Abstract
In this work we compute the effective thermal conductivity of porous Si by means of the phonon Boltzmann transport equation. Simulations of heat transport across aligned square pores reveal that the thermal conductivity can be decreased either by increasing the pore size or decreasing the pore spacing. Furthermore, by including the surface specularity parameter we show that the roughness of the pore walls plays an important role when the pore size is comparable with the phonon mean free path, because to the increase in the surface-to-volume ratio. Thanks to these results, in qualitatively agreement with those obtained with Molecular Dynamics simulations, we gained insights into the scaling of thermal properties of porous materials and interplay between disorder at different length scales. The model, being based on a flexible multiscale finite element context, can be easily integrated with electrical transport models, in order to optimize the figure of merit ZT of thermoelectric devices.
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Majumdar, A.: Enhanced: thermoelectricity in semiconductor nanostructures. Science 303, 777 (2004)
Zebarjadi, M., Esfarjani, K., Dresselhaus, M.S., Ren, Z.F., Chen, G.: Perspectives on thermoelectrics: from fundamentals to device applications. Energy Environ. Sci. 5, 5147 (2011)
Snyder, G.: Complex thermoelectric materials. Nat. Mater. 7, 105 (2008)
Minnich, A.J., Dresselhaus, M.S., Ren, Z.F., Chen, G.: Bulk nanostructured thermoelectric materials: current research and future prospects. Energy Environ. Sci. 2, 466–479 (2009)
Hicks, L.D., Harman, T.C., Dresselhaus, M.S.: Use of quantum-well superlattices to obtain a high figure of merit from nonconventional thermoelectric materials. Appl. Phys. Lett. 3230 (1993)
Mahan, G.D., Sofo, J.O.: The best thermoelectric. Proc. Natl. Acad. Sci. 93, 7436 (1996)
Humphrey, T.E., Linke, H.: Reversible thermoelectric nanomaterials. Phys. Rev. Lett. 94, 096601 (2005)
Song, D., Chen, G.: Thermal conductivity of periodic microporous silicon films. Appl. Phys. Lett. 84(5), 687 (2004)
Yu, J.-K., Mitrovic, S., Tham, D., Varghese, J., Heath, J.R.: Reduction of thermal conductivity in phononic nanomesh structures. Nat. Nanotechnol. 5, 718 (2010)
Lee, J.-H., Galli, G.A., Grossman, J.C.: Nanoporous Si as an efficient thermoelectric material. Nano Lett. 8, 3750 (2008)
Lee, J., Grossman, J., Reed, J.: Lattice thermal conductivity of nanoporous Si: Molecular dynamics study. Appl. Phys. Lett. 91, 223110 (2007)
He, Y., Donadio, D., Lee, J.-H., Grossman, J.C., Galli, G.: Thermal transport in nanoporous silicon: interplay between disorder at mesoscopic and atomic scales. ACS Nano 5, 1839 (2011)
Auf der Maur, M., Penazzi, G., Romano, G., Sacconi, F., Pecchia, A., Di Carlo, A.: The multiscale paradigm in electronic device simulation. IEEE Trans. Electron Devices 58, 1425 (2011)
Sparrow, E.M., Cess, R.D.: Radiation Heat Transfer. CRC Press, Boca Raton (1978)
Hao, Q., Chen, G., Jeng, M.-S.: Frequency-dependent Monte Carlo simulations of phonon transport in two-dimensional porous silicon with aligned pores. J. Appl. Phys. 106, 114321 (2009)
Majumdar, A.: Microscale heat conduction in dielectric thin films. Trans. ASME, J. Heat Transf. 115, 7 (1993)
Joshi, A.A., Majumdar, A.: Transient ballistic and diffusive phonon heat transport in thin films. J. Appl. Phys. 74, 31 (1993)
Chen, G.: Nanoscale Energy Transport and Conversion: A Parallel Treatment of Elections, Molecules, Phonons, and Photons. Oxford Univ. Press, London (2005)
Yang, R.G., Chen, G.: Thermal conductivity modeling of periodic two-dimensional nanocomposites. Phys. Rev. B 69, 195 (2004)
Liu, L.-C., Huang, M.-J.: Thermal conductivity modeling of micro- and nanoporous silicon. Int. J. Therm. Sci. 49(9), 1547 (2010)
Chung, J.D., Kaviany, M.: Effects of phonon pore scattering and pore randomness on effective conductivity of porous silicon. Int. J. Heat Mass Transf. 43, 521 (2000)
Romano, G., Di Carlo, A.: Multiscale electro-thermal modeling of nanostructured devices. IEEE Trans. Nanotechnol. 10, 1285 (2011)
Romano, G., Auf der Maur, M., Pecchia, A., Di Carlo, A.: Handshaking multiscale thermal model of nanostructured devices. In: Proceedings of the 14TH International Workshop on Computational Electronics, p. 68 (2010)
Thompson, J.F., Soni, B.K., Weatherill, N.P.: Handbook of Grid Generation. CRC Press, Boca Raton (1999)
Murthy, J.Y., Mathur, S.R.: Computation of sub-micron thermal transport using an unstructured finite volume method. J. Heat Transf. 124, 1176 (2002)
Murthy, J.Y., Mathur, S.R.: An improved computational procedure for sub-micron heat conduction. J. Heat Transf. 125, 904 (2003)
Chen, G.: Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958 (1998)
Ziman, J.M.: Electrons and Phonons. Oxford University Press, London (1985)
Soffer, S.B.: Statistical model for the size effect in electrical conduction. J. Appl. Phys. 38, 1710 (1967)
Aksamija, Z., Knezevic, I.: Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes. Phys. Rev. B 82(4), 045319 (2010)
Nan, C.-W., Birringer, R., Clarke, D.R., Gleiter, H.: Effective thermal conductivity of particulate composites with interfacial thermal resistance. J. Appl. Phys. 81, 6692 (1997)
Prasher, R.: Transverse thermal conductivity of porous materials made from aligned nano and microcylindrical pores. J. Appl. Phys. 100, 064302 (2006)
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Romano, G., Di Carlo, A. & Grossman, J.C. Mesoscale modeling of phononic thermal conductivity of porous Si: interplay between porosity, morphology and surface roughness. J Comput Electron 11, 8–13 (2012). https://doi.org/10.1007/s10825-012-0390-2
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DOI: https://doi.org/10.1007/s10825-012-0390-2