An ellipsometric procedure for the characterization of very thin surface films on absorbing substrates

The accurate determination of thicknesses well under 100 Å of ultra thin films, such as native, etched or chemically cleaned surface films, from ellipsometric measurements, has always been a difficult problem encountered in the presence of experimental errors, particularly that in the angle of incidence. In this paper, we develop a procedure to determine unambiguously the thickness of such transparent films overlaid on absorbing substrates. From the ellipsometric data measured on two same absorbing substrates overlaid with the same transparent film, but up to different thicknesses, the procedure equally finds out the angle of incidence in addition to the index and the thickness of the two films. Moreover, a very rapid convergence is realized owing to a transformation of the four-parameter problem into a two-dimensional numerical search in which the refractive index and the angle of incidence are found at first independently of the two thicknesses. The validity of the method is also investigated under situations where the assumptions initially made differ slightly. A quantitative error analysis further carried out shows the ability of the method to resist the propagation of experimental angular errors to the parameters sought, in particular to the smaller thickness when the other is chosen relatively thicker. The thicknesses in the order of 10 Å such as that of surface films can hence be obtained from an ellipsometer producing angular errors of a few hundredths of a degree and more. The measured angle of incidence can also be verified. The procedure is finally illustrated with data from simulated and real reflecting systems.