Frequency dependence of the thermal conductivity of semiconductor alloys
Abstract
The distribution of phonons that carry heat in crystals has typically been studied through measurements of the thermal conductivity $\ensuremath{\Lambda}$ as a function of temperature or sample size. We find that $\ensuremath{\Lambda}$ of semiconductor alloys also depends on the frequency of the oscillating temperature field used in the measurement and hence demonstrate a novel and experimentally convenient probe of the phonon distribution. We report the frequency dependent $\ensuremath{\Lambda}$ of ${\mathrm{In}}_{0.49}{\mathrm{Ga}}_{0.51}\mathrm{P}$, ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$, and ${\mathrm{Si}}_{0.4}{\mathrm{Ge}}_{0.6}$ as measured by time-domain thermoreflectance over a wide range of modulation frequencies $0.1<f<10\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and temperatures $88<T<300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The reduction in $\ensuremath{\Lambda}$ at high frequencies is consistent with a model calculation that assumes that phonons with mean free paths larger than the thermal penetration depth do not contribute to the thermal conductivity measured in the experiments.
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This interpretation is the same as that of Koh and Cahill and consistent with Minnich et al. and Johnson et al., who instead used the laser spot diameter and transient grating period as the cutoff dimensions.
“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 [16]
A frequency-dependent thermal conductivity was not observed by time domain thermoreflectance experiments for c-Si at 300 K.
“one unresolved discrepancy is that a frequency-dependent thermal conductivity was not observed by TDTR experiments for c-Si at T ¼ 300 K (ref.16).”
From Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance (2013) · cites this paper as [16]
It is possible to experimentally measure the MFP dependent contributions of phonons to thermal conductivity (the phonon MFP spectrum).
“Recent studies have shown that it is possible to experimentally measure the MFP dependent contributions of phonons to thermal conductivity–the phonon MFP spectrum12345.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [2]
Koh and Cahill hypothesized that the thermal penetration depth limited the diffusive phonons interrogated by TDTR to those having a MFP less than LP.
“Based on observations of suppressed thermal conductivity in semiconductor alloys, Koh and Cahill2 hypothesized that the thermal penetration depth, , limited the diffusive phonons interrogated by TDTR to those having a MFP less than LP, where f was the modulation frequency of the pump laser.”
From Universal phonon mean free path spectra in crystalline semiconductors at high temperature (2013) · cites this paper as [2]
Care should be taken when applying a diffusive thermal transport model to systems where a significant fraction of heat is carried by phonons with long mean-free paths (MFPs).
“However, care should be taken when applying a diffusive thermal transport model to systems where a significant fraction of heat is carried by phonons with long mean-free paths (MFPs). 90-92, 112”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [90]
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 [90]
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References 25 · Cited by 383
- Authors
- Koh, Y. K., & Cahill, D. G.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2007-08-23
- Volume
- 76
- Issue
- 7
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1991872853
- Cited by
- 383
- References
- 25
- Citations by year
- 2026: 7 · 2025: 30 · 2024: 16 · 2023: 8 · 2022: 20 · 2021: 22 · 2020: 25 · 2019: 21 · 2018: 26 · 2017: 31 · 2016: 34 · 2015: 33 · 2014: 23 · 2013: 26 · 2012: 16
- FWCI
- 4.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review B (publishedVersion)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermography and Photoacoustic Techniques
- Physical Sciences › Materials Science › Materials Chemistry › Advanced Thermoelectric Materials and Devices
- Keywords
- phonon distribution, semiconductor alloys, InGaP, InGaAs, SiGe, time-domain thermoreflectance, thermal penetration depth, phonon mean free path
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