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The electronic and excitonic spectra calculations for semiconductor quantum dots (QDs) in the 1980s were all within the ambit of effective mass theory (EMT). This work appeared at the end of this decade1 . Tight-binding (TB) approximation with recursion method for matrix diagonalization were used by the authors to calculate the band gap of small CdS and ZnS crystallites of sizes 10 Ao to 50 Ao. A simple TB parameterization scheme was used. The recursion method does not require storage of all matrix elements and hence was employed to advantage. The TB method needs the detailed atomic structure unlike effective mass theory (EMT) and at the very outset the authors make it clear that zinc-blende is the observed arrangement. But the issues of shape, surface structure and the cluster center cannot be decided unambiguously since there are no experimental confirmations. The authors take as ``spherical'' a structure as possible. These issues have not been resolved and are a matter of concern to this day.
Comparison with experiment is made. The effective mass approximation is shown to overestimate the experimentally obtained band gap for the smallest sizes. The TB model underestimates the band gap but is closer to the experimental results.