Dependence of low frequency flux noise on SQUID-washer dimensions

The 1/f spectral density of low frequency magnetic flux noise at 1 Hz in dc SQUIDs and qubits varies slowly with the dimensions of the superconducting loop, in reasonably good agreement with predictions. Previous measurements on SQUIDs fabricated from a variety of superconductors under different conditions and in a variety of geometries, however, showed that the slope of the power spectrum varied considerably. We report flux noise measurements on six resistively-shunted dc SQUIDs fabricated simultaneously on a single Si chip using a Nb-trilayer process. The noise spectra of all six devices were measured using a SQUID in a single cool-down of our dilution refrigerator. The linewidths of the SQUID loops were varied systematically by a factor of more than 30. The variation in noise power at 1 Hz was small compared with the variation in line width, while the slope varied significantly, from approximately -0.5 to -1. Furthermore, for a given SQUID, the slope depended on temperature.