Calculation of the band gap for small CdS and ZnS crystallites

The tight-binding approximation and the recursion method are used to study the size dependence of the band gap for small CdS and ZnS crystallites (20--2500 atoms). Because of the lack of accurate experimental data, a simple model of the crystal is considered; one which has no dangling bonds and a symmetrical shape. It is then possible to have a good evaluation of the band gap, even for the largest crystallites. The optical-absorption spectra exhibit an excitonic peak; we determine the peak position from a simple evaluation of the binding energy. The results are compared with the results of other calculations based upon the effective-mass approximation and some experimental data.