All-electron projector-augmented-wave GW approximation: Application to theelectronic properties of semiconductors

The so-called GW approximation (GWA) based on an all-electron full-potentia l projector-augmented-wave method (PAW) has been implemented. For the scree ning of the Coulomb interaction W three different plasmon-pole model dielec tric function models have been tested, and it is shown that the accuracy of the quasiparticle energies is hot sensitive to the details of these models . For the decoupling of the valence and core electrons two different scheme s produced quasiparticle energies that differ on average by less than 0.1 e V for Si. This method has been used to study the quasiparticle band structu re of some small, medium, and wideband-gap semiconductors: Si, GaAs,AlAs, I nP, Mg2Si, diamond, and the insulator LiCl. Special attention was devoted t o the convergence of the self-energy with respect to both the k points in t he Brillouin zone and to the number of reciprocal-space G vectors. The most important and surprising result is that although the all-electron GWA impr oves considerably the local-density approximation electronic structure of s emiconductors, it does not always provide the correct energy band gaps for small- and medium-band-gap semiconductors as originally inferred from pseud opotential GWA calculations. The discrepancy between the all-electron and p seudopotential quasiparticle band gaps is mainly traced back to differences between the exchange-correlation matrix elements obtained by the two metho ds.