## 3 Results and Discussion
The implied \(V_{\infty}\) exported from the Sinton-120 lifetime tester (Sinton Instruments, Boulder, CO, USA) for the four samples are shown in Figure 3e. The 1-Sun lifetime values for sample A, B, C, and D are 170, 159.9, 194, and 212 \(\upmu\)s, respectively. As the etching time increases, the lifetime decreases firstly and then increases to its saturation value when the wafer is fully polished. A lifetime drop in sample B can be attributed to the non-uniform pyramid structure with too many turning points (peaks and valleys of pyramids), which may cause film cracks. This damage traps carriers and reduces the lifetime. Another reason for the lower lifetime is related to a less efficient cleaning of the surface due to the presence of narrow valleys between pyramids. Two factors can account for the better performance of samples C and D. First, the polishing process not only smooths the wafer surface but also removes sawing damages, thereby reducing the surface recombination velocity. Second, since sample A and B both have larger rear-side surface areas than that of sample C and D, more defects are present at the Si/Al\({}_{2}\)O\({}_{3}\) interface, acting as recombination centers. This result corresponds well with the observations from the SEM images. Sample D exhibits a slight increase in lifetime at an injection level of 5 \(\times\) 10\({}^{15}\) cm\({}^{-3}\), which is more apparent than that observed for the other cells due to the superior field-effect passivation for the Al\({}_{2}\)O\({}_{3}\) film on the mirror-like polished surface compared with that on the other rougher surfaces. At a low injection level, negligible minority carriers are generated to charge the inversion layer, and a shorter lifetime is gained due to the asymmetry in the electron and hole capture cross sections at the Si/Al\({}_{2}\)O\({}_{3}\) interface [12]. With regard to higher injection levels, the lifetime starts to shorten with increasing Auger recombination. The implied \(V_{\infty}\) exported from the Sinton-120 lifetime tester (Sinton Instruments, Boulder, CO, USA) for the four samples are shown in Figure 3f. The 1-Sun lifetime values for sample A, B, C, and D are 170, 159.9, 194, and 212 \(\upmu\)s, respectively. As the etching time increases, the lifetime decreases firstly and then increases to its saturation value when the wafer is fully polished. A lifetime drop in sample B can be attributed to the non-uniform pyramid structure with too many turning points (peaks and valleys of pyramids), which may cause film cracks. This damage traps carriers and reduces the lifetime. Another reason for the lower lifetime is related to a less efficient cleaning of the surface due to the presence of narrow valleys between pyramids. Two factors can account for the better performance of samples C and D. First, the polishing process not only smooths the wafer surface but also removes sawing damages, thereby reducing the surface recombination velocity. Second, since sample A and B both have larger rear-side surface areas than that of sample C and D, more defects are present at the Si/Al\({}_{2}\)O\({}_{3}\) interface, acting as recombination centers. This result corresponds well with the observations from the SEM images. Sample D exhibits a slight increase in lifetime at an injection level of 5 \(\times\  
Figure 3b to evaluate the maximum \(V_{\rm{oc}}\) before metal deposition. The implied \(V_{\rm{oc}}\) is extracted by the relation proposed by [PERSON] [13]:  
\[\tau_{\textit{eff}}(\Delta n)=\frac{\Delta n(t)}{G-\Delta n(t)/\Delta t} \tag{1}\]  
\[\textit{implied }V_{\rm{oc}}=\frac{kT}{q}ln\bigg{(}\frac{\Delta n(N_{A}+\Delta n )}{{n_{i}}^{2}}\bigg{)} \tag{2}\]  
where \(G\) is the generation rate; \(\tau_{\textit{eff}}\) is the effective minority carrier lifetime; \(\Delta n\) is the excess carrier concentration; \(\Delta t\) is the time taken in seconds; \(k\) is the Boltzmann constant; \(T\) is the temperature; \(N_{A}\) is the acceptor concentration of the wafer; and \(n_{i}\) is the intrinsic carrier concentration.