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The Classical and Quantum Hydrodynamic Models
"... The classical and quantum hydrodynamic equations are presented in a unified formulation and the 3D transport equations are mathematically classified. The 1D steadystate classical and quantum equations are discretized in conservation form using an upwind method. A classical hydrodynamic simulation ..."
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The classical and quantum hydrodynamic equations are presented in a unified formulation and the 3D transport equations are mathematically classified. The 1D steadystate classical and quantum equations are discretized in conservation form using an upwind method. A classical hydrodynamic simulation
Quantum hydrodynamic models for semiconductors with . . .
, 2007
"... In this thesis we study quantum hydrodynamic (QHD) models, particularly the ones used in semiconductor device modeling. The QHD model consists of the conservation laws for the particle density, momentum, and energy density, including quantum corrections from the Bohm potential. We start with a revie ..."
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In this thesis we study quantum hydrodynamic (QHD) models, particularly the ones used in semiconductor device modeling. The QHD model consists of the conservation laws for the particle density, momentum, and energy density, including quantum corrections from the Bohm potential. We start with a
Resonant tunneling in the quantum hydrodynamic model
 VLSI Design 3
, 1995
"... The phenomenon of resonant tunneling is simulated and analyzed in the quantum hydrodynamic (QHD) model for semiconductor devices. Simulations of a parabolic well resonant tunneling diode at 77 K are presented which show multiple regions of negative differential resistance (NDR) in the currentvoltag ..."
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Cited by 10 (3 self)
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The phenomenon of resonant tunneling is simulated and analyzed in the quantum hydrodynamic (QHD) model for semiconductor devices. Simulations of a parabolic well resonant tunneling diode at 77 K are presented which show multiple regions of negative differential resistance (NDR) in the current
The quantum hydrodynamic model for semiconductor devices
 SIAM Journal on Applied Mathematics
, 1994
"... Abstract. The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections. These quantum corrections are O(h2). The full threedimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner ..."
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Cited by 84 (9 self)
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Abstract. The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections. These quantum corrections are O(h2). The full threedimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion
SpaceFrequency Adaptive Approximation for Quantum Hydrodynamic Models
"... Abstract We introduce two spacefrequency adaptive strategies for the numerical approximation of the solutions of quantum hydrodynamic models for semiconductors, based respectively on wavelets and wavelet packets. The two strategies are compared on a test case, and wavelet packets perform better in ..."
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Abstract We introduce two spacefrequency adaptive strategies for the numerical approximation of the solutions of quantum hydrodynamic models for semiconductors, based respectively on wavelets and wavelet packets. The two strategies are compared on a test case, and wavelet packets perform better
Traveling Wave solutions for a Quantum Hydrodynamic Model
, 1999
"... A traveling wave analysis for a quantum hydrodynamic model ist performed. The isobaric, isentropic and isothermal cases are studied. In all three cases the qualitative behaviour of the solutions is analysed. Keywords: quantum hydrodynamics, traveling waves, Painleve II equation. AMS(MOS) subject c ..."
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Cited by 1 (0 self)
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A traveling wave analysis for a quantum hydrodynamic model ist performed. The isobaric, isentropic and isothermal cases are studied. In all three cases the qualitative behaviour of the solutions is analysed. Keywords: quantum hydrodynamics, traveling waves, Painleve II equation. AMS(MOS) subject
On a steadystate quantum hydrodynamic model for semiconductors
 Nonlin. Anal
, 1996
"... A third order quantum perturbation of the stress tensor, and a relaxation approximation to represent averaged collisions, are employed as perturbations of the isentropic model for a collisionless plasma. The model is selfconsistent in the sense that the electric eld, which forms a forcing term in ..."
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Cited by 24 (2 self)
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in the momentum equation, is determined by the coupled Poisson equation. As formulated, the model is a reduced version of the quantum hydrodynamic model for semiconductors. Existence is demonstrated for the model, which is shown to be equivalent to a nonstandard integrodierential equation. An unusual boundary
Recent Progress on Quantum Hydrodynamic Models for Semiconductors
, 2004
"... For ultrasmall semiconductor devices in which quantum effects are present, the corresponding mathematical models have to incorporate the quantum mechanical phenomena. Roughly speaking, these models can be divided into two classes: microscopic and macroscopic quantum models. Microscopic models inc ..."
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include quantum kinetic equations, like the Wigner equation and the Wigner(Poisson)FokkerPlank model, and SchrödingerPoisson systems [4, 30]. It has been known since the early days of quantum mechanics [26, 36] that these microscopic models can be written in hydrodynamic form using macroscopic
A NEW QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTOR DEVICES
"... A new quantum hydrodynamic (QHD) model for semiconductor devices is presented. The quantum hydrodynamic conservation laws have the same form as the classical hydrodynamic model, but the electron potential energy and average energy have additional quantum terms. These quantum terms allow particles ..."
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A new quantum hydrodynamic (QHD) model for semiconductor devices is presented. The quantum hydrodynamic conservation laws have the same form as the classical hydrodynamic model, but the electron potential energy and average energy have additional quantum terms. These quantum terms allow particles
Quantum hydrodynamic models for multiband semiconductor devices.
"... In the modeling of modern semiconductor devices it is essential to incorporate quantum mechanical phenomena, as in the new families of tunneling devices. From the point of view of practical applications, the approaches based on microscopic models are not completely satisfactory. Hence, it is useful ..."
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to formulate semiclassical models in terms of macroscopic variable. Such models are generally built by a hierarchy of coupled moment equations and referred to as quantum hydrodynamic models [1]. A new family of tunneling devices is the family of the heterojunction resonant interband tunneling diodes, which
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