By Topic

Analytic determination of n, κ, and d of an absorbing film from polarimetric data in the thin-film limit

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $31
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Kim, I.K. ; Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695-7911 ; Aspnes, D.E.

Your organization might have access to this article on the publisher's site. To check, click on this link:http://dx.doi.org/+10.1063/1.2434004 

We obtain a solution of the three-phase model in the limit d/λ≪1, where the complex refractive index ñ=n+iκ and thickness d of an isotropic film on an isotropic substrate are given analytically at any single wavelength λ from polarimetric data Δρ/ρ and ΔR/R, where ρ is the complex reflectance ratio and R is either the p- or s-polarized reflectance. We describe several procedures for extending the range of validity of the solution. Analysis of correlations shows that the uncertainty δ(ΔR/R) of ΔR/R is significantly more important than the δ(Δρ/ρ) of Δρ/ρ, which allows us to obtain an expression for the uncertainties δn, δκ, and δd of n, κ, and d, and to identify conditions that optimize the determination of the layer parameters. We find that the relative uncertainties δn/n and δd/d are not equal, as would be expected if they were determined by the optical thickness nd measured by ellipsometry, but that ΔR/R breaks the connection. We verify our results by measurements of H2O reversibly physisorbed on oxidized GaAs, finding, for example, that for our conditions δκ is determined more accurately than δn, and δn more accurately than δd. These data and model calculations show that flu- ctuations in parameters, particularly d, are asymmetric, leading in principle to inaccurate average values. However, we show that the importance of the ΔR/R data together with the remaining high correlation between n and d allows us to define a characteristic curve that can be used to correct the results for this nonlinearity. Finally, we extend our analysis to determine the orthogonal linear combinations of n, κ, and d that the data actually determine, which explains why the data fit the characteristic curve so well. Our results will be useful in various contexts for the analysis of films less than 1 nm thick, for example, in applications involving preparation of next-generation electronic and optoelectronic devices with complicated multilayer structures, real-time control of deposition, and the identification of physisorbed and chemisorbed layers on the monolayer scale.

Published in:

Journal of Applied Physics  (Volume:101 ,  Issue: 3 )