Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

Johnson, Jeremy A.; Maznev, A. A.; Cuffe, J.; Eliason, Jeffrey K.; Minnich, Austin J.; Kehoe, Timothy; Torres, C. M. Sotomayor; Chen, Gang; Nelson, Keith A.

doi:10.1103/physrevlett.110.025901

Cited by 372 publications

(447 citation statements)

References 34 publications

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“…4), (3) the spatial frequency of heating in thermal grating measurements of 400 nm thick Si membranes at 300 K (ref. 10) and (4) the frequency of periodic heating, f, in TDTR measurements of semiconductor alloys and some types of amorphous silicon between 80 and 420 K (refs 6,15). In TDTR, and the related technique of frequency-domain thermoreflectance (FDTR), f sets the time interval over which heat travels and, therefore, controls an important length scale of the temperature profile.…”

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confidence: 99%

“…The breakdown of Fourier theory at small length scales has implications for nanoelectronics 8 and nanostructured thermoelectric devices 9 and has received a great deal of recent attention [1][2][3][4][5][6][7][10][11][12][13][14] . For example, deviations between Fourier theory predictions and experimental data have been reported to depend on (1) the width of the nickel heater lines in nanofabricated Ni/sapphire samples 7 , (2) the diameter of the heating pump laser beam, 2w 0 , in time-domain thermoreflectance (TDTR) measurements of bulk Si between 30 and 100 K (ref.…”

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Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments

2014

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The applicability of Fourier's law to heat transfer problems relies on the assumption that heat carriers have mean free paths smaller than important length scales of the temperature profile. This assumption is not generally valid in nanoscale thermal transport problems where spacing between boundaries is small (o1 mm), and temperature gradients vary rapidly in space. Here we study the limits to Fourier theory for analysing three-dimensional heat transfer problems in systems with an interface. We characterize the relationship between the failure of Fourier theory, phonon mean free paths, important length scales of the temperature profile and interfacial-phonon scattering by time-domain thermoreflectance experiments on Si, Si 0.99 Ge 0.01 , boron-doped Si and MgO crystals. The failure of Fourier theory causes anisotropic thermal transport. In situations where Fourier theory fails, a simple radiative boundary condition on the heat diffusion equation cannot adequately describe interfacial thermal transport.

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Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments

2014

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“…(25) and (26b) into Eqs. (27) and (29), the following system of equations for A, B, and C is obtained:…”

Section: A Steady-state Heat Conductionmentioning

confidence: 99%

“…22,23 This coincidence indicates that the solutions determined by Regner et al could be suitable for high frequencies but not necessarily for materials with sizes comparable to the phonon mean free path. 6 More recently, both the frequency-domain and time-domain thermoreflectance methods have been utilized to extract the mean free path and the relaxation time of phonons as fundamental properties of materials after the inspiring work by Siemens et al [24][25][26][27][28][29] Clearly, there is a strong need of phonon BTE solutions to better understand and validate data reduction schemes in these experiments, which at present are dominantly used through fitting an effective thermal conductivity or conductance with the Fourier's law. 18 The objective of this work is to analytically solve the phonon Boltzmann transport equation for the temperature profile in a dielectric film deposited on a substrate when excited with a modulated laser beam.…”

Section: -8979/2015/118(7)/075103/17mentioning

confidence: 99%

Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

Ordoñez-Miranda

Yang

Volz

et al. 2015

Journal of Applied Physics

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Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both the steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that these components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path (MFP), and they exhibit the diffusive behavior as predicted by the Fourier's law of heat conduction when this ratio is much larger than unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fourier's law. Furthermore, we derive an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gersho work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fourier's law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laserbased transient heating techniques.

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“…So far only a few experiments have followed this guideline to study l's. [13][14][15][16] Alvarez-Quintana et al studied thickness-dependent cross-plane κ of germanium-on-insulator wafer and estimated the l ∼ 20nm. 13 Johnson et al employed laserinduced transient grating method to study in-plane κ of Si membranes and found the κ deviates from diffusive behavior at several micrometers, suggesting l > 1µm.…”

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Length-dependent thermal transport and ballistic thermal conduction

et al. 2015

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Probing length-dependent thermal conductivity of a given material has been considered as an important experimental method to determine the length of ballistic thermal conduction, or equivalently, the averaged phonon mean free path (l). However, many previous thermal transport measurements have focused on varying the lateral dimensions of samples, rendering the experimental interpretation indirect. Moreover, deducing l is model-dependent in many optical measurement techniques. In addition, finite contact thermal resistances and variations of sample qualities are very likely to obscure the effect in practice, leading to an overestimation of l. We point out that directly investigating one-dimensional length-dependent (normalized) thermal resistance is a better experimental method to determine l. In this regard, we find that no clear experimental data strongly support ballistic thermal conduction of Si or Ge at room temperature. On the other hand, data of both homogeneously-alloyed SiGe nanowires and heterogeneously-interfaced Si-Ge core-shell nanowires provide undisputed evidence for ballistic thermal conduction over several micrometers at room temperature.

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Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

Cited by 372 publications

References 34 publications

Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments

Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments

Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

Length-dependent thermal transport and ballistic thermal conduction

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