Thermal resistance of indium coated sapphire–copper contacts below 0.1K

High thermal resistances exist at ultra-low temperatures for solid-solid interfaces. This is especially true for pressed metal-sapphire joints, where the heat is transferred by phonons only. For such pressed joints it is difficult to achieve good physical, i.e. thermal contacts due to surface irregularities in the microscopic or larger scale. Applying ductile indium as an intermediate layer reduces the thermal resistance of such contacts. This could be proven by measurements of several researchers. However, the majority of the measurements were performed at temperatures higher than 1 K. Consequently, it is difficult to predict the thermal resistance of pressed metal-sapphire joints at temperatures below 1 K. In this paper the thermal resistances across four different copper-sapphire-copper sandwiches are presented in a temperature range between 30 mK and 100 mK. The investigated sandwiches feature either rough or polished sapphire discs (empty set 20 mm x 1.5 mm) to investigate the phonon scattering at the boundaries. All sandwiches apply indium foils as intermediate layers on both sides of the sapphire. Additionally to the indium foils, thin indium films are vapour deposited onto both sides of one rough and one polished sapphire in order to improve the contact to the sapphire. Significantly different thermal resistances have been found amongst the investigated sandwiches. The lowest total thermal resistivity (roughly 26 cm(2) K-4/W at 30 mK helium temperature) is achieved across a sandwich consisting of a polished sapphire with indium vapour deposition. The thermal boundary resistance between indium and sapphire is estimated from the total thermal resistivity by assuming the scattering at only one boundary, which is the warm sapphire boundary where phonons impinge, and taking the scattering in the sapphire bulk into account. The so derived thermal boundary resistance agrees at low temperatures very well with the acoustic mismatch theory.