Gallium nitride and its alloys are direct band gap semiconductors with a wide variety of applications. Of particular importance are light emitting diodes and laser diodes. Due to the lack of suitable lattice-matched substrates, epitaxial layers contain a high density of defects such as dislocations. To reduce their number and to design a device with desired specifications, multilayered systems with varying composition (and thus material properties) are grown. Theoretical modelling is a useful tool for gaining understanding of various phenomena and materials properties. The scope of the present work is wide. It ranges from a continuum theory of dislocations treated within the linear elasticity theory, connects the continuum and atomistic level modelling for the case of the critical thickness of thin epitaxial layers, and covers some issues of simulating the electronic structure of III-nitride alloys by means of the first principle methods. The first part of this work discusses several topics involving dislocation theory. The objectives were: (i) to apply general elasticity approaches known from the literature to the specific case of wurtzite materials, (ii) to extend and summarise theoretical studies of the critical thickness in heteroepitaxy. Subsequently, (iii) to develop an improved geometrical model for threading dislocation density reduction during the growth of thick GaN films. The second part of this thesis employs first principles techniques (iv) to investigate the electronic structure of binary compounds (GaN, AlN, InN) and correlate these with experimentally available N K-edge electron energy loss near edge structure (ELNES) data, (v) to apply the special quasi-random structures method to ternary III-nitride wurtzite alloys aiming to develop a methodology for modelling wurtzite alloys and to get quantitative agreement with experimental N K-edge ELNES structures, and (vi) to theoretically study strain effects on ELNES spectra.The EU project PARSEM (contract number MRTN-CT-2004-005583) is acknowledged for financial support
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