Calculated optical properties of Si, Ge, and GaAs under hydrostatic pressure

The macroscopic dielectric function in the random-phase approximation without local-field effect has been implemented using the local-density approximation with an all-electron, full-potential linear muffin-tin orbital basis set. This method is used to investigate the optical properties of the semiconductors Si, Ge, and GaAs under hydrostatic pressure. The pressure dependence of the effective dielectric function is compared with the experimental data of Go\~ni, Syassen, and Cardona [Phys. Rev. B 41, 10 104 (1990)], and excellent agreement is found when the so-called ``scissors-operator'' shift is used to account for the correct band gap at \ensuremath{\Gamma}. The effect of the 3d semicore states in the interband transitions hardly changes the static dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$; however, their contribution to the intensity of absorption for higher photon energies is substantial. The spin-orbit coupling has a significant effect on ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$ of Ge and GaAs, but not of Si. The ${\mathit{E}}_{1}$ peak in the dynamical dielectric function is strongly underestimated for Si, but only slightly for Ge and GaAs, suggesting that excitonic effects might be important only for Si. \textcopyright{} 1996 The American Physical Society.