Uncertainty evaluation of the geometrical thickness and refractive index of silicon wafers

摘要

The uncertainties of measuring the geometrical thickness and refractive index of silicon wafers were evaluated. Both quantities of the geometrical thickness and refractive index were obtained using the previously proposed method based on spectral domain interferometry using the optical comb of a femtosecond pulse laser. The primary uncertainty factor was derived from the determination process of the optical path differences (OPDs) including the phase calculation, measurement repeatability, refractive index of air, and wavelength variation. The uncertainty for the phase calculation contains a Fourier transform in order to obtain the dominant periodic signal as well as an inverse Fourier transform with windowed filtering in order to calculate the phase value of the interference signal. The uncertainty for the measurement repeatability was estimated using the standard deviation of the measured optical path differences. During the experiments, the uncertainty of the refractive index of air should be considered for wavelengths in air because light travels through air. Because the optical path difference was determined based on the wavelength in use, the variation of the wavelength could also contribute to the overall measurement uncertainty. In addition, the uncertainty of the wavelength depends on the wavelength measurement accuracy of the sampling device, i.e. the optical spectrum analyzer. In this paper, the details on the uncertainty components are discussed, and future research for improving the performance of the measurement system is also proposed based on the uncertainty evaluation.