20 Bilayers

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Ellipsometry data for the 20 bilayer ISAM film was acquired on 7-11-02.  One bilayer constitutes a single layer of anionic Poly S-119 and a single layer of cationic Poly(ethylenimine) (PEI).  The substrate was a Fisherfinest premium microscope slide of thickness L=1 mm.  The AFM images and surface analysis for this sample is also available.

A two layer optical model was used for the data analysis.  The first layer is composed of the optical constants of the 1mm thick glass substrate, the optical constants were previously determined by ellipsometry.  The second was a Cauchy layer which is representative of the ISAM film.  In order to determine the thickness of the film the fit must be performed over a spectral region where the film is transparent.  The transmission spectra indicate that the film is transparent the spectral region 700-1100 nm; therefore, the data was restricted to the transparent range for the fit.  The fit parameters that were chosen were An, Bn, Cn, thickness, and thickness uniformity.  The calculated best fit parameter are shown in Table 1, where a normal fit was performed with the fit weighting set to 'experimental standard deviation'.  The mean squared error (MSE) of the model fit was MSE=1.1361.  The calculated film thickness is L=115.75 nm, thus the average bilayer thickness for the 20 bilayer film is l=5.7875 nm/bilayer

Table 1    The calculated parameter values of the Cauchy model in the spectral range 700nm-1100nm.
Parameter Value 90% Confidence Limit
An 1.5969 0.000421
Bn 0.003754 0.00063
Cn 0.0068363 0.000229
Uniformity 26.985 0.628
Thickness (nm) 115.75 0.0629

To interpret the quality of the fit we refer to the correlation matrix shown in Table 2.  The correlation matrix indicates that the fit parameters An, Bn, and Cn are all strongly correlated to each other because their off diagonal elements are all >0.9.   However, the off diagonal components of the thickness and uniformity are small indicating that the solution for these parameters is unique.

Table 2    The correlation matrix for the model parameters in the spectral range 700nm-1100nm.
  An Bn Cn Uniformity Thickness
An 1.000 -0.981 0.936 0.057 0.017
Bn -0.981 1.000 -0.985 -0.189 -0.165
Cn 0.936 -0.985 1.000 0.322 0.274
Uniformity 0.057 -0.189 0.322 1.000 0.747
Thickness 0.017 -0.165 0.274 0.747 1.000

After the thickness and uniformity were determined, the refractive index and extinction coefficients were determined by performing a point by point fit over the entire spectral region 400-1100 nm using n and k as the fitting parameters.  The ellipsometry data and corresponding fit is shown in Figure 1.

Figure 1    Experimental ellipsometric data for (left axis) and (right axis) vs. wavelength, with the model fit for Poly S-119, 20 bilayer ISAM film.

From the model fit the optical constants are determined for the ISAM film as shown in Figure 2.  The refractive index and extinction coefficient calculated from the point by point by point fit are exactly what is expected.  The extinction coefficient follows the transmission spectrum very well and the refractive index shows the anomalous dispersion in the region of high absorption.

Figure 2    Calculated optical constants for the real (left axis) and imaginary (right axis) parts of the complex refractive index for Poly S-119, 20 bilayer ISAM film.

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