Abstract
Studying thermal transport at the nanoscale poses formidable experimental challenges due both to the physics of the measurement process and to the issues of accuracy and reproducibility. The laser-induced transient thermal grating (TTG) technique permits non-contact measurements on nanostructured samples without a need for metal heaters or any other extraneous structures, offering the advantage of inherently high absolute accuracy. We present a review of recent studies of thermal transport in nanoscale silicon membranes using the TTG technique. An overview of the methodology, including an analysis of measurements errors, is followed by a discussion of new findings obtained from measurements on both “solid” and nanopatterned membranes. The most important results have been a direct observation of non-diffusive phonon-mediated transport at room temperature and measurements of thickness-dependent thermal conductivity of suspended membranes across a wide thickness range, showing good agreement with first-principles-based theory assuming diffuse scattering at the boundaries. Measurements on a membrane with a periodic pattern of nanosized holes (135nm) indicated fully diffusive transport and yielded thermal diffusivity values in agreement with Monte Carlo simulations. Based on the results obtained to-date, we conclude that room-temperature thermal transport in membrane-based silicon nanostructures is now reasonably well understood.
Highlights
For silicon membranes with thicknesses comparable to the phonon mean free path (MFP), the in-plane heat transport is normally still described by the diffusion equation, but the thermal diffusivity is reduced compared to the bulk value due to phonon scattering at the boundaries
We have seen that the application of the thermal grating (TTG) method to studying thermal transport in silicon membranes already resulted in some important findings. (i) It permitted a direct observation of nondiffusive phonon-mediated transport at room temperature
“Direct” here means that the deviation from the diffusion model could be seen directly from the deviation of the measured thermal decay rate from a quadratic dependence on the TTG wavevector, without any further analysis. That this experiment could be as well done on a bulk sample;[58] thin membranes were used for technical reasons, to ensure one-dimensional thermal transport to simplify the interpretation of the measurements. (ii) Measurements of thickness-dependent thermal conductivity of suspended membranes across a wide thickness range showed a good agreement with the Fuchs-Sondheimer model employing first-principles-calculated phonon lifetimes and assuming diffuse scattering at the boundaries
Summary
Thermal transport in nanostructures and nanostructured materials has recently become an area of much interest due to novel phenomena that emerge for many materials on the nanoscale, as well as the associated implications for practical engineering efforts in the fields of thermoelectrics and microelectronics.[1,2,3,4] Much recent experimental effort has been concentrated on studying phononmediated thermal transport in silicon nanostructures.[5,6,7,8,9,10,11,12,13,14] The focus on silicon is explained on one hand by the practical importance of this material for many applications, and on the other hand by the fact that silicon serves as a convenient “model material” as it has been very thoroughly studied and is readily amenable to nanofabrication. Oftentimes key conclusions are drawn on the basis of absolute values of the measured thermal conductivity.[5,6] accurate measurements of thermal conductivity are difficult even in bulk materials, as illustrated by the effort involved in quantifying the isotope effect on the room temperature thermal conductivity of Si.[18] The difficulties are greatly amplified in thermal conductivity measurements on nanostructures: for example, the device-based approach, in which the measurement device is fabricated together with the nanostructure to be measured,[19] challenges the notions of reproducibility and benchmarking in metrology. We conclude with a discussion of future prospects, challenges, and opportunities for studying thermal transport in nanostructures using the TTG method
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