Lattice Boltzmann Modeling of Subcontinuum Energy Transport in Crystalline and Amorphous Microelectronic Devices

Numerical simulations of time-dependent energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann method is derived from the continuous Boltzmann transport equation assuming first gray dispersion and then nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that a transition from diffusive to ballistic energy transport is found as the characteristic length of the system becomes comparable to the phonon mean free path. The methodology is used in representative microelectronics applications covering both crystalline and amorphous materials including silicon thin films and nanoporous silica dielectrics. Size-dependent thermal conductivity values are also computed based on steady-state temperature distributions obtained from the numerical models. For each case, reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values. Overall, simulations that consider phonon dispersion yield results more consistent with experimental correlations.

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Thin Film Phonon Heat Conduction by the Dispersion Lattice Boltzmann Method

ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 3 ◽

10.1115/ht2007-32130 ◽

2007 ◽

Author(s):

Rodrigo A. Escobar ◽

Cristina H. Amon ◽

Amador M. Guzma´n

Keyword(s):

Thin Films ◽

Thermal Conductivity ◽

Heat Conduction ◽

Lattice Boltzmann Method ◽

Thermal Energy ◽

Lattice Boltzmann ◽

Energy Transport ◽

Time Dependent ◽

Boltzmann Method ◽

Thermal Energy Transport

Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the Lattice Boltzmann Method applied to phonon transport. The discrete Lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path, and that the thermal energy transport process is characterized by the propagation of multiple, superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray Lattice Boltzmann Method.

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Estimation of an Appropriate Lattice Structure for Phonon Transport Using Lattice Boltzmann Method

Volume 4: Heat and Mass Transfer Under Extreme Conditions; Environmental Heat Transfer; Computational Heat Transfer; Visualization of Heat Transfer; Heat Transfer Education and Future Directions in Heat Transfer; Nuclear Energy ◽

10.1115/ht2013-17188 ◽

2013 ◽

Cited By ~ 2

Author(s):

Ankur Chattopadhyay ◽

Arvind Pattamatta

Keyword(s):

Thermal Conductivity ◽

Heat Conduction ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Energy Transport ◽

Lattice Structure ◽

Detailed Comparison ◽

Phonon Transport ◽

Boltzmann Transport ◽

Boltzmann Method

Heat transport at nanoscales departs substantially from the well established classical laws governing the physical processes at continuum level. The Fourier Law of heat conduction cannot be applied at sub-continuum level due to its inability in modeling non-equilibrium energy transport. Therefore one must resort to a rigorous solution to the Boltzmann Transport Equation (BTE) in the realm of nanoscale transport regime. Some recent studies show that a relatively inexpensive and accurate way to predict the behavior of sub continuum energy transport in solids is via the discrete representation of the BTE referred to as the Lattice Boltzmann method (LBM). Although quite a few numerical simulations involving LBM have been exercised in the literature, there has been no clear demonstration of the accuracy of LBM over BTE; also there exists an ambiguity over employing the right lattice configurations describing phonon transport. In the present study, the Lattice Boltzmann Method has been implemented to study phonon transport in miniaturized devices. The initial part of the study focuses upon a detailed comparison of the LBM model with that of BTE for one dimensional heat transfer involving multiple length and time scales. The second objective of the present investigation is to evaluate different lattice structures such as D1Q2, D1Q3, D2Q5, D2Q8, D2Q9 etc. for 1-D and 2-D heat conduction. In order to reduce the modeling complexity, gray model assumption based on Debye approximation is adopted throughout the analysis. Results unveil that the accuracy of solution increases as the number of lattice directions taken into account are incremented from D2Q5 to D2Q9. A substantial increase in solution time with finer directional resolutions necessitates an optimum lattice. A novel lattice dimension ‘Mod D2Q5’ has been suggested and its performance is also compared with its compatriots. It is also demonstrated that the inclusion of the center point within a particular lattice structure can play a significant role in the prediction of thermal conductivity in the continuum level. However, as the size of the device comes down to allow high Knudsen numbers, in the limiting case of ballistic phonon transport, the choice of lattice seems to have negligible effect on thermal conductivity.

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Thin Film Phonon Heat Conduction by the Dispersion Lattice Boltzmann Method

Journal of Heat Transfer ◽

10.1115/1.2944249 ◽

2008 ◽

Vol 130 (9) ◽

Cited By ~ 22

Author(s):

Rodrigo A. Escobar ◽

Cristina H. Amon

Keyword(s):

Thin Films ◽

Thermal Conductivity ◽

Heat Conduction ◽

Lattice Boltzmann Method ◽

Thermal Energy ◽

Lattice Boltzmann ◽

Energy Transport ◽

Time Dependent ◽

Boltzmann Method ◽

Thermal Energy Transport

Numerical simulations of time-dependent thermal energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann Method is derived from the continuous Boltzmann transport equation assuming nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that the heat conduction in silicon thin films displays a transition from diffusive to ballistic energy transport as the characteristic length of the system becomes comparable to the phonon mean free path and that the thermal energy transport process is characterized by the propagation of multiple superimposed phonon waves. The methodology is used to characterize the time-dependent temperature profiles inside films of decreasing thickness. Thickness-dependent thermal conductivity values are computed based on steady-state temperature distributions obtained from the numerical models. It is found that reducing feature size into the subcontinuum regime decreases thermal conductivity when compared to bulk values, at a higher rate than what was displayed by the Debye-based gray lattice Boltzmann method.

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Numerical prediction of effective thermal conductivity of ceramic fiber board using lattice Boltzmann method

Numerical Heat Transfer Part A Applications ◽

10.1080/10407782.2018.1523599 ◽

2018 ◽

Vol 74 (6) ◽

pp. 1285-1300 ◽

Cited By ~ 4

Author(s):

Mazhar Hussain ◽

Wen-Quan Tao

Keyword(s):

Thermal Conductivity ◽

Lattice Boltzmann Method ◽

Effective Thermal Conductivity ◽

Lattice Boltzmann ◽

Numerical Prediction ◽

Ceramic Fiber ◽

Boltzmann Method

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Lattice Boltzmann method simulation of the gas heat conduction of nanoporous material

Thermal Science ◽

10.2298/tsci180906102h ◽

2020 ◽

Vol 24 (6 Part A) ◽

pp. 3749-3756

Author(s):

Ya Han ◽

Shuai Li ◽

Hai-Dong Liu ◽

Weipeng Cui

Keyword(s):

Thermal Conductivity ◽

Heat Conduction ◽

Lattice Boltzmann Method ◽

Knudsen Number ◽

Lattice Boltzmann ◽

Size Effects ◽

Temperature Jump ◽

Boundary Scattering ◽

Nanoporous Material ◽

Boltzmann Method

In order to deeply investigate the gas heat conduction of nanoporous aerogel, a model of gas heat conduction was established based on microstructure of aerogel. Lattice Boltzmann method was used to simulate the temperature distribution and gas thermal conductivity at different size, and the size effects of gas heat conduction have had been obtained under micro-scale conditions. It can be concluded that the temperature jump on the boundary was not obvious and the thermal conductivity remained basically constant when the value of Knudsen number was less than 0.01; as the value of Knudsen number increased from 0.01 to 0.1, there was a clear temperature jump on the boundary and the thermal conductivity tended to decrease and the effect of boundary scattering increased drastically, as the value of Knudsen number was more than 0.1, the temperature jump increased significantly on the boundary, furtherly, the thermal conductivity decreased dramatically, and the size effects were significantly.

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