Quasi-particles and Excitons

In this Chapter we discuss the different types of calculations which have been performed for the electronic excitations in semiconductor nanostructures. These range from carrier injection (quasi-particle energies, charging effects) to optical excitation and radiative recombination. We start with basic considerations (Sect. 4.1) where confinement effects and self-energy contributions due to surface polarization are formally separated, which will prove useful when analyzing the results of sophisticated calculations. We then treat excitons (Sect. 4.2) in the effective mass approximation (EMA) which, while simple, remains a powerful tool for the interpretation of many data [202]. This is followed by more refined semi-empirical calculations mainly concentrating on evaluations of the exchange splitting (Sect. 4.3). The two following sections (Sects. 4.4 and 4.5) deal with the application of quantitative methods (GW for quasi-particles, Bethe—Salpeter equations for excitons) to the case of silicon nanostructures. The results allow us to discuss the limits of validity of more approximate methods and to derive useful rules. Finally we describe calculations of charging effects and multi-excitonic transitions which can now be described quite satisfactorily (Sect. 4.6).