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

We demonstrate voltage-tunable thermo-optic bi- and tri-stability in silicon photonic microring resonators with lateral p-i-n junctions and present a technique for characterizing the thermo-optic transient response of integrated optical resonators. Our method for thermo-optic transient response measurement is applicable to any integrated photonics platform and uses standard equipment. Thermo-optic relaxation in encapsulated waveguides is found to be approximately logarithmic in time, consistent with the analytic solution for 2D heat diffusion. We develop a model for thermo-optic microring multi-stability and dynamics which agrees with experiment data over a wide range of operating conditions. Our work highlights the fundamental connection in semiconductor waveguides between active free-carrier removal and thermo-optic heating, a result of particular relevance to Kerr soliton state stability and on-chip frequency comb generation. The devices studied here were fabricated in a CMOS foundry process and as a result our model is useful for design of silicon photonic waveguide devices.