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research-article

Solving Non-Gray Boltzmann Transport Equation in Gallium Nitride

[+] Author and Article Information
Ajit K Vallabhaneni

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
ajitkv.purdue@gmail.com

Liang Chen

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
lchen64@gatech.edu

Man Prakash Gupta

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
mp.gupta@gatech.edu

Satish Kumar

G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
satish.kumar@me.gatech.edu

1Corresponding author.

ASME doi:10.1115/1.4036616 History: Received December 16, 2015; Revised April 24, 2017

Abstract

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at sub-micron 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 propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in the temperature prediction for a Gallium Nitride (GaN) based device. The first one is to use 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 method which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involves choosing a cutoff parameter based on the phonon mean free path. 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 multi scale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

Copyright (c) 2017 by ASME
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