Volume 72, Issue 2 - Special Issue: Heat Transfer and Heat Conduction on the Nanoscale / Guest Editors: Svend-Age Biehs, Philippe Ben-Abdallah, Achim Kittel

An electromagnetic theory of thermal radiation is outlined, based on the fluctuation electrodynamics of Rytov and co-workers. We discuss the basic concepts and the status of different approximations. The physical content is illustrated with a few examples on near-field heat transfer.

We present a generalisation of the Debye relaxation model for the dielectric permittivity in the case in which the global relaxation process is the result of many elementary excitations. The relaxation dynamics is in this case non-Markovian. In the case of many events, for which the central limit theorem holds and Gaussianity as well as the assumption of independency are both plausible, the global relaxation time is given by a log-normal function. The hierarchy of relaxation times leads to a generalised expression of the dielectric permittivity.

We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also compare the exact results with predictions from effective medium theory.

We present a theoretical study of the limits and bounds of using effective medium approximations in the calculation of the near field radiative heat transfer between a composite system made of Au nanoparticles in a SiC host and an homogeneous SiC slab. The effective dielectric function of the composite slab is calculated using three different approximations: Maxwell-Garnett, Bruggeman, and Looyenga’s. In addition, we considered an empirical fit to the effective dielectric function by Grundquist and Hunderi. We show that the calculated value of the heat flux in the near field is dependent on the model, and the difference in the effective dielectric function is larger around the plasmonic response of the Au nanoparticles. This, in turn, accounts for the difference in the near field radiative heat flux. For all values of filling fractions, the Looyenga approximation gives a lower bound for the heat flux.

We demonstrate that the energy transport of surface phonon-polaritons can be large enough to be observable in a crystal made up of a three-dimensional assembly of nanorods of silicon carbide. The ultralow phonon thermal conductivity of this nanostructure along with its high surface area-to-volume ratio allows the predominance of the polariton energy over that generated by phonons. The dispersion relation, propagation length, and thermal conductance of polaritons are numerically determined as functions of the radius and temperature of the nanorods. It is shown that the thermal conductance of a crystal with nanorods at 500 K and diameter (length) of 200 nm (20 μm) is 0.55 nW·K −1 , which is comparable to the quantum of thermal conductance of polar nanowires.

We describe a recently developed formulation of coupled conductive and radiative heat transfer (RHT) between objects separated by nanometric, vacuum gaps. Our results rely on analytical formulas of RHT between planar slabs (based on the scattering-matrix method) as well as a general formulation of RHT between arbitrarily shaped bodies (based on the fluctuating–volume current method), which fully captures the existence of temperature inhomogeneities. In particular, the impact of RHT on conduction, and vice versa, is obtained via self-consistent solutions of the Fourier heat equation and Maxwell’s equations. We show that in materials with low thermal conductivities (e.g. zinc oxides and glasses), the interplay of conduction and RHT can strongly modify heat exchange, exemplified for instance by the presence of large temperature gradients and saturating flux rates at short (nanometric) distances. More generally, we show that the ability to tailor the temperature distribution of an object can modify the behaviour of RHT with respect to gap separations, e.g. qualitatively changing the asymptotic scaling at short separations from quadratic to linear or logarithmic. Our results could be relevant to the interpretation of both past and future experimental measurements of RHT at nanometric distances.

The control of electric currents in solids is at the origin of the modern electronics revolution that has driven our daily life since the second half of 20 th century. Surprisingly, to date, there is no thermal analogue for a control of heat flux. Here, we summarise the very last developments carried out in this direction to control heat exchanges by radiation both in near and far-field in complex architecture networks.

We study in this article how heat can be exchanged between two-level systems, each of them being coupled to a thermal reservoir. Calculations are performed solving a master equation for the density matrix using the Born–Markov approximation. We analyse the conditions for which a thermal diode and a thermal transistor can be obtained as well as their optimisation.

The dependence of the Casimir friction force between a graphene sheet and a (amorphous) SiO 2 substrate on the drift velocity of the electrons in the graphene sheet is studied. It is shown that the Casimir friction is strongly enhanced for the drift velocity above the threshold velocity when the friction is determined by the resonant excitation of the surface phonon–polaritons in the SiO 2 substrate and the electron–hole pairs in graphene. The theory agrees well with the experimental data for the current–voltage dependence for unsuspended graphene on the SiO 2 substrate. The theories of the Casimir friction and the near-field radiative energy transfer are used to study the heat generation and dissipation in graphene due to the interaction with phonon–polaritons in the (amorphous) SiO 2 substrate and acoustic phonons in graphene. For suspended graphene, the energy transfer coefficient at nanoscale gap is ~ three orders of magnitude larger than the radiative heat transfer coefficient of the blackbody radiation limit.

Phonons (collective atomic vibrations in solids) are more effective in transporting heat than photons. This is the reason why the conduction mode of heat transport in nonmetals (mediated by phonons) is dominant compared to the radiation mode of heat transport (mediated by photons). However, since phonons are unable to traverse a vacuum gap (unlike photons), it is commonly believed that two bodies separated by a gap cannot exchange heat via phonons. Recently, a mechanism was proposed [J. B. Pendry, K. Sasihithlu, and R. V. Craster, Phys. Rev. B 94 , 075414 (2016)] by which phonons can transport heat across a vacuum gap – through the Van der Waals interaction between two bodies with gap less than the wavelength of light. Such heat transfer mechanisms are highly relevant for heating (and cooling) of nanostructures; the heating of the flying heads in magnetic storage disks is a case in point. Here, the theoretical derivation for modelling phonon transmission is revisited and extended to the case of two bodies made of different materials separated by a vacuum gap. Magnitudes of phonon transmission, and hence the heat transfer, for commonly used materials in the micro- and nano-electromechanical industry are calculated and compared with the calculation of conduction heat transfer through air for small gaps as well as the heat transfer calculation due to photon exchange.

The majority of the silicon devices contain amorphous phase and amorphous/crystalline interfaces which both considerably affect the transport of energy carriers as phonons and electrons. In this article, we investigate the impact of amorphous phases (both amorphous silicon and amorphous SiO 2 ) of silicon nanoporous membranes on their thermal properties via molecular dynamics simulations. We show that a small fraction of amorphous phase reduces dramatically the thermal transport. One can even create nanostructured materials with subamorphous thermal conductivity, while keeping an important crystalline fraction. In general, the a-SiO 2 shell around the pores reduces the thermal conductivity by a factor of five to ten compared to a-Si shell. The phonon density of states for several systems is also given to give the impact of the amorphisation on the phonon modes.