A BGK model for charge transport in graphene

Open access

Abstract

The classical Boltzmann equation describes well temporal behaviour of a rarefied perfect gas. Modified kinetic equations have been proposed for studying the dynamics of different type of gases. An important example is the transport equation, which describes the charged particles flow, in the semi-classical regime, in electronic devices. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a collision operator have been proposed to replace the standard Boltzmann integral term. These new equations are called kinetic models. The most popular and widely used kinetic model is the Bhatnagar-Gross-Krook (BGK) model. In this work we propose and analyse a BGK model for charge transport in graphene.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • 1. A. H. Castro Neto F. Guinea N. M. R. Peres K. S. Novoselov and A. K. Geim The electronic properties of graphene Reviews of Modern Physics vol. 81 no. 1 pp. 109–162 2009.

  • 2. A. Majorana G. Mascali and V. Romano Charge transport and mobility in monolayer graphene Journal of Mathematics in Industry vol. 7 no. 4 2016.

  • 3. V. Romano A. Majorana and M. Coco DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene Journal of Computational Physics vol. 302 pp. 267–284 2015.

  • 4. P. L. Bhatnagar E. P. Gross and M. Krook A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems Physical Review vol. 94 no. 3 pp. 511–525 1954.

  • 5. A. Tomadin D. Brida G. Cerullo A. C. Ferrari and M. Polini Nonequilibrium dynamics of photoex-cited electrons in graphene: Collinear scattering auger processes and the impact of screening Physical Review B vol. 88 no. 035430 pp. 1–18 2013.

  • 6. S. Chapman and T. G. Cowling The Mathematical Theory of Non-uniform Gases. Cambridge University Press 1991.

  • 7. D. W. Snoke The quantum Boltzmann equation in semiconductor physics Annalen der Physik vol. 523 no. 1-2 pp. 97–100 2011.

  • 8. D. Benedetto F. Castella R. Esposito and M. Pulvirenti A short review on the derivation of the nonlinear quantum Boltzmann equations Communications in Mathematical Sciences vol. 5 pp. 55–71 2007.

  • 9. M. Coco A. Majorana and V. Romano Cross validation of discontinuous Galerkin method and Monte Carlo simulations of charge transport in graphene on substrate Ricerche di Matematica vol. 66 no. 1 pp. 201–220 2017.

Search
Journal information
Impact Factor


CiteScore 2018: 0.95

SCImago Journal Rank (SJR) 2018: 0.324
Source Normalized Impact per Paper (SNIP) 2018: 0.73

Mathematical Citation Quotient (MCQ) 2017: 0.38

Target audience:

researchers in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, and medicine

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 29 29 13
PDF Downloads 15 15 2