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| Statistical models are used to describe electron transport in semiconductors at a mesoscopic level.
The basic model is given by the Boltzmann transport equation for semiconductors in the semi-classical approximation coupled with Poisson's equation, since the electric field is self-consistent due to the electrostatics produced by the electrons and the dopants in the semiconductor. However, for small devices the quantum effects must be considered.
And, in this case, the devices are described by the Schr\"odiger-Poisson-Boltzmann system.
In this talk we show WENO-solvers for DG-MOSFETs in both versions: semi-classical approximation for large devices [2] and hybrid quantum-classical approximation for small devices [1,3].
1.- N. Ben Abdallah, M.J. C\'aceres, J. A. Carrillo, F. Vecil, {\em A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs}, J. Comput. Phys. 228 (2009) 6553-6571.
2.-J.M. Mantas, M.J. C\'aceres, {\em Efficient deterministic parallel simulation of 2D semiconductor devices based on WENO-Boltzmann schemes}, Comput. Meth. Appl. Mech. Eng. 198 (2009) 693-704.
3.-F. Vecil, J. M Mantas, M. J. C\'aceres, C. Sampedro, A. Godoy, F. G\'amiz,{\em A parallel deterministic solver for the Schrodinger-Poisson-Boltzmann system in ultra-short DG-MOSFETs:
Comparison with Monte-Carlo}, Preprint. |
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