Studies in the theory of solids

Chapter I: We show that the surface arrangement of atoms in a solid controls the energetically slowly varying features of a LEED spectrum. Because of inelastic collisions within the solid. the LEED electrons mainly sample a surface sandwich of atoms. Thus. the surface sandwich reflectivity. computed by using a method which considers only single reflections of the electron by sheets of atoms in the solid, can be directly compared with the slowly varying. surface dependent features in the data. To concentrate on these fractures of the data. the approximate surface sandwich reflectivity is compared with data which has been smoothed to remove energetically rapidly varying features which·do not depend on surface structure. The spectra, defined as a function of momentum transfer, are smoothed by averaging over momentum shorter than a momentum transfer characteristic of a surface distance. The method, especially adapted to layered materials, was used to determine that the surface of TiS2 is ideal whereas the surface sandwich of TiSe2 expands outward slightly. 2 For the final qeterminations. the smoothing method was used on both the ·data and a theory which includes multiple scattering to confine the comparison to just the slowly varying surface dependent features. Chapter II: We show that energies of deep traps associated with impurities in semiconductors are controlled by the Sand P orbital energies of the impurity atoms. First, the qualitative physics of a deep trap is worked out using a defect molecule model. For very deep traps the trap energy is defined by a pinning energy which is determined by the energies of the nearest neighbors of the impurity. The quantitative theory is worked out using a tight binding Koster-Slater calculation. Using bandstructure at symmetry points to define matrix elements of the host crystal Hamiltonian and a table of atomic energies to define the impurity potential, predictions of energies of deep traps caused by impurities are made for fourteen different semiconductors. The theory is compared with the data for GaP and the alloy GaAs1-xPx before developing a phenomenological model x which depends mainly on the energy centers of the valence and conduction band density. of states as well as atomic energies of impurities. Finally, this phenomenological model is used to make predictions of deep trap energies in S1.U of I OnlyThesi