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

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, 2006.10.1504/IJCSE.2006.012762Search in Google Scholar

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, 2008.10.1080/00411450802536607Search in Google Scholar

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, 2011.10.1088/1751-8113/44/26/265301Search in Google Scholar

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, 2011.10.4208/cicp.080509.310310sSearch in Google Scholar

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, 2015.10.1016/j.jcp.2014.12.026Search in Google Scholar

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, 2016.10.1137/15M1051373Search in Google Scholar

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, 2017.10.1109/TNANO.2017.2741523Search in Google Scholar

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, 2017.10.1016/j.jcp.2017.08.059Search in Google Scholar

9. L. Shifren and D. Ferry, Particle Monte Carlo simulation of Wigner function tunneling, Physics Letters A, vol. 285, pp. 217-221, 2001.10.1016/S0375-9601(01)00344-9Search in Google Scholar

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.Search in Google Scholar

11. D. Querlioz and P. Dollfus, The Wigner Monte Carlo method for nanoelectronic devices. Wiley, 2010.Search in Google Scholar

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, 2017.10.1002/pssr.201700102Search in Google Scholar

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, 2018.10.1016/j.cpc.2018.03.010Search in Google Scholar

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, 2004.10.1103/PhysRevB.70.115319Search in Google Scholar

15. W. Wagner, A random cloud model for the Wigner equation, Kinetic & Related Models, vol. 9, no. 1, pp. 217-235, 2016.10.3934/krm.2016.9.217Search in Google Scholar

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, 2016.10.1137/16M105798XSearch in Google Scholar

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, 2017.10.1515/caim-2017-0012Search in Google Scholar

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, 2019.10.3934/krm.2019003Search in Google Scholar

19. E. Wigner, On the quantum correction for thermodynamic equilibrium, Physical Review, vol. 40, no. 2, pp. 749-759, 1932.10.1103/PhysRev.40.749Search in Google Scholar

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, 2013.10.1007/s11232-013-0128-8Search in Google Scholar

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, 2012.10.1007/s10825-012-0381-3Search in Google Scholar

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, 2014.10.1007/s00161-013-0296-7Search in Google Scholar

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, 2016.10.1515/caim-2016-0003Search in Google Scholar

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, 2016.10.3390/e18100368Search in Google Scholar

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, 2018.10.1186/s13362-018-0056-1Search in Google Scholar