Development of pseudo-random binary gratings and arrays for calibration of surface profile metrology tools

Optical Metrology tools, especially for short wavelength (EUV and X-Ray), must cover a wide range of spatial frequencies from the very low, which affects figure, to the important mid-spatial frequencies and the high spatial frequency range, which produces undesirable flair. A major difficulty in using surface profilometers arises due to the unknown Modulation Transfer Function (MTF) of the instruments. Therefore, accurate calibration of profilometers, the understanding of their MTF limitations, and cross calibration between tools represents a considerable challenge for quantitative optical metrology. In previous work the instrumental MTF of a surface profiler was precisely measured using reference test surfaces based on binary pseudo-random (BPR) gratings. Here, we present results of fabricating and using twodimensional (2D) BPR arrays that allow for a direct 2D calibration of the instrumental MTF. BPR sequences are widely used in engineering and communication applications such as Global Position System, and wireless communication protocol. The ideal BPR pattern has a flat “white noise” response over the entire range of spatial frequencies of interest. The BPR array used here is based on the Uniformly Redundant Array prescription2 initially used for x-ray and gamma ray astronomy applications. The URAs superior imaging capability originates from the fact that its cyclical autocorrelation function very closely approximates a delta function, which produces a flat Power Spectrum Density (PSD).

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