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 goa l of simultaneously dealing with phase-coherence effects and scattering int eractions in quantum-based devices. The proposed method is based on time-de pendent wavepackets and Bohm trajectories and restricts the quantum treatme nt of transport to the device regions where the potential profile significa ntly changes in distances of the order of the de Broglie wavelength of the carriers (the quantum window). Outside this region, electron transport is d escribed in terms of the semiclassical Boltzmann equation, which is solved using the MC technique. In this paper, our proposed description for the ele ctron ensemble inside the quantum window is rewritten in terms of the densi ty matrix. It is shown that, neglecting scattering, the off-diagonal terms of the density matrix remain identically zero even if time-dependent wavepa ckets are used. Bohm trajectories in tunnelling scenarios are reviewed to s how their feasibility to extend the MC technique to mesoscopic devices. A s elf-consistent one-dimensional simulator for resonant tunnelling diodes has been developed to technically validate our proposal. The obtained simulati on results are promising and encourage further efforts to include quantum e ffects into MC simulations.