Infrared Dispersion of Second-Order Electric Susceptibilities in Semiconducting Compounds

A unified study is presented of the infrared behavior of the second-order electric susceptibilities χ⁽²⁾ in semiconducting compounds for both longitudinal and transverse fields. The molecular model used previously for the calculation of χ⁽²⁾ for frequencies above the lattice resonances is extended and applied to the calculation of χ⁽²⁾ for frequencies below the lattice resonances as well. An ab initio calculation of the different contributions is given and the local-field corrections are taken into account in a semiempirical way, consistent with the macroscopic infrared properties of these materials. In particular, the Raman, electro-optic, optical rectification, and far-infrared frequency mixing coefficients are explicitly considered for the seven semiconductors InSb, InAs, InP, GaSb, GaAs, GaP, and AlSb. The agreement with experiment is good. The relation between the ionic part of χ⁽²⁾ and the phonon-damping mechanisms in these compounds is also discussed and a generalization of the Lyddane-Sachs-Teller relation to the nonlinear regime is presented. Further, the relation of the different terms in χ⁽²⁾ to the covalent character of the bonds in these compounds is briefly discussed in terms of the exactly soluble unidimensional δ-function-bond model. This latter approach combined with the recent phenomenological descriptions of the bonding in tetrahedral covalent compounds can also be extended for the calculation of χ⁽²⁾ for the II-VI compounds.