Geometry-Dependent Thermal Transport in Porous Silicon: A Computational Study of Pore Geometry and Porosity Effects
DOI:
https://doi.org/10.51646/jsesd.v14iSTR2E.1180Keywords:
Boltzmann transport equation; Thermal transport; Porous Silicon; Thermal management; SemiconductorAbstract
This study investigates how pore geometry and porosity modulate the thermal conductivity and heat transfer characteristics of porous silicon. Leveraging OpenBTE—an open-source computational tool based on the Boltzmann Transport Equation (BTE)—the research analyzes three distinct pore geometries (circular, rectangular, and hexagonal) with porosity ranging from 5% to 45% in order to quantify their impact on phonon-mediated thermal transport. The results shown a clear dependence of thermal conductivity on pore shape and porosity. Rectangular pores showed the highest thermal conductivity, ranging from 64.4 W/(m·K) at 5% porosity to 26.7 W/(m·K) at 45%. Circular pores yielded intermediate thermal conductivity values, varying from 56.8 W/(m·K) at 5% to 9.5 W/(m·K) at 45%. Hexagonal pores show the lowest thermal conductivity, ranging from 54.6 W/(m·K) to 7.2 W/(m·K). These insights demonstrate the critical role of pore architecture in tailoring heat dissipation pathways, providing actionable guidelines for engineering optimized pore networks. Experimental results advance the understanding of structure-property relationships in porous materials, enabling precise control over thermal performance for applications in thermoelectric, microelectronics, and energy-efficient systems.
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J. Chen and X. Zhang, "Pore-size dependence of the heat conduction in porous silicon and phonon spectral energy density analysis," Physics Letters A, vol. 384, no. 21, p. 126503, 2020. doi: 10.1016/j.physleta.2020.126503
Y. Belaroussi, "High performance porous silicon substrate for the integration of millimeter-wave passive devices," Przegląd Elektrotechniczny, July 2024. doi: 10.15199/48.2024.07.48
E. Amin-Chalhoub et al., "Thermal conductivity measurement of porous silicon by the pulsed-photothermal method," J. Phys. D: Appl. Phys., vol. 44, no. 35, p. 355401, Aug. 2011, doi: 10.1088/0022-3727/44/35/355401.
G. Romano, "Openbte: a solver for ab-initio phonon transport in multidimensional structures," arXiv preprint arXiv:2106.02764, 2021. https://doi.org/10.48550/arXiv.2106.02764
S. A. Hosseini, S. Khanniche, P. A. Greaney, and G. Romano, "Universal effective medium theory to predict the thermal conductivity in nanostructured materials," International Journal of Heat and Mass Transfer, vol. 183, p. 122040, 2022. https://doi.org/10.3390/thermo4010004
M. Isaiev, N. Kyrychenko, V. Kuryliuk, and D. Lacroix, "Features of phonon scattering by a spherical pore: Molecular dynamics insight," Applied Physics Letters, vol. 124, no. 14, p. 142202, 2024.
Z. Deng, X. Liu, Y. Huang, C. Zhang, and Y. Chen, "Heat Conduction in Porous Media Characterized by Fractal Geometry," Energies, vol. 10, p. 1230, 2017. https://doi.org/10.3390/en10081230
A. Pavlenko, "Heat and Mass Transfer in Porous Materials," Materials, vol. 16, p. 5591, 2023. https://doi.org/10.3390/ma16165591
A. Jain, Y.-J. Yu, and A. J. H. McGaughey, "Phonon transport in periodic silicon nanoporous films with feature sizes greater than 100 nm," Physical Review B, vol. 87, p. 195301, 2013. https://doi.org/10.1103/PhysRevB.87.195301
W. Xing, Y. Xu, C. Song, and T. Deng, "Recent Advances in Thermal Interface Materials for Thermal Management of High-Power Electronics," Nanomaterials, vol. 12, p. 3365, 2022. https://doi.org/10.3390/nano12193365
M. Kashiwagi, Y. Sudo, T. Shiga, and J. Shiomi, "Modeling Heat Conduction in Nanoporous Silicon with Geometry Distributions," Physical Review Applied, 2018. DOI: https://doi.org/10.1103/PhysRevApplied.10.044018
U. Ijaz, M. Siyar, and C. Park, "The power of pores: review on porous thermoelectric materials," RSC Sustainability, vol. 2, no. 4, pp. 852-870, 2024. doi: 10.1039/D3SU00451A
