Errors and Sensitivity Analysis

Imperfections or nonidealities of the optical components in an ellipsometer can cause errors in A and il/. Quantitative analyses of errors have been made by Jerrard for inexactness of the quarter-wave plate, by Azzam and Bashara for nonideal optical activity of the quarter-wave plate and surface roughness, and by Smith for finite bandwidths of the monochromatic light source as well as the source polarization. Archer and Shank and Yolken, Waxier, and Kruger considered the effect of multiple reflection within the compensator plate. It is reported that antireflection coatings on the surfaces of the compensator plate are beneficial. Aspnes treated in a formal way the first-order effects from 

The combined ellipsometry-reflectance method—three-parameter ellipsometry—has been subject to error analysis. Cahan showed that, while it is possible in principle to obtain an unambiguous solution for the optical constants and thickness of a film by three-parameter ellipsometry, the method does not guarantee that a solution can be obtained in practice. He also pointed out, by working with sample data from electrochemically produced films, that the numbers obtained as the solution are not necessarily physically real when the three-layer model is inadequate for the particular system. Chung, Lee, and Paik studied the forward and reverse sensitivity analyses for three-parameter ellipsometry to obtain the forward sensitivity coefficients (dMldoi) and the reverse sensitivity coefficients for a passive film on nickel (here 

The most important factor turned out to be the judicious choice of the angle of incidence. Thus, the sensitivity analysis confirms the earlier proposition that, for a successful application of three-parameter ellipsometry, it is essential to choose an incident angle that is well below the principal angle of incidence. At the principal angle of incidence, the relative phase retardation A is near 90° and the sensitivity in the A measurement is near maximum. Therefore, angles near the principal angle are most often 

By a visual inspection of a simulated result, such as Fig. 8, or by the sensitivity analysis by Chung et one can see if the above condition of serious error is encountered at a particular experimental condition (wavelength, angle of incidence, etc.). 

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