## 4 Optical Frequency Comb Generation in Annealing- and Crack-Free Si\({}_{3}\)N\({}_{4}\)  
Kerr optical frequency combs (OFCs) constitute a paradigm shift in the development of high-capacity data transmission, high-precision metrology, frequency synthesis, and integrated spectroscopy [14]. Since 2010, silicon-nitride-on-insulator (SiNOI) has been seen as an attractive chip-based platform for the generation of wideband frequency combs pumped at telecom wavelengths, because of its relatively high nonlinearity (\(\times\)6 larger than that of highly nonlinear Hydex glass [13]), as well as the absence of two-photon absorption and free carrier generation, which plague crystalline silicon. In this context, the monolithic integration of Kerr-based frequency combs with Si photonics and CMOS circuits paves the way for on-chip high-capacity transmitters that would benefit from the maturity and low cost of CMOS manufacturing and scalability. The realization of relatively thick (>7-800 nm) stoichiometric Si\({}_{3}\)N\({}_{4}\) films, as required by microring frequency combs, which imply both a tight confinement of light and anomalous group velocity dispersion (GVD), remains challenging. In particular, all prior works have systematically made use of N\({}_{2}\)-atmosphere long high-temperature annealing of the deposited silicon nitride film at >1200 \({}^{\circ}\)C for at least 3 h [12; 40; 41; 42]. This rather extreme annealing step has been accounted for by the need to densify the silicon nitride film by driving out excess hydrogen and to break N-H bonds, so as to get closer to a stoichiometric Si\({}_{3}\)N\({}_{4}\) film, reducing the material absorption loss in the C-band. Such annealing induces stress, eventually leading to crack formation during device processing unless sophisticated \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Grating** & **Period** & **\(\Delta\)xSi (nm)** & **Unetched/Ficched** & **2D-FDTD** & **2D-FDTD** & **Measured** & **Measured** \\
**Type** & **(nm)** & & **Thickness (nm)** & **CWDM IL** & **1 dB BW** & **CWDM IL** & **1 dB BW** \\  & & & & **(nm)** & **(nm)** & **(dB)** & **(nm)** \\ \hline Si & 468–488 & - & 300/150 & 1.6–15 & 30 & 1.9–13.0 & 26 \\ SiN & 965 & - & 600 & 6.8–10.0 & 54 & 8.0–13.0 & 45 \\ Si/SiN \({}^{\mathrm{a}}\) & 950 & 200 & 600 & 3.0–5.5 & 64 & - & - \\ Si/SiN \({}^{\mathrm{b}}\) & 975 & 150 & 600/50 & 2.7–6.9 & 50 & 2.9–5.2 & 48 \\ \hline \hline \end{tabular} \({}^{\mathrm{a}}\) Simulated and \({}^{\mathrm{b}}\) measured designs with lowest losses over the CWDM band.  
\end{table} 
Table 2: Summary of grating parameters and simulated and measured insertion loss (IL) and bandwidth (BW). pre-patterning strategies are adopted prior to the film deposition [40; 41]. Now, from the perspective of silicon optoelectronics-nonlinear optics co-integration, such extreme annealing cycles would severely degrade the front-end-of-the-line (FEOL) silicon optoelectronic circuits underneath. Specifically, doped components and circuits would be unacceptably affected by the undesirable dopant diffusion in junction-based Si modulators and by the hetero-interface degradation of Ge-on-Si photodetectors. As an alternative, in 2013, optical parametric oscillation was demonstrated by using the proprietary composition of Hydex microresonators [13]. As previously stated, the nonlinear parameter \(\gamma\) of Hydex is 6 times lower than silicon nitride. Consequently, generating frequency combs in such material requires more power, increasing the risk of waveguide fusing, and device failure. In early 2018, we reported a new method that avoids thermal annealing for growing relatively thick (740 nm) crack-free Si\({}_{3}\)N\({}_{4}\)-based straight nanowaveguides with good linear and nonlinear properties measured by self-phase modulation [33].