Quasiparticle band-structure calculations for C, Si, Ge, GaAs, and SiC using Gaussian-orbital basis sets

We report state-of-the-art first-principles calculations of the quasiparticle energies of prototype homopolar and heteropolar covalent semiconductors described in terms of the electron self-energy operator. The wave functions are calculated within density-functional theory using the local-density approximation and employing nonlocal, norm-conserving pseudopotentials. The self-energy operator is evaluated in the GW approximation. Employing the plasmon-pole approximation for the frequency dependence of the dielectric matrix ${\mathrm{\epsilon }}_{\mathbf{G},\mathbf{G}\prime }$(q,ω), its static part is fully calculated within the random-phase approximation (RPA) as well as by using a number of different models. All calculations are carried out employing localized Gaussian orbital basis sets. This will turn out to be very useful for detailed studies of the quasiparticle properties of more complex systems such as bulk defects including lattice relaxation and reconstructed surfaces with large unit cells or interfaces, which are otherwise computationally too demanding. Using an s,p,d,s* basis set of 40 Gaussian orbitals for Si, for example, yields already convergent results in excellent agreement with the results of a 350-plane-wave calculation in the corresponding plane-wave representation. Most of our results for Si, diamond, Ge, and GaAs are in very good agreement with experimental data and with available plane-wave GW calculations. To our knowledge, our results for SiC are the first quasiparticle energies reported so far for this important material of high current technological interest. Also in this case we find very good agreement with the available experimental data except for E(${\mathrm{L}}_{1\mathrm{c}}$). We believe that this deviation may be attributed to experimental uncertainties. In particular, we discuss and scrutinize the applicability of six different models for the static dielectric matrix ${\mathrm{\epsilon }}_{\mathbf{G},\mathbf{G}\prime }$(q,0) in the GW approximation ranging from the simple Hartree-Fock expression over diagonal models to nondiagonal models that take the local fields within the inhomogeneous electronic charge density into account. Some of the nondiagonal models are shown to yield results in very good agreement with the full RPA results.