Disentangling phonon channels in nanoscale heat transport

Samik Mukherjee, Marcin Wajs, Maria de la Mata, Uri Givan, Stephan Senz, Jordi Arbiol, Sebastien Francoeur, and Oussama Moutanabbir

Phys. Rev. B 104, 075429 – Published 16 August 2021

Abstract

Phonon surface scattering has been at the core of heat transport engineering in nanoscale devices. Herein, we demonstrate that this phonon pathway can be the sole mechanism only below a critical, size-dependent temperature. Above this temperature, the lattice phonon scattering coexists along with surface effects. By tailoring the mass disorder at the atomic level, the lattice dynamics in nanowires was artificially controlled without affecting morphology, crystallinity, chemical composition, or electronic properties, thus allowing the mapping of the temperature-thermal conductivity-diameter triple parameter space. This led to the identification of the critical temperature below which the effects of lattice mass disorder are suppressed to an extent that phonon transport becomes governed entirely by the surface. This behavior is discussed based on a modified Landauer-Datta-Lundstrom near-equilibrium transport model. Besides disentangling the main phonon scattering mechanisms, the established framework also provides the necessary input to further advance the design and modeling of heat transport in semiconductor nanoscale systems.

Received 12 October 2020
Accepted 28 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.075429

Physics Subject Headings (PhySH)

Lattice thermal conductivity Nanocrystals Phonons Scattering theory Thermal conductivity

Nanowires Semiconductors

Epitaxy Raman spectroscopy Scanning transmission electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Samik Mukherjee ^1,*, Marcin Wajs¹, Maria de la Mata^2,†, Uri Givan³, Stephan Senz³, Jordi Arbiol ^2,4, Sebastien Francoeur ¹, and Oussama Moutanabbir ^1,‡

¹Department of Engineering Physics, École Polytechnique de Montréal, Case Postale 6079, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3A7
²Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Catalonia, Spain
³Max Planck Institute of Microstructure Physics, Weinberg 2, Halle (Saale) 06120, Germany
⁴ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Catalonia, Spain

^*samik.mukherjee@polymtl.ca
^†Present address: Departamento de Ciencia de los Materiales, Ing. Met. y Qca. Inorg., IMEYMAT, Universidad de Cádiz, 11510 Puerto Real, Spain.
^‡oussama.moutanabbir@polymtl.ca

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Vol. 104, Iss. 7 — 15 August 2021

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Images

Figure 1
HAADF image from HR-STEM analysis of a ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NW at different magnifications.
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Figure 2
(a) Back-scattering micro-Raman spectra, collected at different ambient temperatures, showing the LO phonon mode of a ${}^{30}{Si}$ NWs (left) and a ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NWs (right). The Voigt fits are shown as solid lines. The vertical red dotted line marks the peak positions of the LO modes at 4 K. (b) The evolution of Si-Si peak position ( $ω$ ) as a function of ambient temperature. The fit to the $ω$ vs $T$ data is done using Eq. (1) (solid lines). From the fits, the parameter $A$ in Eq. (1) was found to be $2.63 \times 10^{– 3} K^{– 1}$ and $2.70 \times 10^{– 3} K^{– 1}$ , while the parameter $B$ was found to be $- 3.96 c m^{– 1}$ and $- 3.93 c m^{– 1}$ , for the ${}^{30}{Si}$ NWs and the ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NWs, respectively.
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Figure 3
Evolution of $ω (T_{NW}^{rise})$ and $T_{NW}^{rise}$ of (a) ${}^{30}{Si}$ NWs and (b) ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NWs, as a function of laser power at 140 K. The data are averaged over 10–15 individual NWs. The corresponding error bars in $ω (T_{NW}^{rise})$ are the standard deviation of the data. The error bars associated with the $T_{NW}^{rise}$ comes from two sources: the standard deviation (error bars) associated with the mean value of $ω (T_{NW}^{rise})$ and the uncertainty associated with the value of $ω_{0}$ estimated from the fit. (c) Evolution in the linear regime of $T_{NW}^{rise}$ as a function of the laser power of ${}^{30}{Si}$ NWs and the ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NWs, at 140 K (top) and 60 K (bottom). The dot-dash-dot lines are the linear fit to the corresponding data.
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Figure 4
(a) Evolution of $κ_{T}$ of ${}^{30}{Si}$ NWs and ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NWs as a function of the ambient temperature. The data are normalized to $κ_{T}$ of ${}^{30}{Si}$ NWs at 300 K. The solid-colored lines are fit to the data using Eq. (3) (see text for details). (b) Simulated $κ_{T}$ of ${}^{30}{Si}$ NWs and ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NWs, as a function of ambient temperature, at diameter extremities of 250 and 25 nm. In order to be consistent with the experimental data in (a), the simulated data in (b) were also normalized to $κ_{T}$ of ${}^{30}{Si}$ NWs at 300 K.
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Figure 5
(a) Evolution of $T_{L}^{d_{NW}}$ as a function of the NW diameter ( $d_{NW}$ ). The solid red line is a power-law fit to the simulated data. Inset: Evolution of $T_{L}^{d_{NW}}$ as a function of the fractional composition of ${}^{28}{Si}$ isotope within a ${}^{28}{Si}_{0.4} {}^{30}{Si}_{0.6}$ NW, at diameter extremities of 25 and 250 nm. The solid lines are linear fit to the respective data. (b) The evolution $R_{RT}^{d_{NW}}$ as a function of $d_{NW}$ . The solid green line is an exponential fit to the simulated data, showing a $\sim \exp {(- d_{NW})}^{0.65}$ dependence on $d_{NW}$ . (c) The evolution of $T_{\max}^{d_{NW}}$ as a function of $d_{NW}$ . The solid blue line is the fit to the simulated data, showing a $\sim {(d_{NW})}^{- 1.4}$ dependence. (d) The evolution of $R_{T_{\max}}^{d_{NW}}$ as a function of $d_{NW}$ . The solid brown line is the fit to the simulated data, showing a $\sim \exp {(- d_{NW})}^{0.72}$ dependence. Note that the NWs with $d_{NW}$ of 25 nm never reache $T_{\max}$ within the temperature range of 300 K considered in this work [see Fig. 4]. Consequently, the data in (c) and (d) start at $d_{NW} = 40$ nm and do not show the data point corresponding to $d_{NW} = 25$ nm. In (a)–(d), the simulated data point corresponding to $d_{NW} = 55$ nm (the average diameter of the NWs investigated experimentally in this work) is highlighted using the colored circles.
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