On the theory of amorphous solids and of excitons
This thesis consists of two completely separate parts: In part I some problems related to phonons in amorphous solids are considered, whilst Part II is devoted to the study of excitons in Cuprous Oxide (Cu2O). Part I.- A theoretical model, suitable to treat vibrations in tetrahedrally coordinated amorphous systems is developed and permits the study of a number of situations of current interest. Three of these situations are studied in detail: 1) The local response of hydrogen in amorphous silicon when a single silicon is attached to one, two or three hydrogens. The differences between these three configurations are discussed and a direct connection with experimental results is suggested. 2) The interesting case of an amorphous alloy, where both, topological and substitutional disorder are present. This is treated within the spirit of the Coherent Potential Approximation. The particular alloy chosen (Si-Ge) is readily tractable because oithe similar bond characteristics of both components, which allows the neglect of force constant changes. 3) The Raman spectrum of AX2, glasses. The model adopted permits the investigation of the local response at the defect sites for a number of defects. In order to explain the defect lines observed in the experiments, four plausible defect configurations are considered: a missing A-X bond, a X-A double bond, an A-A bond, and a square ring (two tetrahedra sharing an edge). A simple model to calculate the Raman response in amorphous solids is also outlined. Part II.- The valence band of Cu20 is studied in detail to account for the deviations from the hydrogenic law of the exciton spectrum. The appearance of the two series of excitons is explained in terms of a spin-orbit splitting of the valence band in the centre of the Brillouin Zone, using a Tight-Binding Approximation. The deviations of the lowest exciton levels from their expected values are seen to arise from an admixture of the two components of the split -off valence band due to direct Coulomb and exchange interactions. The Hamiltonian used corresponds to the so called "Spherical Approximation" and the results obtained are in remarkable agreement with the experiments.