A. S. Fedorov and A. S. Teplinskaia, "Thermal Properties of Porous Silicon Nanomaterials," Materials, vol. 15, no. 23, p. 8678, Dec. 2022. https://doi.org/10.3390/ma15238678
J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids, Oxford University Press, 2001. https://doi.org/10.1093/acprof:oso/9780198507796.001.0001
J.-P. M. Péraud, C. D. Landon, and N. G. Hadjiconstantinou, "Monte carlo methods for solving the boltzmann transport equation," Annual Review of Heat Transfer, vol. 17, pp. 205–265, 2014. doi: 10.1615/AnnualRevHeatTransfer.2014007381
W. Cheng, A. Alkurdi, and P.-O. Chapuis, "Coupling Mesoscopic Boltzmann Transport Equation and Macroscopic Heat Diffusion Equation for Multiscale Phonon Heat Conduction," Nanoscale and Microscale Thermophysical Engineering, vol. 24, no. 3-4, pp. 150-167, 2020. doi: 10.1080/15567265.2020.1836095
Z. Wang, J. E. Alaniz, W. Jang, J. E. Garay, and C. Dames, "Thermal Conductivity of Nanocrystalline Silicon: Importance of Grain Size and Frequency-Dependent Mean Free Paths," Nano Letters, vol. 11, no. 6, pp. 2206-2213, Jun. 2011. doi: 10.1021/nl1045395
S. Mazumder and A. Majumdar, "Monte Carlo study of phonon transport in solid thin films including dispersion and polarization," Journal of Heat Transfer, vol. 123, pp. 749-759, 2001. https://doi.org/10.1115/1.1377018
Q. Hao, G. Chen, and M.-S. Jeng, "Frequency-dependent Monte Carlo simulations of phonon transport in two-dimensional porous silicon with aligned pores," Journal of Applied Physics, vol. 106, p. 114321, 2009. https://doi.org/10.1063/1.3266169
C. Ni and J. Y. Murthy, "Parallel computation of the phonon Boltzmann transport equation," Numerical Heat Transfer, Part B, vol. 55, pp. 435-456, 2009. DOI:10.1080/10407780902864771
S. V. J. Narumanchi, J. Y. Murthy, and C. H. Amon, "Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors," Journal of Heat Transfer, vol. 127, no. 7, pp. 713-723, Jul. 2005. doi: 10.1115/1.1924571
D. Lacroix, K. Joulain, and D. Lemonnier, "Monte Carlo transient phonon transport in silicon and germanium at nanoscales," Physical Review B, vol. 72, p. 064305, 2005. https://doi.org/10.1103/PhysRevB.72.064305
A. Mittal and S. Mazumder, "Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons," Journal of Heat Transfer, vol. 132, p. 052402, 2010. https://doi.org/10.1115/1.4000447
G. Romano, "Efficient calculations of the mode-resolved ab-initio thermal conductivity in nanostructures," arXiv preprint arXiv:2002.08940, 2020. DOI: 10.48550/arXiv.2105.08181
R. A. Duncan et al., "Thermal transport in nanoporous holey silicon membranes investigated with optically induced transient thermal gratings," Journal of Applied Physics, vol. 128, p. 235106, 2020. https://doi.org/10.1063/1.5141804
W. Park et al., "Phonon conduction in silicon nanobeam labyrinths," Scientific Reports, vol. 7, p. 6233, 2017. https://doi.org/10.1038/s41598-017-06479-3
W. Li, J. Carrete, N. A. Katcho, and N. Mingo, "ShengBTE: A solver of the Boltzmann transport equation for phonons," Computer Physics Communications, vol. 185, pp. 1747–1758, 2014. https://doi.org/10.1016/j.cpc.2014.02.015
J. Carrete et al., "almaBTE: A solver of the space–time dependent Boltzmann transport equation for phonons in structured materials," Computer Physics Communications, vol. 220, pp. 351–362, 2017. https://doi.org/10.1016/j.cpc.2017.06.023
C. Geuzaine and J.-F. Remacle, "Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities," International Journal for Numerical Methods in Engineering, vol. 79, no. 11, pp. 1309-1331, 2009. https://doi.org/10.1002/nme.2579
R. An, J. Zhao, J. Yang, S. Zhai, L. Dai, Q. Wang, J. Li, W. Hu, G. Sun, Y. Fan, S. Wu, and G. Niu, "Accurate and wide-range measurement of thermal conductivity of semiconductor materials by laser-excited Raman spectroscopy," Journal of Applied Physics, vol. 134, no. 1, p. 015103, Jul. 2023. doi: 10.1063/5.0152963
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