Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux

In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local differential terms (gradients, Laplacians) or integral terms with memory kernels. In contrast to this typical situation, which has led to substantial progress in several fields, we ask ourselves whether in some cases it would be convenient to start from non-local internal variables with non-local evolution equations. We examine this point by considering three main lengths: the observation scale R defining the elementary volumes used in the description of the system, the mean free path l of the microscopic elements of the fluid (particles, phonons, photons, and molecules), and the overall characteristic size L of the global system. We illustrate these ideas by considering three-dimensional rigid heat conductors within the regime of phonon hydrodynamics in the presence of thermal vortices. In particular, we obtain a generalization of the Guyer-Krumhansl equation, which may be of interest for heat transport in nanosystems or in systems with small-scale inhomogeneities.

Super-Ballistic Width Dependence of Thermal Conductivity in Graphite Nanoribbons and Microribbons

The super-ballistic temperature dependence of thermal conductivity, facilitated by collective phonons, has been widely studied. It has been claimed to be unambiguous evidence for hydrodynamic phonon transport in solids. Alternatively, hydrodynamic thermal conduction is predicted to be as strongly dependent on the width of the structure as is fluid flow, while its direct demonstration remains an unexplored challenge. In this work, we experimentally measured thermal conductivity in several graphite ribbon structures with different widths, from 300 nm to 1.2 µm, and studied its width dependence in a wide temperature range of 10-300 K. We observed enhanced width dependence of the thermal conductivity in the hydrodynamic window of 75 K compared to that in the ballistic limit, which provides indispensable evidence for phonon hydrodynamic transport from the perspective of peculiar width dependence. This will help to find the missing piece to complete the puzzle of phonon hydrodynamics, and guide future attempts at efficient heat dissipation in advanced electronic devices.

Universal Behavior of Highly Confined Heat Flow in Semiconductor Nanosystems: From Nanomeshes to Metalattices

Nanostructuring on length scales corresponding to phonon mean free paths provides control over heat flow in semiconductors and makes it possible to engineer their thermal properties. However, the influence of boundaries limits the validity of bulk models, while first-principles calculations are too computationally expensive to model real devices. Here we use extreme ultraviolet beams to study phonon transport dynamics in a 3D nanostructured silicon metalattice with deep nanoscale feature size and observe dramatically reduced thermal conductivity relative to bulk. To explain this behavior, we develop a predictive theory wherein thermal conduction separates into a geometric permeability component and an intrinsic viscous contribution, arising from a new and universal effect of nanoscale confinement on phonon flow. Using experiments and atomistic simulations, we show that our theory applies to a general set of highly confined silicon nanosystems, from metalattices, nanomeshes, porous nanowires, to nanowire networks, of great interest for next-generation energy-efficient devices.

Phonon hydrodynamics in crystalline materials

Phonon hydrodynamics is an exotic phonon transport phenomenon that challenges the conventional understanding of diffusive phonon scattering in crystalline solids. It features a peculiar collective motion of phonons with various unconventional properties resembling fluid hydrodynamics, facilitating non Fourier heat transport. Hence, it opens up several new avenues to enrich the knowledge and implementations on phonon physics, phonon engineering, and micro and nanoelectronic device technologies. This review aims at covering a comprehensive development as well as the recent advancements in this field via experiments, analytical methods, and state-of-the-art numerical techniques. The evolution of the topic has been realized using both phenomenological and material science perspectives. Further, the discussions related to the factors that influence such peculiar motion, illustrate the capability of phonon hydrodynamics to be implemented in various applications. A plethora of new ideas can emerge from the topic considering both the physics and the material science axes, navigating toward a promising outlook in the research areas around phonon transport in non-metallic solids.

Descriptors of intrinsic hydrodynamic thermal transport: screening a phonon database in a machine learning approach

Machine learning techniques are used to explore the intrinsic origins of the hydrodynamic thermal transport and to find new materials interesting for science and engineering. The hydrodynamic thermal transport is governed intrinsically by the hydrodynamic scale and the thermal conductivity. The correlations between these intrinsic properties and harmonic and anharmonic properties, and a large number of compositional (290) and structural (1224) descriptors of 131 crystal compound materials are obtained, revealing some of the key descriptors that determines the magnitude of the intrinsic hydrodynamic effects, most of them related with the phonon relaxation times. Then, a trained black-box model is applied to screen more than 5000 materials. The results identify materials with potential technological applications. Understanding the properties correlated to hydrodynamic thermal transport can help to find new thermoelectric materials and on the design of new materials to ease the heat dissipation in electronic devices.

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

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.