Frequency mismatches between resonators significantly impact the spectral responses of coupled resonator filters, such as high-order microring filters. In this paper, techniques allowing fabrication of frequency-matched high-index-contrast resonators are proposed, demonstrated, and analyzed. The main approach consists of inducing small dimensional changes in the resonators through alteration of the electron-beam dose used to expose either the actual resonator on a wafer or its image on a lithographic mask to be later used in filter fabrication. Third-order microring filters fabricated in silicon-rich silicon nitride, with optical resonator frequencies matched to better than 1 GHz, are reported. To achieve this, the average ring-waveguide widths of the microrings are matched to within less than 26 pm of a desired relative width offset. Furthermore, optimization and calibration procedures allowing strict dimensional control and smooth sidewalls are presented. A 5-nm dimensional control is demonstrated, and the standard deviation of sidewall roughness is reduced to below 1.6 nm.
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Barwicz et al. (2006) studied this question.