Planar superconducting resonators are now being increasingly used at mK
temperatures in a number of novel applications. They are also interesting
devices in their own right since they allow us to probe the properties of both
the superconductor and its environment. We have experimentally investigated
three types of niobium resonators - including a lumped element design -
fabricated on sapphire and SiO_2/Si substrates. They all exhibit a non-trivial
temperature dependence of their centre frequency and quality factor. Our
results shed new light on the interaction between the electromagnetic waves in
the resonator and two-level fluctuators in the substrate.Comment: V2 includes some minor corrections/changes. Submitted to PR
