scholarly journals A New Concept for Solving the Boltzmann Transport Equation in Ultra-fast Transient Situations

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 217-222
Author(s):  
Ming-C. Cheng
Keyword(s):  
Distribution Function ◽  
Equilibrium Distribution ◽  
Electron Distribution Function ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Equilibrium Distribution Function ◽  
Boltzmann Transport ◽  
Hydrodynamic Parameters ◽  
Lower Conduction Band ◽  
Rapid Changes

A concept based on relaxation of the hydrodynamic parameters is introduced to arrive at a computational model for the extreme non-equilibrium distribution function of carriers in multi-valley bandstructure. The relaxation times are taken to describe the evolution scale of the distribution function. The developed model is able to account for transport phenomena at the momentum relaxation scale. The model, together with the Monte Carlo simulation, is applied to obtain the electron distribution function in each valley of the lower conduction band in GaAs, and to study the evolution of the distribution function in GaAs subjected to rapid changes in field.

scholarly journals Validity of the molecular-dynamics-lattice-gas global equilibrium distribution function

2019 ◽  
Vol 30 (10) ◽  
pp. 1941007 ◽  
Author(s):  
M. Reza Parsa ◽  
Aleksandra Pachalieva ◽  
Alexander J. Wagner
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Lattice Gas ◽  
Equilibrium Distribution ◽  
Coarse Graining ◽  
High Volume ◽  
Equilibrium Distribution Function ◽  
Theory Approach ◽  
Lattice Boltzmann Methods ◽  
Definition Of

The molecular-dynamics-lattice-gas (MDLG) method establishes a direct link between a lattice-gas method and the coarse-graining of a molecular dynamics (MD) approach. Due to its connection to MD, the MDLG rigorously recovers the hydrodynamics and allows to validate the behavior of the lattice-gas or lattice-Boltzmann methods directly without using the standard kinetic theory approach. In this paper, we show that the analytical definition of the equilibrium distribution function remains valid even for very high volume fractions.

A LATTICE BGK MODEL FOR SIMULATING SOLITARY WAVES OF THE COMBINED KdV–MKDV EQUATION

2011 ◽  
Vol 25 (04) ◽  
pp. 589-597 ◽  
Author(s):  
CHANGFENG MA
Keyword(s):  
Distribution Function ◽  
Solitary Waves ◽  
Equilibrium Distribution ◽  
Local Equilibrium ◽  
Mkdv Equation ◽  
Equilibrium Distribution Function ◽  
Bgk Model ◽  
Theoretical Results

A lattice BGK model for simulating solitary waves of the combined KdV–MKDV equation, ut+αuux-βu2ux+δuxxx = 0, is established. The tunable parameters in Chapman–Enskog expansion of the local equilibrium distribution function are determined by the coefficient of the combined KdV–MKDV equation. Simulating results fit close in with the theoretical results.

scholarly journals Spherical Harmonic Modeling of a 0.05 μm Base BJT: A Comparison with Monte Carlo and Asymptotic Analysis

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 147-151 ◽  
Author(s):  
C.-H. Chang ◽  
C.-K. Lin ◽  
N. Goldsman ◽  
I. D. Mayergoyz
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Band Structure ◽  
Asymptotic Analysis ◽  
Energy Distribution ◽  
Transport Equation ◽  
Spherical Harmonic ◽  
Boltzmann Transport Equation ◽  
System Of Equations ◽  
Boltzmann Transport

We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm base BJT. We find the SH and the MC methods give very similar results for the energy distribution function, using an analytical band-structure, at all points within the tested devices. However, the SH method can be as much as seven thousand times faster than the MC approach for solving an identical problem. We explain the agreement by asymptotic analysis of the system of equations generated by the SH expansion of the BTE.

scholarly journals Inverse Chapman–Enskog Derivation of the Thermohydrodynamic Lattice-BGK Model for the Ideal Gas

1998 ◽  
Vol 09 (08) ◽  
pp. 1231-1245 ◽  
Author(s):  
B. M. Boghosian ◽  
P. V. Coveney
Keyword(s):  
Thermal Conductivity ◽  
Distribution Function ◽  
Relaxation Time ◽  
Equilibrium Distribution ◽  
Transport Coefficients ◽  
Ideal Gas ◽  
Equilibrium Distribution Function ◽  
Bgk Model ◽  
Constant Relaxation Time ◽  
The Ideal

A thermohydrodynamic lattice-BGK model for the ideal gas was derived by Alexander et al. in 1993, and generalized by McNamara et al. in the same year. In these works, particular forms for the equilibrium distribution function and the transport coefficients were posited and shown to work, thereby establishing the sufficiency of the model. In this paper, we rederive the model from a minimal set of assumptions, and thereby show that the forms assumed for the shear and bulk viscosities are also necessary, but that the form assumed for the thermal conductivity is not. We derive the most general form allowable for the thermal conductivity, and the concomitant generalization of the equilibrium distribution. In this way, we show that it is possible to achieve variable (albeit density-dependent) Prandtl number even within a single-relaxation-time lattice-BGK model. We accomplish this by demanding analyticity of the third moments and traces of the fourth moments of the equilibrium distribution function. The method of derivation demonstrates that certain undesirable features of the model — such as the unphysical dependence of the viscosity coefficients on temperature — cannot be corrected within the scope of lattice-BGK models with constant relaxation time.

Numerical Analysis of Electro-Thermal Phenomena in Metal by Boltzmann Transport Equation for Electron

2005 ◽  
Author(s):  
Kohei Ito ◽  
Ryohei Muramoto ◽  
Isamu Shiozawa ◽  
Yasushi Kakimoto ◽  
Takashi Masuoka
Keyword(s):  
Transport Equation ◽  
Equilibrium Distribution ◽  
Boltzmann Transport Equation ◽  
Quasi Equilibrium ◽  
Boltzmann Transport ◽  
Simulation Based ◽  
Far From Equilibrium ◽  
New Formulation ◽  
Thermal Phenomena ◽  
Non Equilibrium

By the development of micro-fabrication technology, much smaller-size electronic devices will be soon available. In such a smaller device, a non-equilibrium state might appear in metal and/or semiconductor. In this case, it is difficult to estimate the device performance by the macroscopic transport equations that assume quasi-equilibrium distribution. We are developing a numerical simulation based on Boltzmann transport equation (BTE), which can analyze thermal and electric phenomena even when the state is far from equilibrium. In this study, we show a new formulation of BTE for free electron in metal and its calculation result: the thermoelectric power obtained agreed with that of experimental value: the heat flux derived by the non-equilibrium distribution was two-orders small than that estimated by thermal conductivity.

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