## 3 Results and Discussion
The implied \(V_{\rm{oc}}\) following the same trend as the effective minority carrier lifetime with respect to the further polishing time can exactly predict the performance of the surface passivation for the fabricated PERCs, especially in \(V_{\rm{oc}}\). Figure 4 illustrates the reproducible illuminated J-V characteristics for all the PERCs. All of the curves are very close in this figure. The detailed solar cell external parameters are summarized in Table 1. Both \(V_{\rm{oc}}\) and \(J_{\rm{sc}}\) are obviously affected by the rear-side surface, whereas the FF changes little in the range of 0.777 to 0.793, which is attributed to the probable experimental scattering. This reveals that the polishing process is beneficial for \(V_{\rm{oc}}\) and \(J_{\rm{sc}}\) due to better surface passivation and long-wavelength reflection, respectively, but rarely influences the series resistance or shunt resistance. The most obvious variation of the electrical performance for each cell is in the \(V_{\rm{oc}}\), proving that the polishing treatment plays a much more important role in preventing carrier recombination at the rear-side Si/A\({}_{2}\)O\({}_{3}\) interface than gaining the long-wavelength light. Both relatively planar surfaces of samples C and D have \(V_{\rm{oc}}\) over 0.66 V and \(J_{\rm{sc}}\) over 36.6 mA/cm\({}^{2}\), while the further etching time exceeded 20 min. Note that the real \(V_{\rm{oc}}\) for all cells following the same trend as the implied \(V_{\rm{oc}}\) is evidence for reproducibility in this work. Overall, sample D demonstrates the optimized efficiency of 19.27%, with the V\({}_{\rm{oc}}\) of 0.662 V, \(J_{\rm{sc}}\) of 36.69 mA/cm\({}^{2}\), and FF of 0.793. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(V_{\rm{oc}}\) **(V)** & \(J_{\rm{sc}}\) **(mA/cm\({}^{2}\))** & **FF** & **Efficiency (\%)** \\ \hline A & 0.655 & 36.47 & 0.779 & 18.62 \\ B & 0.648 & 36.43 & 0.789 & 18.64 \\ C & 0.660 & 36.64 & 0.777 & 18.80 \\ D & 0.662 & 36.69 & 0.793 & 19.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The detailed electrical external parameters for all PERCs (passivated emitter and rear cells). Figure 3: (**a**) Effective lifetime as a function of injection level; (**b**) Implied \(V_{\rm{oc}}\) for the Al\({}_{2}\)O\({}_{3}\) films with different rear-side surface morphologies. The IQE and reflectance for the PERCs with different surface morphologies are shown in Figure 5. In the short wavelength range before 500 nm, the performance for each curve is similar. Samples C and D represent better spectral responses compared with the other samples at the middle wavelength range from 500 to 900 nm. This may be due to the relatively exceptional rear-side passivation provided by the Al\({}_{2}\)O\({}_{3}\) films on the flatter surfaces; photogenerated electrons at the bottom of wafer are therefore easily repelled to the p-n junction for collection. This can be proven by calculating the effective diffusion length (Leff) using the method proposed by [PERSON] [14]. The Leff for all samples is more than 1450 \(\upmu\)m. As for the wavelengths over 900 nm, an obvious difference in spectral response occurs as well. The smoothed surface of sample D that is functionally analogous to a mirror facilitates the reflection of more unabsorbed long-wavelength light back to the active region of the Si bulk. Both reasons mentioned above make contributions to the higher \(J_{\text{sc}}\) of 36.69 mA/cm\({}^{2}\) for sample D.