Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation
Open accessAbstract
Quasiballistic heat transfer occurs when there is a temperature gradient over length scales comparable to phonon mean free paths (MFPs). This regime has been of interest recently because observation of quasiballistic transport can lead to useful information about phonon MFPs, knowledge of which is essential for engineering nanoscale thermal effects. Here, we use the Boltzmann transport equation (BTE) to understand how observations of quasiballistic transport can yield information about MFPs. We solve the transient, one-dimensional, frequency-dependent BTE for a double-layer structure of a metal film on a substrate, the same geometry that is used in transient thermoreflectance experiments, using a frequency-dependent interface condition. Our results indicate that phonons with MFPs longer than the thermal penetration depth do not contribute to the measured thermal conductivity, providing a means to probe the MFP distribution. We discuss discrepancies between our simulation and experimental observations which offer opportunities for future investigation.
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Solving the transient Boltzmann transport equation in the full 3D geometry of a TDTR experiment is extremely challenging using previously reported numerical methods due to its large spatial extent and 3D geometry.
“Solving the transient BTE in this domain is extremely challenging using previously reported numerical methods 22,27,29,30 due to its large spatial extent and the 3D geometry.”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [22]
In “A. Calculation of the equilibrium distribution” (page unavailable), the paper says that a large domain with a fine spatial grid makes the BTE solution computationally demanding. Its Introduction describes a one-dimensional simulation; our copy does not state that the full 3D geometry of a TDTR experiment makes previously reported numerical methods extremely challenging. (LLM, conf=0.84)
Experimental — accuracy not yet measuredAssigning phonons a constant relaxation time of 1 ps in the metal transducer yields a low thermal conductivity of around 3 W/mK.
“Following Ref. 22, we assign phonon to have a constant relaxation time of 1 ps, yielding a low thermal conductivity of around 3 W/mK.”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [22]
The thermal decay predicted by the Boltzmann transport equation is slower than Fourier's law predicts.
“As in prior works, 22,24 the thermal decay predicted by the BTE is slower than Fourier's law predicts.”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [22]
An actual TDTR experiment measures the response to a modulated pulse train rather than the impulse response from a single pulse.
“We note that an actual TDTR experiment measures the response to a modulated pulse train rather than the impulse response from a single pulse.22”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [22]
The interface transmissivity can be related to the interface conductance G specified in Fourier's law according to the model of Ref. 22.
“At the interface, phonons have a probability to be transmitted or reflected diffusely; this transmissivity can be related to the interface conductance G specified in Fouriers law according to the model of Ref. 22.”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [22]
The reduction in thermal conductivity is due to the suppressed cross-plane heat flux in Fig. 1(b).
“The reduction in thermal conductivity is due to the suppressed cross-plane heat flux in Fig. 1(b), which apparently does not occur in the actual experiment but is consistent with the earlier simulations.22,24”
From Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations (2014) · cites this paper as [22]
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- Authors
- Minnich, A. J., Chen, G., Mansoor, S., & Yilbas, B. S.
- Affiliations
- California Institute of Technology (US)
- Massachusetts Institute of Technology (US)
- King Fahd University of Petroleum and Minerals (SA)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2011-12-15
- Volume
- 84
- Issue
- 23
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2234837974
- Cited by
- 14
- References
- 28
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 1 · 2021: 2 · 2019: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2014: 2 · 2013: 2 · 2012: 1
- FWCI
- 0.79
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical Review B (publishedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- 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 › Civil and Structural Engineering › Thermal Radiation and Cooling Technologies
- Keywords
- phonon mean free path, transient thermoreflectance, thermal penetration depth, thermal conductivity, phonon transport, interface conditions
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