The Kapitza resistance

A thermal contact resistance is the abrupt drop in temperature that occurs when a heat flux crosses an interface. Despite many experiences and several theories, the origin of this phenomenon has remained a mystery since its first observation by Kapitza in 1941.

Silicon / Superfluid Helium interface

By measuring directly the thermal contact resistance at Silicon/Superfluid Helium interface we have demonstrated that heat transmission at interfaces is controlled by the surface roughness.

The Adamenko and Fuck's theory predicts that a resonant scattering occurs when the roughness is approximately one third of the phonon wavelength in the less dense medium (Superfluid Helium here). This resonant scattering can be seen as an enhancement of the heat transfer due to intense roughness/phonon interactions at the interface.

Experimentally, the wavelength was tuned by monitoring both the temperature (0.5 - 2K) and the pressure (saturated vapor pressure - 25bar) in the Superfluid Helium. It was then correlated with the surface roughness of the Silicon crystal which was fully characterized by atomic force microscopy. Our measurements follow remarkably the Adamenko and Fuck's theory, clearly demonstrating that phonons interact selectively with the roughnesses at the interface.

These results can be generalised to control the heat tranfer across any rough interface. Indeed, here helium is used because it's liquid down to the lowest temperature where the thermal resistance is the biggest, but the theory can work with any solid/liquid interface or solid/solid interface.

Artistic view of the phonon transmission at a rough interface between a solid an a liquid

Experimental data of the relation between the surface roughness and the phonon wavelength

Silicon / Solid Helium interface

The quantum aspects of solid Helium are both very interesting and very challenging to study because of the extreme conditions to obtain solid Helium. By increasing the Helium pressure above 25 bars while regulating the temperature at 0.78K, we grew a Helium crystal on the surface of the silicon crystal. As a result, the thermal contact resistance dropped instantly by a factor 2 compared to the resistance just before solidification. It is the signature of a first order transition in the thermal contact resistance.

The observed drop can't be explained only by the transmission of the transverse modes that were not allowed in the liquid Helium, or by the conventional mismatch models used for solid/solid interfaces. Our solution is to combine the resonant scattering effect, due to the roughness at the interface, and the interactions of phonons with the moving dislocations in solid Helium. We show that fluttering dislocations dominate the thermal contact resistance and account for previous experiments.

Transition of the thermal contact resistance upon Helium solidification