Low Temperature Plasma Etching Control through Ion Energy Angular Distribution and 3-Dimensional Profile Simulation.

Plasma etching has become a major part of semiconductor processing because it enables the production of smaller electronics with increased computational power. Plasma etching produces highly anisotropic features, which are needed to maintain feature size critical dimensions (CD) through directional ion wafer bombardment. As the semiconductor industry moves towards smaller feature sizes and higher aspect ratios, a better understanding of ion dynamics and control of the plasma etch processes becomes increasingly necessary. In prior technology nodes, 2-dimensional (2-d) feature profile models served very well to help optimize features and connect reactor scale properties to feature scale CDs. As CDs continue to shrink, the current technology nodes must utilize 3-dimensional (3-d) structures, whose optimization is considerably more difficult and not well represented by 2-d profile simulators. This dissertation investigated the plasma physics and plasma surface interactions in plasma etching chambers using a hybrid plasma equipment model to predict plasma properties and a Monte Carlo feature profile model to predict feature evolution. Algorithms for capturing ion sheath dynamics, controlling dual frequency powers on the same substrate and describing 3-d plasma surface kinetics have been developed and integrated into the models. With the addition of these new algorithms, three challenging areas have been investigated: ion multi-frequency sheath dynamics, control of ion energy angular distributions and 3-d plasma etching. The ion kinetics are found to be controlled through several critical parameters, such as shifting phases, tuning frequencies, and adjusting rf voltage ratios. The 3-d profile model addresses the complex feature pattern layout and aids in the physical understanding of ion 3-d bombardment on surfaces. With this improved capability, correlations of the variability of plasma tool performance with variability of feature dimensions are investigated.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113432/1/yitingz_1.pd

Computing the Tracy-Widom distribution for arbitrary β>0\beta>0

We compute the Tracy-Widom distribution describing the asymptotic distribution of the largest eigenvalue of a large random matrix by solving a boundary-value problem posed by Bloemendal. The distribution is computed in two ways. The first method is a second-order finite-difference method and the second is a highly accurate Fourier spectral method. Since $\beta$ is simply a parameter in the boundary-value problem, any $\beta> 0$ can be used, in principle. The limiting distribution of the $n$th largest eigenvalue can also be computed. Our methods are available in the Julia package TracyWidomBeta.jl

Pyrolysis-Gas Chromatography/Mass Spectrometry Analysis of Oils from Different Sources

Regenerated gutter oil (i.e., waste oil) accounts for 10% of the edible oil market, which has caused serious food safety issues. Currently, there is no standard protocol for the identification of the gutter oil. In this study, the pyrolysis-gas chromatography/mass spectrometry (Py-GC/MS) method was employed to analyze eleven oil samples including edible vegetable oils (tea oil, corn oil, olive oil, sunflower oil, peanut oil and blend vegetable oil) and waste oils (used frying oil, lard, chicken fat, inferior oil and kitchen waste grease). Three factors of pyrolysis temperature, reaction time and sample volume were investigated to optimize the analytical parameters. The optimal pyrolysis conditions were determined to be 600°C, 1 min and an injection volume of 0.3 μL. Five characteristic components (tetradecane, z,z-9,12-octadecadienoic acid, decanoic acid-2-propenyl ester, 17-octadecenoic acid, and z-9-octadecenoic acid) were found in all oil samples. The existence of C11-C16 olefins in the pyrolytic products of the animal fats and the other low-quality oils could be utilized to distinguish vegetable oils from gutter oils.Â

Strong limit theorems for step-reinforced random walks

A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk repeats one of its preceding steps chosen uniformly at random, and with complementary probability 1-p, it has an independent increment. The negatively step-reinforced random walk follows the same reinforcement algorithm but when a step is repeated its sign is also changed. Strong laws of large numbers and strong invariance principles are established for positively and negatively step-reinforced random walks in this work. Our approach relies on two general theorems on invariance principle for martingale difference sequences and a truncation argument. As by-products of our main results, the law of iterated logarithm and the functional central limit theorem are also obtained for step-reinforced random walks

Urban morphology and ecosystem services: a historico-geographical study of fringe belts and urban green spaces in Birmingham, UK

Cities have tended to be treated by ecologists as essentially physical entities unconnected to the concerns of historical geographers. In contrast, urban morphologists have tended to focus on how urban physical expressions of culture have changed over time: such an approach has stimulated research on the characteristics and planning of the form of cities that has been largely divorced from concerns about ecosystem services. This is somewhat paradoxical in light of the significant areas of most cities that are vegetated and the increasing evidence of the value to society of these green spaces. This thesis examines the connection between urban morphological research on the fringe-belt concept, as developed by M. R. G. Conzen and others, and the character and distribution within cities of major areas of green space. The principal focus is on how green spaces within fringe belts that are embedded within cities (for example, parks, allotment gardens, golf courses, and land attached to educational and medical institutions) have changed over time, especially during the past 100 years. Detailed studies of fringe-belt sites in Birmingham reveal a decline in green space over time but maturation of surviving green space towards mature wood-grassland. Comparisons are made with residential areas