Variation of Signal Reflection on Electrodes of Silicon Mach-Zehnder Modulators: Influence of Nanoscale Variation and Mitigation Strategies.

Driving signal reflection on traveling wave electrodes (TWEs) is a critical issue in Mach-Zehnder modulators. Fabrication variation often causes a random variation in the electrode impedance and the signal reflection, which induces modulation characteristics variation. The variation of reflection could be intertwined with the variation of other electrode characteristics, such as microwave signal attenuation, resulting in complexity. Here, we characterize the (partial) correlation coefficients between the reflection and modulation characteristics at different bit rates. Decreasing correlation at higher bit rates is observed. Device physics analysis shows how the observed variation can be related to nanoscale variation of material properties, particularly in the embedded diode responsible for electro-optic modulation. We develop a detailed theory to analyze two variation modes of the diode (P-i-N diode or overlapping P/N regions), which reveal insight beyond simplistic diode models. Microwave signal attenuation tends to reduce the correlation with on-electrode reflection, particularly at high bit rates. The theory shows the relative importance of conductor-induced attenuation and "dielectric"-induced attenuation, with different dependence on the frequency and fabrication variation. Strategies on how to mitigate the effect of variation for better fabrication tolerance are discussed by considering three key factors: pre-shift in structural design, bias condition, and fabrication control accuracy.