## 3 Nonradiative Processes
### Phonon-Assisted Relaxation of Hot Carriers
The electron-phonon interaction can be enhanced in nanocrystals because of the spatial confinement of both electrons and phonons and, therefore, multiple scattering processes are important. It means that the electron-phonon interaction in QDs, in principle, must be treated in a non-perturbative and non-adiabatic way, leading to the energy spectra described by polaronic quasi-particle excitations [146, 147, 148, 149, 150, 151, 152]. In other words, virtual transitions between different electronic levels, assisted by phonons and not requiring energy conservation may be important enough to guarantee a significant modification of the exciton energy spectrum and dynamics [12]. Thus, does the phonon bottleneck in QDs really exist? Experimental results still are not completely conclusive. On the one hand, an efficient relaxation of optically created excitons was reported in a number of works studying self-assembled QDs (SAQDs) [153, 154, 155], with both PL emission rise time [153, 154] and photo-induced intraband absorption decay time [155] below or of the order of 10 ps. Studies performed on nanocrystal QDs [156, 157], where exciton energy level spacings are larger than in SAQDs, also revealed ultrafast intraband relaxation with a characteristic time in the picoseconds' domain, which is characteristic of CdSe and CdTe QDs in general [12]. On the other hand, there are published experimental results indicating that the relaxation of optically created excitons can be slow (in the nanoseconds' range), both in self-assembled [158, 159] and nanocrystal [160, 161] QDs. It is important to realize that the polaron concept by itself cannot explain intraband relaxation of carriers in QDs as polaron is a _stationary_ state of an electron (or exciton) coupled to optical phonons. Some additional interactions should therefore be responsible for the polaron relaxation [152]. Several possible mechanisms of hot carrier relaxation in QDs have been proposed:  
1. The polaron has a rather short lifetime [162] because of the anharmonic effects that lead to a fast decay of nanocrystal's optical phonons forming the polaron. 2. Acoustic phonons can provide the possibility of transitions between different (exciton-) polaron states formed mostly by the interaction with optical phonons; the polaron spectrum is discrete but relatively dense owing to the non-adiabaticity of this interaction [148]. If the acoustic phonon spectrum is continuous, this additional interaction would drive the polaron dynamics towards equilibrium. 3. In the strong confinement regime where the electron's kinetic energy is larger than the electron-hole interaction, the electron (eventually dressed by phonons and forming the polaron) can relax by an Auger-type mechanism. The excess energy is first transferred from the electron to the hole through their Coulomb interaction and the subsequent hole's cooling occurs via emission of acoustic phonons [163, 164]. It can be feasible because the hole level spacings are relatively small in QDs and match the continuum of acoustic phonon energies. There is no final conclusion concerning the relevance of each of the three mechanisms to the breaking of the phonon bottleneck in QDs; however, the first one seems to be the most popular in the literature, even though calculations yielded too low relaxation rates for this mechanism, of the order of 1 ns\({}^{-1}\), for a typical quantum dot considering anharmonic (Gruneisen) parameters characteristic of bulk materials and the Frohlich interaction with spherically confined optical phonons and electrons [152]. Moreover, the electron-phonon interaction in nanocrystals of non-polar materials (see below) may be too weak to make the polaron effect important. If this is the case, the relaxation proceeds via multi-phonon processes (like temperature-induced interband excitation of charge carriers in bulk semiconductors). Usually, multi-phonon processes are much slower compared to the single-phonon transitions. Therefore, the bottleneck effect does not disappear completely.