Linear optical absorption in silicon and GaAs nanocrystals*

The linear optical spectrum of Si and GaAs nanocrystals containing up to 100 atoms is calculated and discussed. We use two first-principles theories: time-dependent density-functional theory in the local adiabatic approximation (TDLDA), and the many-body solution of the Bethe-Salpeter equation (BSE). Both theories predict a strong blue shift in the energy-resolved polarizability and in the absorption cross section, which is characteristic of confined systems in the nanoscale. When many-body effects are included, in the framework of the BSE, the low-energy range of the spectrum is modified in two ways: the energy of excitation lines increases by almost 1 eV, as a result of self-energy and screening corrections; and the oscillator strength of those lines is enhanced. In bulk semiconductors, many-body effects are known to produce exciton lines and enhanced absorption in the low-energy range of the spectrum. Although the size of the nanocrystals studied is much smaller than the radius of Wannier excitons, the enhancement in oscillator strength is suggested to have the same source as excitonic effects in bulk samples.