Polarizable-bond model for second-harmonic generation

We develop a theory for the calculation of the optical second-harmonic generation spectra of Si incorporating the nonlinear surface local field effect. Our model consists of four interpenetrated fcc lattices of nonlinearly polarizable bonds. Each of them is anisotropic and although they are centrosymmetric, they respond quadratically to the spatial inhomogeneities of the polarizing local field. The large gradient of the field induced at a bond due to the dipole moment of a neighbor leads to a second order polarization. In the bulk, each bond lies within a centrosymmetric environment, so this contribution is canceled out after summing over all other bonds. However, at the surface it is not compensated and 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. We calculate a linear anisotropy spectra for the (110) surface in agreement with previous measurements. Our nonlinear spectra show peaks at 1.65 eV for a strained (001) surface and at 1.75 eV for a (111) surface, in agreement with some recent experimental results.