Determination of thickness and optical constants of metal films from an extended ATR spectrum by using a statistical method

Sudden changes in reflectivity within a small angle or wavelength range are very sensitive to both the metal film thickness and optical constants. Metal films such as silver or gold display two sudden changes in their reflectance curve − the first occurring at the critical angle, which is then followed by a sharp surface plasmon resonance (SPR) dip at an incident angle that is a few degrees greater than the critical angle. In this report, we describe a method involving the optimization of the sum of squared difference (SSQ) to produce good fitting amongst the reflectivity data points from a function curve derived from theory. The standard errors on each output parameter for the best curve fit are determined from the covariant matrix eigenvalues.