Coupled drift-diffusion (DD) and multi-subband Boltzmann transport equation (MSBTE) solver for 3D multi-gate transistors

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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ShengBTE: A solver of the Boltzmann transport equation for phonons

Computer Physics Communications ◽

10.1016/j.cpc.2014.02.015 ◽

2014 ◽

Vol 185 (6) ◽

pp. 1747-1758 ◽

Cited By ~ 845

Author(s):

Wu Li ◽

Jesús Carrete ◽

Nebil A. Katcho ◽

Natalio Mingo

Keyword(s):

Transport Equation ◽

Boltzmann Transport Equation ◽

Boltzmann Transport

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

IEEE Transactions on Nanotechnology ◽

10.1109/tnano.2013.2237924 ◽

2013 ◽

Vol 12 (2) ◽

pp. 168-173 ◽

Cited By ~ 7

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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Chebyshev spectral hexahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation

Annals of Nuclear Energy ◽

10.1016/j.anucene.2007.08.021 ◽

2008 ◽

Vol 35 (6) ◽

pp. 1098-1108 ◽

Cited By ~ 4

Author(s):

A.G. Buchan ◽

C.C. Pain ◽

M.D. Eaton ◽

R.P. Smedley-Stevenson ◽

A.J.H. Goddard

Keyword(s):

Transport Equation ◽

Boltzmann Transport Equation ◽

Boltzmann Transport

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Evaluation of quasi-ballistic transport in nano-MOSFETs by deterministic solver of the time dependent multi-subbands Boltzmann Transport Equation

2011 IEEE International Conference of Electron Devices and Solid-State Circuits ◽

10.1109/edssc.2011.6117726 ◽

2011 ◽

Author(s):

Yong Wang ◽

Tiao Lu ◽

Xiaoyan Liu ◽

Gang Du

Keyword(s):

Transport Equation ◽

Ballistic Transport ◽

Boltzmann Transport Equation ◽

Time Dependent ◽

Boltzmann Transport

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PERFORMANCE LIMITS OF SIMULATION MODELS FOR NOISE CHARACTERIZATION OF MM WAVE DEVICES

Fluctuation and Noise Letters ◽

10.1142/s0219477507003957 ◽

2007 ◽

Vol 07 (03) ◽

pp. L299-L312

Author(s):

ALI ABOU-ELNOUR

Keyword(s):

Boltzmann Transport Equation ◽

Simulation Models ◽

Two Dimensions ◽

Boltzmann Transport ◽

Performance Limits ◽

Drift Diffusion ◽

Model Equations ◽

Accuracy Of Results ◽

Noise Characterization

Based on Boltzmann transport equation, the drift-diffusion, hydrodynamic, and Monte-Carlo physical simulators are accurately developed. For each simulator, the model equations are self-consistently solved with Poisson equation, and with Schrödinger equation when quantization effects take place, in one and two-dimensions to characterize the operation and optimize the structure of mm-wave devices. The effects of the device dimensions, biasing conditions, and operating frequencies on the accuracy of results obtained from the simulators are thoroughly investigated. Based on physical understanding of the models, the simulation results are analyzed to fully determine the limits at which a certain device simulator can be accurately and efficiently used to characterize the noise behavior of mm-wave devices.

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

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.777.421 ◽

2018 ◽

Vol 777 ◽

pp. 421-425 ◽

Cited By ~ 1

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.

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