Theoretical analysis of electronic band structure of 2- to 3-nm Si nanocrystals

In this paper, we discuss the validity of the band structure concept in silicon nanocrystals a few nanometers in size. We introduce a general method which allows reconstruction of a fuzzy electronic band structure of nanocrystals from ordinary real-space electronic structure calculations. A comprehensive study of the fuzzy band structure of a realistic nanocrystal is given including full geometric and electronic relaxation with the surface passivating groups. In particular, we combine this method with large-scale density functional theory calculations to obtain insight into the luminescence properties of silicon nanocrystals up to 3 nm in size depending on the surface passivation and geometric distortion. We conclude that the band-structure concept is applicable to silicon nanocrystals with a diameter larger than approximate to 2 nm with certain limitations. We also show how perturbations due to polarized surface groups or geometric distortion can lead to considerable moderation of momentum space selection rules.