Wigner-Boltzmann Monte Carlo approach to nanodevice simulation: from quantum to semiclassical transport

In this paper, we review and extend our recent works based on the Monte Carlo method to solve the Wigner-Boltzmann transport equation and model semiconductor nanodevices. After presenting the different possible approaches to quantum mechanical modelling, the formalism and the theoretical framework are described together with the particle Monte Carlo implementation using a technique fully compatible with semiclassical simulation. Examples are given to highlight the importance of considering both quantum and scattering effects in nanodevices operating at room temperature, such as resonant tunnelling diode (RTD), double-gate MOSFET and carbon nanotube FET. Quantum and semiclassical approaches are compared for transistor simulation. Finally, the phonon-induced electron decoherence in RTD and MOSFET is examined through the analysis of the density matrix elements computed from the Wigner function. This formalism is shown to be relevant for the quantitative analysis of devices operating in mixed quantum/semiclassical regime and to understand the transition between both regimes or between coherent and sequential tunnelling processes.