## 4 Multiple Exciton Generation  
As demonstrated above, the surface halogenation suppresses both radiative and Auger recombination in nanocrystals. These processes are reverse ones with respect to the carrier multiplication (or multi-exciton generation): they tend to decrease the number of excitons in a system, while the process of multi-exciton generation, shown schematically in Figure 4, has an opposite trend. Initially, a high-energy photon creates a highly excited electron-hole pair which then reduces its energy creating one more electron-hole pair with lower energy. As a result, two (or even more) excitons can arise in the system after absorption of a single photon. The multi-exciton generation is a fundamental process for photovoltaics, where light energy transforms into electric current. Its occurrence in NCs has been experimentally confirmed [170; 171; 42; 172; 173; 170; 171; 42]. In order to be more efficient, this process should be faster than other competitive processes taking place along with exciton generation, such as inter-band radiative recombination or Auger recombination. From this point of view, slowing the latter down caused by surface halogenation is an extremely positive factor. It is important to understand how halogen passivation influences the multi-exciton generation itself. The rates of the multi-exciton generation in the Si\({}_{317}\)X\({}_{172}\) crystallite (X = H, Cl, and Br) can be calculated using the following relation,  
\[\tau_{G}^{-1}=\frac{2\Gamma}{\hbar}\sum_{f_{1}}\sum_{i_{2}}\sum_{f_{2}}\frac{| \langle\Psi_{i_{1}i_{2}}|\bar{U}|\Psi_{f_{1}f_{2}}\rangle|^{2}}{\Gamma^{2}+(E _{i_{1}}+E_{i_{2}}-E_{f_{1}}-E_{f_{2}})^{2}}, \tag{9}\]  
where \(\bar{U}=\bar{U}_{0}+\bar{U}_{1}\), as before, while \(\Psi_{i_{1}i_{2}}\) and \(\Psi_{f_{1}f_{2}}\) are the products of the single-particle Kohn-Sham wave functions of the initial or final electron states participating in the transition, as shown in Figure 4. Here, we present calculated the rates for the Si\({}_{317}\)X\({}_{172}\) crystallite within the range of excess energy \(0<\Delta E<0.6\) eV, where \(\Delta E=E_{i_{1}}-E_{LUMO}-E_{g}\) for  
Figure 4: Schematic representation of the electron- (**left**) and hole-initiated (**right**) process of multi-exciton generation in a nanocrystal. Initial electron configurations are shown. Dashed arrow indicates highly excited exciton with the excitation energy \(E_{0}\) created by an absorbed photon. Vertical solid arrows indicate electron transitions to the final states. After the transition, the number of excitons increases by one. the process initiated by highly excited electron, and \(\Delta E=E_{HOMO}-E_{f_{1}}-E_{g}\) for the hole-initiated process. The calculated rates are shown in Figure 5. It is evident that the rates rise globally as the excess energy increases, because of the considerable increase in the number of possible states participating in the transitions with increasing \(\Delta E\), which opens up many new channels for the realization of exciton generation. It is important to emphasize that the bromination of a Si crystallite increases the exciton generation rates compared to an H-passivated crystallite, especially if the process is initiated by a highly excited hole. The rates of exciton generation in chlorinated Si crystallite turn out to be lower than those in the hydrogenated one at small excess energies. Meanwhile, upon approaching \(\Delta E\sim 0.5\) eV, \(\tau_{G}^{-1}\) in the Si\({}_{317}\)Cl\({}_{172}\) crystallite increases and tends to the typical values observed in Si\({}_{317}\)H\({}_{172}\) crystallite. Accordingly, it is possible to conclude that halogen coating of Si crystallites, at least, does not reduce their ability to generate excitons, particularly when the excess energies are not too small. This is in contrast with the radiative and Auger recombination processes, where the rates became substantially lower due to the halogenation.