Determination of microwave material properties at cryogenic temperatures

Quantum information processing systems rely on cryogenic microwave electronics, and printed circuit board (PCB) laminates play an essential role, including integrating quantum chips and connecting microwave circuit elements. In this Letter, we report a method for accurately determining the microwave conductivity and complex permittivity of PCB laminates over a wide temperature range, from 4 to 300 K. The use of higher-order resonant modes of a balanced-type circular disk resonator (BCDR) enables broadband measurements ranging from below 5 GHz to above 20 GHz. Furthermore, a temperature-independent determination scheme is achieved by employing a pair of BCDRs and a cryogenic calibration technique. This method is demonstrated by measuring two commercially available PCB laminates. The results indicate that while dielectric loss is monotonically reduced at cryogenic temperatures, the reduction in conductor loss is strongly suppressed by the surface roughness of the copper foil. Additionally, the obtained conductivity as a function of frequency and temperature fits well with the Gradient Model, allowing for the evaluation of the root mean square roughness parameter.