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 used to develop accurate standard models for cryogenic, probe-level, calibrations substrates. 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. After, these component are simulated using 2.5D EM solvers including their mechanical variation when exposed to cryogenic temperatures, to extract their nominal response at 7 Kelvin. The quality of the resulting calibrations at cryogenic is evaluated first using independent CPW lines on the calibration substrates and then by measuring the response of 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.