## 3 Results and Discussion
### Optical Properties  
To analyze the optical characteristics, the absorbance and transmittance spectra of the samples were measured using a UV-Vis spectrophotometer. The relationship between transmittance (T), reflectance (R), and absorbance (A) for different nitrogen flow ratios can be expressed as A + R + T = 1, where A represents light absorption, and R and T are the reflectance and transmittance, respectively. Figure 8 presents the spectra of the various sample groups under distinct nitrogen flow ratios. The sample exhibits high transparency in the infrared range. In the ultraviolet and visible-light ranges, as the nitrogen flow rate increases, the light absorption rate also increases. This is likely because the increase in nitrogen flow rate increases the sp\({}^{2}\) phase, enhancing the light absorption rate. Moreover, notable variations in transmittance are evident among different sample groups within the same wavelength range. At a wavelength of 368 nm, the difference in ultraviolet transmittance can even reach 25.62%. The optical properties of the N-DLC coatings are influenced by the nitrogen doping and the resulting microstructural changes, contributing to the varied levels of light absorption and transmittance observed in the different sample groups. The determination of the optical bandgap in DLC films is facilitated through absorption spectroscopy. The Tauc equation provides a means to calculate the optical bandgap (Eg) for doped DLC films. In Equation (1), \(\alpha\) denotes the absorption coefficient, h represents the Planck constant, v corresponds to the frequency of incident photons, and A is a constant of proportionality [35]. The value of N is characteristic of the material type, and for DLC \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**C=C**} & \multicolumn{2}{c}{**C-C**} \\ \cline{2-7}  & **Position, eV** & **FWHM, eV** & **Area, \%** & **Position, eV** & **FWHM, eV** & **Area, \%** \\ \hline C1N8 & 284.78 & 0.93 & 58.33 & 285.24 & 0.99 & 21.77 \\ C1N6 & 284.76 & 1.00 & 55.44 & 285.31 & 1.37 & 29.75 \\ C1N4 & 284.8 & 1.00 & 40.78 & 285.14 & 1.36 & 42.02 \\ C1N2 & 284.71 & 1.15 & 53.70 & 285.17 & 1.08 & 31.86 \\ C2N0 & 284.8 & 1.09 & 49.68 & 285.08 & 1.25 & 33.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Some data from XPS C1s spectra of the films. Figure 8: Absorption and transmittance spectra. (**a**) The absorption rate of the sample; (**b**) The transmittance of the sample. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Sample**} & **C** & **N** & **Other Elements** \\ \hline C1N8 & 83.73 & 2.56 & 13.71 \\ C1N6 & 83.68 & 2.16 & 14.26 \\ C1N4 & 81.56 & 2.04 & 16.4 \\ C1N2 & 86.05 & 1.03 & 12.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative content of each element in the sample (at.%). films, N = 2 [36]. The absorption coefficient \(\alpha\) can be estimated utilizing Equation (2), where t denotes the thickness of the sample, R signifies the reflectance, and T represents the transmittance [35]. By plotting \((\alpha\mathrm{h}\
u)^{\frac{1}{N}}\) as the vertical axis and h\(\
u\) as the horizontal axis, the optical bandgap (Eg) can be derived. \[\alpha\mathrm{h}\
u=\mathrm{A}\big{(}\mathrm{h}\
u-\mathrm{E}_{\mathrm{g}} \big{)}^{\mathrm{N}} \tag{1}\]  
\[\alpha=\frac{1}{\mathrm{t}}\mathrm{ln}\,\frac{\left(1-\mathrm{R}\right)^{2}}{ \mathrm{T}} \tag{2}\]  
Figure 9a-e exhibits the Tauc plots for the five sample groups. As shown in the figure, the intersection point between the red line and the x-axis is the value of Eg. Notably, the optical bandgap demonstrates an inverse relationship with the sp\({}^{2}\) content in the samples. With varied nitrogen flow ratios, an increase in sp\({}^{2}\) content results in a reduction in the coatings' bandgap from its maximal value of 3.62 eV to 3.46 eV.