Bulk quadrupole and interface dipole contribution for second harmonic generation in Si(111)

The second harmonic generation (SHG) response was measured for arbitrarily oriented linear input polarization on Si(111) surfaces in rotational anisotropy experiments. We show for the first time, using the simplified bond hyperpolarizability model (SBHM), that the observed angular shifts of the nonlinear peaks and symmetry features-related to changes in the input polarization-help to identify the corresponding interface dipolar and bulk quadrupolar SHG sources, yielding excellent agreement with the experiment. Additionally, we evaluate for the s-in/p-out (sp) and p-in/p-out (pp)-polarization SHG intensities the contributions from the individual Si bonds. Furthermore, a relation between the four parameters arising from SBHM and six coefficients of the phenomenological SHG theory needed to reproduce experimental data is established.