UBC Theses and Dissertations
Electron wavefunctions at crystal interfaces Patitsas, Stathis Nikos
A one dimensional analysis of the boundary conditions of the electron energy eigenfunc-tion at a sharp interface between two crystals was made. An attempt to evaluate these conditions in terms of known band structure was made. It was concluded that this cannot be done in general. It was shown, however, that if the interface has the proper symmetry properties, the boundary conditions can be expressed in terms of only one unknown, energy-dependent parameter. It was concluded that setting this parameter equal to one gives boundary conditions which, though more general, are equivalent to the commonly used effective mass boundary conditions when they are applicable. It was concluded from numerical results for the transmission coefficient of the symmetric interface, that in general, these boundary conditions, which depend only on known band structure, do not give a good approximation to the exact answer. Since the energy dependence of the parameter mentioned above is described quite well qualitatively using the nearly free electron approximation or the tight-binding approximation, the applicability of any boundary conditions depending only on band structure can be predicted using these simple theories. The exact numerical results were calculated using the transfer matrix method. It was also concluded that the presence of symmetry in the interface either maximizes or minimizes the transmission coefficient. A tight-binding calculation showed that the transmission coefficient depends on an interface parameter which is independent of band structure. The transmission coefficient is maximized when this parameter is ignored. It was concluded that the effective mass equation is of little use when applied to this problem. Some transfer matrix results pertaining to the barrier and the superlattice were obtained.
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