Intracollisional field effect: a gauge-invariant formulation in semiconductors

A gauge-invariant formulation of high-field transport in semiconductors is proposed. We revisit the conventional description of carrier–phonon scattering within the Fermi golden rule scheme by means of a gauge-invariant generalization of the scattering rates. With a density-matrix approach, we show that the so-called intracollisional field effect, as usually accounted for, has always been overestimated due to the neglect of the time variation of the basis states, which in turn leads to a ill-defined Markov limit in the carrier–phonon interaction process. This is confirmed by a fully three-dimensional simulation of charge transport in state-of-the-art semiconductor superlattices.