A semi-empirical 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 $s_r$ ranging from 3 $\mu$m to 20 $\mu$m. For a fixed internal power, we find that the frequency noise decreases rapidly with increasing center strip width, scaling as $1/s_r^{1.6}$. We show that this geometrical scaling is readily explained by a simple semi-empirical model which assumes a surface distribution of independent two-level system fluctuators. These results allow the resonator geometry to be optimized for minimum noise. 
Jiansong Gao (1), Miguel Daal (3), John M. Martinis (4), Benjamin A.   Mazin (2), Peter K. Day (2), Henry G. Leduc (2), Anas...