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Title: Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene

Abstract

Standard computational methods used to take account of the Pauli Exclusion Principle into Monte Carlo (MC) simulations of electron transport in semiconductors may give unphysical results in low field regime, where obtained electron distribution function takes values exceeding unity. Modified algorithms were already proposed and allow to correctly account for electron scattering on phonons or impurities. Present paper extends this approach and proposes improved simulation scheme allowing including Pauli exclusion principle for electron–electron (e–e) scattering into MC simulations. Simulations with significantly reduced computational cost recreate correct values of the electron distribution function. Proposed algorithm is applied to study transport properties of degenerate electrons in graphene with e–e interactions. This required adapting the treatment of e–e scattering in the case of linear band dispersion relation. Hence, this part of the simulation algorithm is described in details.

Authors:
 [1];  [2];  [1]
  1. Warsaw University of Technology, Faculty of Physics, ul. Koszykowa 75, 00-662 Warszawa (Poland)
  2. Institut d'Electronique, de Microélectronique et de Nanotechnologies, UMR CNRS 8520, Université Lille 1, Avenue Poincaré, CS 60069, 59652 Villeneuve d'Ascq Cédex (France)
Publication Date:
OSTI Identifier:
22622310
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 341; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
77 NANOSCIENCE AND NANOTECHNOLOGY; ALGORITHMS; COMPUTERIZED SIMULATION; DISPERSION RELATIONS; DISPERSIONS; DISTRIBUTION; DISTRIBUTION FUNCTIONS; ELECTRON GAS; ELECTRON-ELECTRON INTERACTIONS; GRAPHENE; IMPURITIES; MONTE CARLO METHOD; NANOSTRUCTURES; PAULI PRINCIPLE; PHONONS; SCATTERING

Citation Formats

Borowik, Piotr, Thobel, Jean-Luc, and Adamowicz, Leszek. Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.04.011.
Borowik, Piotr, Thobel, Jean-Luc, & Adamowicz, Leszek. Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene. United States. https://doi.org/10.1016/J.JCP.2017.04.011
Borowik, Piotr, Thobel, Jean-Luc, and Adamowicz, Leszek. Sat . "Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene". United States. https://doi.org/10.1016/J.JCP.2017.04.011.
@article{osti_22622310,
title = {Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene},
author = {Borowik, Piotr and Thobel, Jean-Luc and Adamowicz, Leszek},
abstractNote = {Standard computational methods used to take account of the Pauli Exclusion Principle into Monte Carlo (MC) simulations of electron transport in semiconductors may give unphysical results in low field regime, where obtained electron distribution function takes values exceeding unity. Modified algorithms were already proposed and allow to correctly account for electron scattering on phonons or impurities. Present paper extends this approach and proposes improved simulation scheme allowing including Pauli exclusion principle for electron–electron (e–e) scattering into MC simulations. Simulations with significantly reduced computational cost recreate correct values of the electron distribution function. Proposed algorithm is applied to study transport properties of degenerate electrons in graphene with e–e interactions. This required adapting the treatment of e–e scattering in the case of linear band dispersion relation. Hence, this part of the simulation algorithm is described in details.},
doi = {10.1016/J.JCP.2017.04.011},
url = {https://www.osti.gov/biblio/22622310}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 341,
place = {United States},
year = {2017},
month = {7}
}