Technical Issues - n,k for Films on Metallic Substrates

Recently users have attempted to determine n,k,t of films deposited on silicon. This could not be accomplished with INDEX's Solve...Calculate n,k 'envelope method' algorithm (multiple peaks) which assumes transparent substrates. To meet this new requirement, INDEX 2.50.0400 adds a separate algorithm (#3 below) for transparent (k<<n) films on reflective substrates. The substrate must be opaque or ground on the uncoated surface to eliminate Side 2 reflection.

Unfortunately this is not as straightforward as a transparent film on a transparent substrate. Consider an Al2O3 film deposited on Silicon. Using Gedankenspektrum techniques we create test spectra (12, 13 QWOT Al2O3 @ 770nm) and see whether calculations return our known values (red curve). As shown below, results are close but not exact, a consequence of wavelength shifts resulting from k>0.

The envelope method requires that peak/valley positions not depend on substrate index. The problem with semiconductors and much worse with metals is that these wavelengths are shifted. This can be seen below where the peak wavelength for SiO2 on Si is shifted relative to the same calculation with Si, k=0 and with n=3.945, k=0.

Care must be taken to choose film-substrate combinations that converge in Gedankenspektrum calculations. We can then be hopeful that the combination will work with actual measurements. Consider Si3N4 on Si. A solution cannot be found because the index of Si3N4 is nearly equal to the square root of the index of Si (derivative of the QWOT reflectance ~0). Ultimately, one cannot apply any film to any substrate and expect to deduce n,k vs. wavelength.