Structural relaxation in Si and Ge nanocrystallites: Influence on the electronic and optical properties

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Abstract
A complex atomic relaxation pattern for hydrogen-saturated Ge and Si nanocrystallites with diameters between 10 and 25 Å has been found by means of ab initio calculations. While the bonds at the center of the nanocrystals expand beyond their length in the corresponding bulk material, the bonds near the surface are shortened. The average bond lengths decrease. The atoms at the surface facets move inward, those at the edges and corners outward, leaving the volume of the crystallite almost unchanged. As a consequence of the structural relaxation, the pair excitation energies increase as compared to the values for the respective ideal structures, and they do so stronger for Ge than for Si. The main effect on the overall absorption spectra is an upward shift of the different spectral features. Most important for Ge crystallites is the change of the energetic ordering of the electronic states close to the HOMO-LUMO (highest occupied molecular orbital–lowest unoccupied molecular orbital) gap, leading their radiative lifetimes to decrease by orders of magnitude.