Accurate measurement of the phase shift on reflection of light from opaque materials.

Abstract

Because the phase shift on reflection is a function of the optical properties, it provides an excellent tool for the study of the microstructure of materials. However, there is a significant amount of confusion and error in its measurement in previous work. Therefore, a new method for accurately measuring the phase shift on reflection from opaque materials that is based upon a mathematical comparison of step height measurements made with stylus and phase shifting interferometric profilometers is presented. The presentation of this new measurement method consists of a comprehensive account of its theoretical and experimental basis and validation. The theoretical portion begins with the development of the initial mathematical models used for calculating the phase shift from stylus and afocal, normal incidence interferometric step height measurements and verifying the results with the Fresnel relations. As a result of the first measurements, both the measurement and verification models are modified to account for the use of focused, unpolarized light by the interferometric profilometer, and the verification model is also modified to include the possible existence of a dielectric overlayer on the surface of the opaque material. The experimental portions consist of the descriptions and results of accurate step height measurements made with a Rank Taylor Hobson Talystep diamond stylus profilometer and a Wyko TOPO-2D interferometric surface profiling system. Also included are comprehensive descriptions of both profilometers and their operation, and accurate assessments of the number and magnitude of sources of experimental error. The opaque materials used to demonstrate and validate this technique consisted of thick films of chromium on glass and gold on fused silica. The phase shifts, which were measured at different locations on each of the samples, are verified with the predictions of published values of the optical and structural properties of the particular material, and the averages of the measured phase shifts agreed extremely well with those predictions. In the gold measurements, which had a precision of 0.7%, a 4% spatial variation in the phase shift on reflection was discovered and strongly supported by a second set of measurements with a refined version of the experimental technique.