Study of nonlinear effects and self-heating in a silicon microring resonator including a Shockley-Read-Hall model for carrier recombination

Abstract

A detailed description of the non-linear effects in silicon is needed when designing ring resonators in the silicon platform. The optical field propagating in the ring waveguide is strongly absorbed due to two-photon-absorption (TPA) and free-carrier-absorption (FCA), which become more prominent with increasing the input power in the ring. We present a new approach for the modelling of non-linear effects in silicon based ring resonators. We have numerically solved the non-linear problem coupling the variation of refractive index and loss due to TPA, FCA , self-heating and Shockley-Read-Hall (SRH) theory for trap-assisted recombination process. The model is validated by reproducing experimental measurements on a ring and a racetrack resonator having different Q-factors and waveguide cross-sections. As a result, we show that the SRH recombination is the origin of the dependence of free carrier lifetime on the power circulating in the ring and how this dependence is affected by the surface trap density and trap energy level. The model is then applied to the calculation of the maximum power that can incident the silicon rings designed for the Si PIC mirror of a hybrid III-V/Si widely tunable laser.

Dynamics of Free Carrier Absorption and Refractive Index Dispersion in Si and Si/PolySi Microrings

“…With this approach, the carrier lifetimes in both structures can be retrieved demonstrating that in poly-Si they are one order of magnitude smaller than in Si waveguides. We validate our procedure by comparing the experimental results with ad hoc simulations, including trap-assisted recombination [2]. II.…”

“…Silicon microring resonators (MRRs) are important components in photonics integrated circuits due to their lowcost, low-power, and small-size properties achievable with CMOS fabrication processes [1]. One of the main drawbacks of using silicon at optical communication wavelengths is that Two-photon absorption (TPA), free carrier absorption (FCA), and dispersion (FCD) pose limitations to the power entering the MRR [2]. This problem is of great importance when employing microrings for hybrid tunable lasers based on the Vernier effect [3].…”

“…shift of the ring resonant wavelength. It is determined by trapassisted non-radiative Shockley-Read-Hall (SRH) recombination [6] and thus by the density of holes in the valence band and of electrons in the conduction band [2]. Unfortunately, given the same electron and hole density in the Si and poly-Si core, the FCA in polysilicon is higher compared to crystalline silicon [7] since the FCA scales, as a first approximation, as 1/µ n,p [8] (with µ n,p the carrier mobility) and the mobility in poly-Si is lower depending on the grain size and the number of grain boundaries that populate the material [9].…”

“…Since the pump repetition rate (4 kHz) is much larger than the pump pulse, we avoid any thermal effects. To understand the experimental results, we employ the model we developed in [2] to simulate the CW nonlinear response of silicon MRR. The model in [2] can be extended to the time domain [10] to simulate the nonlinear response of the ring after the pump pulse.…”

“…To understand the experimental results, we employ the model we developed in [2] to simulate the CW nonlinear response of silicon MRR. The model in [2] can be extended to the time domain [10] to simulate the nonlinear response of the ring after the pump pulse. FC recombination is modeled by trap-assisted Shockley-Read-Hall (SRH) rate equations [2].…”