Optical spectra of Si nanocrystallites: Bethe-Salpeter approach versus time-dependent density-functional theory

Two state-of-the-art approaches based on the quasiparticle-Bethe-Salpeter equation (QP-BSE) and time-dependent density-functional theory (TDDFT) for different functionals are applied to calculate optical-absorption spectra of Si nanocrystallites passivated with hydrogen. All-electron wave functions are generated within the projector-augmented wave method. The results of the two many-body approaches are used to discuss the interplay of quasiparticle, local-field (LF), and excitonic effects. The QP approach gives rise to blueshifts of the absorption spectra, whereas the LF effects and electron-hole exchange redistribute the oscillator strengths toward higher energies. The screened electron-hole attraction leads to slightly larger optical gaps than the ones found for independent particles described within the local-density approximation (LDA) for exchange and correlation (XC). The results within the TDDFT using the LDA kernel confirm the influence of LF effects. When a hybrid functional for XC is used, the TDDFT spectra show the same tendencies as the QP-BSE ones but still indicate a reduced electron-hole attraction. An effective-medium theory is used to examine the role of local fields due to the nanocrystal arrangement.