Electrical and Computer Engineering ETDs

Publication Date

10-8-1973

Abstract

This dissertation is concerned with energy levels and the density of states in random crystals.

By developing a non-linear differential equation for the phase process in random crystals, it is shown how to calculate the density of states in one-dimensional random arrays. The method used ha􀀕 the virtues of simplic­ity and, where comparison with previous numerical results can be made, accuracy, with minimal computing time. Various analytical results are found with the phase process method and these are equivalent with results found by other workers.

In the three-dimensional case, it is shown how to use the phase process to help construct the Green's function and, from it, the density of states. No applications are given. By expanding in plane waves, a secular determinant is found for the determination of the energy eigen­values in a random crystal. Applications of the result show that in the presence of impurities, the band gap is narrowed and that states in the forbidden bands of a perfect crystal are then filled. The model used shows that the distribution of states in the forbidden zone is exponentially distributed in energy away from the gap edge.

Document Type

Dissertation

Language

English

Degree Name

Electrical Engineering

Level of Degree

Doctoral

Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

William Jackson Byatt

Second Committee Member

Ahmed Erteza

Third Committee Member

Harold Dean Southward

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