Research Papers: Experimental Techniques

From the Casimir Limit to Phononic Crystals: 20 Years of Phonon Transport Studies Using Silicon-on-Insulator Technology

[+] Author and Article Information
Amy M. Marconnet

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 01239
e-mail: amymarco@mit.edu

Kenneth E. Goodson

Fellow ASME
Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305

References cited in Table 1 are [7,11-22,25,26,30,31,42,11-22,25-26,30-31,42].

References cited in Table 2 are [27-30,32-33,50].

Manuscript received October 14, 2012; final manuscript received December 20, 2012; published online May 16, 2013. Assoc. Editor: Leslie Phinney.

J. Heat Transfer 135(6), 061601 (May 16, 2013) (10 pages) Paper No: HT-12-1561; doi: 10.1115/1.4023577 History: Received October 14, 2012; Revised December 20, 2012

Silicon-on-insulator (SOI) technology has sparked advances in semiconductor and MEMs manufacturing and revolutionized our ability to study phonon transport phenomena by providing single-crystal silicon layers with thickness down to a few tens of nanometers. These nearly perfect crystalline silicon layers are an ideal platform for studying ballistic phonon transport and the coupling of boundary scattering with other mechanisms, including impurities and periodic pores. Early studies showed clear evidence of the size effect on thermal conduction due to phonon boundary scattering in films down to 20 nm thick and provided the first compelling room temperature evidence for the Casimir limit at room temperature. More recent studies on ultrathin films and periodically porous thin films are exploring the possibility of phonon dispersion modifications in confined geometries and porous films.

