Non-equilibrium induction of tin in germanium: towards direct bandgap Ge1-xSnx nanowires

The development of non-equilibrium group IV nanoscale alloys is critical to achieving new functionalities, such as the formation of a direct bandgap in a conventional indirect bandgap elemental semiconductor. Here, we describe the fabrication of uniform diameter, direct bandgap Ge1-xSnx alloy nanowires, with a Sn incorporation up to 9.2[thinsp]at.%, far in excess of the equilibrium solubility of Sn in bulk Ge, through a conventional catalytic bottom-up growth paradigm using noble metal and metal alloy catalysts. Metal alloy catalysts permitted a greater inclusion of Sn in Ge nanowires compared with conventional Au catalysts, when used during vapour-liquid-solid growth. The addition of an annealing step close to the Ge-Sn eutectic temperature (230[thinsp][deg]C) during cool-down, further facilitated the excessive dissolution of Sn in the nanowires. Sn was distributed throughout the Ge nanowire lattice with no metallic Sn segregation or precipitation at the surface or within the bulk of the nanowires. The non-equilibrium incorporation of Sn into the Ge nanowires can be understood in terms of a kinetic trapping model for impurity incorporation at the triple-phase boundary during growth.

Statistical considerations in the kinetic analysis of PET-FDG brain tumour studies

Dynamic positron emission tomography (PET) imaging can be used to track the distribution of injected radio-labelled molecules over time in vivo. This is a powerful technique, which provides researchers and clinicians the opportunity to study the status of healthy and pathological tissue by examining how it processes substances of interest. Widely used tracers include 18F-uorodeoxyglucose, an analog of glucose, which is used as the radiotracer in over ninety percent of PET scans. This radiotracer provides a way of quantifying the distribution of glucose utilisation in vivo. The interpretation of PET time-course data is complicated because the measured signal is a combination of vascular delivery and tissue retention effects. If the arterial time-course is known, the tissue time-course can typically be expressed in terms of a linear convolution between the arterial time-course and the tissue residue function. As the residue represents the amount of tracer remaining in the tissue, this can be thought of as a survival function; these functions been examined in great detail by the statistics community. Kinetic analysis of PET data is concerned with estimation of the residue and associated functionals such as ow, ux and volume of distribution. This thesis presents a Markov chain formulation of blood tissue exchange and explores how this relates to established compartmental forms. A nonparametric approach to the estimation of the residue is examined and the improvement in this model relative to compartmental model is evaluated using simulations and cross-validation techniques. The reference distribution of the test statistics, generated in comparing the models, is also studied. We explore these models further with simulated studies and an FDG-PET dataset from subjects with gliomas, which has previously been analysed with compartmental modelling. We also consider the performance of a recently proposed mixture modelling technique in this study.