Alloying effects on the optical properties of Ge1-xSix nanocrystals from time-dependent density functional theory and comparison with effective-medium theory

We present the optical spectra of Ge1-xSix alloy nanocrystals of a fixed size calculated with time-dependent density functional theory in the adiabatic local-density approximation (TDLDA). The spectra change smoothly as a function of the composition x. On the Ge side of the composition range, the lowest excitations at the absorption edge are almost pure Kohn-Sham independent-particle highest occupied molecular orbital\textendashlowest occupied molecular orbital transitions, while for higher Si contents strong mixing of transitions is found. Within TDLDA the first peak is slightly higher in energy than in earlier independent-particle calculations. However, the absorption onset and in particular its composition dependence is similar to independent-particle results. Moreover, classical depolarization effects are responsible for a very strong suppression of the absorption intensity. We show that they can be taken into account in a simpler way using Maxwell-Garnett classical effective-medium theory. Emission spectra are investigated by calculating the absorption of excited nanocrystals at their relaxed geometry. The structural contribution to the Stokes shift is about 0.5 eV. The decomposition of the emission spectra in terms of independent-particle transitions is similar to what is found for absorption. For the emission, very weak transitions are found in Ge-rich clusters well below the strong absorption onset.