Frequency- and Time-Domain Modeling and Characterization of PN Phase Shifters in All-Silicon Carrier-Depletion Modulators

We present a systematic study on PN junction phase shifters in silicon Mach-Zehnder modulators (MZMs) in both frequency and time domains, with an emphasis on their impact on MZMs' RF loss. The RF loss associated with PN phase shifters dominates the overall RF loss of a MZM's transmission line and determines a MZM's bandwidth. The RF loss is also evident in the time domain, which for the first time is investigated. We find that the dielectric loss and conductor loss of a PN-loaded, lossy transmission line result in downhill and uphill features on the instantaneous impedance curve, which features are typically observed on the instantaneous impedance of an inductor and a capacitor, respectively. This is aligned with our model, which shows that the impedance of a PN-loaded lossy line includes an inductor term and a capacitor term and their values are expressed in terms of RF loss. Our model on RF loss and impedance agrees well with experiment in both domains for a variety of doping levels. Finally, we conduct performance test on modulators and discuss the constraints on the baud-rates and BERs in our QAM tests.