On the interplay between kinetic inductance fraction and Kerr non-linearities in superconducting resonators for millimeter wave detection

Following their proof-of-concept paper published in 2003, in the span of ten years Microwave Kinetic Inductance Detectors (MKIDs) found both widespread scientific interest in the superconducting electronics community and in technological applications as particle detectors. We explore the possibility of using Granular Aluminum (GrAl) with the goal of decreasing the Noise Equivalent Power (NEP) of the resulting MKIDS. One of the most attractive features of GrAl films is the wide-range tunability of the sheet resistance, which is in turn directly linked to the kinetic inductance. To exploit this resource we propose a theoretical model for the dependence of the NEP with the kinetic inductance fraction of the detector. We quantify the interplay between kinetic inductance fraction and non-linearities and we determine the kinetic inductance fraction value that gives the lowest NEP.