Steady state solution of the relativistic Boltzmann transport equation

1960 ◽  
Vol 11 (3) ◽  
pp. 169-175 ◽  
Author(s):  
Ivan Abonyi
Keyword(s):  
Steady State ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Steady State Solution ◽  
State Solution ◽  
Boltzmann Transport

Local Excitation as Transport Phase Transition in Phonon Systems

1977 ◽  
Vol 32 (7) ◽  
pp. 697-703
Author(s):  
Fr. Kaiser
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Steady State ◽  
Transport Equation ◽  
Thermal Equilibrium ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Local Excitation ◽  
Steady State Solutions ◽  
Transport Phase

Abstract The Peierls-Boltzmann transport equation for phonons, which was re-formulated and modified in a previous paper, is extended to be applicable to arbitrary interactions and phonon processes. As a rule, it turns out that only two types of steady state solutions are possible: hysteresis and threshold. These two solutions reveal the possibility of “transport phase transitions”, i. e. a transition from the “thermodynamic” branch to a “nonthermodynamic” one via a cumulative excitation. It is shown that both the threshold and the hysteresis situation exhibit pronounced analogies to phase transi­tions in thermal equilibrium. The dependence of the steady states from the relevant parameters is discussed.

Streamline upwind Petrov–Galerkin methods for the steady-state Boltzmann transport equation

2006 ◽  
Vol 195 (33-36) ◽  
pp. 4448-4472 ◽  
Author(s):  
C.C. Pain ◽  
M.D. Eaton ◽  
R.P. Smedley-Stevenson ◽  
A.J.H. Goddard ◽  
M.D. Piggott ◽  
...  
Keyword(s):  
Steady State ◽  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Galerkin Methods ◽  
Boltzmann Transport

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar
Keyword(s):  
Gallium Nitride ◽  
Transport Equation ◽  
Thermal Transport ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Significant Loss ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

ShengBTE: A solver of the Boltzmann transport equation for phonons

2014 ◽  
Vol 185 (6) ◽  
pp. 1747-1758 ◽  
Author(s):  
Wu Li ◽  
Jesús Carrete ◽  
Nebil A. Katcho ◽  
Natalio Mingo
Keyword(s):  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport

Chebyshev spectral hexahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation

2008 ◽  
Vol 35 (6) ◽  
pp. 1098-1108 ◽  
Author(s):  
A.G. Buchan ◽  
C.C. Pain ◽  
M.D. Eaton ◽  
R.P. Smedley-Stevenson ◽  
A.J.H. Goddard
Keyword(s):  
Transport Equation ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport
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