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Nguyen, B.-Y., Celler, G., and Mazure, C., 2009, “A Review of SOI Technology and Its Applications,” J. Integr. Circuit Syst., 4(2), pp. 51–54.
Loncar, M., Doll, T., Vuckovic, J., and Scherer, A., 2000, “Design and Fabrication of Silicon Photonic Crystal Optical Waveguides,” J. Lightwave Tech., 18(10), pp. 1402–1411. [CrossRef]
Lutz, M., Partridge, A., Gupta, P., Buchan, N., Klaassen, E., McDonald, J., and Petersen, K., 2007, “MEMS Oscillators for High Volume Commercial Applications,” 14th International Conference on Solid-State Sensors, Actuators and Microsystems Conference (TRANSDUCERS & EUROSENSORS '07), Lyon, France, June 10–14, IEEE, pp. 49–52. [CrossRef]
Goodson, K. E., Flik, M. I., Su, L. T., and Antoniadis, D. A., 1995, “Prediction and Measurement of Temperature Fields in Silicon-on-Insulator Electronic Circuits,” ASME J. Heat Transfer, 117(3), pp. 574–581. [CrossRef]
McConnell, A. D., and Goodson, K. E., 2005, “Thermal Conduction in Silicon Micro- and Nanostructures,” Ann. Rev. Heat Transf., 14, pp. 129–168. [CrossRef]
Cahill, D. G., Ford, W. K., Goodson, K. E., Mahan, G. D., Majumdar, A., Maris, H. J., Merlin, R., and Phillpot, S. R., 2003, “Nanoscale Thermal Transport,” J. Appl. Phys., 93(2), pp. 793–818. [CrossRef]
Liu, W., and Asheghi, M., 2004, “Phonon–Boundary Scattering in Ultrathin Single-Crystal Silicon Layers,” Appl. Phys. Lett., 84(19), pp. 3819–3821. [CrossRef]
Casimir, H. B. G., 1938, “Note on the Conduction of Heat in Crystals,” Physica, 5(6), pp. 495–500. [CrossRef]
Yoneoka, S., Liger, M., Yama, G., Schuster, R., Purkl, F., Provine, J., Prinz, F. B., Howe, R. T., and Kenny, T. W., 2011, “ALD-Metal Uncooled Bolometer,” 2011 IEEE 24th International Conference on Micro Electro Mechanical Systems (MEMS), Jan. 23–27, pp. 676–679. [CrossRef]
Niklaus, F., Vieider, C., and Jakobsen, H., 2007, “MEMS-Based Uncooled Infrared Bolometer Arrays: A Review,” MEMS/MOEMS Technologies and Applications III, J.-C. Chiao, X. Chen, Z. Zhou, and X. Li, eds., SPIE Proceedings, Beijing, China, Vol. 6836, p. 68360D. [CrossRef]
Asheghi, M., Leung, Y. K., Wong, S. S., and Goodson, K. E., 1997, “Phonon-Boundary Scattering in Thin Silicon Layers,” Appl. Phys. Lett., 71(13), pp. 1798–1800. [CrossRef]
Asheghi, M., Touzelbaev, M. N., Goodson, K. E., Leung, Y. K., and Wong, S. S., 1998, “Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates,” ASME J. Heat Transfer, 120(1), pp. 30–36. [CrossRef]
Aubain, M. S., and Bandaru, P. R., 2011, “In-Plane Thermal Conductivity Determination Through Thermoreflectance Analysis and Measurements,” J. Appl. Phys., 110(8), p. 084313. [CrossRef]
Aubain, M. S., and Bandaru, P. R., 2010, “In-Plane Thermal Conductivity Determination in Silicon on Insulator (SOI) Structures Through Thermoreflectance Measurements,” Materials Research Society Spring Meeting, San Francisco, CA, Cambridge University Press, Vol. 1267, p. 1267-DD-01.
Aubain, M. S., and Bandaru, P. R., 2010, “Determination of Diminished Thermal Conductivity in Silicon Thin Films Using Scanning Thermoreflectance Thermometry,” Appl. Phys. Lett., 97(25), p. 253102. [CrossRef]
Ju, Y. S., 2005, “Phonon Heat Transport in Silicon Nanostructures,” Appl. Phys. Lett., 87(15), p. 153106. [CrossRef]
Ju, Y. S., and Goodson, K. E., 1999, “Phonon Scattering in Silicon Films With Thickness of Order 100 Nm,” Appl. Phys. Lett., 74(20), pp. 3005–3007. [CrossRef]
Hao, Z., Zhichao, L., Lilin, T., Zhimin, T., Litian, L., and Zhijian, L., 2006, “Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Films Using Improved Structure,” 8th International Conference on Solid-State and Integrated Circuit Technology (ICSICT '06), Shanghai, China, Oct. 23–26, pp. 2196–2198. [CrossRef]
