Table 2 Resonator properties. Extracted parameters for the two films with varying dielectric configurations. The sheet resistance \(R^{\mathrm{sq,dc}}\) and critical temperature \(T_{c}^{\mathrm{dc}}\) are obtained from a dc measurement. The rf sheet kinetic inductance \(L_{\mathrm{k}}^{\mathrm{sq,rf}}\) is independently inferred from the 8 measured resonance frequencies of either film, where the error represents the root variance. \(Q_{\mathrm{TLS}}\), \(Q_{\mathrm{other}}\), \(n_{c}\) and β are fit parameters of Eq. (3). The paramagnetic impurities leading to the feature in Fig. 4a) are characterized by the minimum internal Q-factor \(Q_{i}^{s}\) and feature width \(\Delta _{s}\). The values of D, \(Q_{\mathrm{TLS}}\), \(Q_{\mathrm{other}}\), \(n_{c}\), β, \(Q_{i}^{s}\), and \(\Delta _{s}\) represent weighted averages over the data sets of 4 resonators of either dielectric configuration with weights proportional to the inverse of the error bar of the fit, resulting in a maximum weight, if \(Q_{c}\sim Q_{i}\) for which the resonance is most pronounced. \(g_{s}\) is the Landé g-factor extracted from Fig. 4b). The color code corresponds to Fig. 1b)

From: Performance of high impedance resonators in dirty dielectric environments