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We demonstrate voltage-tunable thermo-optic bi- and tri-stability in siliconphotonic microring resonators with lateral p-i-n junctions and present atechnique for characterizing the thermo-optic transient response of integratedoptical resonators. Our method for thermo-optic transient response measurementis applicable to any integrated photonics platform and uses standard equipment.Thermo-optic relaxation in encapsulated waveguides is found to be approximatelylogarithmic in time, consistent with the analytic solution for 2D heatdiffusion. We develop a model for thermo-optic microring multi-stability anddynamics which agrees with experiment data over a wide range of operatingconditions. Our work highlights the fundamental connection in semiconductorwaveguides between active free-carrier removal and thermo-optic heating, aresult of particular relevance to Kerr soliton state stability and on-chipfrequency comb generation. The devices studied here were fabricated in a CMOSfoundry process and as a result our model is useful for design of siliconphotonic waveguide devices.

Thermo-Optic Multi-Stability and Relaxation in Silicon Microring Resonators with Lateral Diodes