scholarly journals Quantum Energy-Transport and Drift-Diffusion Models for Electron Transport in Graphene An Approach by The Wigner Function

2021 ◽  
Author(s):  
Vito Dario Camiola ◽  
Giovanni Mascali ◽  
Vittorio Romano
Keyword(s):  
Boltzmann Equation ◽  
Energy Transport ◽  
Diffusion Models ◽  
Diffusion Equations ◽  
Numerical Treatment ◽  
Drift Diffusion ◽  
Quantum Energy ◽  
Quantum Hydrodynamic Model ◽  
Mathematical Properties ◽  
Quantum Hydrodynamic

Abstract The present work aims at formulating quantum energy-transport and drift- diffusion equations for charge transport in graphene from a quantum hydrodynamic model proposed in [1], obtained from the Wigner-Boltzmann equation via the mo- ment method. In analogy with the semiclassical case, we are confident that the energy- transport and drift-diffusion models have mathematical properties which allow an easier numerical treatment.

scholarly journals Quantum Energy-Transport and Drift-Diffusion Models

2005 ◽  
Vol 118 (3-4) ◽  
pp. 625-667 ◽  
Author(s):  
Pierre Degond ◽  
Florian M�hats ◽  
Christian Ringhofer
Keyword(s):  
Energy Transport ◽  
Diffusion Models ◽  
Drift Diffusion ◽  
Quantum Energy

scholarly journals Parameter-free continuous drift–diffusion models of amorphous organic semiconductors

2015 ◽  
Vol 17 (35) ◽  
pp. 22778-22783 ◽  
Author(s):  
Pascal Kordt ◽  
Sven Stodtmann ◽  
Alexander Badinski ◽  
Mustapha Al Helwi ◽  
Christian Lennartz ◽  
...  
Keyword(s):  
Organic Semiconductors ◽  
Diffusion Models ◽  
Diffusion Equations ◽  
Atomistic Simulations ◽  
Drift Diffusion ◽  
Current Voltage ◽  
Current Voltage Characteristics ◽  
Semiconducting Film

Current–voltage characteristics of an organic semiconducting film via a direct parametrization of drift–diffusion equations by atomistic simulations.

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.

The combined semi-classical and relaxation limit in a quantum hydrodynamic semiconductor model

2010 ◽  
Vol 140 (1) ◽  
pp. 119-134 ◽  
Author(s):  
Yeping Li
Keyword(s):  
Diffusion Model ◽  
Hydrodynamic Model ◽  
Drift Diffusion Model ◽  
Smooth Solutions ◽  
Drift Diffusion ◽  
One Dimensional ◽  
Quantum Hydrodynamic Model ◽  
Highly Nonlinear ◽  
Isentropic Euler Equations ◽  
Quantum Hydrodynamic

We discuss the combined semi-classical and relaxation limit of a one-dimensional isentropic quantum hydrodynamical model for semiconductors. The quantum hydrodynamic equations consist of the isentropic Euler equations for the particle density and current density, including the quantum potential and a momentum relaxation term. The momentum equation is highly nonlinear and contains a dispersive term with third-order derivatives. The equations are self-consistently coupled to the Poisson equation for the electrostatic potential. With the help of the Maxwell-type iteration, we prove that, as the relaxation time and Planck constant tend to zero, periodic initial-value problems of a scaled one-dimensional isentropic quantum hydrodynamic model have unique smooth solutions existing in the time interval where the classical drift-diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the classical drift-diffusion model from the quantum hydrodynamic model.

scholarly journals On quantum hydrodynamic and quantum energy transport models

2007 ◽  
Vol 5 (4) ◽  
pp. 887-908 ◽  
Author(s):  
Pierre Degond ◽  
Samy Gallego ◽  
Florian Mehats
Keyword(s):  
Energy Transport ◽  
Transport Models ◽  
Quantum Energy ◽  
Quantum Hydrodynamic
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