Effect of surface roughness on the anomalous heat conductance at solid/superfluid helium interfaces: a way of quantifying phonon scattering in microstructures

Heat transfer mechanisms at very small length scales are studied at the boundary between solid and superfluid helium-4 (He II) at temperatures of 1-2 K. We shall show that this configuration is interesting and may prove useful in future heat conduction analysis in microstructures and across film/substrate boundaries. We define two possible heat conduction regimes, namely a classical surface effect regime and a scattering effect regime for the solid/He II system. The distinction between these regimes depends upon the (l/λ) ratio, where the surface roughness extent is l at a given length scale and the phonon wavelength is λ. We analyse our results of heat conduction across solid-superfluid helium interfaces and we show that the conductance can be entirely explained by the scattering effect regime where diffuse phonon scattering from surface irregularities of nanometric scale lengths play a dominant role. We also provide evidence of the existence of a frequency dependence of the heat transmission coefficient and, we compare the heat conduction with that in microstructures