Optical absorption spectra of doped and codoped Si nanocrystallites

The effects of the incorporation of group-III (B and Al), group-IV (C and Ge), and group-V (N and P) impurities on the formation energies, electronic density of states, optical absorption spectra, and radiative lifetimes of Si nanocrystallites of different shape and with diameters up to 2 nm are studied by means of an ab initio pseudopotential method that takes into account spin polarization. The single doping with group-III or group-V impurities leads to significant changes on the onsets of the absorption spectra that are related to the minority-spin states. In contrast to the optical absorption spectra, the radiative lifetimes are sensitively influenced by the shape of the nanocrystallites, though this influence tends to disappear as the size of the nanocrystallites increase. Codoping is investigated for pairs of group-III and group-V impurities. We show that the impurity formation energies decrease significantly when the nanocrystallites are codoped with B and P or with Al and P. Additional peaks are introduced in the absorption spectra due to codoping, giving rise to a redshift of the absorption onset with respect to the undoped nanocrystallites. Those additional peaks are more intense when codoping is performed with two different species either of the group III or of the group V. The values of radiative lifetimes for the codoped nanocrystallites are mostly in between the values for the nanocrystallites doped with the impurities separately.