## 3 Electron Spin-Dependent Processes in Si Nanocrystals
### Phenomenological Model of the Photosensitization by Si Nanocrystals
The experimental pressure dependence of the photosensitization efficiency is well described by theoretical predictions (solid lines in Figure 27). As expected, in the entire pressure range a decrease of the temperature increases the mean number of adsorbed molecules and enhances the efficiency of energy transfer to O\({}_{2}\) molecules. The steady state concentration of \({}^{(1)}\)O\({}_{2}\) is a product of its generation  
Figure 27: Dependences of the exciton PL quenching strength at 1.63 eV on oxygen pressure at different temperatures: \(T=120\) K (squares), \(T=200\) K (circles), \(T=300\) K (triangles). Solid lines are fits by Equation (18). (From Reference [65]). Figure 26: (**a**) Spectra of the PL quenching strength in por-Si with adsorbed O\({}_{2}\) molecules at T = 110 K, 100 mbar (solid line) and 2 mbar (dotted line). (**b**) the same spectra at T = 295 K, 1 bar (solid line) and 100 mbar (dotted line). (From Reference [65]). rate and the collision-related deactivation one. Because both quantities are rising with oxygen ambient pressure [67], there is an optimal \(P_{ox}\) for the maximal steady state concentration of \({}^{(1)}\)O\({}_{2}\)[65]. Additional information about the \({}^{(1)}\)O\({}_{2}\) photosensitization at room temperature is obtained from the PL transient measurements. Figure 28 presents several transients of the exciton PL of por-Si MPs in gaseous oxygen ambient. The inset of Figure 28 shows the transients after the pumping of oxygen molecules. The PL transients are not actually single exponential. However, they can be well fitted by single exponential decays for times about 50-70 \(\upmu\)s after the excitation laser pulse [83]:  
\[I_{PL}(t)\ =\ I_{PL}(0)\exp(-t/\tau_{PL}), \tag{19}\]  
where \(\tau_{PL}\) is the PL lifetime and \(I_{PL}(0)\) is the PL intensity just after excitation. The values of \(\tau_{PL}\) for the samples in vacuum are found to be within a microsecond time scale that is in good agreement with the singlet lifetimes of excitons in nc-Si [60; 61]. The admission of O\({}_{2}\) causes a decrease of \(\tau_{PL}\) and this effect is stronger at higher oxygen pressure (curve 3 in Figure 28). The PL lifetime shortening after oxygen adsorption with \(P_{ox}>10\) Torr is partially reversible (inset of Figure 28). The strongest lifetime shortening occurs at the PL energy of 1.6 eV, which correlates with the spectral maximum of the PL intensity quenching. While the energy transfer time at room temperature can be obtained from the PL decay times by applying Equation (13), in which \(\tau_{ex}\) has to be substituted by \(\tau_{PL}\) in vacuum, the energy transfer efficiency is estimated by using the following expression [83]:  
\[\eta\ =\ 1-\int_{0}^{\infty}I_{PL}{}^{\alpha}(t)dt/\int_{0}^{\infty}I_{PL}{}^{ nuc}(t)dt. \tag{20}\]  
It is obvious that \(\eta\approx 1\)-\(Q^{-1}\) where \(Q\) is described by Equation (14). If the PL quenching is not completely reversible due to the oxidation of nc-Si by photosensitized \({}^{(1)}\)O\({}_{2}\)[81], Equations (15) and (20) will give the lower and upper limits of the corresponding energy transfer time and photosensitization efficiency, respectively [83]. It was found that the photosensitization efficiency in por-Si layers and powder is strongly dependent on the porosity of nc-Si assemblies (Figure 29). The minimal value of \(\tau_{\rm ET}\) and maximal  
Figure 28: Transients of the exciton PL intensity of nc-Si in por-Si at 1.6 eV at oxygen pressures \(P_{ox}=1\) Torr (1), 100 Torr (2) and 200 Torr (3). Inset: the same PL transients in vacuum after oxygen adsorption at \(P_{ox}\)= 1 Torr (1’), 100 Torr (2’) and 200 Torr (3’). \(T\) = 300 K. (Reprinted from Reference [83] by permission from John Wiley and Sons © 2007). value of \(\eta\) are supposed for highly porous layers and powder of MPs, which consist of smallest nc-Si. The porosity dependence of \(\eta\) and \(\tau_{\rm ET}\) can be explained by considering the following reasons.