Estimation of the FR4 Microwave Dielectric Properties at Cryogenic Temperature for Quantum-Chip-Interface PCBs Design

Ad-hoc interface PCBs are today the standard connection between cryogenic cabling and quantum chips. Besides low-loss and low-temperature-dependent-dielectric-permittivity materials, FR4 provides a low-cost solution for fabrication of cryogenic PCBs. Here, we report on an effective way to evaluate the dielectric performance of a FR4 laminate used as substrate for cryogenic microwave PCBs. We designed a coplanar waveguide {\lambda}/2 open-circuit series resonator and we fabricated the PCB using a low-cost manufacturing process. Such a geometry allows to exploit the resonance peak of the resonator to measure the variation of the complex dielectric permittivity as a function of the temperature. Resonance peak frequency and magnitude were used as sensing parameters for the real part of dielectric permittivity and dielectric loss tangent, respectively. We estimated a 9 % reduction of the real part of the dielectric permittivity and a 70 % reduction of the dielectric loss tangent in the temperature range from 300 to 4 K. The proposed approach can be immediately extended to the detection of cryogenic temperature-dependent dielectric performance of any kind on substrate.