Understanding and minimizing resonance frequency deviations on a 4-inch kilo-pixel kinetic inductance detector array

One of the advantages of kinetic inductance detectors is their intrinsic frequency domain multiplexing capability. However, fabrication imperfections usually give rise to resonance frequency deviations, which create frequency collision and limit the array yield. Here we study the resonance frequency deviation of a 4-inch kilo-pixel lumped-element kinetic inductance detector (LEKID) array using optical mapping. By measuring the resonator dimensions and the film thickness, most of the fractional deviation can be explained within $\pm 20\times 10^{-3}$ with a standard deviation of $8\times 10^{-3}$ ($\sim$18~MHz) of the residuals. Using the capacitor trimming technique, the fractional deviation is decreased by a factor of 10. The yield of the trimming process is found to be 97%. The mapping yield, measured under a 110~K background, is improved from 69% to 76%, which can be further improved to 81% after updating our readout system. With the improvement in yield, the capacitor trimming technique will benefit future large-format LEKID arrays.