Peter Kratzer Universität Duisburg-Essen Defects and impurities in semiconductors and their diffusion are topics with a long-standing tradition in the first-principles community. This is due to their great practical importance, in particular for the electrical or magnetic properties of semiconductors, but also for the materials transport during growth. Recently, the epitaxial growth of nanowires catalysed by gold particles has opened the possibility to grow traditional III-V semi-conductors, such as GaAs, in the wurtzite crystal structure (as opposed to conventional zincblende GaAs). Furthermore, wide-band-gap oxides, such as ZnO, continue to pose challenging questions for theorists in the context of doping. For our calculations of defects, we use density functional theory in conjunction with the plane-wave supercell approach. Motivated by GaAs nanowire growth, we investigated the role of arsenic vacancies and Ga antisites in both GaAs polytypes. [1] The thermodynamic stability and the charge transfer levels of these defects are similar in wurtzite and zincblende GaAs. However, we find clear differences in the diffusion barriers of arsenic vacancies: For diffusion along the wurtzite c-axis, the As atom must pass through a tetrahedral interstitial site to fill the vacancy, while in cubic GaAs this role of an intermediate state is played by the more spacious octahedral interstitial site. Consequently, As vacancy diffusion in zincblende GaAs and in the hexagonal wurtzite GaAs crystal is highly anisotropic: fast within the hexagonal lattice planes, but slow in c-direction. Furthermore, I shall discuss the behavior of the As vacancies at the interface of the GaAs nanowire with the gold catalyst particle. Our calculations give evidence for various As diffusion mechanisms with activation barriers lower than in bulk GaAs. Consequences for our understanding of the atomistic processes in catalytic nanowire growth will be discussed. In another recent study [2], we addressed the doping of ZnO by carbon. We find that the carbon atom replacing Zn (CZn) is thermodynamically more stable than CO or interstitial carbon. In all cases we investigated, the C atom induces deep charge transfer levels in the band gap of ZnO. This means that C must be considered unsuitable for controlled doping of ZnO. However, in some electronic configurations, the C impurities show a magnetic moment. We relate this theoretical finding [3] to experimental observations of magnetism in ZnO allegedly caused by carbon doping. [1] Y. Du, S. Sakong, and P. Kratzer, to be published. [2] S. Sakong and P. Kratzer, Semicond. Sci. Technol. 26, 01438 (2011). [3] H. Wu, A. Stroppa, S. Sakong, S. Picozzi, M. Scheffler, and P. Kratzer, Phys. Rev. Lett. 105, 267203 (2010).