Macroscopic quantum models with and without collisions
Vol. 2 No. 2 (2007) P.251~P.279
Recent progress on the derivation of macroscopic quantum models, particularly used in semiconductor device modeling, is reviewed. The first part of the survey is concerned with collisionless models, namely quantum hydrodynamic equations. These models are derived from the mixed-state Schrödinger system or from the Wigner equation. In the second part, starting from a Wigner-Boltzmann-type equation, quantum diffusion models like the viscous quantum hydrodynamic and the quantum drift-diffusion equations are derived. For these quantum diffusion models, new numerical results for a simple semiconductor resonant tunneling diode are presented. Moreover, some hybrid macroscopic-microscopic models for semiconductor devices are reviewed.
Quantum hydrodynamic equations, quantum drift-diffusion equations, moment method, semiconductor, viscosity, hybrid models, resonant tunneling diode
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35G30, 76Y05
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Revised : 2005-04-04