Second-Order Optical Susceptibilities of III-V Semiconductors

An ab initio calculation of the low-frequency limit of the second-order optical susceptibility $\chi _{14}^{}{}_{}{}^{\mathrm{}\left(2\right)\mathrm{}}$ is presented for eight III-V compounds possessing the zinc-blende symmetry. In the frequency range considered (above the lattice absorption and below the onset of real electronic transitions), the molecular model due to Coulson, Rédei, and Stocker can be used. The susceptibilities ${\chi }^{\mathrm{}\left(1\right)\mathrm{}}$ and $\chi _{14}^{}{}_{}{}^{\mathrm{}\left(2\right)\mathrm{}}$ are expressed in terms of bond polarizabilities. These last quantities are calculated, using a variational perturbation procedure. Effective-field corrections are included in a semiempirical way. Numerical results are given for the following compounds: InSb, InAs, InP, GaSb, GaAs, GaP, AlSb, and BP. They are in good agreement with the available experimental values. For boron phosphide, for which no such data exist, our predicted value is very low, in disagreement with the usual formulation of Miller's rule. This is discussed within the framework of a linear correlation shown by our results to exist between Miller's reduced coefficient and the bond dipole moment $p$.