Wave-like heat propagation is shown to emerge as a consequence of a rapidly varying temperature field in Ge.

We present a formalism to solve the phonon Boltzmann transport equation (BTE) for finite Knudsen numbers that supplies a hydrodynamic heat transport equation similar to the Navier-Stokes equation for general semiconductors. This generalization of Fourier's law applies in general cases, from systems dominated by momentum-preserving normal collisions, as is well known, to kinetic materials dominated by resistive collisions, where it captures nonlocal effects. The key feature of our framework is that the macrostate is described in terms of the heat flux and its first derivatives. We obtain explicit expressions for the nonequilibrium phonon distribution and for the geometry-independent macroscopic parameters as a function of phonon properties that can be calculated from first principles. Ab initio model predictions are found to agree with a wide range of experiments in silicon. In contrast to approaches directly based on the BTE, the hydrodynamic equation can be solved in arbitrary geometries, thus providing a powerful tool for nanoscale heat modeling at a low computational cost.

Significance: Oxygen heterogeneity in solid tumors is recognized as a limiting factor for therapeutic efficacy. This heterogeneity arises from the abnormal tumor vascular structure. We investigate the role that anomalies in red blood cell transport plays in establishing oxygen heterogeneity in tumor tissue. We introduce a metric to characterize tumor vasculature (mean vessel length-to-diameter ratio, λ ) and demonstrate how it predicts tissue-oxygen heterogeneity. We also report an increase in λ following treatment with the antiangiogenic agent DC101. Together, we propose λ as an effective way of monitoring the action of antiangiogenic agents and a proxy measure of oxygen heterogeneity in tumor tissue. Unraveling the causal relationship between tumor vascular structure and tissue oxygenation will pave the way for new personalized therapeutic approaches.

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.

A multiscale hydrodynamic-heat-transport model applicable to arbitrary geometries using finite-element methods is compared with the experimental effective thermal conductivity of silicon thin films and periodic holey membranes for different sizes and temperatures. The range of system length scales and temperatures in which the model predictions agree with experimental data is discussed and quantitatively determined. The model agrees with experimental results when the smallest system size is larger than twice the nonlocal length, an intrinsic property of the material that depends only on temperature. These results open the door to the use of the hydrodynamic equation instead of an effective Fourier model to interpret current heat-transport experimental data.

The hydrodynamic heat transport equation with appropriate boundary conditions and ab initio calculated coefficients is validated by comparing the corresponding analytical and numerical solutions with frequency-domain thermoreflectance experimental measurements in silicon. Special attention is devoted to identifying the resistive effects appearing at the interface between the metal transducer and the silicon substrate. We find that a Fourier model using frequency-dependent effective thermal conductivity cannot simultaneously explain the experimental phase shifts and the amplitude of the temperature oscillations, whereas the hydrodynamic model using intrinsic parameters provides good agreement across a wide temperature range. In addition, phenomenology appearing at reduced length and time scales in this kind of experiment at different temperatures is shown. Specifically, we find hydrodynamic modes of thermal transport that are analogous to pressure- and shear-wave propagation in viscoelastic media.