Asheghi, M., Kurabayashi, K., Kasnavi, R., and Goodson, K. E., 2002, “Thermal Conduction in Doped Single-Crystal Silicon Films,” J. Appl. Phys., 91(8), pp. 5079–5088. [CrossRef]
Kim, B., Nguyen, J., Clews, P. J., Reinke, C. M., Goettler, D., Leseman, Z. C., El-Kady, I., and Olsson, R. H., 2012, “Thermal Conductivity Manipulation in Single Crystal Silicon via Lithographycally Defined Phononic Crystals,” IEEE 25th International Conference on Micro Electro Mechanical Systems (MEMS), Paris, France, Jan. 29–Feb. 2, pp. 176–179. [CrossRef]
Song, D., and Chen, G., 2004, “Thermal Conductivity of Periodic Microporous Silicon Films,” Appl. Phys. Lett., 84(5), pp. 687–689. [CrossRef]
Sverdrup, P. G., Sinha, S., Asheghi, M., Uma, S., and Goodson, K. E., 2001, “Measurement of Ballistic Phonon Conduction Near Hotspots in Silicon,” Appl. Phys. Lett., 78(21), pp. 3331–3333. [CrossRef]
Chen, G., 1996, “Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles,” ASME J. Heat Transfer, 118(3), pp. 539–545. [CrossRef]
Liu, W., and Asheghi, M., 2006, “Thermal Conductivity Measurements of Ultra-Thin Single Crystal Silicon Layers,” ASME J. Heat Transfer, 128(1), pp. 75–83. [CrossRef]
Liu, W., and Asheghi, M., 2005, “Thermal Conduction in Ultrathin Pure and Doped Single-Crystal Silicon Layers at High Temperatures,” J. Appl. Phys., 98(12), p. 123523. [CrossRef]
Liu, W., Etessam-Yazdani, K., Hussin, R., and Asheghi, M., 2006, “Modeling and Data for Thermal Conductivity of Ultrathin Single-Crystal SOI Layers at High Temperature,” IEEE Trans. Elec. Device., 53(8), pp. 1868–1876. [CrossRef]
Bourgeois, O., Fournier, T., and Chaussy, J., 2007, “Measurement of the Thermal Conductance of Silicon Nanowires at Low Temperature,” J. Appl. Phys., 101(1), p. 016104. [CrossRef]
Heron, J. S., Fournier, T., Mingo, N., and Bourgeois, O., 2009, “Mesoscopic Size Effects on the Thermal Conductance of Silicon Nanowire,” Nano Lett., 9(5), pp. 1861–1865. [CrossRef] [PubMed]
Heron, J.-S., Bera, C., Fournier, T., Mingo, N., and Bourgeois, O., 2010, “Blocking Phonons via Nanoscale Geometrical Design,” Phys. Rev. B, 82(15), p. 155458. [CrossRef]
Yu, J.-K., Mitrovic, S., Tham, D., Varghese, J., and Heath, J. R., 2010, “Reduction of Thermal Conductivity in Phononic Nanomesh Structures,” Nat. Nanotechnol., 5(10), pp. 718–721. [CrossRef] [PubMed]
Tang, J., Wang, H.-T., Lee, D. H., Fardy, M., Huo, Z., Russell, T. P., and Yang, P., 2010, “Holey Silicon as an Efficient Thermoelectric Material,” Nano Lett., 10(10), pp. 4279–4283. [CrossRef] [PubMed]
Hippalgaonkar, K., Huang, B., Chen, R., Sawyer, K., Ercius, P., and Majumdar, A., 2010, “Fabrication of Microdevices With Integrated Nanowires for Investigating Low-Dimensional Phonon Transport,” Nano Lett., 10(11), pp. 4341–4348. [CrossRef] [PubMed]
Boukai, A. I., Bunimovich, Y., Tahir-Kheli, J., Yu, J.-K., Goddard, W. A., III, and Heath, J. R., 2008, “Silicon Nanowires as Efficient Thermoelectric Materials,” Nature, 451(7175), pp. 168–171. [CrossRef] [PubMed]
Thomas, J. A., Turney, J. E., Iutzi, R. M., Amon, C. H., and McGaughey, A. J. H., 2010, “Predicting Phonon Dispersion Relations and Lifetimes From the Spectral Energy Density,” Phys. Rev. B, 81(8), p. 081411. [CrossRef]
Henry, A. S., and Chen, G., 2008, “Spectral Phonon Transport Properties of Silicon Based on Molecular Dynamics Simulations and Lattice Dynamics,” J. Comput. Theor. Nanos., 5(2), pp. 141–152.
