Direct measurement of the extinction coefficient by differential transmittance

Abstract

A new procedure to measure the extinction coefficient k of film materials that are relatively transparent is presented. This procedure does not require the use of an optical-constant model or the knowledge of extra physical properties of the material, such as the specific heat capacity. It involves preparing a sample with two areas, at least one of them coated with the film, whereas the other may remain uncoated or may be coated with a different thickness of the same material. The differential transmittance between the two sample areas is shown to be proportional to k of the film material in the following measurement conditions: the incident light is p polarized and it impinges at the film material Brewster angle. The differential transmittance is obtained with a single measurement by making the light beam or the sample to oscillate with respect to one another and by using a lock-in amplifier; for normalization purposes, the transmittance in one of the sample areas is also measured. The proportionality factor between the normalized differential transmittance and k only involves the wavelength, the film thickness, and the Brewster angle. The knowledge of the film Brewster angle requires that the film refractive index (n) is measured beforehand; this can be performed with standard procedures, such as ellipsometry, since such techniques are efficient at measuring n of a transparent material, but are inefficient at measuring a small k. The procedure is exemplified with the calculation of k in the far ultraviolet of AlF3 films deposited by evaporation. The dependence of the uncertainty of k obtained with this procedure is analyzed in terms of the uncertainty of the film n, of wavelength, and of the degree of polarization of the incident beam. The selection of a substrate with similar n to the film material is also discussed. The uncertainties involved with the present procedure were analyzed for a specific example and an uncertainty of 2 × 10−5 in k calculation is considered feasible.