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On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

Author

Listed:
  • Giuseppe Alì

    (Department of Physics, University of Calabria, 87036 Arcavacata, Italy
    National Institute for Nuclear Physics (INFN), Associated Group of Cosenza, Arcavacata di Rende, 87036 Cosenza, Italy)

  • Francesco Lamonaca

    (Department of Computer Science, Modelling, Electronic and Systems (DIMES), University of Calabria, 87036 Arcavacata, Italy)

  • Carmelo Scuro

    (Department of Physics, University of Calabria, 87036 Arcavacata, Italy)

  • Isabella Torcicollo

    (Istituto per le Applicazioni del Calcolo “Mauro Picone” (IAC), CNR, 80131 Naples, Italy)

Abstract

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents.

Suggested Citation

  • Giuseppe Alì & Francesco Lamonaca & Carmelo Scuro & Isabella Torcicollo, 2021. "On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility," Mathematics, MDPI, vol. 9(17), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2152-:d:628659
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