A new matrix method for tunnelling in heterostructures: Γ, X effects in single-barrier systems

Abstract

The authors present the results on the band-structure effects in single-barrier tunnelling, calculated using a new scattering matrix method. Their results show that the transmission amplitude may be divided into two regions. The first is for electron energies in the band gap of the barrier material, where the transmission is found to be a single state property, with the Gamma state dominant. The appropriate barrier height, regardless of the direct/indirect nature of the barrier band gap, is the Gamma - Gamma band offset. The tunnelling behaviour is therefore single state like. The other regime is for electrons with energies above the barrier material's conduction band edge where, for indirect band-gap barriers, a sharp transition to an X dominated behaviour is observed. Coupling between the barrier Gamma and the X states are found in thin barriers and X well resonances are obtained. The single barrier transmission in this regime is therefore a multistate property.