Reducing Frequency Scatter in Large Arrays of Superconducting Resonators with Inductor Line Width Control

Superconducting resonators are now found in a broad range of applications that require high-fidelity measurement of low-energy signals. A common feature across almost all of these applications is the need for an increased number of resonators to further improve sensitivity, combined with the desire to limit cryogenic readout channels and complexity. One of the major limitations of current resonator arrays is the observed scatter in the resonator frequencies when compared to the initial design. Here we present recent progress toward identifying one of the dominant underlying causes of resonator scatter - inductor line width fluctuation. We designed and fabricated an array of lumped-element resonators in which the inductor line width changes from 1.8 m to 2.2 m in steps of 0.1 m . The inductor is defined using electron-beam lithography to probe and quantify the systematic variation of resonance frequencies. Paired with two different capacitor geometries the resonators showed a linear frequency spacing of ≈20 MHz and 30 MHz, respectively, or 1.48 % and 1.96 % in fractional frequency shift ( f/f_o ). This linear relationship matches our theoretical prediction. Our result demonstrates significant improvement in resonator array frequency scatter is readily achievable if inductor line width variation is sufficiently controlled.