Continuum Mechanics and Thermodynamics

, Volume 31, Issue 3, pp 751–773 | Cite as

An improved 2D–3D model for charge transport based on the maximum entropy principle

  • Vito Dario Camiola
  • Giovanni Mascali
  • Vittorio RomanoEmail author
Original Article


To study the electron transport in a some tens of nanometers long channel of a metal oxide field effect transistor, in order to reduce the computational cost of simulations, it can be convenient to divide the electrons into a 2D and a 3D population. Near the silicon/oxide interface the two populations coexist, while in the remaining part of the device only the 3D component needs to be considered because quantum effects are negligible there. The major issue is the description of the scattering mechanisms between the 2D and the 3D electron populations, due to interactions of electrons with nonpolar optical phonons and interface modes. Here, we propose a rigorous treatment of these collisions based on an approach similar to that used in Fischetti and Laux (Phys Rev B 48:2244–2274, 1993), in the context of a Monte Carlo simulation. We also consider all the other main scatterings, which are those with acoustic phonons, surface roughness, and impurities.


Quantum confinement 2DEG Semiconductors Maximum entropy principle Hydrodynamical models 


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G.M. acknowledges the financial support from the P.R.A. of the University of Calabria. V.R. acknowledges the financial support by progetto FIR 2016-2018 Modellistica, simulazione e ottimizzazione del trasporto di cariche in strutture a bassa dimensionalità, University of Catania. The authors G.M and V. R. are members of the INdAM research group GNFM.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Vito Dario Camiola
    • 1
  • Giovanni Mascali
    • 2
  • Vittorio Romano
    • 1
    Email author
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità della Calabria and INFN-Gruppo c. CosenzaCosenzaItaly

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