Numerical solutions of a viscous‐hydrodynamic model for semiconductors:: the supersonic case

• Luca Ballestra ^[1] ; Fausto Saleri ^[1]
  1. [1] University of Milan

     University of Milan

     Milán, Italia

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 22, Nº 2, 2003, págs. 205-230
• Idioma: inglés
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• Resumen

  • In this paper, we solve by a finite difference upwinded method an extended hydrodynamic model for semiconductors, with viscous terms in the momentum equation. In particular, we consider the simulation of a one‐dimensional n+‐n ‐n+ diode, whose solution exhibits at low temperatures strong discontinuities, and investigate the effect of the momentum viscosity on the shock waves. Numerical experiments, performed also on a two‐dimensional test case, demonstrate that the numerical scheme, working on non‐uniform grids, is suitable to describe solutions with strong variations in time and space. Well‐posedness for the boundary conditions is discussed, and a linear stability estimate is established for the one‐dimensional n+‐n ‐n+ diode benchmark problem.