Uncertainty Quantification for Charge Transport in GNRs Through Particle Galerkin Methods for the Semiclassical Boltzmann Equation
Year: 2025
Author: Andrea Medaglia, Giovanni Nastasi, Vittorio Romano, Mattia Zanella
Communications in Computational Physics, Vol. 37 (2025), Iss. 4 : pp. 1055–1084
Abstract
In this article, we investigate some issues related to the quantification of uncertainties associated with the electrical properties of graphene nanoribbons. The approach is suited to understand the effects of missing information linked to the difficulty of fixing some material parameters, such as the band gap, and the strength of the applied electric field. In particular, we focus on the extension of particle Galerkin methods for kinetic equations in the case of the semiclassical Boltzmann equation for charge transport in graphene nanoribbons with uncertainties. To this end, we develop an efficient particle scheme which allows us to parallelize the computation and then, after a suitable generalization of the scheme to the case of random inputs, we present a Galerkin reformulation of the particle dynamics, obtained by means of a generalized Polynomial Chaos approach, which allows the reconstruction of the kinetic distribution. As a consequence, the proposed particle-based scheme preserves the physical properties and the positivity of the distribution function also in the presence of a complex scattering in the transport equation of electrons. The impact of the uncertainty of the band gap and applied field on the electrical current is analysed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2024-0103
Communications in Computational Physics, Vol. 37 (2025), Iss. 4 : pp. 1055–1084
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Charge transport graphene uncertainty quantification semiclassical Boltzmann equation stochastic Galerkin particle methods.