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table to making self-consistent calculation of a big supercell since its computational load is relatively small but its calculating precision is able to meet usual demands. In Chapter1, the computational principles and methods used in this thesis are presented. Besides the LMTO-ASA method, the special k points and the statistical supercell method are also introduced in detail. In Chapter 2, as an instance of studying luminescence centers, we investigated the electronic structure of wurtzite ZnS doped with Cu. The calculating results show that, the levels of Cu luminescence centers depend on the oxide-state of copper and the existence of codopants. In the cases of ZnS:Cu,Cl and ZnS:Cu,Al , Cu acceptor states are anomalously deep and located near the bottom of conduction band. However, the Cu+ center is an associated center for ZnS:Cu+ with sulfur vacancies. As to ZnS:Cu2+, the Cu d-like states are situated above the top of valence band. The luminescence mechanisms of above-mentioned Cu luminescence-centers accord with the Lambe-Klick model, the Williams-Prener model and the Schön-Klasens model, respectively. In Chapter 3, as an example of investigating the crystal with point defects, we calculated the electronic structure of the arsenic antisite (AsGa) defect in as-grown GaAs. The AsGa attracts great interest because of its close relation with EL2 center in GaAs. Our calculating results manifest that it is the central AsGa atom that antibonds with nearest neighbor arsenic atoms and induces gap states. Moreover, the gap states are composed of the A1-like and the T2-like state with energy EA1 = Ev+ 0.70 eV and ET2 = EA1+1.07 eV respectively. Our results are in agreement with experiments and previously theoretical results obtained by other self-consistent methods. In Chapter 4, we studied TiNx mixed crystal system. According to the phase diagram for Ti-N bulk system, TiNx possesses a two-phase structure of the mixture of either a-Ti with e-Ti2N, or d-TiN with e-Ti2N. The electronic structure of a-Ti, e-Ti2N and d-TiN micro-crystals was calculated by using the LMTO-ASA method and the supercell approach, while the electronic structure of TiNx system for all substoichiometric x value (0 < x < 1) was obtained by means of statistical distribution of the micro-crystals. In order to compare our results with experiments, we further analyzed the variation of the electric resistivity of TiNx system with composition x. We found that the general trend of variation agrees basically with each other. In Chapter 5, we researched another mixed crystal system, Ba1-xKxBiO3. In the field of x < 0.3, the breathing-mode distortions of BiO6 octahedra create two kinds of inequivalent Bi atoms. In order to simulate 3+ valence for Bi(I) and 5+ valence for Bi(II), the 6s states of Bi were treated as core states for Bi(I) and as valence configurations for Bi(II) in our calculations. The electronic structure of some ordered alloys of the Ba1-xKxBiO3 was first calculated, and then the effect of disorder of K-for-Ba substitutions was included by resorting to the statistical supercell method. Our computational results are in agreement with experiments in the following aspects. First, pure BaBiO3 is a semiconductor with a gap of 1.6 eV (compared with experimental gap of 2.0 eV). Second, Ba1-xKxBiO3 system exhibits semiconductor behavior in x < 0.3, and the forbidden gap reduces gradually with the increase of x. Third, Ba1-xKxBiO3 system possesses metal behavior in