Validity of effective-medium theory for optical properties of embedded nanocrystallites from ab initio supercell calculations

The optical properties of Ge and Si nanocrystals embedded in a crystalline matrix are calculated using an ab initio supercell method. Spectra of effective nanocrystallite materials including confinement effects are extracted by means of effective-medium theory. Spectra for different composites are calculated and compared to results obtained directly. The applicability of the Maxwell-Garnett effective-medium theory is demonstrated for photon energies below the main absorption peak of the host material. The minimum crystallite diameter treatable by effective-medium theory is found to be approximately 1 nm. The transferability of the crystallite spectra is discussed, its limits are investigated.