Hyperpolarizabilities of Si clusters: model calculations to interpret second-harmonic generation from SiO2/Si(111) interface

We have evaluated molecular hyperpolarizability β of Si clusters either with or without a dangling bond normal to Si(111) surface, and discussed the results in relation to the second-harmonic-generation (SHG) measurement from SiO2/Si(111) interface. The simplified sum-over-states calculation and missing-orbital analysis are extended to handle an open shell system, i.e. a dangling bond. In the presence of the dangling bond, β is caused by charge-transfers from the cluster interior to the dangling bond, while its absence by hydrogen termination greatly reduces β. This is consistent with the experiment that SHG is reduced by termination of interfacial Si atoms by annealing under hydrogen ambient.