Matrix formalism for the triple-band effective-mass equation

Abstract

We propose a transfer matrix formalism of the triple-band effective-mass equation to describe the transport process of carriers through an arbitrary structure with layers of different materials. We use the coherent tunnelling approach in the flat band approximation. Special attention is paid to the boundary conditions. The triple-band matrix formalism is applied to AlAs/GaAs resonant tunnelling diodes and n- and p-type InAs/AlSb/GaSb resonant interband tunnelling diodes. We compare the results of the single- and double-band effective-mass equation with the triple-band effective-mass equation. We show that the influence of the non-parabolicity of the bands on the position of the energy levels in the quantum well for the simple resonant tunnelling structure is of the same order as the shifts induced by the charging of the quantum well. In the case of the p-type resonant interband tunnelling diode, we calculate that the effect of the split-off band is not negligible.