Evaluation of quality factors in superconductor microresonators with proximity enhancement

Abstract

The quality factor of microstrip line resonators made of 20/50/20 nm Nb/NbN/Nb trilayer films has been calculated as microwave transmission through the cascade of three single layers, and in agreement with experimental data. Each layer is evaluated with an explicit extended Zimmermann expression. The formula is generalized from the standard expression by including electron mean free path and the imaginary part of the gap energy of the material [1]. The quality factor of the microresonator consisting of a 50 nm thick single layer Nb film is also calculated by this compact expression and quantitatively agrees with the measured results as well. The quality factor of the microresonator made of trilayer films is shown to be larger than that of the microresonator with only a single Nb film.