Second-Harmonic Generation At Surfaces

A method for computing the intensity of electric dipole second-harmonic generation from semiconductor surfaces and interfaces is presented. It uses third-order perturbation theory and a Green's function technique to embody Fresnel's formulas. Calculations for As/Si(111) are compared to experimental data, and show fair agreement for the spectral and angular dependence of the second-harmonic signal; the calculated absolute intensity, however, is too high. To investigate the origin of the discrepancy, we generalize the theory to all orders in the electron-photon coupling. The new scheme, based on the method of excitation amplitudes, is outlined. It allows to set up a theory of the second-harmonic generation response and other inelastic light scattering phenomena, like the dynamical Stark effect. Many-photon effects can modify the response in a qualitative way, and the maximum intensity of the second-harmonic fields does not generally correspond exactly to twice the incident frequency. This formalism also leads to new exact sum rules for nonlinear optics, that complement those obtained recently by Bassani and Scandolo.