Simultaneous film thickness and refractive index measurement using a constrained fitting method in a white light spectral interferometer.

Film is widely used in optoelectronic and semiconductor industries. The accurate measurement of the film thickness and refractive index, as well as the surface topography of the top and bottom surfaces are necessary to ensure its processing quality. Multiple measurement methods were developed; however, they are limited by the requirements of a known dispersion model and initial values of thickness and refractive index. Further, their systems are rarely compatible with surface topography measurement methods. We propose a constrained nonlinear fitting method to simultaneously measure the thickness and refractive index of film in a simple white-light spectral interferometer. The nonlinear phase extracted by the spectral phase-shifting is fitted with the theoretical nonlinear phase obtained by multiple reflection model. The constraints of nonlinear fitting are obtained by the interferometric signal of vertical scanning, reconstructed by the integration of the white-light spectral signal to avoid local minima. The proposed method does not require a priori knowledge of the dispersion model and initial values of thickness and refractive index, and its system is compatible with the vertical scanning interferometry (VSI) method to reconstruct the surface topography of the top and bottom surfaces of film. Three SiO ₂ films with different thicknesses are measured, and the results show that the measured refractive index is within the theoretical value range of wavelength bandwidth and the measured thicknesses are closely aligned with the values provided by the commercial instrument. The measurement repeatability of refractive index reaches 10 ^-3 . Measurements on a polymer film demonstrate that this method is feasible for measuring the film without a priori information.