STEADY-STATE SOLUTIONS AND ASYMPTOTIC LIMITS ON THE MULTI-DIMENSIONAL SEMICONDUCTOR QUANTUM HYDRODYNAMIC MODEL

2007 ◽  
Vol 17 (02) ◽  
pp. 253-275 ◽  
Author(s):  
BO LIANG ◽  
KAIJUN ZHANG
Keyword(s):  
Relaxation Time ◽  
Steady State ◽  
Hydrodynamic Model ◽  
Planck Constant ◽  
Quantum Hydrodynamic Model ◽  
Uniqueness Results ◽  
Qhd Model ◽  
Quantum Hydrodynamic ◽  
Dispersive Limit ◽  
Steady State Solutions

In this paper we study the steady-state quantum hydrodynamic model for semiconductors. The existence of solutions on the bipolar QHD model is obtained in the case of sufficiently small relaxation time. Uniqueness results are showed both in the thermal equilibrium states and the scaled Planck constant being large enough. The relaxation time and dispersive limit are performed on the bipolar and unipolar equations, respectively. In a sense, we have made a complete answer to the original unsolved problems of the steady-state QHD model.

scholarly journals Theory and Simulation of the Smooth Quantum Hydrodynamic Model

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 351-355
Author(s):  
Carl L. Gardner
Keyword(s):  
Hydrodynamic Model ◽  
Differential Resistance ◽  
Classical Electron ◽  
Model Simulations ◽  
Quantum Hydrodynamic Model ◽  
Tunneling Diode ◽  
Qhd Model ◽  
Quantum Hydrodynamic ◽  
Quantum Semiconductor ◽  
Classical Hydrodynamic

The “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. 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(ħ2) QHD model. In addition, smooth QHD simulations of a classical electron shock wave are presented which agree with classical hydrodynamic model simulations and which do not exhibit the spurious dispersive oscillations of the O(ħ2) QHD model.

scholarly journals Weak Limits of the Quantum Hydrodynamic Model

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 427-434 ◽  
Author(s):  
Paola Pietra ◽  
Carsten Pohl
Keyword(s):  
High Frequency ◽  
Numerical Study ◽  
Planck Constant ◽  
Quantum Hydrodynamic Model ◽  
High Frequency Oscillations ◽  
Weak Limits ◽  
Quantum Hydrodynamic ◽  
Formal Limit ◽  
Dispersive Limit ◽  
Quantum Hydrodynamic Equations

A numerical study of the dispersive limit of the quantum hydrodynamic equations for semiconductors is presented. The solution may develop high frequency oscillations when the scaled Planck constant is small. Numerical evidence is given of the fact that in such cases the solution does not converge to the solution of the formal limit equations.

scholarly journals The Chapman-Enskog Expansion and the Quantum Hydrodynamic Model for Semiconductor Devices

VLSI Design ◽  
2000 ◽  
Vol 10 (4) ◽  
pp. 415-435 ◽  
Author(s):  
Carl L. Gardner ◽  
Christian Ringhofer
Keyword(s):  
Heat Flux ◽  
Boltzmann Equation ◽  
Potential Energy ◽  
Hydrodynamic Model ◽  
Semiconductor Devices ◽  
Quantum Hydrodynamic Model ◽  
Qhd Model ◽  
Quantum Hydrodynamic ◽  
Classical Potential ◽  
Quantum Semiconductor

A “smooth” quantum hydrodynamic (QHD) model for semiconductor devices is derived by a Chapman-Enskog expansion of the Wigner-Boltzmann equation which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A dispersive quantum contribution to the heat flux term in the QHD model is introduced.

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