Measurement of the absorption edge of thick transparent substrates using the incoherent reflection model and spectroscopic UV-visible-near IR ellipsometry

A model taking into account the incoherent reflection in a thick transparent substrate (approx. 1 mm) is described and tested. The incoherent model makes it possible to calculate the averaged elements of the Mueller matrix describing the sample, for comparison with data obtained by Spectroscopic Phase Modulated Ellipsometry (SPME). By performing PME in two different configurations, the degree of polarisation is calculated from the measured intensities and compared to the theory. The strong transition from incoherent to coherent reflection at the onset of the extinction or absorption edge, makes it possible to measure extremely weak extinction coefficients (k ∼ 10^-5) using ellipsometry. In particular, the electronic absorption edge in the UV-visible region, giving the transition from incoherent to coherent reflection, is found to be adequately modelled by the Forouhi-Bloomer (F and B) or the Tauc-Lorentz (TL) dispersion formulas. Industrial applications of ellipsometry often involve transparent substrates and examples of characterisation of thin films on glass are given.