Transfer Hamiltonian description of resonant tunnelling

Abstract

The transmission coefficient of a tunnel barrier can become very large when the incident energy matches the energy of a localised level in the barrier whereupon resonant tunnelling occurs. Ricco and Azbel (1970) have pointed out that many properties of the resonant tunnelling process, such as the tunnelling time, depend critically on the magnitude of the wavefunction at the position of the resonant level. However, they were unable to calculate the magnitude of the wavefunction with the transfer matrix method they used. In this paper a transfer Hamiltonian formalism is developed to describe resonant tunnelling which enables the occupancy of the resonant level to be calculated. It is shown that the method gives the correct magnitude for the total tunnel current through a one-dimensional double barrier. The time dependences of the occupancies of the resonant levels are calculated for two model systems.