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Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane
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The "textbook" phonon mean free path of heat carrying phonons in silicon at room temperature is ∼40 nm. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range ∼1-10 μm. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.
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“This interpretation is the same as that of Koh and Cahill 16 , and consistent with Minnich et al. 1 and Johnson et al. 19,20 who instead used the laser spot diameter and transient grating period as the cutoff dimensions.”
From Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance (2013) · cites this paper as [19]
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“The thermal conductivity exhibits a marked dependence on grating period up to ∼10 μm, a value comparable to that observed in other covalent crystals with higher thermal conductivity such as silicon60,65.”
From Origin of high thermal conductivity in disentangled ultra-high molecular weight polyethylene films: ballistic phonons within enlarged crystals (2022) · cites this paper as [60]
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“More recently, transient grating experiments have varied the grating period to study related ballistic phonon transport effects in Si membranes4.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [4]
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Thermal diffusivity determination using heterodyne phase insensitive transient grating spectroscopy
Dennett, C. A., & Short, M. P. (2018) · Journal of Applied Physics · doi:10.1063/1.5026429 · Cited by 50
Ma, H., & Tian, Z. (2017) · Nano Letters · doi:10.1021/acs.nanolett.7b02867 · Cited by 49
Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment
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Self-citationThermal transport in suspended silicon membranes measured by laser-induced transient gratings
Vega-Flick, A., Duncan, R. A., Eliason, J. K., Cuffe, J., Johnson, J. A., Péraud, J.-P. M., Zeng, L., Lu, Z., Maznev, A. A., Wang, E. N., et al. (2016) · AIP Advances · doi:10.1063/1.4968610 · Cited by 49
Self-citationSpectrally Resolved Specular Reflections of Thermal Phonons from Atomically Rough Surfaces
Ravichandran, N. K., Zhang, H., & Minnich, A. J. (2018) · Physical Review X · doi:10.1103/physrevx.8.041004 · Cited by 48
Self-citationHsiao, T.-K., Huang, B.-W., Chang, H.-K., Liou, S., Chu, M., Lee, S., & Chang, C. (2015) · Physical Review B · doi:10.1103/physrevb.91.035406 · Cited by 47
Engineering Nanoscale Thermal Transport: Size- and Spacing-Dependent Cooling of Nanostructures
Frazer, T. D., Knobloch, J. L., Hoogeboom-Pot, K. M., Nardi, D., Chao, W. L., Falcone, R. W., Murnane, M. M., Kapteyn, H. C., & Hernández-Charpak, J. N. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.11.024042 · Cited by 46
Maznev, A. A., Bencivenga, F., Cannizzo, A., Capotondi, F., Cucini, R., Duncan, R. A., Feurer, T., Frazer, T. D., Foglia, L., Frey, H., et al. (2018) · Applied Physics Letters · doi:10.1063/1.5048023 · Cited by 47
Self-citationLocal temperatures out of equilibrium
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Metadata
- Authors
- Johnson, J. A., Maznev, A. A., Cuffe, J., Eliason, J. K., Minnich, A. J., Kehoe, T., Torres, C. M. S., Chen, G., & Nelson, K. A.
- Affiliations
- Massachusetts Institute of Technology (US)
- University College Cork (IE)
- Institut Català de Nanociència i Nanotecnologia (ES)
- Institució Catalana de Recerca i Estudis Avançats (ES)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2013-01-08
- Volume
- 110
- Issue
- 2
- Pages
- 025901-025901
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2161591557
- Cited by
- 421
- References
- 28
- Citations by year
- 2026: 15 · 2025: 24 · 2024: 21 · 2023: 13 · 2022: 32 · 2021: 40 · 2020: 27 · 2019: 46 · 2018: 41 · 2017: 38 · 2016: 39 · 2015: 38 · 2014: 30 · 2013: 16
- FWCI
- 18.52
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Arrow@dit (Dublin Institute of Technology) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Cork Open Research Archive (University College Cork, Ireland) (submittedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, other-oa)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, other-oa)
- arXiv (Cornell University)
- APS
- Funders
- U.S. Department of Energy
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Physical Sciences › Engineering › Mechanics of Materials › Thermography and Photoacoustic Techniques
- Keywords
- ballistic thermal transport, low-frequency phonons, phonon mean free path, silicon, thermal conductivity, thermal grating, silicon membranes
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