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International audience; We provide a derivation allowing the calculation of thermal conductance at interfaces by equilibrium molecular dynamics simulations and illustrate our approach by studying thermal conduction mechanisms in Si/Ge superlattices. Thermal conductance calculations of superlattices with period thicknesses ranging from 0.5 to 60 nm are presented as well as the temperature dependence. Results have been compared to complementary Green-Kubo thermal conductivity calculations demonstrating that thermal conductivity of perfect superlattices can be directly deduced from interfacial conductance in the investigated period range. This confirms the predominant role of interfaces in materials with large phonon mean free paths.

In the ballistic regime of transport, we derive the thermal resistance of metal nanowires connected to two heat baths. We find that the thermal resistances for any metal nanowire remain in a narrow and temperature-dependent interval between 0.447/$T$ and 14/$T$ ${\mathrm{m}}^{2}$ K/W. For cross-section edges larger than 20 nm, the thermal resistance can actually be estimated from $\frac{{R}_{0}}{(3\ensuremath{\pi}{n}_{V}^{2}){}^{3}}$, where ${R}_{0}$ is the quantum of resistance and ${n}_{V}$ refers to the electron density. This prediction yields a contact resistance one order of magnitude larger than the one of previous estimations. Significant consequences for application fields such as nanoelectronics, where nanowire sizes involve ballistic transport, are expected.

At low temperatures, thermal transport in single crystalline nanowires with sub-10-nm diameters is defined in terms of the universal quantum of conductance. In the case of a nanowire connected to plane substrates, additional conductances appear due to the contacts. We calculate the contact conductances and prove that they are much smaller than the conductance of the nanowire. The reason is that the number of excited modes per unit volume in the substrates becomes smaller than the one in the wire at low temperatures. The substrate then generates the predominant thermal resistance because its specific heat becomes smaller than the one of the wire. From these considerations, the wire-membrane and membrane-plane substrate thermal conductances can also be predicted.