Graduation date: 1967

The dissertation first investigates the single-scattering properties of inhomogeneous ice crystals containing air bubbles. Specifically, a combination of the ray-tracing technique and the Monte Carlo method is used to simulate the scattering of light by randomly oriented large hexagonal ice crystals containing spherical or spheroidal air bubbles. The effect of the air bubbles within ice crystals is to smooth the phase functions, diminish the 22° and 46° halo peaks, and reduce the backscatter in comparison with the case of bubble-free ice crystals. Cloud reflectance look-up tables were generated at the wavelengths of 0.65 μm and 2.13 μm to examine the impact of accounting for air bubbles in ice crystal morphology on the retrieval of ice cloud optical thickness and effective particle size. To investigate the effect of the representation of aggregates on electromagnetic scattering calculations, an algorithm is developed to efficiently specify the geometries of aggregates and to compute some of their geometric parameters such as the projected area. Based on in situ observations, aggregates are defined as clusters of hexagonal plates with a chain-like overall shape. An aggregate model is developed with 10 ensemble members, each consisting of between 4-12 hexagonal plates. The scattering properties of an individual aggregate ice particle are computed using the discrete dipole approximation or an Improved Geometric Optics Method, depending upon the size parameter. The aggregate model provides an accurate and computationally efficient way to represent all aggregates occurring within ice clouds. We developed an algorithm to determine an appropriate ice cloud model for application to satellite-based retrieval of ice cloud properties. Collocated Moderate Resolution Imaging Spectroradiometer and Multi-angle Imaging SpectroRadiometer (MISR) data are used to retrieve the optical thicknesses of ice clouds as a function of scattering angle in the nine MISR viewing directions. The difference between cloud optical thickness and its averaged value over the nine viewing angles can be used to validate the ice cloud models. Using the data obtained on 2 July 2009, an appropriate ice cloud model is determined. With the presence of all the uncertainties in the current operational satellite-based retrievals of ice cloud properties, this ice cloud model has excellent performance in terms of consistency in cloud property retrievals with the nine MISR viewing angles.

Researchers analyzing the upper clouds of Jupiter and Saturn are unable to theoretically reproduce the data returned by Pioneers 10 and 11 and Voyagers 1 and 2 with an approach based on Mie theory. Ammonia crystals are believed to be an important constituent of Jupiter's upper clouds, but both their shape and scattering properties were unknown at the start of this work. Ammonia crystals and water crystals were grown in a cold chamber at temperatures 20°C below their freezing points (0°C and -77.7°C, respectively). The H₂O crystals formed had shapes in agreement with published growth habit diagrams. The NH₃ crystals formed were usually irregular in shape, but regular four-sided pyramids were commonly observed. This four-sided pyramidal shape is in agreement with ammonia's primitive cubic crystal structure. Ammonia crystals could not be formed at temperatures above -95°C due to nucleation problems. A scattering measuring instrument was constructed with fifteen separate lens-detector combinations aimed at a common point in the center of the cold chamber. A laser beam (6328Å wavelength) traversed the chamber center, illuminating any crystal aerosal clouds present. A computer was used to rapidly sample the outputs of the fifteen detectors and to drive a photoelectric modulator to change the slow speed polarization properties of the laser beam. The measurements resulted in a determination of the single scattering phase function and degree of linear polarization for the crystal species present. Water crystals were found to have scattering properties similar to that reported by previous researchers. The H₂O crystal scattering possesses a smaller backscatter peak and smaller polarization features than is common for water spheres of similar size. A negative polarization of 5% occurred in the forward scattering hemisphere and a positive polarization of 10% in the rear. Ammonia particles were observed to have a backscattering peak four times higher than for water crystals. The NH₃ particle light scattering produced very little polarization of the scattered light. A small (∼ 4%) negative polarization occurred in the forward scattering hemisphere. Work is continuing here to make scattering measurements using blue light illumination nearly simultaneous with the red HeNe laser wavelength illumination.

No description available.

No description available.

