A Comprehensive Equivalent Circuit Model of Silicon Microring Modulators for Photonics-Electronics Codesign

Silicon microring modulators have huge potential for applications in co-packaged optics (CPO) and optical I/O (OIO) owing to the superior bandwidth, small footprint, and inherent wavelength multiplexing characteristics. To enable efficient and robust optical transceiver systems, codesign and cosimulation environments are essential for optimization of photonic devices, transceiver circuitry and electronic-photonic integrated circuits (EPIC). We introduce a comprehensive equivalent circuit model for single- and dual-segment silicon microring modulators (MRMs), which accurately capture the device behavior during high-speed modulation. This model includes electrical parasitics, nonlinear optical steady state and dynamics, and thermo-optic effects. Model parameters are extracted by curve fitting MRM optical transmission spectrum and small signal characteristics. The simulated eye diagrams exhibit excellent alignment with the measured eye diagrams at data rates of 80 Gb/s and 106 Gb/s. A cosimulation environment with a MRM driver in 28 nm CMOS and a MRM in 130 nm silicon photonics is demonstrated on an electronics design automation (EDA) platform. An optical eye diagram at a data rate of 212 Gb/s PAM8 is successfully achieved by optimizing the driver equalizer and the MRM two segment ratio. Then an EPIC with photonics-electronics closed-loop feedback control algorithm is demonstrated, achieving a significantly larger eye opening after thermal tuning, thanks to the accurate equivalent circuit model of the MRM.