scholarly journals A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

2015 ◽  
Vol 117 (13) ◽  
pp. 135102 ◽  
Author(s):  
Jesse Maassen ◽  
Mark Lundstrom
Keyword(s):  
Transport Equation ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport

Study of an Iterative Solution for Boltzmann Transport Equation and Calculation of Thermal Conductivity

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Iterative Method ◽  
Transport Equation ◽  
Linear Systems ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Boltzmann Transport

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.

Simulations of Heat Transport During Transient Electrostatic Discharge Events in a Sub-Micron Transistor

Volume 4 ◽  
2004 ◽  
Author(s):  
Sreekant V. J. Narumanchi ◽  
Jayathi Y. Murthy ◽  
Cristina H. Amon
Keyword(s):  
Transport Equation ◽  
Heat Transport ◽  
Electrostatic Discharge ◽  
Boltzmann Transport Equation ◽  
The Other ◽  
Comprehensive Model ◽  
Boltzmann Transport ◽  
Thermal Problem ◽  
Model Based ◽  
Silicon Transistors

The thermal problem associated with the transient electrostatic discharge phenomena in sub-micron silicon transistors is fast becoming a major reliability concern in IC packages. Currently, Fourier diffusion and some simple models based on the solution to the phonon Boltzmann transport equation (BTE) are used to predict failure (melting of silicon) in these transistors. In this study, a more comprehensive model, based on the phonon BTE and incorporating considerable details of phonon physics, is proposed and used to study the ESD problem. Transient results from the model reveal very significant discrepancies when compared to results from the other models in the literature.

Analytical Solutions of Enhanced Gray Boltzmann Transport Equation on Transient Thermal Grating and Time-Domain Thermoreflectance Experiments

2017 ◽  
Author(s):  
Dadong Wang ◽  
Zhengxian Qu ◽  
Yanbao Ma
Keyword(s):  
Experimental Data ◽  
Data Analysis ◽  
Transport Equation ◽  
Heat Transport ◽  
Analytical Solutions ◽  
Time Domain ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Transient Thermal ◽  
Experimental Data Analysis

As reported by many studies, Fourier’s law breaks down in micro/nanoscale due to the nondiffusive heat transport. To account for the nondiffusive heat transport, high-fidelity nondiffusive models with good efficiency for the experimental data analysis in nanothermometry are necessary but unfortunately missing. In this paper, based on a validated enhance Gray Boltzmann transport equation, we offer the analytical solutions for two important nanothermometry techniques, namely the transient thermal gratings (TTG) and time-domain thermoreflectance (TDTR) experiments. The analytical solutions obtained by inverse Fourier transform are compared to the experimental signals in both TTG and TDTR cases. The excellent agreements between the analytical solutions and the experiments demonstrate the applicability of the EG-BTE in experimental data analysis as an efficient replacement of Fourier’s law.

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
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