## 3 Results and Discussion
The \(Q_{f}\) decreases from 9 \(\times\) 10\({}^{12}\) to 6.9 \(\times\) 10\({}^{11}\) cm\({}^{-2}\) when the annealing temperature increases from 400 to 650 \({}^{\circ}\)C. As shown by the FTIR results, the bonding configuration changes from Si-O to Hf-O, so the oxygen vacancies of HfO\({}_{2}\) near the interface reduce when the annealing temperature increases. Another reason for the smaller \(Q_{f}\) values of the annealed samples compared to the as-deposited one is the crystallization of HfO\({}_{2}\) at these annealing temperatures. In particular, the HfO\({}_{2}\) films are completely crystallized when the annealing temperature reaches 550 \({}^{\circ}\)C or above, leading to very low \(Q_{f}\) values of around 0.5 \(\times\) 10\({}^{11}\) cm\({}^{-2}\). The value of \(D_{it}\) decreases from 5.1 \(\times\) 10\({}^{13}\) cm\({}^{-2}\)eV\({}^{-1}\) for the as-deposited sample to a minimum 6.1 \(\times\) 10\({}^{12}\) cm\({}^{-2}\)eV\({}^{-1}\) for the sample annealed at 500 \({}^{\circ}\)C, and then increases to 1.4 \(\times\) 10\({}^{13}\) cm\({}^{-2}\)eV\({}^{-1}\) when the temperature further increases to 650 \({}^{\circ}\)C. Several studies have suggested that interfacial SiO\({}_{x}\) plays a critical role in the reduction of interface defect density [12]. The high \(D_{it}\) of the as-deposited sample is due to the fact that SiO\({}_{x}\) deposited at low temperatures has many pores and defects near the SiO\({}_{x}\)/Si interface. Increasing the deposition temperature of SiO\({}_{x}\) can increase film density, therefore decreasing the \(D_{it}\). However, for the annealing temperatures from 550 and 650 \({}^{\circ}\)C, the nearly disappeared SiO\({}_{x}\) interfacial layer is responsible for the increased \(D_{it}\). Table 1 lists the values of \(\tau_{\textit{eff}}\) for the HfO\({}_{2}\)/Si with different annealing conditions. Lifetimes with two injection levels, 1 \(\times\) 10\({}^{14}\) cm\({}^{-3}\) (\(\tau_{\textit{eff,low}}\)) and 1 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) (\(\tau_{\textit{eff,high}}\)), are specified. The higher injection level corresponds to the evaluation of a solar cell operating under normal conditions, while the degradation of the lifetime at low injection levels can be used for assessing the field effect passivation [16]. In this work, the latter was done by introducing the ratio \(\tau_{\textit{eff,low}}\)/\(\tau_{\textit{eff,high}}\). Note that the passivation of the as-deposited HfO\({}_{2}\)/Si sample is poor such that the high-injection-level lifetime is not measurable. The \(\tau_{\textit{eff,high}}\) value increases from 15.2 us to the maximum of 74.7 us when the annealing temperature increases from 400 to 500 \({}^{\circ}\)C, and it then decreases to 19.4 us when the temperature further increases to 650 \({}^{\circ}\)C. As the 500 \({}^{\circ}\)C-annealed sample has the highest lifetime and the lowest \(D_{it}\), this result supports the claim that low \(D_{it}\) is the prerequisite of high passivation quality. The ratio of \(\tau_{\textit{eff,low}}\) to \(\tau_{\textit{eff,high}}\) can be divided into two groups. A ratio is around 0.61-0.68 for annealing temperatures of 550-650 \({}^{\circ}\)C. This indicates that annealing temperatures equal to or greater than 550 \({}^{\circ}\)C can deteriorate the field effect passivation. This is also in agreement with the low \(Q_{f}\) values of these  
Figure 2: (a) n-type passivated emitter and rear contact (PERC) cell structure; (b) transmission electron microscopy (TEM) image of the HfO\({}_{2}\)/Si interface annealed at 550 \({}^{\circ}\)C.  
samples. On the other hand, annealing temperatures of 400, 450, and 500 \({}^{\circ}\)C result in a ratio around 0.9-0.94. The high values and small variation indicate that the \(Q_{f}\) of 4.4 \(\times\) 10\({}^{12}\) cm\({}^{-3}\) is enough to achieve field-effect passivation. In order to obtain the influence of the annealing temperature on the performance of n-type PERC solar cells, PC1D simulation was performed.