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Thesis (Ph.D.)--York University, 2005. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 114-123). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR19804

The magnetophonon effect was used to investigate the uniaxial stress dependence of the effective mass in n-type InSb (indium antimonide).

The origin of the Shubnikov-de Haas effect, the strain theory developed by Bir and Pikus, and a simple, classical beating-effects model are discussed. The equipment and the experimental techniques used in recording the Shubnikov-de Haas oscillations of n-type indium antimonite are described. The analysis of the experimental data showed that the angular anisotropy of the period of SdH oscillations at zero stress was unmeasurable for low concentration samples as discussed by other workers. Thus the Fermi surfaces of InSb are nearly spherical at low concentration. It was also shown that the Fermi surface of a high concentration sample of InAs is also nearly spherical. The advantages of using the magnetic field modulation and phase sensitive detection techniques in determining the beats are given. The simple, classical beating-effects model is able to explain the experimental beating effect data in InSb. The computer programs used to obtain the theoretical values of the beat nodal position, SdH frequencies, average frequency, the Fermi surface contours, and the energy eigenvalues are given.

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This dissertation presents the results of experimental research on the nonlinear refraction in InSb and the experimental demonstration of two nonlinear etalon devices using InSb as the active material. The first portion of the dissertation considers the Dynamic Burstein-Moss Shift model for nonlinearities in narrow-gap semiconductors. The physics and the equations are reviewed, and limitations in describing intensity dependent refraction in a semiconductor are considered. These limitations arise from the nonlinear dependence of charge carrier density upon irradiance. The second portion of the dissertation presents experimental measurements made on the nonlinear refraction of InSb at temperatures between 80 K and 182 K, for wavelengths from 5.75 μm to 6.10 μm, where the photon energy lay in the band tail below 100 cm⁻¹. Measurements of the linear absorption were first made with an infrared spectrometer for temperatures from 80 K to 300 K. The nonlinearity was measured by analyzing the transmission through InSb etalons. Nonlinear transmission curves were digitized and stored with an IBM PC-XT, then a curve fit was performed using the nonlinear refractive index as a fiting parameter. Observations are reported of increasing absorption, due in part to a thermal shift of the absorption edge. The second portion of the work presents the theory and demonstration of a bistable etalon using an edge-injected control beam. Plane-wave nonlinear etalon theory is used to describe the operation of such a device, illustrating the way in which switching and logic gate operation can be obtained. Two devices based on this concept are demonstrated: the 3-port device using a single control beam, and the 2SON gate using two control beams to perform two-input logic operation. The extension of the 2SON gate to an array of pixels, and some considerations for optimizing array performance, are considered. Two appendices follow the body of the dissertation, the first describing the preparation of the InSb etalon samples, and the second detailing several procedures for maintenance and operation of the CO laser used.

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This thesis investigation concerns the optical and nonlinear electrical properties of n-InSb. Two specific areas have been studied. First is the magneto-optical study of magneto-donors, and second is the nonlinear dynamic study of nonlinear and chaotic oscillations in InSb. The magneto-optical study of InSb provides a physical picture of the magneto-donor levels, which has an important impact on the physical model of nonlinear and chaotic oscillations. Thus, the subjects discussed in this thesis connect the discipline of semiconductor physics with the field of nonlinear dynamics.

The Shubnikov-de Haas effect is an oscillation in the electrical resistivity or conductivity of a metal, semimetal, or semiconductor as a function of changing magnetic field which occurs at low temperatures. The effect is caused by the quantization of the momentum and energy of the charge carriers by the magnetic field. Since the nature of the oscillation depends strongly on the energy band structure of the material in which it is measured, the effect could be quite useful as an investigative tool. Its usefulness has been limited, however, by the uncertainty as to the functional form of the relationship between the measured oscillations and the parameters characterizing the material. One purpose of the present study is to extend the usefulness of the Shubnikov-de Haas effect by experimentally determining the functional form appropriate for a material such as n-type indium antimonide. The second purpose of the study is to determine values for the parameters which characterize the band structure of indium antimonide. The curve fitting procedure is found to be a powerful tool for investigating band structure. All computer programs used in processing the data, fitting the data, and comparing the results with the Kane model are given.