Calculation of the nonlinear susceptibility for optical second-harmonic generation in III-V semiconductors

We calculate both linear and nonlinear optical response in the static limit for AlP, AlAs, GaP, and GaAs in the local-density approximation with and without a scissors operator, including local-field effects. The calculation agrees with the measurement of Levine and Bethea to within 15%. The derivatives d ln${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$/d lna, for lattice constant a, are predicted to be from 1.7 to 6.6 times the values obtainable from existing models. The calculated static dielectric constants ${\mathrm{\epsilon }}_{\mathrm{\infty }}$ are within 2% of measured values; calculated results for d ln${\mathrm{\epsilon }}_{\mathrm{\infty }}$/d lna are also presented. The scissors operator alters ${\mathrm{\epsilon }}_{\mathrm{\infty }}$ up to 25% but alters ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ by a factor of 2.