Local-field effect in the second-harmonic-generation spectra of Si surfaces

Abstract

We calculate the second-harmonic-generation spectra of Si͑100͒ and ͑111͒ surfaces introducing the nonlinear surface local-field effect. Our model consists of four interpenetrated fcc lattices of polarizable bonds, each of which is centrosymmetric, but responds nonlinearly to the spatial inhomogeneities of the polarizing local field. The gradient of the field induced at a bond due to the dipole moment of a neighbor leads to a secondorder polarization that is canceled out in the bulk after summing over all other bonds, but it is not compensated at the surface, where it leads to a large nonlinear macroscopic response. Our model parameters are fitted to the nonlinear anisotropy measured at 1.17 and 2.34 eV. The linear anisotropy spectra calculated for the Si͑110͒ surface are in accordance with reflectance difference measurements. The same parameters yield a nonlinear spectrum that has peaks at 1.65 eV for a strained ͑100͒ surface and at 1.75 eV for a ͑111͒ surface, in agreement with recent experimental results.

Optical circular dichroism of single-wall carbon nanotubes

“…Furthermore, local field effect has been pointed out as the main source of the induced optical anisotropy at surfaces of cubic crystals. 21,22,23 However, quantum mechanical approaches are still inappropriate for systems with hundreds and thousands of atoms due to the huge computational effort that is involved in these type of calculations.…”

Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding

“…For example, a calculation for which the last layer of atoms was displaced inward by 5% of the interplane distance shows an enhanced SHG E 1 peak (dashed-dotted curve; RDS remains trivially zero), illustrating the possible role of near-surface strain. 99 Additionally, calculations based on the equilibrated asymmetric 2 ð 1 reconstruction (dotted, thin solid curves), in which both backbond strain and polarized bonds are present, also show a strong E 1 SHG signal, as well as RDS that qualitatively reproduces experimental features at 1.6, 3.7 and 4.3 eV. Roughly equivalent agreement with both experiments is obtained using either the same polarizable bond parameters as for the previous calculation (dotted) or optimized parameters (thin solid), including displacing the dimer's dipole towards the upper Si by 1/4 of the dimer bond length to account for the charge transfer.…”

“…Nevertheless, such calculations quickly identify plausible microscopic causes of prominent features in both types of spectra from a simple computational basis. 99,129 For the calculation in Fig. 7, the surface was modeled as a slab of up to N sl D 30 atomic (001) layers.…”

Eigenfunctions of the Inverse Dielectric Functions and Response Functions of Silicon and Argon

“…Discrete dipole models have been used to calculate the surface [1][2][3][4][5] and bulk [6,7] optical properties of semiconductors. These models consist of point dipolar polarisabilities located at bond or atom centres, interacting via electrostatic fields and driven by external electromagnetic fields.…”