## 3 Electron Spin-Dependent Processes in Si Nanocrystals
### Phenomenological Model of the Photosensitization by Si Nanocrystals
Figure 25:0 Dependences of the of \({}^{(1)}\)O\({}_{2}\) luminescence intensity, \(I_{\rm oxy}\), (open triangles) and defect-related PL, \(I_{d}\), for initial por-Si (solid triangles) and por-Si powder (solid squares) for the photoexcitation time of por-Si powder in oxygen atmosphere at \(P_{\rm ox}=1\) bar. \(E_{\rm exc}=2.33\) eV, \(I_{\rm exc}=0.1\) W/cm\({}^{2}\), \(T=300\) K. (Reprinted from Reference [73] by permission from Springer Nature Customer Service Centre GmbH: Springer © 2010.) Figure 25:1 Spectra of the photoluminescence of por-Si powder in vacuum (lowest curve) and in oxygen atmosphere at \(P_{\rm ox}=1\) bar for different times after illumination (indicated near the corresponding curves). \(E_{\rm exc}=2.33\) eV, \(I_{\rm exc}=0.1\) W/cm\({}^{2}\), \(T=300\) K. (Reprinted from Reference [73] by permission from Springer Nature Customer Service Centre GmbH: Springer © 2010). Beside the PL diagnostics of the nc-Si-induced photosensitization the EPR technique was shown to be efficient for the quantitative analysis of the \({}^{(1)}\)O\({}_{2}\) photosensitization [84]. It is known that por-Si possesses intrinsic defects as Si DBs, which can act as _spin labels_ for \({}^{(1)}\)O\({}_{2}\). Typical EPR spectra of por-Si are shown in Figure 25:2 The EPR signal is characterized by the effective \(g\)-factor of 2.0055 \(\pm\) 0.0005. The corresponding paramagnetic defects are usually attributed to so-called P\({}_{\text{b}}\)-like centers, which are Si DBs at Si/SiO\({}_{2}\) interface [85]. The EPR signal intensity (I\({}_{\text{EPR}}\)) of por-Si in vacuum is the weakest at high microwave power because of the saturation effect of the microwave power absorbance by Si DBs [74]. The \({}^{1}\)O\({}_{2}\) can be also detected by monitoring a decrease of the concentration of paramagnetic \({}^{(3)}\)O\({}_{2}\)[75]. It was found that por-Si in O\({}_{2}\) atmosphere was characterized by larger I\({}_{\text{EPR}}\) in darkness than under illumination. Furthermore, I\({}_{\text{EPR}}\) for the sample under short time illumination in O\({}_{2}\) atmosphere decreased almost reversibly [74]. Note, that prolonged intensive illumination led to an irreversible increase of I\({}_{\text{EPR}}\) due to the defect formation under photo-oxidation [81]. The saturation effect of the EPR signal of por-Si results from relatively long time of the spin relaxation of P\({}_{\text{b}}\)-centers [85]. In general, I\({}_{\text{EPR}}\) depends on the number of paramagnetic centers (Si DBs in the case of nc-Si) and their relaxation time, which can be expressed in the following way [75]:  
Figure 25:3  
where \(T_{1}^{DB}\) is the longitudinal relaxation time (spin-lattice relaxation) and \(T_{2}^{DB}\) is the transverse relaxation time, associated with spin-spin relaxation. For nc-Si systems with low defect density--\(T_{1}^{DB}\)\(<<T_{2}^{DB}\) and then \(T\approx 2T_{1}\). While the value of \(T_{1}\) for bulk c-Si at the room temperature lies typically in the range of several microseconds [85], this time can be longer in small nc-Si because of a low density of phonon modes. Indeed, I\({}_{\text{EPR}}\) for the sample in vacuum exhibits the strong saturation even at relatively low microwave power (Figure 33). The spectral shape of the EPR signal of the sample in vacuum does not change significantly under illumination [75]. Note, the factor of phonon mode depletion in nc-Si can also influence the longitudinal relaxation time of nuclear spin as \({}^{29}\)Si what is essential for the hyperpolarization method (see Section 2). Figure 25:4 Electron paramagnetic resonance (EPR) spectra of por-Si powder in vacuum and in oxygen ambient (\(P_{\text{ox}}\) = 760 Torr) in darkness and under illumination. Measurements were done at high microwave power of about 200 mW. (Reprinted from Reference [84] with permission from Elsevier). The \(T_{2}\) value is reciprocal to the paramagnetic center concentration, which depends on the number of adsorbed triplet O\({}_{2}\) molecules on nc-Si surface.