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Vacuum and non‐vacuum solutions of the quasi‐hydrodynamic semiconductor model in thermal equilibrium
Author(s) -
Unterreiter A.
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180304
Subject(s) - monotonic function , semiconductor , boundary value problem , range (aeronautics) , transformation (genetics) , boundary (topology) , thermal equilibrium , mathematics , thermal , physics , mechanics , mathematical analysis , thermodynamics , materials science , chemistry , quantum mechanics , biochemistry , composite material , gene
The quasi‐hydrodynamical model for bipolar semiconductor devices in thermal equilibrium admits in general solutions for which the non‐negative electron‐ or hole‐density is not strict positive. In this paper sufficient conditions depending on the device's data which lead to or prevent vacuum are presented. The transformation of the model equations to a single semilinear elliptic mixed boundary value problem for the electrostatic potential V reduces the vacuum‐non‐vacuum discussion to an investigation of the range of V . Monotonicity arguments and the employment of local sub‐ and supersolutions allow to estimate the size as well as the distance from the Dirichlet boundary of the respective vacuum sets. An one‐dimensional model is analysed in some detail.