## 3 Results and Discussion
If DLC thin films can be regarded as a homogeneous medium, the absorption coefficient \(\alpha(\lambda)\) and the absorbance \(A_{abs}\) were described by Beer-Lambert law and estimated by using Formulas (2) and (3):  
\[A(\lambda)=I(\lambda)-R(\lambda)-T(\lambda), \tag{1}\]  
\[A_{abs}=-ln\frac{T(\lambda)}{I(\lambda)-R(\lambda)}, \tag{2}\]  
\[\alpha(\lambda)=\ \frac{A_{abs}}{d}\ =d^{-1}ln\frac{I(\lambda)-R(\lambda)}{T( \lambda)}, \tag{3}\]  
where \(d\) is the film thickness, \(A(\lambda)\) is the intensity of light absorbed by the film, \(I(\lambda)\) is the intensity of incident light to the film, \(R(\lambda)\) is the intensity of reflected light on the  
Figure 4: (**a**) G-peak position and I\({}_{\rm D}\)/I\({}_{\rm G}\) ratio, and (**b**) G-peak width and intensity in the RF-PECVD DLC thin films with various film thicknesses: 20, 40, 60, and 80 nm. surface, and \(T(\lambda)\) is the intensity of illumination that passes through the film at a certain wavelength of \(\lambda\). The increase in the thickness of the DLC thin films resulted in increased absorbance, which resulted from the decrease in the transmittance and/or reflectance. It can be concluded that there is a negligible effect of light scattering from the surface because the rms surface roughness was lower than 0.94 nm for all film thicknesses (Figure 1) [27]; therefore, the transmittance will be diminished if the reflectance of the thin films increases with increasing thickness [27]. The transmittance decreased because of the change in the thin-film microstructure due to the decrease in the \(sp^{3}\) bonding fraction [28; 29] owing to the increase in the ratio of hydrogen bonds [26], while these results are also associated with an increase in \(sp^{2}\) sites or clusters [26], as shown by the Gaussian curve fitting for the Raman spectrum [8; 9; 10; 11]. The increased refractive index was caused by the increase in \(sp^{2}\) sites or clusters, which resulted from the reduced bound hydrogen content and structurally densified thin films as the thickness of the DLC thin films increased [28]. Figure 6 shows the I-V curve showing the characteristics of DSSCs with the DLC ARC as a function of thickness, and the electrical characteristics of DSSCs with the DLC ARC are summarized in Table 1. The open-circuit voltage (\(V_{\infty}\)) is determined by the difference between the Fermi level of the TiO\({}_{2}\) working electrode and the oxidation/reduction level of the electrolyte. The fill factor (FF) is generally due to the internal DSSC resistances, such as FTO sheet resistance, resistance to charge movement in working/counter electrodes, and diffusion resistance of ion species in the electrolyte. The short-circuit current density (\(J_{\infty}\)) of DSSCs could be controlled at a similar level from 11.93 without the DLC ARC to 12.11 and to 11.38 mA/cm\({}^{2}\) with the DLC ARC. For DSSCs, the increase in \(J_{\infty}\) is associated with an increase in incident photons; an improved \(J_{\infty}\) of 12.11 mA/cm\({}^{2}\) was obtained at a thickness of 20 nm with an increase in the incident photons through reflection protection, while a diminished \(J_{\infty}\) of 9.79 mA/cm\({}^{2}\) was observed for a thickness of 80 nm with a sharp decrease in the transmittance from the thicker ARC. The increase in \(V_{\infty}\) of the DSSCs results from a passivation effect of DLC thin films that suppresses the recombination current [30]. The measured \(V_{\infty}\) and FF values show differences with changes in the thickness of the DLC ARC. Thus, a significant improvement in the CE was obtained from 4.92% to 5.35% when applying the DLC ARC owing to the amount of photons in the DSSCs with the proper thickness of ARC. In particular, the DSSCs with the DLC ARC of 60 nm showed an improvement of 8.73% in CE compared with the establ  
Figure 5: (**a**) Transmittance, (**b**) refractive index (\(n\)), and absorption coefficient (\(k\)) of the RF-PECVD DLC thin films with various film thicknesses: 20, 40, 60, and 80 nm.