Modeling and Simulation of 3D Subcontinuum Phonon Energy Transport Using Lattice Boltzmann Method
Date Issued
2011
Date
2011
Author(s)
Hu, Chia-Li
Abstract
The feature size of electronic devices in current integrated circuits has become comparable to or even smaller than the mean free path (MFP) of the energy carrier. It has been well known that the continuum-based Fourier heat conduction law may lead to erroneous results when the phonon mean free path becomes comparable or larger than the characteristic size of the material studied. The prevailing approach to calculate the thermal conductivity of semiconductors and dielectric materials is based on phonon Boltzmann transport equation as the energy carriers at temperatures of interest are phonons.
In this thesis, an efficient three-dimensional lattice Boltzmann method based on the phonon Boltzmann-BGK transport equation is developed for solving energy transfer in the subcontinuum regime. The lattice Boltzmann method is derived by expanding the phonon Bose-Einstein distribution in the tensor Hermite polynomials space and standard D3Q19 lattice model is employed. Depending on the order of expansion adopted, different level of approximation of the transport phenomenon can be modeled. The implementations of periodic boundary conditions and constant temperature wall conditions are described. The present phonon lattice Boltzmann method is validated against existing direct discrete ordinate method by modeling and simulation of thermal conductivities for two-dimensional problems. Modeling and simulations of the micro-/nano-scale phonon energy transfer covering broad range of Knudsen numbers range are presented. It is found that the present lattice Boltzmann method solutions are in good agreement with those from the discrete ordinate phonon Boltzmann solver. Results suggest that reducing feature size will decrease the thermal conductivity, and temperature will become non-continuum distributions in the interface. And the effective thermal conductivity changes not only with the length of the thin film, but also with the boundary thermal resistance.
Subjects
Phonon Boltzmann Transport
Subcontinuum Regime Heat Transfer
Thermal Conductivity
Lattice Boltzmann Method
Hermite Tensor Polynomials
Type
thesis
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