## 3 Results
### Silicon Surface Passivation of ALD TiO\({}_{2}\)  
Figure 5 shows the effective minority carrier lifetime as a function of the carrier density for 8-nm-thick TiO\({}_{2}\) film on Si. Its minority carrier lifetime value is 921 \(\upmu\)s at a carrier density of 1.0 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) which was extracted using the quasi-steady-state photo-conductance (QSSPC) mode with a light bias of 0.1 suns. The result shows that the Si wafer is effectively passivated by the 8-nm-thick TiO\({}_{2}\) film deposited at a temperature of 200 \({}^{\circ}\)C. The effective lifetime (\(\tau\_\)_eff_) is a combination of the bulk lifetime (\(\tau\_\)_bulk_) and the surface lifetime (\(\tau\_\)_sur_) described as follows [38]:  
\[\frac{1}{\tau\_eff}=\frac{1}{\tau\_bulk}+\frac{1}{\tau\_sur},\ \ \frac{1}{\tau\_sur}=\frac{2S}{W} \tag{1}\]  
where \(W\) is the sample thickness, and \(S\) is the surface recombination velocity. Since the FZ Si wafer has a long bulk lifetime, the measured effective lifetime can be approximated to the surface lifetime. Consequently, a low surface recombination velocity of 14.93 cm/s for 8-nm-thick TiO\({}_{2}\) films on Si wafers is deduced. The effective minority carrier lifetimes of the other three samples with different thicknesses of TiO\({}_{2}\) (i.e., 15 nm, 35 nm, and 66 nm) were also investigated according to the procedures of 8-nm-thick TiO  
Figure 4: The extracted index of refraction (\(n\)) and extinction coefficient (\(k\)) of upper and lower layers as functions of wavelength (the inset shows the fitting model). Figure 5: Minority carrier lifetime as function of carrier density for 8-nm-thick TiO\({}_{2}\) film deposited at substrate temperature 200 \({}^{\circ}\)C.  
films. The effective lifetimes of four samples at the injection level of 1.0 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) are summarized in Figure 6. The effective lifetime decreases dramatically from 921 \(\upmu\)s for the 8-nm-thick TiO\({}_{2}\) film to 32 \(\upmu\)s for the 66-nm-thick TiO\({}_{2}\) film. The results show that the Si surface passivation of TiO\({}_{2}\) films by ALD at a substrate temperature 200 \({}^{\circ}\)C declines as the cycle number increases. Thin TiO\({}_{2}\) films in amorphous phase can provide better Si surface passivation in the mechanisms of field-effect passivation and chemical passivation. The degradation of the surface passivation quality with increasing the TiO\({}_{2}\) thickness could be caused by stress effects and phase transformation, which has been reported and proved [26; 27; 32]. Phase transformation of TiO\({}_{2}\) at the interface could change the band structure and the interface trap density to decrease the field-effect passivation. Capacitance-voltage measurements of these films could be possible to study fixed charges and the interface trap density of TiO\({}_{2}\) films. Besides, atomic hydrogen, which terminates the dangling bonds of Si for chemical passivation, plays an important role in silicon surface passivation [39]. From the results of SIMS in Figure 2, we can find that atomic hydrogen accumulates at the interface of Si and TiO\({}_{2}\) films. We proposed that it might be another reason that ultrathin TiO\({}_{2}\) films have a better performance of surface passivation. The TiO\({}_{2}\) films with a lower thermal budget during the deposition and in the amorphous phase could keep more hydrogen atoms at the interface of the Si and TiO\({}_{2}\). Therefore, as the thickness of the TiO\({}_{2}\) thin films increases during ALD growth, stress effects, phase transformation of TiO\({}_{2}\) films, atomic hydrogen and a greater thermal budget from the chamber could be reasons to decrease the silicon surface passivation of TiO\({}_{2}\) films. Forming gas annealing (FGA) of TiO\({}_{2}\) films was a strategy to enhance chemical surface passivation by the diffusion of atomic hydrogen. However, FGA at high temperatures will degrade the field-effect passivation of TiO\({}_{2}\) films due to the phase transformation from amorphous to anatase [26].