Analytical Solutions of the Boltzmann Transport Equation. I. Carrier Transport Phenomena in Nondegenerate Semiconductors at Low Fields

1971 ◽  
Vol 4 (8) ◽  
pp. 2524-2534 ◽  
Author(s):  
H. C. Law ◽  
K. C. Kao
Keyword(s):  
Transport Equation ◽  
Analytical Solutions ◽  
Carrier Transport ◽  
Transport Phenomena ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport

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.

Sign in / Sign up

Export Citation Format

Share Document