A semiempirical model for two-level system noise in superconducting microresonators

We present measurements of the low-temperature excess frequency noise of four niobium superconducting coplanar waveguide microresonators, with center strip widths sr ranging from 3to20μm. For a fixed internal power, we find that the frequency noise decreases rapidly with increasing center strip width, scaling as 1∕sr1.6. We show that this geometrical scaling is readily explained by a simple semiempirical model which assumes a surface distribution of independent two-level system fluctuators. These results allow the resonator geometry to be optimized for minimum noise.