All-electron local-density and generalized-gradient calculations of the structural properties of semiconductors

The lattice constant, bulk modulus, and single-particle eigenvalues of Si, Ge, and GaAs are evaluated by using the local-density approximation (LDA) and the generalized-gradient approximation (GGA) for the exchange-correlation energy. We consider two different generalized-gradient functionals, the exchange correlation recently proposed by Perdew and Wang and the Becke exchange combined with a previous version of the Perdew-Wang correlation. We perform an all-electron calculation with the linear-augmented-plane-wave method to test the capability of these generalized-gradient exchange-correlation functionals to describe structural properties of semiconductor systems. Our results differ from previous calculations of the same quantities within the pseudopotential scheme although the qualitative trends are the same. The LDA yields lattice constants that are smaller by less than 0.6% than the experimental values. Both GGA's overcorrect, giving lattice constants that are larger than the experimental ones by about 2% for the earlier GGA and by about 1.5% for the later GGA. The LDA predicts bulk moduli that are within 3% of the experimental value whereas the GGA's underestimate the bulk moduli by 14--22 %. The underestimate of the LDA band gaps is not improved by either of the GGA's.