A General and Predictive Understanding of Thermal Transport from 1D- and 2D-Confined Nanostructures: Theory and Experiment

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 geometrydependent 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.

Atomistic evidence of hydrodynamic heat transfer in nanowires

“…However, it has recently been shown that this description is also relevant for room temperature applications in general semiconductors like Si [9,11]. The derived set of equations can be solved using the finite element method, to model the thermal relaxation of nanostructured heat sources on Si substrate [12] or thermoreflectance experiments [13].…”

Non-monotonic heat dissipation phenomenon in close-packed 2D and 3D hotspot system

“…Except above situations, recent studies have revealed the importance of the distance between adjacent nanoscale heat sources on heat dissipations in hotspot systems [30,31,32,33,34]. In 2014, Zeng et al [32] studied quasiballistic heat conduction for quasi-2D nanoline heat sources periodically deposited on a substrate based on the frequency-independent phonon Boltzmann transport equation (BTE) under the single-mode relaxation time approximation model.…”

“…However, the fundamental physical mechanisms of this novel phenomenon are still not unified. In addition, it's worth noting that various macroscopic constitutive relationships between the heat flux and temperature are used to fit the experimental data in different research groups [32,30,36,33]. By artificial fitting, an effective thermal conductivity can be obtained, which varies non-monotonously when the distance between the nanoscale hotspot decreases gradually.…”

“…By artificial fitting, an effective thermal conductivity can be obtained, which varies non-monotonously when the distance between the nanoscale hotspot decreases gradually. Usually, the heat diffusion equation with a constant effective thermal conductivity is widely used during data post-processing, as did by Hoogeboom-Pot et al [30] and Zeng et al [32], but this model cannot simultaneously fit both amplitude and phase well [35,33,36]. Under the semi-infinite assumption, Hua and Minnich [36] obtained a constitutive relationship between the heat flux and temperature by analytically deriving the phonon BTE under the single-mode relaxation time approximation model, which is valid for all phonon transport regimes.…”

“…However, this analytical strategy is much challenging for complex geometries and hotspot systems with finite size. Beardo et al used a macroscopic moment equation with adjustable parameters to fit the experimental data, and both the nonlinear and nonlocal terms of the heat flux are accounted in their model [33]. They uncovered the existence of two time scales: an interface resistance regime that dominates on short time scales and a quasiballistic phonon transport regime that dominates on longer time scales.…”