PARALLEL COMPUTATION OF THE PHONON BOLTZMANN TRANSPORT EQUATION FOR THE PREDICTION OF THERMAL TRNSPORT ACROSS SILICON/GERMANIUM INTERFACES

2015 ◽  
Author(s):  
Syed Ashraf Ali ◽  
Sandip Mazumder
Keyword(s):  
Transport Equation ◽  
Parallel Computation ◽  
Silicon Germanium ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport

Prediction of Non-Equilibrium Heat Conduction Using Parallel Computation of the Phonon Boltzmann Transport Equation

2014 ◽  
Author(s):  
Syed A. Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Parallel Computation ◽  
Large Scale ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Computational Time ◽  
Spectral Space ◽  
Boltzmann Transport ◽  
Non Equilibrium

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.

Large-scale parallel computation of the phonon Boltzmann Transport Equation

2014 ◽  
Vol 86 ◽  
pp. 341-351 ◽  
Author(s):  
Syed Ashraf Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan ◽  
Arpit Mittal
Keyword(s):  
Transport Equation ◽  
Parallel Computation ◽  
Large Scale ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport

Phonon Heat Conduction in Multidimensional Heterostructures: Predictions Using the Boltzmann Transport Equation

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Syed Ashraf Ali ◽  
Sandip Mazumder
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Silicon Germanium ◽  
Large Scale ◽  
Boltzmann Transport Equation ◽  
Three Dimensional ◽  
Interfacial Thermal Resistance ◽  
Boltzmann Transport ◽  
Interfacial Resistance ◽  
Silicon And Germanium

In this article, two models for phonon transmission across semiconductor interfaces are investigated and demonstrated in the context of large-scale spatially three-dimensional calculations of the phonon Boltzmann transport equation (BTE). These include two modified forms of the classical diffuse mismatch model (DMM): one, in which dispersion is accounted for and another, in which energy transfer between longitudinal acoustic (LA) and transverse acoustic (TA) phonons is disallowed. As opposed to the vast majority of the previous studies in which the interface is treated in isolation, and the thermal boundary conductance is calculated using closed-form analytical formulations, the present study also considers the interplay between the interface and intrinsic (volumetric) scattering of phonons. This is accomplished by incorporating the interface models into a parallel solver for the full seven-dimensional BTE for phonons. A verification study is conducted in which the thermal boundary resistance of a silicon/germanium interface is compared against the previously reported results of molecular dynamics (MD) calculations. The BTE solutions overpredicted the interfacial resistance, and the reasons for this discrepancy are discussed. It is found that due to the interplay between intrinsic and interface scattering, the interfacial thermal resistance across a Si(hot)/Ge(cold) bilayer is different from that of a Si(cold)/Ge(hot) bilayer. Finally, the phonon BTE is solved for a nanoscale three-dimensional heterostructure, comprised of multiple blocks of silicon and germanium, and the time evolution of the temperature distribution is predicted and compared against predictions using the Fourier law of heat conduction.

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

Simulation Study of Quasi-Ballistic Transport in Asymmetric DG-MOSFET by Directly Solving Boltzmann Transport Equation

2013 ◽  
Vol 12 (2) ◽  
pp. 168-173 ◽  
Author(s):  
Gai Liu ◽  
Gang Du ◽  
Tiao Lu ◽  
Xiaoyan Liu ◽  
Pingwen Zhang ◽  
...  
Keyword(s):  
Transport Equation ◽  
Simulation Study ◽  
Ballistic Transport ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Dg Mosfet
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