## 3 Electron Spin-Dependent Processes in Si Nanocrystals
### Phenomenological Model of the Photosensitization by Si Nanocrystals
The time constants used in the model are obtained from the experimental data discussed above whereas \(\sigma\) is known from Reference [61]. Solutions of Equation (16) fit the experimental dependences of the PL intensity of por-Si on excitation intensity \(I_{\rm ex}\) (solid lines in Figure 25). The described model assumes that the larger number of adsorbed O\({}_{2}\) molecules results in shorter \(\tau_{\rm ET}\) at the same conditions of the energy transfer. The energy transfer efficiency is described by \(\beta\) and it is obviously dependent on nc-Si size and surface conditions [79]. Hydrogen terminated nc-Si assembles with lowest number of nonradiative surface defects as Si DBs are preferable for the \({}^{(1)}\)O\({}_{2}\) photosensitization [81]. For por-Si aged in air at room temperature, the photosensitization process is additionally complicated by the thermally activated desorption of O\({}_{2}\) molecules as well as by the thermally activated exciton migration and nonradiative recombination. Besides, it should be analyzed both the generation rate and the quenching process of \({}^{(1)}\)O\({}_{2}\) via the interaction with internal surface of por-Si and ambient molecules. The quenching processes are especially important for por-Si suspended in different solvents. The theoretical description of the photosensitized generation of \({}^{(1)}\)O\({}_{2}\) by real systems based on por-Si needs rather sophisticate analysis. The experimental results presented in the next sections of this chapter can be used as experimental basis for future complete theory of the photosensitized generation of \({}^{(1)}\)O\({}_{2}\) by nc-Si. Contrary to cryogenic temperatures, the conditions of efficient interaction between excitons in nc-Si and O\({}_{2}\) molecules adsorbed on the surfaces of nc-Si are not fulfilled at elevated temperatures. First of all, because of the thermally activated desorption, a small spatial separation between excitons and O\({}_{2}\) molecules is realized only during a short time of collisions [65]. Furthermore, the exciton lifetime and spin-triplet state occupation drop down with rising temperature [59; 60; 61]. It results in a weaker PL quenching, which scales with the collision rate, that is, the gas pressure and in a broad spectral resonance of the energy transfer to the \({}^{1}\Sigma\) state [64]. Spectra of the photosensitization efficiency of nc-Si in por-Si at different temperatures are shown in Figure 26 [65]. At intermediate temperatures (\(T=110\) K) the second quenching band in the spectral region of 1.75-1.95 eV is observed and it becomes better pronounced with increasing oxygen concentration (Figure 26a). This quenching band is attributed to the energy transfer from excitons confined in nc-Si to \({}^{(1)}\)O\({}_{2}\) dimers, that is, to the 2(\({}^{1}\Delta\)) state formation [65]. The energy transfer to the 2(\({}^{1}\Delta\)) states is enhanced at higher pressures due to increasing the probability of dimer formation. A decrease of the dimer-related quenching band is observed at higher temperature because the dimer formation is less probable. For temperatures above 250 K the energy transfer to the \({}^{(1)}\)O\({}_{2}\) dimers cannot be resolved spectroscopically (see Figure 26b). This fact agrees with results of the spectroscopic investigation of \({}^{(1)}\)O\({}_{2}\)[67]. Dependence of the exciton PL quenching detected at 1.63 eV on the O\({}_{2}\) ambient pressure at different temperatures are shown in Figure 27[65]. The pressure dependence is well described by using the Langmuir approach for molecular adsorption on a surface [82], that considers the dynamic equilibrium between the rates of adsorption and desorption by the following Equation:  
\[Q^{-1}\ =\ 1-A\frac{Kp_{ox}}{1+Kp_{ox}}, \tag{18}\]  
where \(K\) is the equilibrium constant, \(P_{ox}\) is the oxygen gas pressure and \(A\) is the part of exciton energy transferred to adsorbed O\({}_{2}\) molecules [65].