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

Abstract

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.

Bond Model of Second‐ and Third‐Harmonic Generation in Body‐ and Face‐Centered Crystal Structures

“…For the case of bcc (001) surface, we just need to insert Equations (10) and (11) into Equation (13) for arbitrary zaxis rotation ϕ and set ϕ 0 at the end. e result is…”

“…where α 2j is the interface dipolar SHG hyperpolarizability and E int (ω) is the electric field at the interface E 0 is the EFISH DC field. e fields arising from quadrupole, spatial dispersion, and EFISH are linearly mixed together with the surface dipolar SHG field contribution; hence, they may be hard to distinguish in low symmetry lattices although it is possible in some cases to separate their contributions for certain surface orientation using arbitrary polarization [11]. It is thus reasonable to measure the third-harmonic generated far field when probing the bulk especially in centrosymmetric materials where dipolar SHG contribution is forbidden inside the bulk, but dipolar THG and odd-order nonlinear effects are not.…”

“…Just using these two complex parameters is a major advantage compared to previous phenomenological description for the same case [7][8][9]. Later on, SBHM was applied to model surface rotational anisotropy (RA) SHG experiment for a nonvicinal Si(111) surface with success [10] although it has recently been shown by using arbitrary input polarization that bulk quadrupolar effects also contribute to SHG [11]. However, SBHM was also criticised and tested against experiment by using Si(111) with different offcut directions and different offcut magnitude [12].…”

Optical rectification and Pockels effect as a method to detect the properties of Si surfaces

“…Local electric-field-induced (EFI) second-order nonlinear optical effects, such as EFI SHG [11,12] , EFI PE, and EFI OR [13][14][15] , were observed. EFI SHG and EFI second-harmonic spectroscopy have been widely used for characterization of Si-SiO 2 interfaces in metal-oxide-semiconductor (MOS) devices [16][17][18][19][20][21][22][23][24] . In these investigations, researchers mainly focused on Si(111) or Si(001) surfaces, and there have been very few papers on the nonlinear optical effects of Si(110) surfaces.…”

“…[18][19][20] for the EFI OR also was used in this work. If the azimuth with respect to the x axis of the linearly polarized light is θ, the dc polarization along the z axis (namely the [110] orientation) can be expressed as …”