Indications of Phonon Hydrodynamics in Telescopic Silicon Nanowires

Abstract

The validity of Fourier's law in telescopic nanowires is tested by means of molecular dynamics simulations. We observe that the radial dependence of the heat-flux profile, the temperature jump, and the appearance of vorticity obtained in molecular dynamics telescopic wires near the contact point acquire a hydrodynamic character, and we show that they are incompatible with Fourier's law. We propose the Guyer-Krumhansl equation as a generalization capable of capturing these hydrodynamic effects. Latticedynamics results show that the thermal average of the confined modes shows no radial dependence of the vibrating energy inside the wire. This means that hydrodynamic effects could not be related to the confinement effects in these small systems.

Atomistic evidence of hydrodynamic heat transfer in nanowires

“…NWs [27]. Again, it is worth noting that both κ Hyd and in equation ( 5) are linked to the phonon lifetime, that increases as the radius increases, so this can explain the variations of κ Hyd and (see appendix Appendix C).…”

“…In the present work, the use of the ab initio calculated volumic parameters and κ Hyd is precluded due to the small NW diameters [39]. However, the model can be still used with effective parameters to interpret the MD simulations as done for previous studies [27].…”

“…A decrease of the thermal conductivity can be obtained, either by inducing back-scattering or by promoting diffusive scattering over reflection [23]. This influence of the boundaries leads to a non-uniform radial flux distribution, that can be observed in MD or in Monte-Carlo solvers of the PB equation [26,27].…”

“…In this work, the radial flux distribution in pristine and core/shell Si NWs is obtained with MD and then analyzed at the mesoscopic level of description using the hydrodynamic heat transport equation. Such comparative studies between phonon hydrodynamic transport and MD have already been carried in telescopic Si NW [27], and used to model second sound in germanium [37]. First, the methods used and the NWs studied will be presented.…”

A novel transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport

“…Note: There are some disputes about the term "hydrodynamic phonon transport" or "phonon hydrodynamic" in different references [11,3,43,32,33]. One of them [11,23] focus on the hydrodynamic phenomena of phonon transport due to strong N-scattering, while the other [43,44,3,45] uses the hydrodynamic equations to describe the quasiballistic or non-diffusive phonon transport, where the strong N scattering is not required. In this study, the hydrodynamic phonon transport happens when the N scattering is much stronger than the boundary scattering and the boundary scattering is much stronger than the R scattering [8,7,32,33].…”