Properties of superconducting planar resonators at millikelvin temperatures

Planar superconducting resonators are now being increasingly used at mK temperatures in a number of novel applications. We have experimentally investigated three types of niobium resonators including a lumped-element design fabricated on sapphire and SiO₂/Si substrates. They all exhibit a nonmonotonic temperature dependence of their center frequency which could be accurately described by resonant absorption by two-level fluctuators (TLF). By analyzing the temperature dependence we extracted information about the distribution of TLF. Our results are consistent with there being a spread of TLF at the interface between superconductor and substrate.