hole states in the momentum space. We find that the coupling between light and heavy holes depends strongly on the doping level of the injection electrode. Higher doping causes stronger coupling and distortion of the I-V curve because of the contribution from larger in-plane k vectors. A comparison with the parabolic-band model is also made. The parabolic-band model shows that the transmitted current density due to the incident light hole is larger than that due to the heavy hole because of the much higher transmission coefficient of the light hole, even though the heavy hole has a higher concentration in the injection region. However, the multiband model shows the opposite since the transmission coefficients of HH-in–HH-out and HH-in–LH-out become comparable to those of LH-in–HH-out and LH-in–LH-out because of the strong mixing between light and heavy holes. This study suggests that the band mixing has an important influence on the high-speed tunneling of photogenerated carriers in photodetectors and electro-optical modulators when the carrier concentration is high.