| dc.contributor |
Gerald J. Iafrate, Committee Member |
|
| dc.contributor |
David E. Aspnes, Committee Co-Chair |
|
| dc.contributor |
John F. Muth, Committee Chair |
|
| dc.contributor |
Salah M. Bedair, Committee Member |
|
| dc.creator |
Kim, In Kyo |
|
| dc.date |
2010-04-02T18:25:41Z |
|
| dc.date |
2010-04-02T18:25:41Z |
|
| dc.date |
2007-08-07 |
|
| dc.date.accessioned |
2023-02-28T17:08:29Z |
|
| dc.date.available |
2023-02-28T17:08:29Z |
|
| dc.identifier |
etd-07312006-120203 |
|
| dc.identifier |
http://www.lib.ncsu.edu/resolver/1840.16/3001 |
|
| dc.identifier.uri |
http://localhost:8080/xmlui/handle/CUHPOERS/265690 |
|
| dc.description |
The problem of the simultaneous determination on a wavelength-by-wavelength basis of the complex refractive index ñ = n + iκ and thickness d of an isotropic thin film deposited on an isotropic substrate has never been solved analytically over the last 35 years. Here I find the analytic solution of the three-phase model in the limit d/λ << 1 on a wavelength-by-wavelength (λ-by-λ) basis from polarimetric data Δρ/ρ and ΔR⁄R, where ρ and R are the complex reflectance ratio and either the p- or s-polarized power reflectance, respectively. My relatively simple quadratic equation eliminates several disadvantages of previous numerical-analysis approaches, including intrinsic instabilities and a need for accurate estimates of starting parameters for convergence, which become particularly acute as d⁄λ→0. I also investigate the source of the numerical difficulties, the correlations in both parameters and data, with an approach based on the Jacobian of the exact equations. These correlations prevent a simple quadrature addition of uncertainties in Δρ⁄ρ and ΔR⁄R in the calculation of uncertainties in the parameters. I also show that a simple mathematical transformation of the data can improve the accuracy of the first-order equations. The results will be useful directly for optically analyzing films with d ≤ 1 nm, and for providing starting values for more accurate numerical calculations for thicker films. Results are demonstrated for the cyclic physisorption and desorption of a layer of H₂O on oxidized GaAs, and as numerical estimates of performance specifications for application to several materials combinations important to semiconductor technology. |
|
| dc.rights |
I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
|
| dc.subject |
polarimetry |
|
| dc.subject |
thin film |
|
| dc.subject |
analytic solution |
|
| dc.subject |
ellipsometry |
|
| dc.subject |
three-phase model |
|
| dc.title |
The Simultaneous Determination of Thickness and Complex Refractive Index of a Thin Film on a Substrate |
|