Impedance Standard Substrate Characterization and EM model definition for Cryogenic and Quantum-Computing Applications

In this contribution, we describe the modeling approaches and the characterization procedures to develop accurate standard models for cryogenic, probe-level, calibrations of planar devices. The key electrical and mechanical parameters of the impedance terminations and the lines used in commercially available impedance standard substrates are first characterized versus temperature, then simulated considering their mechanical deviations due to the temperature variations, employing 2.5D EM solvers to extract accurate standard models. The quality of the resulting calibrations at cryogenic is evaluated using independent CPW lines on the calibration substrates and a transformer-based resonator realized on a Si-based technology. Ambient temperature models are used as a comparison, to highlight the accuracy improvement that can be achieved employing optimized Cryo-EM based models.