Film-thickness dependence of 10 GHz Nb coplanar-waveguide resonators

TL;DR

This study investigates how the film thickness of Nb coplanar-waveguide resonators affects their resonant frequency and kinetic inductance, revealing significant thickness dependence due to kinetic inductance effects.

Contribution

It provides experimental evidence of film-thickness dependence on resonant frequency and kinetic inductance in Nb CPW resonators, surpassing predictions from simple circuit models.

Findings

Resonant frequency varies significantly with film thickness.

Kinetic inductance explains the observed thickness dependence.

Temperature dependence aligns with kinetic inductance theory.

Abstract

We have studied Nb lambda/2 coplanar-waveguide (CPW) resonators whose resonant frequencies are 10-11 GHz. The resonators have different film thicknesses, t=0.05, 0.1, 0.2, and 0.3 um. We measured at low temperatures, T=0.02-5 K, one of the scattering-matrix element, S_21, which is the transmission coefficient from one port to the other. At the base temperatures, T=0.02-0.03 K, the resonators are overcoupled to the input/output microwave lines, and the loaded quality factors are on the order of 10^3. The resonant frequency has a considerably larger film-thickness dependence compared to the predictions by circuit simulators which calculate the inductance of CPW taking into account L_g only, where L_g is the usual magnetic inductance determined by the CPW geometry. By fitting a theoretical S_21 vs. frequency curve to the experimental data, we determined for each film thickness, the phase velocity of the CPW with an accuracy better than 0.1%. The large film-thickness dependence must be due to the kinetic inductance L_k of the CPW center conductor. We also measured S_21 as a function of temperature up to T=4-5 K, and confirmed that both thickness and temperature dependence are consistent with the theoretical prediction for L_k.