AVS 53rd International Symposium
    Thin Film Friday Sessions
       Session TF+EM-FrM

Paper TF+EM-FrM1
Parameter Uncertainties and Higher-Order Effects in the Analytic First-Order Solution for the Complex Refractive Index and Thickness of a Thin Film on a Substrate

Friday, November 17, 2006, 8:00 am, Room 2022

Session: In-Situ/Ex-Situ & Real-Time Monitoring and Characterization
Presenter: I.K. Kim, North Carolina State University
Authors: I.K. Kim, North Carolina State University
D.E. Aspnes, North Carolina State University
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We recently reported a solution in the thin-film limit of the general problem of determining the complex refractive index ñ = n+i@kappa@ and thickness d of an isotropic film on an isotropic substrate from the changes induced in polarimetric data by deposition or removal. Here, we consider uncertainties in n, @kappa@, and d in terms of uncertainties in the measured Fourier coefficients of the intensity. Taking advantage of the fact that the uncertainty @delta@(@DELTA@R/R) in the reflectance is much higher than the uncertainty @delta@(@DELTA@@rho@/@rho@) in the relative complex reflectance ratio, we obtain an analytic expression that gives the uncertainties of n, @kappa@, and d in both relative and absolute terms. The expression can be used to establish conditions where one or the other is determined with maximum accuracy. In contrast to expectations from ellipsometry, the relative uncertainties @delta@n/n and @delta@d/d can be significantly different. By adding noise to simulated data, we investigate the range of linearity and higher-order nonlinearities. Symmetric fluctuations of the Fourier coefficients about their average values can yield highly asymmetric fluctuations about the parameter values corresponding to the coefficient averages, particularly d. We describe a procedure for correcting the results for these asymmetries. Finally, we confirm all results with polarimetric data obtained by cyclically physisorbing and desorbing a monolayer of H@sub 2@O on oxidized GaAs.