Theoretical Study of the Transverse Dielectric Constant of Superlattices and Their Alloys (Refraction, Absorption)
Kahen, Keith Brian
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https://hdl.handle.net/2142/69343
Description
Title
Theoretical Study of the Transverse Dielectric Constant of Superlattices and Their Alloys (Refraction, Absorption)
Author(s)
Kahen, Keith Brian
Issue Date
1986
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Optics
Abstract
The optical properties of III-V binary and ternary compounds and GaAs-Al(,x)Ga(,1-x)As superlattices are determined by calculating the real and imaginary parts of the transverse dielectric constant, (epsilon)((omega)) = (epsilon)(,1)((omega)) + i(epsilon)(,2)((omega)). Emphasis is given to determining the influence of different material and superlattice (layer thickness and Al composi- tion) parameters on the values of the index of refraction. (eta)((omega)) and absorption coefficient, (alpha)((omega)).
In order to calculate the optical properties of a material, it is necessary to compute its electronic band structure. We accomplish this by introducing a partition band structure approach based on a combination of the (')k(.)(')p and nonlocal pseudopotential techniques. In this approach the bulk Brillouin zone is partitioned into the (GAMMA), X, and L regions by performing (')k(.)(')p expansions about these three symmetry points. The results for (eta)((omega)) and (alpha)((omega)) of bulk III-V compounds com- pare well with other one-electron band structure models, and our calculations show that for small frequencies, the index of refraction is determined mainly by the contributions of the outer regions of the Brillouin zone.
The effects of alloy scattering are incorporated into the model using a perturbative CPA approach which only includes the influence of compositional disorder. The results for the disorder-induced, (GAMMA) point, energy-gap bowings are shown to be nearly comparable to those calculated using more sophisticated CPA approaches. Further- more, the calculated absorption coefficient of Al(,x)Ga(,1-x)As is found to be in good agreement with the experimental data.
The model is extended to heterostructures by using the envelope-function approximation. Valence-band mixing and (GAMMA)-region exciton effects are also included in the model. Our results show that the anisotropy and structure dependence of the refractive index of superlattices result mainly from the contribution of the (GAMMA) region, while the contributions of the outer regions of the zone are rather insensitive to the superlattice structure. The superlattice index of refraction values is determined to attain maxima at the various (GAMMA)-region, quantized, transition energies, where for certain structures the difference between the refractive indices of the superlattice and its corresponding Al(,x)Ga(,1-x)As alloy can be as large as 2%. (Abstract shortened with permission of author.)
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