Localised electronic states in model systems and semiconductors

Accurately modelling charge trapping phenomena is a vital part of understanding and improving the behaviour of semiconductors in both current and future devices. While charge traps are frequently observed in doped crystals, the formation of socalled self-trapped polarons means that charges can trap even in defect-free bulk crystals. This in turn reduces charge carrier mobility in materials, sometimes to the detriment of the underlying device. More effective methods of modelling self-trapping typically introduce a few free parameters, each of which can significantly influence results obtained by the model. The focus of this thesis is on developing parameterfree, computationally inexpensive and accurate approaches to modelling charge trapping, with a focus on titanium dioxide, a material used in promising new photovoltaics. Through comparison to both experimental data and solutions to the exact many-electron Schr¨odinger equation, this thesis demonstrates that use of the generalised Koopmans’ theorem in conjunction with hybrid functionals can yield strikingly accurate results. This technique is subsequently used to predict the formation of selftrapped charges in a number of titania phases, including the well-studied rutile and anatase, and less-known brookite, TiO2(H), TiO2(R) and TiO2(B). Intrinsic point defects are also investigated in rutile and anatase, where it is found that several interesting and unique electronic phenomena occur in their vicinity.