Calorimetric measurements of microwave surface resistance at cryogenic temperatures

The measurement of the surface resistance has always been a difficult challenge at microwave frequencies, especially if it concerns superconductors in the transition region where the accuracy of the measurements is strongly influenced by the temperature fluctuations. In this paper we present a new method to measure the microwave surface resistance of superconducting thin-films at cryogenic temperatures. The method, based on the principle of the equivalence of the thermal effects, is effective for the superconductors that generally have a good bolometric behavior in the transition region. It is a complementary approach to the usual resonant cavity methods which fail near the T_c because of thermal instability. In practice we use a microcalorimeter whose thermal load is a superconducting thin-film that works as a matched bolometer in a quasiadiabatic environment and in a well known thermodynamical equilibrium. The total uncertainty of the surface resistance measurements made with our method is estimated to be about 1.5%. The apparatus has been tested in the Ka frequency band (26.5 to 40) GHz for low-T_c superconductors and it is also proposed for the high-T_c thin-films that require a thermal environment less critical than liquid helium