AVS 52nd International Symposium
    Thin Films Wednesday Sessions
       Session TF+EM-WeM

Paper TF+EM-WeM7
Analytic First-Order Solution for the Simultaneous Determination of Complex Refractive Indices and Thicknesses of Thin Films Deposited on Substrates

Wednesday, November 2, 2005, 10:20 am, Room 310

Session: In-Situ/ Ex-Situ & Real- Time Monitoring
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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The problem of the simultaneous determination of the complex refractive index = n + i@kappa@ and thickness d of an isotropic thin film deposited on an isotropic substrate from polarimetric data (the so-called nkt problem) has never been solved analytically for a general , although solutions are available for the case of a transparent film (@kappa@ = 0). Here, we present an analytic solution for arbitrary n and @kappa@ that is valid to first order in d/@lambda@, where @lambda@ is the wavelength of light. The solution requires a knowledge of the change of pseudodielectric function <@epsilon@>, or alternatively the relative change @Delta@@rho@/@rho@ in the complex reflectance ratio @rho@, and either the relative change @Delta@Rp/Rp or @Delta@Rs/Rs, where Rp and Rs are the reflectances for p- or s-polarized light. Ranges of validity are obtained by comparing results to those obtained numerically using the exact three-phase-model expressions, and a procedure is presented for improving the accuracy. Numerical evaluation of the exact equations, which proceeds by least-squares analysis, is facilitated by using the first-order solution as a starting point. Depending on the sample the first-order solution is more effective at some energies than others, emphasizing the need for multiwavelength measurements over finite energy ranges. The most effective ranges can be determined from the correlation coefficients obtained in the least-squares analysis. As previously noted, the highest correlation generally occurs between n and d, although under some situations a high correlation can also occur between @kappa@ and d. The results should be particularly useful for systems involving reversible configurations, such as the cyclic adsorption and desorption of gases on clean surfaces, where accuracy can be improved by modulation techniques.