Transmission coefficient and stationary-phase tunneling time of an electron through a heterostructure

In this paper we calculate the tunneling time and transmission coefficient for an electron wave packet passing through a barrier formed by a two-dimensional heterostructure. We assume that the direction of propagation of the wave packet makes an arbitrary angle with respect to the layers of the heterostructure and that the effective mass of the electron is position dependent. Neglected in earlier publications, both these factors when taken in combination produce changes up to 30% in the tunneling time and up to 150% in the transmission coefficient from their respective values obtained assuming a constant electron effective mass. The calculated results apply for electron energies above and below the barrier height.