# Design of a 90 GHz SOI Fin Electro-Optic Modulator for High-Speed Applications
## 1 Introduction  
Optical interconnects demonstrate core advantages over their traditional electrical counterparts in many aspects such as immunity to electromagnetic interference, high data transfer rates, and low losses [1; 2]. Having integrated systems with such characteristics will be also very advantageous if the systems are complementary metal-oxide semiconductor (CMOS) compatible. Such compatibility adds compactness, low-cost and ease of fabrication to the previous list of advantages. This concept gave a big momentum for silicon photonics for almost three decades. Currently, with many components being mature enough [3; 4; 5; 6; 7; 8; 9; 10; 11; 12], silicon photonics stands ready to serve in many speed-demanding applications, such as 5G networks [13], central processing unit (CPU)-memory interconnects [14] and radio-over-fiber (RoF) [15]. A key device in such applications is the electro-optic modulator where electrical data converts into optical data [16], before commencing its trip over low-loss optical fibers. The main method to modulate laser in a silicon waveguide is the plasma dispersion effect which was quantitatively described by [PERSON] about three decades ago [17]. This technique is the practical way to get around the small electro-optic coefficient of silicon. In this method, the modulating voltage manipulates the charge carrier concentration in doped silicon. The result is the variation of both parts of the effective refractive index, the real, \(n_{e}\), which is responsible for the mode phase shift and the imaginary, \(k\), which is responsible for the optical power loss. Based on this idea, two families of modulators can be studied. The first family, which includes carrier-injection modulators, is the one that grabbed attention earlier. Here, electric current flows through the waveguide leading to an increase in the charge concentration, which decreases \(n_{e}\) but increases \(k\). Although this current flow results in a big change in \(n_{e}\) and hence enables a relatively short phase shifter length, the speed is limitedbecause of the carrier recombination time [18; 19; 20]. Another drawback is the DC power consumption. The second family, which includes carrier-depletion modulators, is a more successful one. In this approach, usually a reverse-biased PN junction is positioned within the phase shifter [21]. With the reverse bias, the junction works as a voltage-controlled capacitor. The concentration of the carriers changes between two states, where recombination does not take place in any. This way, the device 3-dB bandwidth \(f_{\rm 3 dB}=\frac{1}{2\pi RC}\) is limited by the junction capacitance, \(C\), and the circuitry resistance, \(R\). Hence, higher speeds can be achieved. There is also zero DC power consumption in this technique. An extensive work was invested in this direction, where different PN junction-based structures were introduced to maximize the interaction between the optical mode and the junction [22; 23; 24]. However, the depletion cannot be increased arbitrarily because of the silicon breakdown limit, a fact that sets a limit to the modulation efficiency [25]. This approach can also make use of metal-oxide semiconductor (MOS) devices [26]. Here, not only depletion can be utilized, but also accumulation of charge. One of these two modes of operation can be used, or even both, to create a larger contrast of \(n_{e}\) and hence minimize the phase shifter length. Unfortunately, the inversion mode is not useful at high frequencies of operation [26]. In MOS based modulators, the modulator speed can be limited if the oxide thickness is small [25]. Besides, having a small oxide thickness might result in high optical insertion loss if the metallic electrodes come close enough to the optical mode. The only benefit of a thin oxide layer is the low modulating voltage. Apart from silicon modulation using plasma dispersion, different alternatives were suggested.