Wigner Monte Carlo simulation without discretization error of the tunneling rectangular barrier

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Abstract

The Wigner transport equation can be solved stochastically by Monte Carlo techniques based on the theory of piecewise deterministic Markov processes. A new stochastic algorithm, without time discretization error, has been implemented and studied in the case of the quantum transport through a rectangular potential barrier.

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  • 1. H. Kosina Wigner function approach to nano device simulation International Journal of Computa- tional Science and Engineering vol. 2 no. 3-4 pp. 100-118 2006.

  • 2. O. Morandi and L. Demeio A Wigner-function approach to interband transitions based on the multiband-envelope-function model Transport Theory and Statistical Physics vol. 37 no. 5-7 pp. 473-459 2008.

  • 3. O. Morandi and F. Schürrer Wigner model for quantum transport in graphene Journal of Physics A: Mathematical and Theoretical vol. 44 no. 26 p. 265301 2011.

  • 4. S. Shao T. Lu and W. Cai Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport Communications in Computational Physics vol. 9 no. 3 pp. 711-739 2011.

  • 5. A. Dorda and F. Schürrer A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes Journal of Computational Electronics vol. 284 pp. 95-116 2015.

  • 6. Y. Xiong Z. Chen and S. Shao An advective-spectral-mixed method for time-dependent many-body Wigner simulations SIAM Journal on Scientific Computing vol. 38 no. 4 pp. B491-B520 2016.

  • 7. J.-H. Lee and M. Shin Quantum transport simulation of nanowire resonant tunneling diodes based on a Wigner function model with spatially dependent effective masses IEEE Transactions on Nan- otechnology vol. 16 no. 6 pp. 1028-1036 2017.

  • 8. M. L. V. de Put B. Soree and W. Magnus Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field Journal of Computational Physics vol. 350 pp. 314-325 2017.

  • 9. L. Shifren and D. Ferry Particle Monte Carlo simulation of Wigner function tunneling Physics Letters A vol. 285 pp. 217-221 2001.

  • 10. M. Nedjalkov R. Kosik H. Kosina and S. Selberherr A Wigner equation for nanometer and femtosecond transport regime in Proceedings IEEE Conference on Nanotechnology pp. 277-281 IEEE 2001.

  • 11. D. Querlioz and P. Dollfus The Wigner Monte Carlo method for nanoelectronic devices. Wiley 2010.

  • 12. P. Ellinghaus J. Weinbub M. Nedjalkov and S. Selberherr Analysis of lense-governed Wigner signed particle quantum dynamics Physica Status Solidi RRL vol. 11 no. 7 p. 1700102 2017.

  • 13. M. Nedjalkov P. Ellinghaus J. Weinbub T. Sadi A. Asenov I. Dimov and S. Selberherr Stochastic analysis of surface roughness models in quantum wires Computer Physics Communications vol. 228 pp. 30-37 2018.

  • 14. M. Nedjalkov H. Kosina S. Selberherr C. Ringhofer and D. K. Ferry Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices Physical Review B vol. 70 p. 115319 2004.

  • 15. W. Wagner A random cloud model for the Wigner equation Kinetic & Related Models vol. 9 no. 1 pp. 217-235 2016.

  • 16. O. Muscato and W. Wagner A class of stochastic algorithms for the Wigner equation SIAM Journal on Scientific Computing vol. 38 no. 3 pp. A1438-A1507 2016.

  • 17. O. Muscato A benchmark study of the signed-particle Monte Carlo algorithm for the Wigner equation Communications in Applied and Industrial Mathematics vol. 8 no. 1 pp. 237-250 2017.

  • 18. O. Muscato and W. Wagner A stochastic algorithm without time discretization error for the Wigner equation Kinetic & Related Models vol. 12 no. 1 pp. 59-77 2019.

  • 19. E. Wigner On the quantum correction for thermodynamic equilibrium Physical Review vol. 40 no. 2 pp. 749-759 1932.

  • 20. V. F. Los and N. Los Exact solution of the one-dimensional time-dependent Schrödinger equation with a rectangular well/barrier potential and its applications Theoretical and Mathematical Physics vol. 177 no. 3 pp. 1706-1721 2013.

  • 21. O. Muscato and V. Di Stefano Hydrodynamic modeling of silicon quantum wires Journal of Com- putational Electronics vol. 11 no. 1 pp. 45-55 2012.

  • 22. O. Muscato and V. Di Stefano Hydrodynamic simulation of a n+ - n - n+ silicon nanowire Continuum Mechanics and Thermodynamics vol. 26 no. 2 pp. 197-205 2014.

  • 23. O. Muscato and T. Castiglione Electron transport in silicon nanowires having different cross-sections Communications in Applied and Industrial Mathematics vol. 7 no. 2 pp. 8-25 2016.

  • 24. O. Muscato and T. Castiglione A hydrodynamic model for silicon nanowires based on the maximum entropy principle Entropy vol. 18 no. 10 p. 368 2016.

  • 25. O. Muscato T. Castiglione V. Di Stefano and A. Coco Low-field electron mobility evaluation in silicon nanowire transistors using an extended hydrodynamic model Journal of Mathematics in Industry vol. 8 p. 14 2018.

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CiteScore 2018: 0.95

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

Mathematical Citation Quotient (MCQ) 2018: 0.27

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