Homodyne Detection of Free Carrier Induced Electro-Optic Modulation in Strained Silicon Resonators

In the last few years, strained silicon has been proposed as a potential electro-optic material, paving the way to the realization of ultrafast modulators which are compatible with the CMOS fabrication technology. The linear Pockels effect has been used for measuring the magnitude of the induced $\chi ^{(2)}$ components, with values reaching hundreds of $\text{pm/V}$. Recently, it has been shown that these values could have been overestimated due to the contribution of free carriers to the electro-optic modulation. In this work, this hypothesis is validated by a series of experimental observations, which are performed on strained silicon racetrack resonators. These are fabricated with different waveguide widths and orientations. We use a low frequency (KHz) homodyne detection technique to monitor the electro-optic response of the devices. The results indicate that the modulation strength is not dependent on the waveguide geometry or direction. A lot of anomalies are encountered in the device response, which are not compatible with a modulation mechanism of $\chi ^{(2)}$ origin. To this purporse, a theory based on the nonlinear injection of free carriers inside the waveguide is presented. This is able to account for all the observed anomalies.