## 2 Light Emission in Nanocrystals
### Silicon Nanocrystals
In this case, the rate values become \(\sim\)16 times lower compared to the case of Si NCs embedded in silicon dioxide due to the factor \(\kappa\sqrt{\epsilon_{1}}\). As seen in Figure 1, generally, doped crystallites demonstrate 1-2 orders of magnitude faster transitions than intrinsic ones. For Si crystallites doped with phosphorus, increasing rates of the radiative transitions have been explained by the efficient mixing of the electronic states in the \(\Gamma\) and X points of the Brillouin zone (\(\Gamma\)-X mixing) caused by the short-range field of the phosphorus ion [87; 99]. Meanwhile, the radiative decay in the Li-doped crystallites becomes faster due to the high density of states above the inter-band energy gap (in the range \(\hbar\omega-E_{g}\lesssim k_{B}T\), where \(k_{B}\) is the Boltzmann constant) [107]. Surface chemistry is another method capable of modifying electronic structure of nanocrystals [124; 125]. This method is especially efficient for small crystallites, where the role of surface rises. It has been demonstrated experimentally [104; 126; 127] that chemical synthesis allows to fabricate Si nanocrystals with various ligand coatings, which emit light in visible range with typical nanosecond radiative lifetimes [104; 128; 129]. Calculations based on the tight-binding model [105] performed for CH\({}_{3}\)-capped Si nanocrystals confirmed the conclusion on the increase of the radiative recombination rate due to the formation of direct-like electronic structure of the crystallite. Let us now consider some other kind of the surface reconstruction of the crystallites, the halogenation. Table 1 presents calculated rates of radiative transitions between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in completely halogenated with Cl-, Br- and H-coated silicon crystallites. It is possible to see from Table 1 that the surface halogenation significantly slows down the radiative recombination in silicon nanocrystals, especially in the case of the bromine coating. Such a slowing down is due to the spatial separation of the electron densities of the HOMO and LUMO states, which takes place in halogenated Si crystallites [130; 131; 132]. \begin{table}
\begin{tabular}{c c c c} \hline  & **X = H** & **X = Cl** & **X = Br** \\ \hline Si\({}_{35}\)X\({}_{36}\) & \(3.7\times 10^{5}\) & 3.3 & 2.7 \\ Si\({}_{59}\)X\({}_{60}\) & \(2.9\times 10^{4}\) & \(4.2\times 10^{4}\) & \(3.0\times 10^{2}\) \\ Si\({}_{87}\)X\({}_{76}\) & \(1.6\times 10^{3}\) & \(2.4\times 10^{2}\) & 36 \\ Si\({}_{123}\)X\({}_{100}\) & \(3.6\times 10^{3}\) & \(4.2\times 10^{3}\) & 1.7 \(\times 10^{5}\) \\ Si\({}_{147}\)X\({}_{100}\) & \(2.2\times 10^{4}\) & \(4.3\times 10^{2}\) & 15 \\ Si\({}_{163}\)X\({}_{116}\) & \(6.1\times 10^{3}\) & \(3.0\times 10^{4}\) & \(3.1\times 10^{3}\) \\ Si\({}_{175}\)X\({}_{116}\) & \(3.5\times 10^{4}\) & \(1.3\times 10^{2}\) & \(3.5\times 10^{2}\) \\ Si\({}_{317}\)X\({}_{172}\) & \(1.4\times 10^{4}\) & \(2.4\times 10^{3}\) & 63 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated rates (s\({}^{-1}\)) of the radiative HOMO–LUMO transitions in H-, Cl- and Br-passivated silicon nanocrystals. Figure 1: Calculated rates of radiative transitions for undoped (small violet dots), P-doped (big blue dots) and Li-doped (big red dots) Si nanocrystals. The separation turns out to be more pronounced in the Br-passivated crystallites, in which the HOMO states are strongly concentrated near the Br atoms. Presumably, the bromine atoms produce strong lattice distortions, and the stress fields have an additional localizing effect on the electron density. An effect of the rate reduction was also found for completely fluorine-passivated Si nanocrystals [102].