Tunneling time asymmetry in semiconductor heterostructures

Analytical expressions are given for the difference between left-to-right and right-to-left tunneling times in asymmetric single- and multiple-barrier heterostructures. This tunneling time asymmetry is related to the phase difference of the reflection coefficients of the electron wavefunction for the two tunneling directions. Examples for single- and double-barrier heterostructures are given. The treatment in this paper can be used for designing devices with asymmetric frequency characteristics with respect to the electron tunneling direction