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Numerical simulation of the smooth quantum hydrodynamic model for semiconductor devices. (English) Zbl 0966.76100

Summary: We review an extension of classical hydrodynamic model for semiconductor devices to include quantum transport effects. This “smooth” quantum hydrodynamic (QHD) model is derived specifically to handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. We discuss a conservative upwind discretization of the one-dimensional steady-state smooth QHD equations. Smooth QHD model simulations of the resonant tunneling diode are presented which exhibit enhanced negative differential resistance when compared with simulations using the original \(O(\hbar^2)\) QHD model.

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76M20 Finite difference methods applied to problems in fluid mechanics
82D37 Statistical mechanics of semiconductors
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