# Low-Cost 400 Gbps DR4 Silicon Photonics Transmitter for Short-Reach Datacenter Application
## 3 Modulator Design and Characterization  
Our modulator is based on the Mach-Zehnder Interferometer (MZI), which is insensitive to fabrication error and temperature changes, but with a relatively large device size. An optical cavity structure, such as microring (MR), theoretically consumes less power but needs smart designs to withstand the resonance perturbation [27] and nonlinearity [28].  
In our design, the optical waveguide of the MZI was formed on a silicon-on-insulator (SOI) wafer and a light dose (-10\({}^{17}\) cm\({}^{-3}\)) of boron and phosphorus was injected to create the PN junction. The junction is reverse biased, to establish a depletion region that overlaps with the optical TE\({}_{0}\) mode confined in the waveguide. The effective index of the waveguide is then modulated by the applied reversed bias that changes the depletion width. To balance the performance among the carrier drifting speed, dopant-induced optical loss and variation range of the effective index, we considered all factors such as: the waveguide geometry, doping profile and junction offset from the waveguide center. Outside of the waveguide, heavy doses (-10\({}^{20}\) cm\({}^{-3}\)) of boron and phosphorus were injected into the slab region to create ohmic contacts between the metals and PN junction.  
As the PN junctions are always several millimeters long to achieve sufficient modulation depth, the traveling wave electrode (TWE) was carefully designed to meet both electric-optical phase matching and impedance matching. A polysilicon-based 50 \(\Omega\) termination resistor was integrated at the end of the TWE. Followed by the TWE, an NIN junction was embedded in the waveguide of each arm to form a low-loss thermal phase shifter, by which the MZI was tuned to quadrature. The MZM was finally buried in oxide dielectric layers when the fabrication processing was completed. A simplified cross-section view of the silicon MZM is shown in Figure 2.  
Figure 2: Cross-section view of the silicon photonics modulator.  
For the DC measurement, The MZM had an insertion loss of <5 dB and Vpi \(\times\) L of \(\sim\)2.5 V.cm under \(-\)2 V bias. The small signal electro-optical (EO) response of the MZM was characterized by a Vector Network Analyzer (VNA) with frequency sweeping from 100 MHz to 50 GHz. Port 1 and Port 3 from the VNA were differentially paired and connected to each arm of the MZM and thus formed a push-pull driving scheme. The output optical signal was received by a 70 GHz commercial InGaAs photodetector (11241-01P), which connected to Port 2 from the VNA. The optical wavelength was fixed at 1310 nm, and the modulator was reverse-biased at 2 V. The tested differential S11 response of the MZM is shown in Figure 3a. The reflection in the frequency range of 100 MHz to 30 GHz was \(<\)\(-\)20 dB and slowly increased to \(\sim\)\(-\)10 dB at higher frequencies, indicating a good impedance matching. The tested differential S21 response of the MZM is shown in Figure 3b. The 3-dB bandwidth of the MZM was \(\sim\)43 GHz. As the S21 curve had no sharp roll-off, the bandwidth compensation by FFE could be easily performed with fewer taps. Both the tested S11 and S21 curve match with the simulated data from our HFSS model, as shown in Figure 3a,b. In addition, the 6.4-dB electro-electrical (EE) bandwidth of the TWE was \(\sim\)45 GHz as calculated, which suggests that the optical signal was efficiently modulated by the electrical signal, as a result of good phase matching.  
A performance summary of silicon modulators is listed in Table 1.