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 Smooth Quantum Hydrodynamic Model Simulation of the Resonant Tunneling Diode

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 143-146 ◽  
Author(s):  
Carl L. Gardner ◽  
Christian Ringhofer
Keyword(s):  
Negative Differential Resistance ◽  
Resonant Tunneling ◽  
Model Simulation ◽  
Differential Resistance ◽  
Resonant Tunneling Diode ◽  
Model Simulations ◽  
Quantum Hydrodynamic Model ◽  
Tunneling Diode ◽  
Qhd Model ◽  
Quantum Hydrodynamic

Smooth quantum hydrodynamic (QHD) model simulations of the resonant tunneling diode are presented which exhibit enhanced negative differential resistance (NDR) when compared to simulations using the original O(ℏ2) QHD model. At both 300 K and 77 K, the smooth QHD simulations predict significant NDR even when the original QHD model simulations predict no NDR.

scholarly journals Resonant Tunneling in the Quantum Hydrodynamic Model

VLSI Design ◽  
1995 ◽  
Vol 3 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Carl L. Gardner
Keyword(s):  
Quantum Interference ◽  
Resonant Tunneling ◽  
Differential Resistance ◽  
Quantum Hydrodynamic Model ◽  
Tunneling Diode ◽  
Voltage Curve ◽  
Current Voltage Curve ◽  
Multiple Regions ◽  
Qhd Model ◽  
Quantum Hydrodynamic

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-voltage curve. These are the first simulations of the QHD equations to show multiple regions of NDR.Resonant tunneling (and NDR) depend on the quantum interference of electron wavefunctions and therefore on the phases of the wavefunctions. An analysis of the QHD equations using a moment expansion of the Wigner-Boltzmann equation indicates how phase information is retained in the hydrodynamic 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.

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.

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