Limitations to the determination of the optical properties of a thin film by combined ellipsometric and surface plasmon resonance measurements

We consider the use of the ellipsometric constant Delta and the surface plasmon excitation angle theta of a metal substrate covered by a thin transparent isotropic film for the determination of the refractive index n and thickness d of the film. It is proved, using an expression for Delta(n,d) and theta(n,d) valid to firstorder in d, that it is in general not possible to find a unique n and d from measured values of Delta and theta. Exact calculation of Delta(n,d) and theta(n,d) for the case of a silver substrate covered by an organic thin film and 632.8-nm radiation confirms this result and establishes that the range of d where the proof applies is below ~35 nm. For a value of d of ~40 nm we find that the theoretical limit of uncertainty in n and d when both Delta and theta are known to +/-0.01 degrees is 0.01 and 0.05 nm, respectively.