The magnetic penetration depth is a key parameter governing the electrodynamic response of superconductors and provides important insight into the superconducting state. High Q superconducting microstripline resonator, where the resonant frequency is dependent on the kinetic inductance of the superconductor, provides a sensitive tool to study the penetration depth of the superconducting thin films at microwave frequencies. While this technique gives the change in penetration depth with temperature with very high resolution, it is not easy to obtain the absolute value of the penetration depth, which has to be estimated from other measurements.

In this work, we present a new method to obtain the absolute value of the penetration depth over a wide temperature range, by combining microstripline resonator measurements with Finite-element electromagnetic simulations using COMSOL multiphysics. Superconductivity is incorporated here through a complex conductivity, [ ]​, along with appropriate boundary conditions. The imaginary component of the conductivity is related to the penetration depth via this formula . Temperature-dependent changes in penetration depth modify the film’s kinetic inductance, shifting the resonant frequency. Using COMSOL simulations, we extract the temperature dependence of the penetration depth from the measured frequency shifts. Applying this approach, we determine the absolute penetration depth of NbN films with different thicknesses.

Furthermore, we extend this technique to probe superconducting films with lower critical temperatures than NbN using NbN microstripline resonator. By placing the film above the NbN resonator and using a small insulating gap created by a Mylar sheet, we form a coupled superconducting structure. The changes in the electromagnetic field distribution and the effective inductance of the resonator lead to measurable shifts in the resonant frequency. By comparing these measurements with the simulations of the multilayer structure, we can determine temperature dependence of the penetration depth of the additional superconducting film with high sensitivity. This method offers a reliable and non-destructive way to get precise penetration depth measurements in superconducting thin films with different critical temperatures.