Dispersive white-light spectral interferometry used to measure thickness of a thin film on a substrate

We present a white-light spectral interferometric technique for measuring the thickness of a thin film on a substrate. First, the spectral interferogram is expressed analytically for a setup of a slightly dispersive Michelson interferometer with a cube beam splitter and a fiber-optic spectrometer of a Gaussian response function when one of the interferometer mirrors is replaced by the thin film on the substrate. We reveal that the visibility of the spectral interference fringes is dependent on the reflectance of the thin-film structure and that the phase change on reflection from the structure is inscribed in the phase of the spectral interference fringes. We model the wavelength dependences of the reflectance and of the so-called nonlinear phase function for SiO2 thin film on a silicon wafer of known optical constants taking into account multiple reflection within the thin-film structure. Second, we perform experiments with the SiO2 thin film on the silicon wafer and record the spectral interferograms for determining the thin-film thickness. We confirm very good agreement between theory and experiment and determine precisely various thicknesses of the SiO2 thin film.