Abstract
In wavelength-tuning interferometry, the surface profile of the optical component is a key evaluation index. However, the systematic errors caused by the coupling error between the higher harmonics and phase shift error are considerable. In this research, a new 10N − 9 phase-shifting algorithm comprising a new polynomial window function and a DFT is developed. A new polynomial window function is developed based on characteristic polynomial theory. The characteristic of the new 10N − 9 algorithm is represented in the frequency domain by Fourier description. The phase error of the new algorithm is also discussed and compared with other phase-shifting algorithms. The surface profile of a silicon wafer was measured by using the 10N − 9 algorithm and a wavelength-tuning interferometer. The repeatability measurement error across 20 experiments was 2.045 nm, which indicates that the new 10N − 9 algorithm outperforms the conventional phase-shifting algorithm.
Highlights
In the semiconductor industry, high-purity and high-quality polished silicon wafers are the best and most widely used material for the manufacturing of integrated circuits (ICs)
The repeatability measurement error across 20 experiments was 2.045 nm, which indicates that the new 10N − 9 algorithm outperforms the conventional phase-shifting algorithm
The results demonstrated that the new algorithm can more strongly compensate for phase shift miscalibration in the presence of harmonics in comparison with other conventional algorithms, even for a phase shift miscalibration of −30% and high reflectivity (30%) sample surface
Summary
High-purity and high-quality polished silicon wafers are the best and most widely used material for the manufacturing of integrated circuits (ICs). Silicon wafers will still be the most basic and important functional material of the IC industry for the several decades. This kind of material has high quality characteristics; for example, the current passes the wafer more quickly than other conductors and has excellent mobility under high temperature. One of the basic parameters for measuring the performance of a silicon wafer is the surface profile. The surface shape measurement methods can be divided into non-optical methods and optical methods. For testing large aperture optical devices, the limitations of non-optical methods are their nonlinearity and narrow dynamic range; they do not meet the requirements of surface shape measurement. Optical methods mainly include confocal microscopy [4], structured light microscopy [5], and optical interferometry [6,7,8,9,10,11,12,13,14,15]
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