Stresses in semiconductors:Ab initiocalculations on Si, Ge, and GaAs

Explicit formulas for the calculation of stress are presented based on the stress theorem and the local-density-functional approximation. Norm-conserving pseudopotentials are applied in a plane-wave basis for calculations on the semiconductors Si, Ge, and GaAs. Besides the lattice constants and bulk moduli, complete sets of elastic constants are given, together with the optical {Γ} phonon frequencies and internal-strain parameter {ζ}. Electronic charge density structure factors, deformation potentials, and strain-induced splittings of phonons are given, as well as the nonlinear third-order elastic constants. Good agreement with experiment is found throughout, except for persistent deviations from the x-ray diffraction values for {ζ}.