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Strategies for reducing frequency scatter in large arrays of superconducting resonators

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 increased numbers of resonators to further improve sensitivity, and the ability to read out large numbers of resonators without the need for additional cryogenic complexity is a primary motivation. 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 with inductor line width changing from 1.8um to 2.2um in step of 0.1um defined with electron-beam lithography to probe and quantify the systematic variation of resonance frequency across a 6-inch wafer. The resonators showed a linear frequency shift of 20MHz (140FWHM) and 30MHz (214FWHM), respectively, as they are connected to two different capacitors. This linear relationship matches our theoretical prediction. The widely used MLA photon lithography facility for MKID fabrication has a resolution on the order of 600nm, which could cause frequency fluctuation on the order of 100MHz or 710FWHM.