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Defects in the functional oxides play an important role in electronic devices like metal oxide semiconductor field effect transistors (MOSFETs) and resistive random-access memories (ReRAMs). The continuous scaling of CMOS has brought the Si MOSFET to its physical technology limit and the replacement of Si channel with Ge channel is required. However, the performance of Ge MOSFETs suffers from Ge/oxide interface quality and reliability problems, which originates from the charge traps and defect states in the oxide or at the Ge/oxide interface. The sub-oxide layers composed of GeII states at the Ge/GeO2 interface seems unavoidable with normal passivation methods like hydrogen treatment, which has poor electrical properties and is related to the reliability problem. On the other hand, ReRAM works by formation and rupture of O vacancy conducting filaments, while how this process happens in atomic scale remains unclear. In this thesis, density functional theory is applied to investigate the defect behaviours in oxides to address existing issues in these electronic devices. In chapter 3, the amorphous atomic structure of doped GeO2 and Ge/GeO2 interface networks are investigated to explain the improved MOSFET reliability observed in experiments. The reliability improvement has been attributed to the passivation of valence alternation pair (VAP) type O deficiency defects by doped rare earth metals. In chapter 4, the oxidation mechanism of GeO2 is investigated by transition state simulation of the intrinsic defect diffusion in the network. It is proposed that GeO2 is oxidized from the Ge substrate through lattice O interstitial diffusion, which is different from SiO2 which is oxidized by O2 molecule diffusion. This new mechanism fully explains the strange isotope tracer experimental results in the literature. In chapter 5, the Fermi level pinning effect is explored for metal semiconductor electrical contacts in Ge MOSFETs. It is found that germanides show much weaker Fermi level pinning than normal metal on top of Ge, which is well explained by the interfacial dangling bond states. These results are important to tune Schottky barrier heights (SBHs) for n-type contacts on Ge for use on Ge high mobility substrates in future CMOS devices. In chapter 6, we investigate the surface and subsurface O vacancy defects in three kinds of stable TiO2 surfaces. The low formation energy under O poor conditions and the +2 charge state being the most stable O vacancy are beneficial to the formation and rupture of conducting filament in ReRAM, which makes TiO2 a good candidate for ReRAM materials. In chapter 7, we investigate hydrogen behaviour in amorphous ZnO. It is found that hydrogen exists as hydrogen pairs trapped at oxygen vacancies and forms Zn-H bonds. This is different from that in c-ZnO, where H acts as shallow donors. The O vacancy/2H complex defect has got defect states in the lower gap region, which is proposed to be the origin of the negative bias light induced stress instability.

The problem of accounting for spatial dependence in statistical analyses has received considerable attention due to the prevalence of spatial data in many disciplines. Typically, statistical analyses proceed by first testing if there is spatial dependence in the data. Then, if we find it, we want to measure its strength. Previous studies either do not provide obvious estimators of spatial-dependence parameters in commonly used models, or they cannot be expressed in closed form. For example, maximum likelihood estimators (MLEs) cannot typically be expressed in closed form. In this dissertation, we develop alternative closed-form measures of spatial dependence, which we call APLEs, as they are approximate profile likelihood estimators of parameters in spatial lattice models. While we consider three commonly used spatial lattice models, this dissertation primarily focuses on the APLEs for the simultaneous autoregressive (SAR) model. For this model, we derive APLEs under different scenarios where the nuisance parameters are known or unknown. We include both theoretical and simulation-based motivation (including comparison to the MLE) for using APLE as an estimator, and we explore its asymptotic properties. In conjunction, we propose the APLE scatterplot and local APLEs for assessing the strength of spatial dependence visually and for identifying “spatial outliers”. Crime data from Columbus, Ohio are used to illustrate the use of our APLE statistics in exploratory data analyses. In addition to considering the properties of APLE as an estimator of spatial dependence, we show that APLE can be used as a test statistic. Finally, we derive APLEs in the presence of measurement error, as well as heteroskedasticity. Beyond the SAR-based APLE, we also derive APLEs for spatial-dependence parameters in the conditional autoregressive (CAR) and spatial moving-average (SMA) models. To accommodate features of these models, the APLE approach must be modified slightly. The efficiency of the APLEs for these two lattice models is evaluated, and heteroskedasticity extensions are provided.