Gauge-invariant formulation of Fermi's golden rule: Application to high-field transport in semiconductors

INFM and Dipartimento di Fisica, Politecnico di Torino Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received: 22 September 2003
Accepted: 5 November 2003

Abstract

A gauge-invariant formulation of Fermi's golden rule is proposed. We shall revisit the conventional description of carrier-phonon scattering in the presence of high electric fields by means of a gauge-invariant density-matrix approach. We show that the so-called intracollisional field effect, as usually accounted for, has been always overestimated due to the neglect of the time variation of the basis states, which in turn leads to an ill-defined Markov limit in the carrier-phonon interaction process. This may account for the surprisingly good agreement between semiclassical and rigorous quantum-transport calculations previously reported, and is confirmed by our fully three-dimensional simulations of charge transport in state-of-the-art semiconductor superlattices, which show significant current overestimations.