## 3 Electron Spin-Dependent Processes in Si Nanocrystals
### Photosensitized Generation of Singlet Oxygen
A local maximum separated by 57 meV from the main maximum at 1.63 eV is an evidence of the indirect radiative transition in nc-Si, where the participation of the momentum conserving TO phonon with energy of 57 meV is required [61]. The excess of the exciton energy with respect to the energies of the \({}^{1}\Delta\) and \({}^{1}\Sigma\) states is compensated by emission of the TO phonons with energy of 63 meV [64; 65]. Figure 21: PL spectra of por-Si in vacuum (dashed line) and those with adsorbed oxygen molecules (solid line). Transition energies from the excited states (\({}^{1}\Delta\), \({}^{1}\Sigma\)) of (\({}^{1}\))O\({}_{2}\) to the ground state are indicated by dashed vertical lines. The spin configuration and spectroscopic labeling of the oxygen states are shown in the right inset. The left inset depicts the PL line related to the \({}^{1}\Delta\rightarrow\)\({}^{3}\Sigma\) transition in O\({}_{2}\). Temperature \(T\) = 5 K, excitation at 2.41 eV. (From Reference [65]). Figure 22: Spectral dependence of the PL quenching strength of por-Si with adsorbed O\({}_{2}\) molecules at \(T\) = 5 K. Inset shows the second derivative of the PL quenching strength. For convenient presentation, the data are partially scaled by the indicated multiplication factor. Vertical dotted lines are guide for the eye. (From Reference [65]). The dynamics of the energy transfer is deduced from the PL transients of por-Si in the presence of adsorbed O\({}_{2}\) molecules [65]. The PL spectra of por-Si at different quenching level by the energy transfer to O\({}_{2}\) at low temperatures and the corresponding PL decay times \(\tau_{\rm PL}\) are shown in Figure 23. In vacuum \(\tau_{\rm PL}\) is approximately equal to the radiative lifetime of excitons \(\tau_{\rm ex}\) of the order of 10\({}^{-3}\) s and it does not depend on the photon energy (see Figure 23). The PL quenching by O\({}_{2}\) adsorption is accompanied by a significant decrease of the PL decay time because the adsorbed O\({}_{2}\) molecules on the nc-Si surface represent a channel for the nonradiative recombination of the excitons. The spectral dependence of \(\tau_{\rm PL}\) follows the quenching strength spectrum. The shortest \(\tau_{\rm PL}\) is observed at the PL photon energies, which correspond the strongest PL quenching. Increasing the concentration of adsorbed O\({}_{2}\) molecules results in a stronger PL quenching and further decrease of \(\tau_{\rm PL}\)[65]. The time resolved PL studies performed with nanosecond time resolution confirm this spectral behavior of the exciton lifetime [71]. The average time of the energy transfer from excitons in nc-Si assembly to O\({}_{2}\) molecules can be calculated from the following expression [65]:  
\[\tau_{\rm ET}{}^{-1}=\tau_{\rm PL}{}^{-1}\mbox{--}\tau_{\rm ex}{}^{-1}. \tag{15}\]  
In the regime of the strongest quenching the values of \(\tau_{\rm ET}\) for the \({}^{1}\Delta\) and \({}^{1}\Sigma\) states are 50 to 100 \(\upmu\)s and \(<\)3 \(\upmu\)s, respectively. A uniform concentration of O\({}_{2}\) molecules for all nc-Si would result in a quenching strength that scales as \(\tau_{\rm ex}\)/\(\tau_{\rm PL}\). Obviously this simple relation is not valid. A decay time longer than that expected from the quenching strength is observed because of statistical fluctuations of the number of adsorbed O\({}_{2}\) molecules--while mainly the slowest PL emission from nc-Si with a small number of the adsorbed molecules contributes to the PL decay, the PL intensity spectrum reflects the response of all nanocrystals [65]. A mechanism of the direct electron exchange between nc-Si and O\({}_{2}\) molecule is explained the triplet-triplet annihilation of excitons accompanied by spin-flip excitation of an O\({}_{2}\) molecule and followed by the \({}^{(1)}\)O\({}_{2}\) formation [65]. The energy transfer rate is supposed to be determined by the spatial overlap of the electronic wave functions of the interacting species and depends exponentially on the donor-acceptor distance [78].