A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Abstract

The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case. Keywords:Nanostructures, Wigner transport equation, Direct simulation Monte Carlo AMS subject classification: 82D80, 82S30, 65M75The Wigner equation is a full quantum transport model able to capture the relevant physics in next generation semiconductor devices. It is well known that the pure state Wigner equation is an equivalent phase-space reformulation of the Schrödinger equation. At the same time the Wigner equation can be augmented by a Boltzmann-like collision operator accounting for the process of decoherence. However, this equation has represented a numerically daunting task and it has raised more problems than solutions. A numerical treatment of the Wigner equation can be dealt with deterministic schemes [1][2][3][4], Direct Simulation Monte Carlo [5][6][7][8], and it is often used to derive reduced transport models, such as quantum-hydrodynamic models [9][10][11][12].Among the several particle Monte Carlo methods developed during these years (see [13] for a review), we have focused in the so called Signed Monte Carlo method [14], where the Wigner potential is treated as a scat-

Solving the Wigner Equation with Signed Particles Monte Carlo for Chemically Relevant Potentials

“…We leave more complex scenarios for future work. In addition to these two models we have also reproduced results previously reported in the literature of scattering from a Gaussian barrier 15,20 . Please see Appendix B for these results and discussion.…”

Improved mobility models for charge transport in graphene

“…Further developments could include the effects of crystal heating and quantum effects in the mobility models. Although the subject is still in an early stage, attempts in this direction can be found in [10,11] regarding the thermal influence on the electric performance, and in [12][13][14][15] regarding the inclusion of quantum corrections.…”

A stochastic algorithm without time discretization error for the Wigner equation

“…The kernel (13) without a majorant (or, withV W = |V W |) was considered in [17]. The kernel (13) with a majorant was used in [10], [7] in the context of a class of time splitting algorithms (transport and creation steps were separated).…”