Calculation of optical properties for systems with large supercells

Si and Ge nanocrystals embedded in a wide-gap semiconductor like $\alpha$-SiC are potentially interesting systems for possible electroluminescence applications. A theoretical understanding of these systems is yet to be achieved, both for the optical properties under inclusion of the relevant many-body effects and for the structural and electronic properties. We present first attempts to describe these properties using parameter-free electronic structure calculations and large supercells. A plane-wave-pseudopotential code (VASP ) is used to calculate the electronic structure within density-functional theory (DFT) in local-density approximation (LDA). Ultrasoft non-normconserving pseudopotentials allow the {\it ab-initio} treatment of supercells with up to 512 atoms, even in the case of first-row elements. Each supercell contains one cluster, the remaining space is filled with matrix material. The maximum dot diameters are about 1 nm. Examples are mainly structures made of group-IV materials. In the present talk we focus our attention on three main problems. The problem of wave-function augmentation for non-normconserving pseudopotentials is solved by constructing all-electron wave functions using Bl\"ochl's projector-augmented wave (PAW) method [1]. As an advantage nonlocal contributions to the optical matrix elements do not occur. Spectra are compared with those obtained using normconserving pseudopotentials and the FLAPW method. The huge supercell size drastically restricts the number of $k$-points. Nevertheless we prefer to use the tetrahedron method for the optical calculations. Unfortunately the increase of the supercell size gives rise to many band crossings which prevent the identification of the same band at the tetrahedron vertices. We present a highly efficient and robust extrapolative Brillouin-zone integration scheme based on second-order $k\cdot p$ perturbation theory (cf. [2]). We use the simplified treatment of the GW self-energy developed by Cappellini et al. [3] in the beginning of the 90's to calculate the quasiparticle corrections for supercells with several hundreds of atoms . The dielectric constant and the electron density determining the RPA screening are obtained within DFT-LDA. Despite the complications with the augmentation of the Bloch integrals we show agreement with calculations using two-atom cells. Computations for embedded clusters are in progress.