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This thesis presents theoretical studies of the optical and electronic properties of defects in diamond and of the mechanisms of doping graphene. The birefringence of the four petalled defect commonly observed in CVD diamond is explained by four linear arrays of dislocations along ⟨110⟩ directions with ⟨110⟩ Burgers vectors. Such an arrangement of dislocations reproduces the extension and the features of the birefringence patterns observed experimentally. Density functional theory via the AIMPRO code was used to study the electronic and optical properties of different nitrogen-related point defects in diamond. It was found that the zero-phonon luminescence line of the NV− defects can split in the presence of a surface or other NV− defects. Since VNH and VN2 are expected to have similar optical properties, the optical transi- tions for VN2 were used to correct the transitions for VNH calculated by local density approximation. The absorption band at 2.38 eV (520 nm) observed in CVD diamond is then attributed to an internal transition of VNH. The weak zero-phonon line and broad vibronic sidebands for VN− and VN−2 and its absence for VNH− is explained by the large structural change when the defect is excited. Finally, different mechanisms for doping graphene were considered. The calculations predict the electropositive metals, such as Ti and Cr, act as donors, while molecules with strong electron affinity, such as F4-TCNQ, act as acceptors in graphene. An unexpected mechanism of doping graphene was shown by Au which dopes bilayer graphene but not single layer. In the presence of water, electrochemical reactions on the graphene can also lead to p or n-type doping.

In this thesis first-principles calculations of point and extended defects in diamond and silicon are reported. In single crystal diamond grown by chemical vapour deposition (CVD) dislocations are observed as mixed-type 45° and edge-type dislocations lying along <100> with 1/2<110> Burgers vectors. Results are presented on the core structures, core energies and electrical properties of both types of dislocations and their interaction with nitrogen is investigated. Then the focus turns to the brown diamond problem. Despite concerted research efforts, the origin of the brown colouration of diamond is still under discussion. Recently, the attention was drawn to vacancy-related defects. Experiments on type IIa diamonds indicate that the brown colour is caused by vacancy-type extended defects, however the shape and size of these defects remained unclear. In this work, the structural, electrical and optical properties of large spherical vacancy clusters and thin vacancy disks are investigated by means of density functional theory and the calculations are compared with recent experimental measurements on brown diamond. High pressure high temperature treatment (HPHT) of brown type Ia diamonds above 2000°C results in the loss of the brown colour and the formation of nitrogen-vacancy defects. The generation of such defects requires a source of mobile vacancies during the annealing process. It is suggested that the vacancy cluster model described in this thesis can explain the observed annealing behaviour since the break-up of the clusters leads to a supersaturation of mobile vacancies which readily complex with substitutional nitrogen atoms present in the material. Therefore, the effect of HPHT treatment of brown type Ia diamond is investigated by studying the formation energies of common and rare defects and estimates of their equilibrium concentrations at different annealing stages are given. Finally, an open problem also involving nitrogen, but in a different group IV semiconductor is considered. In Czochralski-silicon, nitrogen-related shallow thermal donors are formed between 500 and 750°C. Until now the exact chemical composition and atomic structure of these defects are not well established. Here, it is shown that NO and NO_2 belong to the family of nitrogen-oxygen related shallow thermal donors. Based on the law of mass action the equilibrium defect concentrations are predicted. Finally, the theoretical results are compared to recent Fourier transform infrared (FTIR) spectroscopy measurements.