Recombination, multiplication, and transfer of electron-hole pairs in silicon nanocrystals: Effects of quantum confinement, doping, and surface chemistry

Highlights: • Rates of exciton tunneling in Si crystallites are comparable with those of Auger process. • Doping with P increases the rates of radiative transitions and slows down Auger process. • Halogenation of the crystallite surface increases an efficiency of exciton generation. In the present review some basic radiative and non-radiative processes occurring with strongly confined electron-hole pairs (excitons) in silicon nanocrystals are discussed, and rates of these processes are calculated. We explore both intra-crystallite processes, such as the photon absorption or emission, Auger recombination, phonon-assisted exciton relaxation, multi-exciton generation, and inter-crystallite processes realized through the exciton migration in ensembles of nanocrystals. Dependence of the rates on a nanocrystal size is analyzed, and physical and chemical factors, such as doping with shallow donors and surface passivation, is examined from the point of view of their influence on the nanocrystal electronic structure and all the processes investigated. We consider nanocrystals in a wide range of their sizes. For small crystallites (less than $~2$ nm in diameter), the presented results are based on the stationary and non-stationary density functional theory (DFT and TD DFT, respectively). For greater crystallites, for which some semiempirical methods, such as the envelope function approximation, tight binding model, or empirical pseudopotential, are usually employed, we discuss the results obtained within the framework of these methods.