Experimental investigation of band structure modification in silicon nanocrystals

Abstract

Experimental studies of size-related effects in silicon nanocrystals are reported. We present investigations carried out on nanocrystals prepared from single-crystal Si:P wafer by ball milling. The average final grain dimension varied depending on the way of preparation in the range between 70 and 230 nm. The ball milling was followed by sedimentation and selection of the smallest grains. The initial grain size distribution was measured by scanning electron microscopy. Further reduction in size was achieved by oxidation at $1000\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ which creates a silicon dioxide layer around a silicon core. The oxidation process was monitored by transmission electron microscopy and the growth speed of ${\mathrm{SiO}}_{2}$ was estimated in order to model the grain size of nanocrystals. Crystallinity of silicon grains was confirmed by x-ray diffraction and by transmission electron microscopy using a bright/dark field method and selected area diffraction pattern. In the silicon nanocrystals the electron energy levels are shifted which was observed separately for conduction band, valence band and energy band gap. Electron paramagnetic resonance was applied to investigate variation of the conduction band minimum by monitoring its influence on the hyperfine interaction of phosphorus shallow donor. On the basis of these results an explicit expression for conduction band upshift as a function of average grain size has been derived. Information about the downshift of the valence band was obtained from measurements on a photoluminescence band related to a deep to shallow level transition. A perturbation of a few meV for grain sizes of the order about 100 nm has been observed. Internal consistency of these findings has been examined by investigation of the photoluminescence band due to an electron-hole recombination whose energy is directly related to the band gap of silicon.