Abstract
Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Past experimental and theoretical works exploring nanoscale heat transport in semiconductors addressed known deviations from Fourier’s law modeling by including effective parameters, such as a size-dependent thermal conductivity. However, recent experiments have qualitatively shown behavior that cannot be modeled in this way. Here, we combine advanced experiment and theory to show that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be described using a general hydrodynamic heat transport model, contrary to previous understanding of heat flow in bulk silicon. We use a comprehensive set of extreme ultraviolet scatterometry measurements of nondiffusive transport from transiently heated nanolines and nanodots to validate and generalize our ab initio model, that does not need any geometry-dependent fitting parameters. This allows us to uncover the existence of two distinct time scales and heat transport mechanisms: an interface resistance regime that dominates on short time scales and a hydrodynamic-like phonon transport regime that dominates on longer time scales. Moreover, our model can predict the full thermomechanical response on nanometer length scales and picosecond time scales for arbitrary geometries, providing an advanced practical tool for thermal management of nanoscale technologies. Furthermore, we derive analytical expressions for the transport time scales, valid for a subset of geometries, supplying a route for optimizing heat dissipation.
Highlights
Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime
We show that heat transport away from nanoscale sources on bulk silicon can be predicted by the hydrodynamic equation
For the thermal boundary resistance, which is an intrinsic property that depends only on the materials and the fabrication process, we use R1 = 2.25 nKm2/W for all nanostructure geometries, which agrees with previous extreme ultraviolet (EUV) scatterometry measurements on these samples[9] and is close (∼2×) to the value obtained from time-domain thermoreflectance.[45]
Summary
Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Recent works have used this effective Fourier model to analyze heat dissipation away from metallic nanostructures of varying size and spacing.[5−9,11] This can quantify the deviation from the diffusive prediction by fitting either an effective thermal boundary resistance between the transducer and substrate[7−9] or an effective thermal conductivity of the substrate.[5,6,12,34−36] These techniques have significantly advanced our understanding, making it possible to develop new experimental mean free path spectroscopy techniques,[1] as well as uncovering new transport regimes dominated by the heat source spacing.[7,8] using Fourier’s law as a mesoscopic model, even with effective parameters, can obscure the underlying physics and fails to predict thermal transport observed for all time and length scales.[19,22] Most importantly, this approach is difficult to generalize to arbitrary geometries or materials
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