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Convergent Iterative Schemes for a Non‐isentropic Hydrodynamic Model for Semiconductors
Author(s) -
Amster P.,
Pinnau R.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200208)82:8<559::aid-zamm559>3.0.co;2-6
Subject(s) - decoupling (probability) , convergence (economics) , iterative method , isentropic process , local convergence , mathematics , semiconductor device , diffusion , physics , mathematical analysis , mechanics , mathematical optimization , thermodynamics , materials science , layer (electronics) , control engineering , engineering , economics , composite material , economic growth
Two iterative schemes for the solution of the one‐dimensional stationary full hydrodynamic model for semiconductor devices are studied. This model consists of a system of balance equations for the electron density, temperature, and the electric field. The first iterative scheme relies on a decoupling of the equations in the spirit of the well‐known Gummel‐iteration for the standard drift diffusion model. Convergence is proven in the case of small deviations from the equilibrium state. Secondly, a full Newton‐iteration is analyzed and its local second order convergence is proven.