Lacroix, D., Joulain, K., Terris, D., and Lemonnier, D., 2006, “Monte Carlo Simulation of Phonon Confinement in Silicon Nanostructures: Application to the Determination of the Thermal Conductivity of Silicon Nanowires,” Appl. Phys. Lett., 89(10), p. 103104. [CrossRef]
Schelling, P. K., Phillpot, S. R., and Keblinski, P., 2002, “Comparison of Atomic-Level Simulation Methods for Computing Thermal Conductivity,” Phys. Rev. B, 65(14), p. 144306. [CrossRef]
Volz, S. G., and Chen, G., 1999, “Molecular Dynamics Simulation of Thermal Conductivity of Silicon Nanowires,” Appl. Phys. Lett., 75(14), pp. 2056–2058. [CrossRef]
Ziman, J. M., 1960, Electrons and Phonons, Oxford University Press, London.
Baillis, D., and Randrianalisoa, J., 2009, “Prediction of Thermal Conductivity of Nanostructures: Influence of Phonon Dispersion Approximation,” Int. J. Heat Mass Transf., 52(11–12), pp. 2516–2527. [CrossRef]
Holland, M. G., 1963, “Analysis of Lattice Thermal Conductivity,” Phys. Rev., 132(6), pp. 2461–2471. [CrossRef]
Hopkins, P. E., Reinke, C. M., Su, M. F., Olsson, R. H., Shaner, E. A., Leseman, Z. C., Serrano, J. R., Phinney, L. M., and El-Kady, I., 2010, “Reduction in the Thermal Conductivity of Single Crystalline Silicon by Phononic Crystal Patterning,” Nano Lett., 11(1), pp. 107–112. [CrossRef] [PubMed]
Sondheimer, E. H., 1952, “The Mean Free Path of Electrons in Metals,” Adv. Phys., 1(1), pp. 1–42. [CrossRef]
Berman, R., Foster, E. L., and Ziman, J. M., 1955, “Thermal Conduction in Artificial Sapphire Crystals at Low Temperatures. I. Nearly Perfect Crystals,” Pr. Roy. Soc. Lond. A Mat., 231(1184), pp. 130–144. [CrossRef]
Ho, C. Y., Powell, R. W., and Liley, P. E., 1972, “Thermal Conductivity of the Elements,” J. Phys. Chem. Ref. Data, 1(2), pp. 279–421. [CrossRef]
Torres, C. M. S., Zwick, A., Poinsotte, F., Groenen, J., Prunnila, M., Ahopelto, J., Mlayah, A., and Paillard, V., 2004, “Observations of Confined Acoustic Phonons in Silicon Membranes,” Phys. Status Solidi C, 1(11), pp. 2609–2612. [CrossRef]
Cuffe, J., Chávez, E., Shchepetov, A., Chapuis, P.-O., El Boudouti, E. H., Alzina, F., Kehoe, T., Gomis-Bresco, J., Dudek, D., Pennec, Y., Djafari-Rouhani, B., Prunnila, M., Ahopelto, J., and Sotomayor Torres, C. M., 2012, “Phonons in Slow Motion: Dispersion Relations in Ultrathin Si Membranes,” Nano Lett., 12(7), pp. 3569–3573. [CrossRef] [PubMed]
Johnson, J. A., Maznev, A. A., Eliason, J. K., Minnich, A., Collins, K., Chen, G., Cuffe, J., Kehoe, T., Torres, C. M. S., and Nelson, K. A., 2011, “Experimental Evidence of Non-Diffusive Thermal Transport in Si and GaAs,” MRS Proceedings, San Francisco, CA, Apr. 25–29, Cambridge University Press, Vol. 1347. [CrossRef]
Johnson, J. A., Maznev, A., Cuffe, J., Eliason, J. K., Minnich, A. J., Kehoe, T., Sotomayor Torres, C. M., Chen, G., and Nelson, K. A., 2012, “Direct Measurement of Room Temperature Non-Diffusive Thermal Transport Over Micron Distances in a Silicon Membrane,” ArXiv eprint No. arXiv:1204.4735.
Marconnet, A. M., Kodama, T., Asheghi, M., and Goodson, K. E., 2012, “Phonon Thermal Conduction in Periodically Porous Silicon Nanobridges,” Microscale Nanoscale Therm. Eng., 16(4), pp. 199–219. [CrossRef]
Nordheim, L. W., 1934, “Die Theorie Der Thermoelektrischen Effekte,” Actes Scientifiques et Industrielles, Vol. 131, Hermann & Cie, Paris.
Hochbaum, A. I., Chen, R., Delgado, R. D., Liang, W., Garnett, E. C., Najarian, M., Majumdar, A., and Yang, P., 2008, “Enhanced Thermoelectric Performance of Rough Silicon Nanowires,” Nature, 451(7175), pp. 163–167. [CrossRef] [PubMed]
