Towards the Monte Carlo simulation of resonant tunnelling diodes using time-dependent wavepackets and Bohm trajectories

Following the path of a previous letter, a generalization of the classical Monte Carlo (MC) device simulation technique is proposed with the final goal of simultaneously dealing with phase-coherence effects and scattering interactions in quantum-based devices. The proposed method is based on time-dependent wavepackets and Bohm trajectories and restricts the quantum treatment of transport to the device regions where the potential profile significantly changes in distances of the order of the de Broglie wavelength of the carriers (the quantum window). Outside this region, electron transport is described in terms of the semiclassical Boltzmann equation, which is solved using the MC technique. In this paper, our proposed description for the electron ensemble inside the quantum window is rewritten in terms of the density matrix. It is shown that, neglecting scattering, the off-diagonal terms of the density matrix remain identically zero even if time-dependent wavepackets are used. Bohm trajectories in tunnelling scenarios are reviewed to show their feasibility to extend the MC technique to mesoscopic devices. A self-consistent one-dimensional simulator for resonant tunnelling diodes has been developed to technically validate our proposal. The obtained simulation results are promising and encourage further efforts to include quantum effects into MC simulations.