Parallel Computation of the Phonon Boltzmann Transport Equation

2009 ◽  
Vol 55 (6) ◽  
pp. 435-456 ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Author(s):  
Syed A. Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan

Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In this article, strategies and algorithms for large-scale parallel computation of the phonon BTE are presented. An unstructured finite volume method for spatial discretization is coupled with the control angle discrete ordinates method for angular discretization. The single-time relaxation approximation is used to treat phonon-phonon scattering. Both dispersion and polarization of the phonons are accounted for. Three different parallelization strategies are explored: (a) band-based, (b) direction-based, and (c) hybrid band/cell-based. Subsequent to validation studies in which silicon thin-film thermal conductivity was successfully predicted, transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral cells. The angular space was discretized using 400 angles, and the spectral space was discretized into 40 spectral intervals (bands). This resulted in ∼9.7×109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-based and hybrid band/cell-based parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy — about 88% — was found to be superior to that of the direction-based strategy, and is recommended as the preferred strategy for even larger scale computations.


2014 ◽  
Vol 86 ◽  
pp. 341-351 ◽  
Author(s):  
Syed Ashraf Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan ◽  
Arpit Mittal

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar

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.


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

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

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