Li, D., Wu, Y., Kim, P., Shi, L., Yang, P., and Majumdar, A., 2003, “Thermal Conductivity of Individual Silicon Nanowires,” Appl. Phys. Lett., 83(14), pp. 2934–2936. [CrossRef]
Josell, D., Burkhard, C., Li, Y., Cheng, Y. W., Keller, R. R., Witt, C. A., Kelley, D. R., Bonevich, J. E., Baker, B. C., and Moffat, T. P., 2004, “Electrical Properties of Superfilled Sub-Micrometer Silver Metallizations,” J. Appl. Phys., 96(1), pp. 759–768. [CrossRef]
Dingle, R. B., 1950, “The Electrical Conductivity of Thin Wires,” Pr. Roy. Soc. Lond. A Mat., 201(1067), pp. 545–560. [CrossRef]
Gong, Y., Ellis, B., Shambat, G., Sarmiento, T., Harris, J. S., and Vuckovic, J., 2010, “Nanobeam Photonic Crystal Cavity Quantum Dot Laser,” Optics Exp., 18(9), pp. 8781–8789. [CrossRef]
Makarova, M., Yiyang, G., Szu-Lin, C., Nishi, Y., Yerci, S., Rui, L., Negro, L. D., and Vuckovic, J., 2010, “Photonic Crystal and Plasmonic Silicon-Based Light Sources,” IEEE J. Quant. Electron., 16(1), pp. 132–140. [CrossRef]
Laude, S., Beugnot, J. C., Benchabane, S., Pennec, Y., Djafari-Rouhani, B., Papanicolaou, N., and Martinez, A., 2010, “Design of Waveguides in Silicon Phoxonic Crystal Slabs,” IEEE Ultrasonics Symposium (IUS), San Diego, CA, Oct. 11–14, pp. 527–530. [CrossRef]
Sadat-Saleh, S., Benchabane, S., Baida, F. I., Bernal, M.-P., and Laude, V., 2009, “Tailoring Simultaneous Photonic and Phononic Band Gaps,” J. Appl. Phys., 106(7), p. 074912. [CrossRef]
Olsson, R. H., III, and El-Kady, I., 2009, “Microfabricated Phononic Crystal Devices and Applications,” Measure. Sci. Tech., 20(1), p. 012002. [CrossRef]
El-Kady, I., Su, M. F., Reinke, C. M., Hopkins, P. E., Goettler, D., Leseman, Z. C., Shaner, E. A., and Olsson, R. H., III, 2011, “Manipulation of Thermal Phonons: A Phononic Crystal Route to High-ZT Thermoelectrics,” Photonic and Phononic Properties of Engineered Nanostructures, A. Adibi, S.-Y. Lin, and A. Scherer, eds., Proc. SPIE, San Francisco, CA, Jan. 22–27, p. 794615. [CrossRef]
Hopkins, P. E., Rakich, P. T., Olsson, R. H., El-Kady, I. F., and Phinney, L. M., 2009, “Origin of Reduction in Phonon Thermal Conductivity of Microporous Solids,” Appl. Phys. Lett., 95(16), p. 161902. [CrossRef]
Hopkins, P. E., Phinney, L. M., Rakich, P. T., Olsson, R. H., and El-Kady, I., 2010, “Phonon Considerations in the Reduction of Thermal Conductivity in Phononic Crystals,” Appl. Phys. A, 103(3), pp. 575–579. [CrossRef]
Benchabane, S., Khelif, A., Daniau, W., Robert, L., Petrini, V., Assouar, B., Vincent, B., Elmazria, O., Kruger, J., and Laude, S., 2005, “Silicon Phononic Crystal for Surface Acoustic Waves,” IEEE Ultrasonics Symposium, Rotterdam, Netherlands, Sept. 18–21, Vol. 2, pp. 922–925. [CrossRef]
Lee, J.-H., Galli, G. A., and Grossman, J. C., 2008, “Nanoporous Si as an Efficient Thermoelectric Material,” Nano Lett., 8(11), pp. 3750–3754. [CrossRef] [PubMed]
Mohammadi, S., Eftekhar, A. A., Hunt, W. D., and Adibi, A., 2008, “Demonstration of Large Complete Phononic Band Gaps and Waveguiding in High-Frequency Silicon Phononic Crystal Slabs,” IEEE International Frequency Control Symposium, Honolulu, HI, May 19–21, pp. 768–772. [CrossRef]
El-Kady, I., Olsson, R. H., III,Hopkins, P. E., Leseman, Z. C., Goettler, D. F., Kim, B., Reinke, C. M., and Su, M. F., 2012, “Phonon Manipulation With Phononic Crystals,” Sandia National Labs, Albuquerque, NM, Report No. SAND2012-0127.
Reinke, C. M., Su, M. F., Davis, B. L., Kim, B., Hussein, M. I., Leseman, Z. C., Olsson, R. H., III, and El-Kady, I., 2011, “Thermal Conductivity Prediction of Nanoscale Phononic Crystal Slabs Using a Hybrid Lattice Dynamics-Continuum Mechanics Technique,” AIP Adv., 1(4), p. 041403. [CrossRef]


