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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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.

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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].

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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.

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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.

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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.

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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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