Mr T. J. Sono, an MSc student during the period January 2001 to January 2003, developed an apparatus to measure the pressure and temperature dependence of the electric-field induced birefringence (or electro-optic Kerr effect) in gases. Mr Sono obtained experimental results for dimethyl ether at a wavelength of 632.8 nm resulting in polarizability tensor components, first and second Kerr hyperpolarizabilities, and second Kerr-effect virial coefficients for this particular molecular species. One of the primary concerns of this thesis has been to obtain new measured Kerr-effect data for dimethyl ether and for trifluoromethane over a range of temperature. The cell has been calibrated using hydrogen as a primary standard, and has been carefully aligned to avoid multiple reflections of the incident laser beam off the closely-spaced electrode surfaces. The data has been analyzed to extract values of the polarizability anisotropy and the second Kerr hyperpolarizability for these molecules. In addition, precise values for the second Kerr-effect virial coefficients have been obtained from measurements of the Kerr effect a function of pressure. The molecular-tensor theory of the second Kerr-effect virial coefficient BK is reviewed. This theory describes the effects of intermolecular interactions on the molar Kerr constant, and it has been used to compute BK for dimethyl ether and trifluoromethane over the experimental temperature range. Agreement between experiment and theory is generally good. BK for ammonia has also been calculated, and compared to recent measured data found in the literature. The theory of the Cotton-Mouton effect (the magnetic analogue of the Kerr-effect) in a dilute gas is reviewed, and a new molecular-tensor theory describing the effects of molecular pair-interactions is developed. Calculations for a test molecule, namely chloromethane, indicate that density-dependent effects for this molecule are extremely tiny (of the order of 1% for typical experimental pressures). This new theory could be profitably used in selecting molecules which might demonstrate a larger effect which might be more readily measured in the laboratory. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2008.

During the period January 2001 to January 2003, M Sc student Mr Tleyane Jonas Sono developed an apparatus to measure the pressure- and temperature-dependence of the electro-optic Kerr effect (electric-field-induced birefringence) in gases. Mr Sono presented experimental results for dimethyl ether at a wavelength of 632.8 nm, extracting polarizability tensor components, first and second Kerr hyperpolarizabilities, and second Kerr-effect virial coefficients for this molecular species. This thesis has been primarily concerned with a thorough re-investigation of the Keneffect for the dimethyl ether molecule. Of primary concern is the reproducibility of the measured data, which depend upon precise and accurate knowledge of various experimental parameters. These include calibrations of the high-voltage power supply which is used to establish the electric field across the medium, the pressure transducer, the platinum thermistors, as well as the Faraday cell which forms the heart of the compensator. There is also a possibility of the 316-stainless-steel electrodes buckling and warping as they are cycled over ±200°C, leading to variations in the applied field and a consequent hysteresis in the results. In essence, we have been loath to publish our Kerr-effect investigation of dimethyl ether before making a thorough investigation of the reproducibility of our measured data. Here we present our investigations, and compare our new Kerr virial coefficients and the molecular (hyper)polarizability data extracted from them against the previous work of Sono. It will become apparent agreement is excellent, and that the findings for dimethyl ether are now ready for publication. The molecular-tensor theory of the Kerr-effect; including the second Kerr-effect virial coefficient BK, which describes the effects of intermolecular collisions on the molecular Kerr constant; is reviewed. The computed data is compared with the experimental data, yielding good agreement over the full experimental temperature range of 280 to 450 K. Attempts to obtain measured data at 260 K proved fruitless in the present study, though efforts are underway to complete this task. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2005.

No description available.

No description available.