Grahic Jump Location
Fig. 1

SOI thermal measurement structures. (a) On-substrate steady-state joule heating structure. (b) Suspended steady-state joule heating structure. (c) Suspended heater bridge structure. (d) Suspended heater-thermometer structure.

Grahic Jump Location
Fig. 2

Thickness dependence of the thermal conductivity of silicon thin films [7,11-22,25,26,30,31,42,11-22,25-26,30-31,42]. For the reported in-plane thermal conductivity data; red rings around the solid circular data markers indicate nearly pure samples (intrinsic, nearly pure, or < 1015 cm−3 dopant atoms). The Sondheimer model (Eq. (5)) for the reduced thermal conductivity as a function of film thickness is shown for a mean free path of 100 nm and 300 nm, assuming purely diffuse scattering (p = 0) at the film boundaries.

Grahic Jump Location
Fig. 3

Temperature-dependent thermal conductivity of several different SOI-based silicon structures: thin films (Asheghi and colleagues [7,12]), 20 nm × 28 nm rectangular nanobeams (Yu et al. [30]), and 22 nm thick nanoporous films (results shown for both 11 and 16 nm diameter holes spaced by 34 nm from Yu et al. [30]). The thermal conductivity of bulk silicon (Ho et al. [45]) is shown for comparison. While the modeling results agree fairly well for the thin film data, the nanobeam and nanomesh results fall below the predicted thermal conductivities.

Grahic Jump Location
Fig. 4

Impact of doping on the thermal conductivity of (a) 3 μm and (b) 30 nm thick silicon films. Figures reprinted with permission from (a) Asheghi et al. [19] and (b) Asheghi and Liu [25].

Grahic Jump Location
Fig. 5

Thermal conductivity of silicon nanobeams [30,32,33] as a function of (a) critical thickness and (b) temperature. The thermal conductivity of rough [52] and smooth [53] cylindrical nanowires are shown in panel (a) for comparison to the nanobeam data. The results of the simple model for nanowire thermal conductivity from Eq. (7) are shown with the solid line in panel (a), while the data for the rectangular nanobeams appear to follow an approximate trend of k~dc2. In panel (b), the temperature-dependent thermal conductivity results from a thermal conductivity integral model with the Sondheimer-type reduction function to account for the boundary scattering in rectangular nanobeams are shown for in comparison to the experimental data. The large nanowires from Boukai et al. [33] fall significantly higher than the model for nanobeams (and also the prediction for 35 nm thick films), while the smaller nanowires from Boukai et al. [33] and Yu et al. [30] fall below the predictions.

Grahic Jump Location
Fig. 6

Room temperature thermal conductivity of 2D periodically porous thin films [20,21,30,31] and 1D periodically porous nanobeams [50] as a function of the film thickness. The porous film data are compared to the predictions from Eq. (5) for in-plane thermal conductivity of solid films.

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Fig. 7

Room temperature thermal conductivity of 2D periodically porous thin films [20,21,30,31] and 1D periodically porous nanowires [50] as a function of (a) the limiting dimension and (b) the porosity. In panel (a), for the films, the limiting dimension is the intrapore distance (S-D). For the 1D porous nanoladders Marconnet et al. [50], the limiting dimension is the smaller of the intrapore distance and the distance from the edge of the nanowire to the pore wall, (W-D)/2. Film thicknesses ds are indicated in the legend. The thermal conductivity data are compared to the results of the thermal conductivity integral model with the mean free path reduced using Matthiessen's rule and the limiting dimension. The results of the thermal conductivity integral model are independent of film thickness.



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