# Design of a 90 GHz SOI Fin Electro-Optic Modulator for High-Speed Applications
## 3 Optimizing the Modulator Parameters  
In this section, the dimensions of the waveguide cross section, the silica thickness and the core doping, are optimized in order to achieve the best performance of the modulator in terms of losses, speed and size. In this work, the mode profile and the effective index are found using the commercially available software, MODE, while the plasma dispersion is simulated using DEVICE, both from Lumerical [42]. The simulation settings are shown in Appendix A. Three waveguide cross sections are tested. The heights are taken as \(H=150\) nm, \(220\) nm, and \(300\) nm with the corresponding width values \(W=600\) nm, \(450\) nm, and \(400\) nm, respectively. Those dimensions ensure single mode operation at \(\lambda_{o}=1.55\) um. The mode of interest in this work is the transverse electric field like (TE-like) mode which has its major electric field component parallel to the substrate. The electric field intensity, for the mode supported by each of the three different waveguides, is shown in Figure 2. In this design, acceptors are chosen for the doping, since holes have a stronger effect on the change of \(n_{e}\) than electrons [17]. The doping concentration, \(N_{A}\), is varied from \(1\times 10^{16}\) cm\({}^{-3}\) to \(3\times 10^{17}\)cm\({}^{-3}\). For each value of \(N_{A}\), the values of \(y_{o}\) and \(z_{o}\) are swept from \(200\) nm to \(500\) nm in steps of \(100\) nm while the value of the modulating voltage, \(V\), is swept from \(-20\) Volt to \(20\) Volt in steps of \(1\) Volt. Figure 1: (**a**) A cross section of the phase shifter. The silicon core is separated from the silicon substrate by a buried oxide layer that is \(2\) μm thick. (**b**) Three-dimensional view of the proposed MZI modulator. The insertion loss for this device comprises four mechanisms. Three loss mechanisms are related to the propagation through the waveguide. First, the free carrier absorption loss, which depends on \(N_{A}\) and \(V\). Second, the optical absorption due to the overlap between the optical mode and the metallic electrodes. The total of the two losses is found through DEVICE and MODE simulations, in dB/cm, and is given the symbol \(\alpha_{0}\). Third, the passive waveguide scattering losses, taken here as 1 dB/cm [43]. This loss is to be added to \(\alpha_{0}\) to give the total phase shifter loss, which is designated by \(\alpha\), in dB/cm. The fourth loss mechanism is the insertion loss due to the two Y-junctions of the MZI, which is taken here as 0.3 dB for each junction, totalling 0.6 dB of optical losses for the MZI [44]. With all of the dimensions and the doping dose combinations, a selection criterion is necessary to pick the desired device. First, the results are filtered for the smallest \(IL\) at each doping concentration when \(V=0\). This selection criterion simply picks the configurations with maximum silica thickness in the range of this study, \(y_{o}=z_{o}=500\) nm, because the overlap of optical mode with the electrodes is minimal. According to this criterion, the phase shifter loss, \(\alpha L\), when \(L=L_{\pi}\), is plotted versus the doping concentration in Figure 3a. In Figure 3b, the corresponding effective length, \(L_{\pi}\), is plotted versus the doping concentration. The first remark here is that the waveguide with \(H=300\) nm, which has the largest cross-sectional area, is the one that shows the largest \(L_{\pi}\) at all concentrations. This finding follows from the fact that a larger cross section means more charge resides inside the phase shifter. Hence, manipulating the charge density with the modulating voltage is less effective. This results in a smaller change of the effective index and consequently a longer \(L_{\pi}\). Figure 3: _Cont._  
Figure 2: Electric field intensity distribution over the cross section of a waveguide with (**a**) \(H=150\) nm and \(W=600\) nm, (**b**) \(H=220\) nm and \(W=450\) nm, and (**c**) \(H=300\) nm and \(W=400\) nm. The buried oxide layer lies below \(z=0\).