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

Giuseppe Alì, Francesco Lamonaca, Carmelo Scuro and Isabella Torcicollo
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Giuseppe Alì: Department of Physics, University of Calabria, 87036 Arcavacata, 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

Mathematics, 2021, vol. 9, issue 17, 1-9

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.

Keywords: subsonic solutions; unipolar semiconductor; saturation velocity; steady-state hydrodynamical model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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