Breakdown of the linear approximation to the Boltzmann transport equation in quasi-one-dimensional semiconductors

1989 ◽  
Vol 39 (11) ◽  
pp. 8025-8028 ◽  
Author(s):  
S. Briggs ◽  
J. P. Leburton
Keyword(s):  
Transport Equation ◽  
Linear Approximation ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
One Dimensional

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.

scholarly journals Self-Consistent Solution of the Multi Band Boltzmann, Poisson and Hole-Continuity Equations

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 257-260
Author(s):  
Surinder P. Singh ◽  
Neil Goldsman ◽  
Isaak D. Mayergoyz
Keyword(s):  
Boltzmann Transport Equation ◽  
The Novel ◽  
Boltzmann Transport ◽  
One Dimensional ◽  
Bipolar Junction Transistor ◽  
Continuity Equations ◽  
The Poisson Equation ◽  
Curvilinear Grid ◽  
Consistent Solution ◽  
Junction Transistor

The Boltzmann transport equation (BTE) for multiple bands is solved by the spherical harmonic approach. The distribution function is obtained for energies greater than 3 eV. The BTE is solved self consistently with the Poisson equation for a one dimensional npn bipolar junction transistor (BJT). The novel features are: the use of boundary fitted curvilinear grid, and Scharfetter Gummel type discretization of the BTE.

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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