# Design of a 90 GHz SOI Fin Electro-Optic Modulator for High-Speed Applications
## 3 Optimizing the Modulator Parameters
The second remark is that the waveguide with the largest \(H\) exhibits the lowest optical losses at low levels of doping concentrations, despite the previous finding. This can be explained by the small carrier absorption loss which allows the electrode absorption to be the dominant loss. Using MODE, the waveguide with \(H=300\) nm has a confinement factor, defined as the ratio of the core power to the total mode power, \(\Gamma=84\%\). This is the largest amongst the three and hence its mode has the least overlap with the electrodes at the same \(y_{o}\) and \(z_{o}\). The waveguide with \(H=220\) nm has \(\Gamma=77\%\) and the one with \(H=150\) nm has \(\Gamma=60\%\). However, as the doping dose increases, apparently, the carrier absorption loss becomes the dominant and hence the waveguide with \(H=300\) nm becomes the most lossy. Based on the previous discussion, the device that shows the lowest \(IL\) is found from Figure 3a, as the one with \(H=300\) nm, \(W=400\) nm, \(L=L_{\pi}=3\) mm, \(N_{A}=3\times 10^{16}\) cm\({}^{-3}\), \(IL=0.75+0.6=1.35\) dB. The other parameters for this design are \(V_{\pi}=30\) Volt and \(ER=29.5\) dB. Using DEVICE, we find the capacitance per micrometer of the propagation path, \(C^{\prime}=0.04\frac{fF}{\mu m}\). Then, the total device capacitance \(C=C^{\prime}L=121\)\(fF\) which gives \(f_{\rm 3 dB}=\frac{1}{2\pi RC}=26\) GHz. Note that in the bandwidth calculations we employ the commonly used value of contact resistance \(R=50\)\(\Omega\). This design shows a small \(IL\) and a very high \(ER\). This device is referred to as 'Modulator A' in the next discussion. Next, the selection criterion could be altered to target a higher speed of modulation, at the expense of the insertion loss. With closer electrodes at \(z_{o}=300\) nm and \(y_{o}=500\) nm and for \(H=150\) nm, \(W=600\) nm and \(N_{A}=2\times 10^{17}\)cm\({}^{-3}\) we get \(L_{\pi}=1.6\) mm, \(IL=6.9+0.6=7.5\) dB, \(ER=26.7\) dB \(V_{\pi}=40\) Volt, \(C^{\prime}=0.044\frac{fF}{\mu m}\), and \(f_{\rm 3 dB}=44\) GHz. This interesting case has its main device parameters shown in Figure 4. As the modulating voltage, \(V\), increases above zero, the holes deplete and therefore the effective index increases and the phase shifter loss decreases [17]. With depletion, the capacitance decreases in value since the charge inside the silicon waveguide moves away from the silicon edges which effectively enlarges the capacitor width [45]. With negative \(V\), the hole concentration increases which results in a decrease in \(n_{e}\) and increase in \(\alpha_{o}\). The charge accumulating at the silicon edge makes the effective thickness of the capacitor determined by the oxide thickness [45]. Therefore, the capacitance is higher in the accumulation regime. To account for the slowest response, this value is used in the 3-dB bandwidth calculations, although the maximum change of the capacitance is approximately 2% over the entire range of the modulating voltage. Figure 3: (**a**) Minimum phase shifter loss versus the doping concentration. (**b**) Corresponding effective length versus the doping concentration. \(IL=3.4+0.6=4\) dB while the extinction ratio decreases to \(ER=3\) dB. Although being much smaller, this \(ER\) value is widely reported in literature as an acceptable value [22; 46; 47; 48; 49; 50]. This design is referred to as 'Modulator B'. A third alternative is a design with low modulation voltage. We find that the device with \(H=150\) nm, \(W=600\) nm, \(N_{A}=10^{16}\) cm\({}^{-3},z_{o}=400\) nm, \(y_{o}=500\) nm has the following: \(V_{\pi}=22\) Volt, \(L_{\pi}=3\) mm, \(IL=3+0.6=3.6\) dB, \(ER=28\) dB, \(f_{\rm 3 dB}=24\) GHz. The depletion reaches its maximum when the applied voltage to one arm is 2 _Volt_ only. The rest of the \(V_{\pi}\) which is 20 Volt are employed in the accumulation regime for the other arm. Seeking a low voltage of operation, this device can be operated between \(V=0\) and \(V=2\) Volt, sacrificing the accumulation contribution to \(\Delta n_{\epsilon}\).