Bond calculation of optical second-harmonic generation at gallium- and arsenic-terminated Si(111) surfaces

An ab initio valence bond method based on finite-sized clusters is proposed for calculating the non-linear electric susceptibilities of covalent solids, particularly those that are directly related to their efficiency for second-harmonic generation. It is presented as a radical alternative to electronic land-structure methods for these dielectric response functions and it is applied here to two Si surfaces. In its present form it is limited to the response to static fields. linear and non-linear parts of the electric susceptibility are obtained from generalised valence bond calculations on clusters representing gallium- and arsenic-terminated (1*1) Si(111) surfaces. In the valence bond model for these covalent systems the self-consistent orbitals are localized in bond pairs and lone pairs. Electric susceptibilities are constructed by summing bond polarizabilities or hyperpolarizabilities of electron pairs in the surface layer. The major sources of non-linear polarization in the cluster lie along bond axes, hence optical second-harmonic generation at a covalently bonded surface may depend strongly on the surface structure. An additional major source of non-linear polarization exists perpendicular to the axes of bent bonds which becomes dominant when the bond is severely bent. Calculated non-linear susceptibilities are in good agreement with absolute measurements of second-harmonic generation intensity.