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.
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Solving Nongray Boltzmann Transport Equation in Gallium Nitride
Ajit K. Vallabhaneni,
Ajit K. Vallabhaneni
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: ajitkvallabhaneni@gmail.com
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: ajitkvallabhaneni@gmail.com
Search for other works by this author on:
Liang Chen,
Liang Chen
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Search for other works by this author on:
Man P. Gupta,
Man P. Gupta
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
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Satish Kumar
Satish Kumar
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Search for other works by this author on:
Ajit K. Vallabhaneni
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: ajitkvallabhaneni@gmail.com
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: ajitkvallabhaneni@gmail.com
Liang Chen
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Man P. Gupta
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Satish Kumar
G. W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 16, 2015; final manuscript received April 24, 2017; published online June 6, 2017. Assoc. Editor: Alan McGaughey.
J. Heat Transfer. Oct 2017, 139(10): 102701 (8 pages)
Published Online: June 6, 2017
Article history
Received:
December 16, 2015
Revised:
April 24, 2017
Citation
Vallabhaneni, A. K., Chen, L., Gupta, M. P., and Kumar, S. (June 6, 2017). "Solving Nongray Boltzmann Transport Equation in Gallium Nitride." ASME. J. Heat Transfer. October 2017; 139(10): 102701. https://doi.org/10.1115/1.4036616
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