Thickness Profiling of a Large-aperture Transparent Plate immune to nonlinear errors

Abstract

According to the increased demand for large-aperture silicon wafers, a transparent plate, used as a mask for patterning a silicon wafer, should be thoroughly measured for the high performance of the semiconductor chips. In the wavelength-tuning interferometry, the optical thickness of the large-aperture transparent plate can be precisely measured without destruction, but it is inevitable to avoid the occurrence of nonlinear errors by environmental factors. The nonlinearities generate uniform and nonuniform errors in the final phase distorting the original phase information. In this paper, for suppressing the nonlinearities, uniform, and nonuniform errors, a new algorithm designing method, extended averaging method, is developed. With the use of the minimum number of interferograms, we can get the extended averaging phase-extracting algorithm which has immunity to nonlinearities, uniform, and nonuniform error. Two types of numerical error analyses show the novel algorithm has superior error-suppression ability.