## 6 Overview and Conclusions  
CIPMRM is a kind of insensitive micro-ring for its huge waveguide loss. By utilizing the low Q of CIPMRMs, the ER is less insensitive to temperature. The micro-rings with low Q are hard to modulate. Therefore, more minority carriers need to be injected. Moreover, the resonant wavelength can be tuned based on the carrier concentration when the linewidth varies. CIPMRMs and the method of tuning the resonant wavelength based on the carrier concentration are first proposed here. Two main issues need to be improved in future work. First, the compensation method for a \(\pm\)10% variation in linewidth matters, which will boost the yields. Second, the insertion loss of CIPMRMs needs to be improved in future work. If the insertion loss can be reduced to \(-\)4 to \(-\)6 dB, the performance of CIPMRMs \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Linewidth** & **Bit Rate (Gbps)** &
\begin{tabular}{c} **Energy Consumption** \\ **(p/bit)** \\ \end{tabular} & **IL (dB)** & **ER (dB)** \\ \hline \(-\)5\% & 28.5 & 3.53 & \(-\)8 & 14 \\ \(-\)2.5\% & 32 & 5.39 & \(-\)6 & 18.7 \\ \(0\)\% & 45 & 4.50 & \(-\)8 & 22 \\ \(2.5\)\% & 36 & 4.99 & \(-\)6.3 & 37.7 \\ \(5\)\% & 34 & 6.05 & \(-\)6.4 & 23.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The performance of CIPMRMs for different linewidths. Figure 11: (**a**) The carrier concentration varies with time for different widths of CIPMRMs. (**b**) The calculated energy consumption for different widths of CIPMRMs. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Linewidth** & **Vbias** & \
\begin{tabular}{c} **Pre-Emphasize** \\ **Voltage** \\ \end{tabular} &
\begin{tabular}{c} **Pre-Emphasize** \\ **Voltage Time** \\ \end{tabular} & **Vwork** \\ \hline \(-\)5\% & 1 V & 2.5 V & 8 ps & 1.1 V \\ \(-\)2.5\% & 1.08 V & 2.5 V & 10 ps & 1.18 V \\ \(0\)\% & 1.14 V & 2.5 V & 8 ps & 1.21 V \\ \(2.5\)\% & 1.18 V & 2.5 V & 9 ps & 1.1 V \\ \(5\)\% & 1.23 V & 2.5 V & 11 ps & 1.15 V \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The initialization voltage condition for different widths of CIPMRMs. will be comparable with that of photonic MZMs. For MZMs, the energy consumption is only few pJ/bit and the bit rate is 30-50 Gbps (BPSK) [25; 26; 27]. However, CIPMRMs present a compacted footprint of 43.4 \(\upmu\)m\({}^{2}\), which is promising for integration and saving costs. In summary, a fully CMOS-compatible CIPMRM based on a Cu-SiO\({}_{2}\)-Si plasmonic waveguide has been proposed and numerically demonstrated. It has a compacted footprint of 43.4 \(\upmu\)m\({}^{2}\), a data rate of 45 Gbps, an insertion loss of \(-8\) dB, a static extinction ratio of 22 dB, and an energy consumption of 4.5 pJ/bit when 2.5 V peak-to-peak voltage is applied. Due to the low Q of CIPMRMs, an ER of 9 dB is achieved when temperature varies within 60 K. A method of tuning the resonant wavelength based on the carrier concentration is proposed by initializing the voltage condition. Compared with MRMs utilized in the method of tuning the resonant wavelength based on the thermo-optic characteristic of silicon, there is no need for complex temperature control and a feedback circuit. The performances (except IL) of CIPMRMs are comparable with MZMs although it is smaller in size. CIPMRMs provide another technological route for achieving a CMOS-compatible compacted modulator. Conceptualization, [PERSON]; methodology, [PERSON]; software, [PERSON]; validation, [PERSON]; formal analysis, [PERSON]; investigation, [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON]; visualization, [PERSON]; supervision, Z.L. ; project administration, W.W.; funding acquisition, W.W. All authors have read and agreed to the published version of the manuscript. This research was funded by National Key R&D Program of China (Grant No. 2018 YFB2200203). Not applicable. The data that support the findings of this study are available from the corresponding author upon reasonable request.