Superdiffusive heat conduction in semiconductor alloys. II. Truncated Lévy formalism for experimental analysis
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Nearly all experimental observations of quasiballistic heat flow are interpreted using Fourier theory with modified thermal conductivity. Detailed Boltzmann transport equation (BTE) analysis, however, reveals that the quasi-ballistic motion of thermal energy in semiconductor alloys is no longer Brownian but instead exhibits L\'evy dynamics with fractal dimension $\ensuremath{\alpha}<2$. Here, we present a framework that enables full three-dimensional experimental analysis by retaining all essential physics of the quasiballistic BTE dynamics phenomenologically. A stochastic process with just two fitting parameters describes the transition from pure L\'evy superdiffusion as short length and time scales to regular Fourier diffusion. The model provides accurate fits to time domain thermoreflectance raw experimental data over the full modulation frequency range without requiring any ``effective'' thermal parameters and without any a priori knowledge of microscopic phonon scattering mechanisms. Identified $\ensuremath{\alpha}$ values for InGaAs and SiGe match ab initio BTE predictions within a few percent. Our results provide experimental evidence of fractal L\'evy heat conduction in semiconductor alloys. The formalism additionally indicates that the transient temperature inside the material differs significantly from Fourier theory and can lead to improved thermal characterization of nanoscale devices and material interfaces.
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The majority of experimental work in the literature deduced thermal properties based on Fourier's law of heat conduction with an effective thermal conductivity.
“Similarly, while TDTR can be used to study non-equilibrium phenomena such as quasi-ballistic phonon transport 90, 91, 109-111 and electronphonon coupling 55 due to its ability to detect temperature evolutions at micrometer-scale and picosecond-scale resolutions, the majority of the experimental work in the literature deduced thermal properties based on Fourier's”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [111]
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Kim, Y., Kodama, T., Kim, Y., Kim, B. S. Y., Ko, C., Lim, J., & Park, W. (2022) · NPG Asia Materials · doi:10.1038/s41427-022-00375-7 · Cited by 1 · see citing works
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Neophytou, N., & Karamitaheri, H. (2016) · IEEE Transactions on Nanotechnology · doi:10.1109/tnano.2016.2524593 · Cited by 1 · see citing works
Collective thermal transport in pure and alloy semiconductors
Torres, P., Mohammed, A. M. S., Torelló, À., Bafaluy, J., Camacho, J., Cartoixà, X., Shakouri, A., & Álvarez, F. X. (2018) · Physical Chemistry Chemical Physics · doi:10.1039/c7cp07738f · Cited by 1 · see citing works
Self-citationMonte Carlo Study on Anomalous Carrier Diffusion in Inhomogeneous Semiconductors
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Torres, P. (2018) · Springer theses · doi:10.1007/978-3-319-94983-3_7
Torres, P. (2018) · Springer theses · doi:10.1007/978-3-319-94983-3_2
Singh, S. K., & Ávila, M. A. (2024) · Springer eBooks · doi:10.1007/978-981-97-7610-8_4
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Zenji, A. (2022) · theses.fr (ABES) · doi:10.70675/9667875bz39edz4748z8b49z2f92f27c680a
Nkenfack, I. M., Pascale, F., Pernot, G., & Lacroix, D. (2026) · Journal of Applied Physics · doi:10.1063/5.0348120
Self-citation
- Authors
- Vermeersch, B., Mohammed, A. M. S., Pernot, G., Koh, Y. R., & Shakouri, A.
- Affiliations
- Purdue University West Lafayette (US)
- Laboratoire Ondes et Matière d'Aquitaine (FR)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2015-02-10
- Volume
- 91
- Issue
- 8
- Pages
- 085203 (1-7)
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1975344085
- Cited by
- 78
- References
- 33
- Citations by year
- 2026: 2 · 2025: 7 · 2024: 4 · 2023: 1 · 2022: 7 · 2021: 7 · 2020: 7 · 2019: 8 · 2018: 11 · 2017: 7 · 2016: 9 · 2015: 8
- FWCI
- 4.73
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- HAL (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-SC0001009)
- Defense Advanced Research Projects Agency
- Army Research Office (W911NF0810347)
- Air Force Office of Scientific Research (FA9550-08-1-0340)
- 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
- Lévy flight, semiconductor alloys, truncated Lévy distribution, time-domain thermoreflectance, InGaAs, SiGe, lattice thermal conductivity, fractal dimension, Boltzmann equation, non-Fourier heat conduction
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