Computation of quantum electron transport with local current conservation using quantum trajectories

A recent proposal for modeling time-dependent quantum electron transport with Coulomb and exchange correlations using quantum (Bohm) trajectories (Oriols 2007 Phys.Rev.Lett.98 066803) is extended towards the computation of the total (particle plus displacement) current in mesoscopic devices. In particular, two different methods for the practical computation of the total current are compared. The first method computes the particle and the displacement currents from the rate of Bohm particles crossing a particular surface and the time-dependent variations of the electric field there. The second method uses the Ramo-Shockley theorem to compute the total current on that surface from the knowledge of the Bohm particle dynamics in a 3D volume and the time-dependent variations of the electric field on the boundaries of that volume. From a computational point of view, it is shown that both methods achieve local current conservation, but the second is preferred because it is free from 'spurious' peaks. A numerical example, a Bohm trajectory crossing a double-barrier tunneling structure, is presented, supporting the conclusions. © 2009 IOP Publishing Ltd.