Surface profilometry of silicon wafers using wavelength-tuned phase-shifting interferometry

Abstract

Surface profile is one of the key evaluation indexes in the optical industry. With the development of optical technology, wavelength-tuned phase-shifting interferometry has been widely used for measuring the surface profiles of optical components based on the high accuracy of this technique. However, coupling errors caused by higher harmonics and phase-shift errors may lead to systematic errors in the calculated phase. In this research, to suppress coupling errors effectively, we propose an 8N - 7 phase-shifting algorithm consisting of a novel polynomial window function and discrete Fourier transform. By locating eight multiple roots on the characteristic diagram, the polynomial window function of the proposed algorithm is derived based on the theory of characteristic polynomials. The characteristic polynomial of the 8N - 7 algorithm is estimated based on a Fourier representation. Phase errors are discussed and compared to the errors in other algorithms. The results indicate that the 8N - 7 algorithm has the smallest phase error among the compared algorithms and can compensate for up to sixth-order nonlinearity in phase measurements. Finally, the proposed algorithm was applied to profile the surface of a silicon wafer. The results revealed that the standard deviation across 20 experiments was 3.231 nm, which is much smaller than the standard deviations of conventional phase-shifting algorithms.