When no theoretical model (e.g. Drude) will fit n & k over a given range, fitting at each wavelength may be required. While investigating n & k determination via Gedankenspektrum simulations (15 nm Ta on BK7) we found 'bad' solutions where n & k values appeared switched. [Method: 1. Calculate R/T based on known n,k, 2. Add random errors and convert to optimization targets, 3. Solve using LM algorithm {$NK function}, 4. Save data with BASIC Sub XLwrite, 5. Plot in Excel.] Switching is seen in plots below (normal distribution, S.D. = 1%, R & T @ 0°). Red traces are Sopra Ta values.

By way of explaining n & k switching, we utilized two index files: normal (Sopra Ta as in the red traces above) and n & k switched. The nearly overlapping curves below diverge as film thickness increases. One imagines that an n & k solution can take the other road.

In the FSPlot graph below we compare phase difference Ø at 45° with %R difference. This suggests that there is no substitute for an ellipsometer! It may be of interest to note that the wavelength where red and green phase curves overlap seems to be the point at which solutions diverge.

Hoping to discover general rules, we also examined results for constant indices, as shown below for S.D. = 1%, t = 10 nm, n = 2 and k = 3. In the cases below targets are R & T @ 0°, 45° S & P, 60° S & P.

In the graphs below t = 5 nm, n = 2 , k = 10 and n & k switching was not observed.

Advanced FilmStar users familiar with BASIC are invited to request the macro used to create the above graphs. All readers can download an Excel Workbook using formulas from Heavens's Optical Properties of Thin Solid Films. As films become thinner, ultimately (zero) the values for n & k no longer matter. As films become thicker %R and %T values diverge, but at that point films may be too thick for reliable %T.

Seen n & k switching reported in the literature? If so, please contact us.
We have consulted with industrial and academic experts; thus far
it appears that 'Fred's nk anomaly' has not been reported.

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