Introduction

Applications involving AI and in particular ML are on the rise Villalobos et al., 2022. The single operations performed in typical ML algorithms are of low complexity. However, ML algorithms improve when exposed to datasets of increasing size Prusa et al., 2015. To tackle increasingly difficult tasks the amount of data processed grew rapidly over the last decades Villalobos et al., 2022. This trend forced communication hardware to provide increasing bandwidth at decreasing power budget, which led to the adoption of fiber optic communications for links of decreasing distance Wade, 2019. For more than a decade "fiber optic technologies [have provided] the bloodstream for datacenter operations" Lam et al., 2010[p. 39]. New technologies are investigated by academia and industry, which tightly integrate electronics and photonics, to continue the scaling to shorter link distances. A promising candidate is graphene photonics, which allows the construction of photonics in the BEOL of any electronic chip.

Graphene allows to fabricate integrated modulators Liu et al., 2011 and detectors Schall et al., 2018 by covering a waveguide with a graphene sheet. To achieve modulation electrostatic gating is used. However, semiconductor processing involving graphene has proven to be challenging, especially depositing a high-quality insulator on top of large-scale and high-quality graphene Illarionov et al., 2020. Due to doping degradation, finite operating temperature, limited drive voltage, border traps, etc., the optical absorption in the transmissive and absorptive state of a graphene modulator are tightly coupled together, leading to a proportionality relation between MD and IL. The ratio is directly determined by the graphene conductivity switching factor $f$ as $\mathrm{MD}/\mathrm{IL}=f-1$.

It has been shown in literature, that MD diverges to infinity at critical coupling of a resonant modulator, while IL remains finite Phare et al., 2015. Thus the fixed relation between MD and IL can be lifted using optical resonators. The goal of this work is to investigate to what extent modulators including one or more optical resonators are able to improve the modulation performance with respect to MD and IL. Initially, it was tested to optimize the modulator geometry by inverse design Molesky et al., 2018 to maximize the ratio of MD/IL. For this purpose, a collection of modulator architectures were conceptualized, implemented, and subjected to optimization. It was observed that the inverse design algorithm was more effective at maximizing the bespoke ratio for a strong interaction of the slab mode with the graphene. Moreover, the ratio only significantly surpassed the straight waveguide limit in a regime of high IL and MD.

The single resonator modulator was evaluated with respect to the MD/IL ratio to better understand this limitation. A semi-analytical expression for the relation between MD and IL was found.

The nonlinear MD(IL) was used to evaluate the modulator performance in optical links. In the expected thermal noise limited links, the laser power could only be lowered by less than \qty{4.7}{%} when leveraging resonance, while in the shot noise limit more than \qty{82}{%} improvement is possible. In links limited by RIN and thermal noise, the potential improvement depends on the cumulative RIN over the electrical bandwidth.

Additionally, resonant modulators offer the potential to reduce the size of the graphene capacitor, which in turn reduces the switching energy and has been experimentally demonstrated to improve the EOBW Hu et al., 2016Agarwal et al., 2021Wu et al., 2021. Here it is demonstrated by a numerical model that reducing the graphene size beyond the autocorrelation length $L_{corr}$ of the local variations in doping can alleviate the switching penalty imposed by these variations. Depending on the length scales of doping variations this can be enabled by resonant modulators. Spatially resolved confocal Raman maps were used, to investigate the microscopic doping variations. It was shown, that the doping levels in the analyzed samples either exhibit tremendous variations on small length scales, or the variations are governed by multiple length scales including $L_{corr}$ of multiple hundreds of nanometers. This suggests that it is possible to eliminate some effects of doping variations using resonant devices. This leads to an improvement in $f$ and thus laser power beyond the limitations mentioned before. A mask design is provided which can be used to evaluate the minimum graphene size necessary with the current photonic processing capabilities at hand.

This work is structured into five chapters, starting with the introduction followed by a brief overview of the current state of the art and the underlying concepts of graphene modulators. Next, the used methods for simulation, modeling, and characterization will be summarized. Chapter Results showcases the results of this work. Lastly, the conclusions drawn from those findings will be presented and an outlook of useful future experiments will be given.