Electron-electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the effective bandgap.

We model, in an elementary way, the excited electronic states of semiconductor crystallites sufficiently small (~50 angstrom diameter) that the intrinsic bulk band gap does not form. In this limit the excited states and ionization processes assume a molecular like character. However, diffraction bonding electrons by the periodic lattice potential remains of paramount importance in the crystallite electronic structure. Calculations were undertaken to understand the experimental optical properties of small in situ CdS colloidal crystallites. The absorption edge shifts blue for diameters in the range of 20-25 angstrom. At a diameter of 28 angstrom, the electron-hole pair is confined to a volume ~=1/8 if that occupied in the corresponding bulk 1S exciton. The band gap shows a blue shift of about 0.8 eV, as described in a forthcoming memorandum.