## 3 Results and Discussion  
The XRD patterns of the Al\({}_{2}\)O\({}_{3}\) films after annealing treatment from 350 \({}^{\circ}\)C to 650 \({}^{\circ}\)C are shown in Figure 1. The only (100) peaks, which represent crystalline silicon substrates, are observed in all samples. This result indicates that all the Al\({}_{2}\)O\({}_{3}\) films are amorphous phase, and the thermal stability of the Al\({}_{2}\)O\({}_{3}\) films are outstanding. In this study, Al\({}_{2}\)O\({}_{3}\) films annealed at 450 \({}^{\circ}\)C are used, due to their longer lifetimes compared with Al\({}_{2}\)O\({}_{3}\) films annealed at other temperatures. As the annealing temperature increases over 500 \({}^{\circ}\)C, the lifetime starts to decrease. Lifetime reduction at high annealing temperature has also been obtained by other research groups [9,10]. The rear-side surface morphologies for the samples treated with the standard texture process and further polishing processes for 10, 20, and 30 min are shown in Figure 2. The typical textured surface morphology containing uniformly sized pyramids of around 5 to 8 \(\upmu\)m (width of the base) can be seen in Figure 2a. In Figure 2b, large and small pyramids start to coexist with the additional polishing process as the duration approaches 10 min. By extending the duration to 20 min, all the pyramids become uniformly smaller and thinner as shown in Figure 2c. Increasing the duration to 30 min produces a smoothed surface like a mirror; most pyramids almost disappear as seen in Figure 2d. Overall these four stages constitute a substantially texturing cycle. Figure 3a shows the injection level dependent effective minority carrier lifetime and Auger lifetime for the four samples. The effective lifetime is calculated from the photoluminescence intensity by the self-consistent calibration method, and the Auger lifetime is calculated by the model proposed by [PERSON] et al. [11]. The effective lifetime for samples A, B, C, and D are 174.4, 163.7, 200.1, and 225.3 \(\upmu\)s at the injection level of 5 \(\times\) 10\({}^{15}\) cm\({}^{-3}\), respectively. 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 3b.