Investigation of numerical atomic orbitals for first-principles calculations of the electronic and transport properties of silicon nanowire structures

This thesis is focused on the application of numerical atomic basis sets in studies of the structural, electronic and transport properties of silicon nanowire structures from first-principles within the framework of Density Functional Theory. First we critically examine the applied methodology and then offer predictions regarding the transport properties and realisation of silicon nanowire devices. The performance of numerical atomic orbitals is benchmarked against calculations performed with plane waves basis sets. After establishing the convergence of total energy and electronic structure calculations with increasing basis size we have shown that their quality greatly improves with the optimisation of the contraction for a fixed basis size. The double zeta polarised basis offers a reasonable approximation to study structural and electronic properties and transferability exists between various nanowire structures. This is most important to reduce the computational cost. The impact of basis sets on transport properties in silicon nanowires with oxygen and dopant impurities have also been studied. It is found that whilst transmission features quantitatively converge with increasing contraction there is a weaker dependence on basis set for the mean free path; the double zeta polarised basis offers a good compromise whereas the single zeta basis set yields qualitatively reasonable results. Studying the transport properties of nanowire-based transistor setups with p+-n-p+ and p+-i-p+ doping profiles it is shown that charge self-consistency affects the I-V characteristics more significantly than the basis set choice. It is predicted that such ultrascaled (3 nm length) transistors would show degraded performance due to relatively high source-drain tunnelling currents. Finally, it is shown the hole mobility of Si nanowires nominally doped with boron decreases monotonically with decreasing width at fixed doping density and increasing dopant concentration. Significant mobility variations are identified which can explain experimental observations.

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.

The development of new methods for high resolution radio astronomy imaging

Very Long Baseline Interferometry (VLBI) polarisation observations of the relativistic jets from Active Galactic Nuclei (AGN) allow the magnetic field environment around the jet to be probed. In particular, multi-wavelength observations of AGN jets allow the creation of Faraday rotation measure maps which can be used to gain an insight into the magnetic field component of the jet along the line of sight. Recent polarisation and Faraday rotation measure maps of many AGN show possible evidence for the presence of helical magnetic fields. The detection of such evidence is highly dependent both on the resolution of the images and the quality of the error analysis and statistics used in the detection. This thesis focuses on the development of new methods for high resolution radio astronomy imaging in both of these areas. An implementation of the Maximum Entropy Method (MEM) suitable for multi-wavelength VLBI polarisation observations is presented and the advantage in resolution it possesses over the CLEAN algorithm is discussed and demonstrated using Monte Carlo simulations. This new polarisation MEM code has been applied to multi-wavelength imaging of the Active Galactic Nuclei 0716+714, Mrk 501 and 1633+382, in each case providing improved polarisation imaging compared to the case of deconvolution using the standard CLEAN algorithm. The first MEM-based fractional polarisation and Faraday-rotation VLBI images are presented, using these sources as examples. Recent detections of gradients in Faraday rotation measure are presented, including an observation of a reversal in the direction of a gradient further along a jet. Simulated observations confirming the observability of such a phenomenon are conducted, and possible explanations for a reversal in the direction of the Faraday rotation measure gradient are discussed. These results were originally published in Mahmud et al. (2013). Finally, a new error model for the CLEAN algorithm is developed which takes into account correlation between neighbouring pixels. Comparison of error maps calculated using this new model and Monte Carlo maps show striking similarities when the sources considered are well resolved, indicating that the method is correctly reproducing at least some component of the overall uncertainty in the images. The calculation of many useful quantities using this model is demonstrated and the advantages it poses over traditional single pixel calculations is illustrated. The limitations of the model as revealed by Monte Carlo simulations are also discussed; unfortunately, the error model does not work well when applied to compact regions of emission.