Discrete duality finite volume schemes for two-dimensional drift-diffusion and energy-transport models

2009 ◽  
Vol 59 (3) ◽  
pp. 239-257 ◽  
Author(s):  
C. Chainais-Hillairet
Keyword(s):  
Finite Volume ◽  
Energy Transport ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Drift Diffusion ◽  
Transport Models

scholarly journals Formulation of Macroscopic Transport Models for Numerical Simulation of Semiconductor Devices

VLSI Design ◽  
1995 ◽  
Vol 3 (2) ◽  
pp. 211-224 ◽  
Author(s):  
Edwin C. Kan ◽  
Zhiping Yu ◽  
Robert W. Dutton ◽  
Datong Chen ◽  
Umberto Ravaioli
Keyword(s):  
Numerical Simulation ◽  
Computational Efficiency ◽  
Recent Progress ◽  
Energy Transport ◽  
Semiconductor Devices ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Drift Diffusion ◽  
Thermoelectric Effects ◽  
Transport Models

According to different assumptions in deriving carrier and energy flux equations, macroscopic semiconductor transport models from the moments of the Boltzmann transport equation (BTE) can be divided into two main categories: the hydrodynamic (HD) model which basically follows Bløtekjer's approach [1, 2], and the Energy Transport (ET) model which originates from Strattton's approximation [3, 4]. The formulation, discretization, parametrization and numerical properties of the HD and ET models are carefully examined and compared. The well-known spurious velocity spike of the HD model in simple nin structures can then be understood from its formulation and parametrization of the thermoelectric current components. Recent progress in treating negative differential resistances with the ET model and extending the model to thermoelectric simulation is summarized. Finally, we propose a new model denoted by DUET (Dual ET)which accounts for all thermoelectric effects in most modern devices and demonstrates very good numerical properties. The new advances in applicability and computational efficiency of the ET model, as well as its easy implementation by modifying the conventional drift-diffusion (DD) model, indicate its attractiveness for numerical simulation of advanced semiconductor devices

scholarly journals Simulating Quasi-ballistic Transport in Si Nanotransistors

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 5-13 ◽  
Author(s):  
Kausar Banoo ◽  
Jung-Hoon Rhew ◽  
Mark Lundstrom ◽  
Chi-Wang Shu ◽  
Joseph W. Jerome
Keyword(s):  
Numerical Simulation ◽  
Energy Transport ◽  
Ballistic Transport ◽  
Mean Free Path ◽  
Simulation Methods ◽  
Field Region ◽  
Drift Diffusion ◽  
Transport Models ◽  
Low Field ◽  
Hydrodynamic Energy

Electron transport in model Si nanotransistors is examined by numerical simulation using a hierarchy of simulation methods, from full Boltzmann, to hydrodynamic, energy transport, and drift-diffusion. The on-current of a MOSFET is shown to be limited by transport across a low-field region about one mean-free-path long and located at the beginning of the channel. Commonly used transport models based on simplified solutions of the Boltzmann equation are shown to fail under such conditions. The cause for this failure is related to the neglect of the carriers' drift energy and to the collision-dominated assumptions typically used in the development of simplified transport models.

scholarly journals A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model

2020 ◽  
Author(s):  
Clément Cancès ◽  
Claire Chainais-Hillairet ◽  
Jürgen Fuhrmann ◽  
Benoît Gaudeul
Keyword(s):  
Stability Analysis ◽  
Numerical Analysis ◽  
Finite Volume ◽  
Numerical Experiments ◽  
Chemical Potential ◽  
Existence Results ◽  
Drift Diffusion Model ◽  
Finite Volume Schemes ◽  
Drift Diffusion ◽  
Charged Species

Abstract In this paper we consider a unipolar degenerate drift-diffusion system where the relation between the concentration of the charged species $c$ and the chemical potential $h$ is $h(c)=\log \frac{c}{1-c}$. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes.

scholarly journals A Stability Analysis of Finite-Volume Advection Schemes Permitting Long Time Steps

2007 ◽  
Vol 135 (7) ◽  
pp. 2658-2673 ◽  
Author(s):  
Peter Hjort Lauritzen
Keyword(s):  
Stability Analysis ◽  
Finite Volume ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Courant Number ◽  
Von Neumann ◽  
Dispersion Properties ◽  
Advection Schemes ◽  
Long Time ◽  
The Stability

Abstract Finite-volume schemes developed in the meteorological community that permit long time steps are considered. These include Eulerian flux-form schemes as well as fully two-dimensional and cascade cell-integrated semi-Lagrangian (CISL) schemes. A one- and two-dimensional Von Neumann stability analysis of these finite-volume advection schemes is given. Contrary to previous analysis, no simplifications in terms of reducing the formal order of the schemes, which makes the analysis mathematically less complex, have been applied. An interscheme comparison of both dissipation and dispersion properties is given. The main finding is that the dissipation and dispersion properties of Eulerian flux-form schemes are sensitive to the choice of inner and outer operators applied in the scheme that can lead to increased numerical damping for large Courant numbers. This spurious dependence on the integer value of the Courant number disappears if the inner and outer operators are identical, in which case, under the assumptions used in the stability analysis, the Eulerian flux-form scheme becomes identical to the cascade scheme. To explain these properties a conceptual interpretation of the flux-based Eulerian schemes is provided. Of the two CISL schemes, the cascade scheme has superior stability properties.

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