Ab initio investigations of the intrinsic optical properties of germanium and silicon nanocrystals

Ab initio calculations of Si and Ge nanocrystals of up to 363 Ge atoms have been carried out. After relaxation, the structure shows an expansion at the center. Structural relaxation is indispensable for the description of the electronic and optical properties. Germanium nanocrystals show much shorter radiative lifetimes than those of silicon, leading to the expectation of applicability to luminescence. The Delta-self-consistent-field method is used to calculate excitation energies within the DFT-LDA framework. Exchange splitting energies between singlet and triplet excitons are likewise calculated, within LSDA. Optical spectra in independent-particle approximation compare rather well with experiment. Alloying and confinement are found to act approximately independently. Embedded crystallites are treated using a special extrapolative version of the linear tetrahedron integration method. Compression is shown to change the character of the crystallites. This can be explained with reference to the bulk band behavior. Stokes shifts are calculated for fixed symmetry. The effect of the symmetry break due to an optical excitation is found to be strong.