Czochralski (Cz) silicon wafers are used almost exclusively for the fabrication of VLSI devices. Such silicon contains excess oxygen which precipitates as oxide particles either when the initial ingot is grown or subsequently during the wafer device fabrication. Such oxide particles can produce reduced device performance or failure if they occur within the active device regions. However, they can be used to improve the device performance by a process known as internal oxide gettering. The wafers are given a series of preanneal treatments to produce controlled precipitation in which a surface zone of the wafer to a depth of typically in the range of 10 to 50 μm is denuded of oxide particles, while the remainder of the wafer contains large numbers of well formed particles. The devices are fabricated in the surface denuded zone and harmful contaminating metal impurities are attracted during the heat treatment stages away from the device regions to precipitate at the underlying oxide particles or their associated dislocations. In this way device yields can be significantly increased. Because of the importance of these oxide particles and the oxygen precipitation process for VLSI fabrication, considerable efforts have been made to develop methods to assess the numbers and distributions of such particles within the wafers. The number density range of most interest is 10⁷ to 10¹⁰ cm^-3, and the particle size range is typically 30 to 300 nm. The method that has mostly been used is surface etching followed by optical microscopy to obtain etch pit densities. Transmission electron microscopy is a research method used for obtaining detailed information concerning a small number of individual particles. However, because these methods are destructive, much attention has been given during the last few years to the development of infra-red microscopy methods to directly image the particles within the silicon wafers. Although the particles are smaller than the resolution of these methods, individual particles can nevertheless be imaged. This is because the particles are mostly further apart than the resolution limit, and the sensitivity can be sufficient high that adequate contrast occurs. The contrast arises from scattering or absorption of the light by the particle. Infra-red imaging methods developed include infra-red microscopy (IRM), laser scattering tomography (LST), optical precipitate profiler (OPP) and scanning infra-red microscopy (SIRM), all described more fully in Chapter 2. The SIRM has been developed and used to investigate a variety of semiconductor specimens in the Materials Department, Oxford University, during the last ten years. The SIRM has a good performance and flexibility making it especially suitable as a research instrument. Although all of these infra-red imaging methods have been successful to different degrees in assessing oxide particles in Cz silicon wafers, their performance has at least initially been assessed by comparing the number densities and distributions thus obtained with the corresponding results produced by etch pit studies. Furthermore, no serious attempt has yet been made to develop a rigorous theory of the imaging process and to compare the predictions with the experimental images. One of the main objectives of the present work is to do this or at least to make a significant start to such a project based on the SIRM. The outline of an ideal project which aims at a full understanding of the imaging process and the contrast mechanisms is as follows. The performance of the present Oxford SIRM should be improved and the number of imaging modes increased. The improved performance, i.e. better lateral and depth resolutions and higher sensitivity, would enable smaller particles and higher number densities to be imaged, and hence better quantitative data obtained. The larger number of imaging modes would enable the optimum method to be used to image different types of particle. A rigorous theory should be developed that can describe the imaging process and the contrast mechanisms. First, the illumination system should be studied, and in particular the structure of the focussed probe within the specimen and how the structure changes on focussing deeper into the specimen. Second, the interaction of the light with the specimen should be investigated and especially how light is scattered by individual oxide particles in silicon for the case of the particle size being smaller than the light wavelength. Third, the detection system should be considered. For example, for the reflection confocal SIRM, how the light back scattered by the particles is collected by the probe forming lens and imaged at a pin-hole aperture placed in the front of the detector. Well designed experiments are required to determine the imaging properties of the different modes and comparisons should be made between the experimental and theoretical data. The successful conclusion of such a project would enable SIRM images of the particles to be more fully interpreted and hence more detailed information obtained concerning the particles. Furthermore, the images expected from different types of particle could be more closely predicted, e.g. whether they are detectable or not, and hence materials projects could be better planned at the outset. In this thesis we describe the methods that are presently being used to assess oxide particles in bulk silicon (Chapter 2). We review the literature on scanning optical microscopy covering both visible and infra-red light, present some considerations regarding the design of a high performance and versatile SIRM, and describe the various microscope modes that have been or could be used to image particles in semiconductors with infra-red light (Chapter 3). We give a detailed rigorous theoretical analysis of the energy distributions in the probe for the case when the light is focussed by a high numerical aperture lens from air into silicon (Chapters 4, 5). Numerically computed distributions are obtained to illustrate how the probe changes under different conditions, e.g. different focussing depths (Chapter 6). The relationship between the penetration depth of the probe and the spherical aberration coefficient arising from the silicon specimen is determined (Chapter 7). The classical theory of light scattering is applied to individual spherical silicon dioxide particles embedded in silicon. Numerical results are presented and a contrast mechanism is proposed to describe how the scattered intensity depends on particle size (Chapter 8). A formal solution relevant to the reflection confocal SIRM is given to treat the backward propagation of light using a model which takes into account the polarisation state of the incident light, the spherical aberration introduced by the silicon wafer, the polarisation state of the scattered light and the size of the pin-hole (Chapter 9). Experimental results are obtained for most of the imaging modes described in Chapter 3, specimens being selected so that the wide range of the imaging capabilities of the SIRM is shown, and experimental contrast values are compared with theoretical values (Chapter 10). Finally, overall conclusions are drawn and suggestions are made for completing the work started here (Chapter 11).