Macroscopic quantum models with and without collisions
by
Ansgar Jüngel
Josipa-Pina Milišić
Vol. 2 No. 2 (2007) P.251~P.279
ABSTRACT
Recent progress on the derivation of macroscopic quantum models, particularly used in semiconductor device modeling, is reviewed. The fi rst 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-di ffusion 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.
KEYWORDS
Quantum hydrodynamic equations, quantum drift-diff usion equations, moment method, semiconductor, viscosity, hybrid models, resonant tunneling diode
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35G30, 76Y05
MILESTONES
Received: 2004-11-24
Revised : 2005-04-04
Accepted:
Download Full Content