Group delay in semiconductor structures with energy dependent effective mass

Abstract

We investigate tunneling times of a particle with energy dependent effective mass for a one-dimensional real potential. General relations between phase, group and dwell times are obtained for a desired potential shape. For the textbook case of a real rectangular potential barrier the explicit relations for relevant times are derived, which reveal that the nonparabolicity, depending on the energy of incident particle, may substantially increase the group time in realistic structures. Further, we extend this theory to the case of absorptive media described by complex potentials, via introduction of a new absorptive tunneling time τa. Depending on whether the short wavelength or long wavelength limit is considered, maximization of τa results in a very different shape of a complex rectangular potential.