Compact behavioral model and parametric extraction for optical phase shifters in carrier-depletion Mach-Zehnder silicon modulators

Testing of active photonic devices is totally different from testing of pure electronics; in particular, reduction of testing time in silicon photonics has been a significant issue. In this study, a compact behavioral model of optical phase shifters is constructed for carrier-depletion Mach-Zehnder (MZ) silicon modulators in the push-pull regime. The target characteristics, i.e., the dynamic extinction ratio (ER), absorption loss, and chirp parameter, are expressed in simple forms in terms of parameters representing the voltages-dependent modulation efficiency (ME) and the imaginary part of the effective index. The parameters reflecting manufacturing variability can be quickly extracted from fast DC measurements, which shortens the testing time. The theoretical concept relies on the proposal of a generalized form of the large-signal ME and an effective approximation for model construction that avoids the problem of the conventional small-signal definition being not applicable and large signal definition leading to a cumbersome and non-intuitive formulation. It is shown that the constructed model suitably explains the physics and the reported experimental results for the slightly positive chirp characteristics of balanced phase shifters. Moreover, a parametric extraction applying the model is demonstrated in the C-band wavelength on a 300-mm SOI wafer.