Design of Digital Filters for Si Wafer Surface Profile Measurement - Denoising by Total Variation

Hirotaka Ojima; Kazutaka Nonomura; Li Bo Zhou; Jun Shimizu; Teppei Onuki

doi:10.4028/www.scientific.net/KEM.516.332

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HomeKey Engineering MaterialsKey Engineering Materials Vol. 516Design of Digital Filters for Si Wafer Surface...

Design of Digital Filters for Si Wafer Surface Profile Measurement - Denoising by Total Variation

Abstract:

In the semiconductor industry, high resolution and high accuracy measurement is needed for the geometric evaluation of Si wafers. The flatness parameters are important to evaluate the wafer profile and are required to be the same level as the design rule of IC, and the tolerance for flatness is very tight. According to SEMI (Semiconductor Equipment and Materials International) standards, the required wafer flatness will be 22 nanometres by the year 2016. However, to obtain a higher resolution for sensors, the uncertainty becomes very large compared to the resolution and influences the measured data when the noise is increased. High resolution instruments always incorporate a certain degree of noise. In the presence of noise, form parameters are normally biased. Correction and compensation need a large population of measurements to analytically estimate both bias and uncertainty. The estimation is still far from perfect because of the nature of noise. Another approach is to extract a true profile by filtering noise from the measured data. For the purpose of noise reduction, low-pass filters by Gaussian smoothing and Fourier transform are often used. The noise is normally considered to be a component of small deviation (amplitude) with high frequency which also takes a normal distribution around zero. However these conventional filters can remove the noise in the spatial frequency domain only. So, it is essential to design a filter capable of removing the noise both in the spatial frequency domain and the amplitude component. Thus, we have designed and developed new type of digital filter for denoising. We introduce two new digital filters. One is wavelet transform capable of denoising in the spatial frequency domain and amplitude component, and the other is total variation that can be applied to discontinuous signals without introducing artificial Gibbs Effects.

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Periodical:

Key Engineering Materials (Volume 516)

Pages:

332-336

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.516.332

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Online since:

June 2012

Authors:

Hirotaka Ojima, Kazutaka Nonomura, Li Bo Zhou, Jun Shimizu, Teppei Onuki

Keywords:

De-Noising, Digital Filter, Profile Measurement, Total Variation

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References

[1] H. Haitjema, Uncertainty Propagation in Surface Plate Measurement, Proc. of the 4th Int. Symp. on Dimensional Metrology in Production and Quality Control (1992) 304-320.