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The anisotropic Fourier Heat Conduction Equation (FHCE) and the multidimensional phonon Boltzmann Transport Equation (BTE) were solved numerically in cylindrical coordinates and in time domain to simulate a Time Domain Thermo-Reflectance (TDTR) experimental silicon/aluminum substrate/transducer setup. The out-of-phase response of the probe laser was predicted at various beam offset distances for a pump laser pulse frequency of 80 MHz and modulation frequency of 10 MHz and compared against experimental measurements for a silicon substrate. The isotropic FHCE was also solved for comparison. Results show that the isotropic FHCE with bulk thermal conductivity of 145 W/m/K significantly underpredicts the out-of-phase temperature difference, particularly at smaller beam offsets. With an isotropic thermal conductivity of 105 W/m/K, the computed results match experimental data at smaller beam offsets well, but overpredicts the experimental data at larger beam offsets. An almost-perfect match is obtained by using an anisotropic thermal conductivity wherein the radial (in-plane) thermal conductivity is set to 85 W/m/K and the axial (through-plane) conductivity is set to 130 W/m/K. The multidimensional frequency and polarization dependent phonon BTE is next solved. The BTE results for the out-of-phase temperature difference match experimental observations well at small and intermediate beam offsets, but overpredicts the experimental data at larger beam offsets. FHCE results are fitted to the BTE predictions, and the extracted (best fit) thermal conductivity is found to be 110 W/m/K.
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Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium
Abstract Phonon Boltzmann transport equation (BTE) is a key tool for modeling multiscale phonon transport, which is critical to the thermal management of miniaturized integrated circuits, but assumptions about the system temperatures (i.e., small temperature gradients) are usually made to ensure that it is computationally tractable. To include the effects of large temperature non-equilibrium, we demonstrate a data-free deep learning scheme, physics-informed neural network (PINN), for solving stationary, mode-resolved phonon BTE with arbitrary temperature gradients. This scheme uses the temperature-dependent phonon relaxation times and learns the solutions in parameterized spaces with both length scale and temperature gradient treated as input variables. Numerical experiments suggest that the proposed PINN can accurately predict phonon transport (from 1D to 3D) under arbitrary temperature gradients. Moreover, the proposed scheme shows great promise in simulating device-level phonon heat conduction efficiently and can be potentially used for thermal design.
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- PAR ID:
- 10338465
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 8
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41524-022-00712-y
