Calculation of the characteristics of coplanar resonators for kinetic inductance detectors

Photon detectors based on the change of kinetic inductance of a thin superconducting film have a number of applications, particularly in astronomy, owing to their high sensitivity and ease of integration into large arrays. Here we discuss in detail the analysis of kinetic inductance detectors that use thin film microwave coplanar resonators. Photon absorption decreases the electron pair density, increasing the magnetic penetration depth λ, which causes a decrease in the resonant frequency (or phase) of an irradiated resonator. To quantify this effect, we first compute the resonator current distribution, from which the λ-dependent parameters (such as kinetic inductance) are calculated. Optimum responsivity for phase measurement is achieved by using the thinnest film with the narrowest center conductor width at the lowest possible temperature. However, the responsivity is compromised by extrinsic microwave losses, in particular due to residual surface resistance, which is likely to be significant in the thinnest films.