Development of pseudo-random binary 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 scattering. A major difficulty in using surface profilometers arises due to the unknown Point-Spread Function (PSF) of the instruments [1] that is responsible for distortion of the measured surface profile. Generally, the distortion due to the PSF is difficult to account because the PSF is a complex function that comes to the measurement via the convolution operation, while the measured profile is described with a real function. Accounting for instrumental PSF becomes significantly simpler if the result of measurement of a profile is presented in a spatial frequency domain as a Power Spectral Density (PSD) distribution [2]. For example, the measured PSD distributions provide a closed set of data necessary for three-dimensional calculations of scattering of light by the optical surfaces [3], [4]. The distortion of the surface PSD distribution due to the PSF can be modeled with the Modulation Transfer Function (MTF), which is defined over the spatial frequency bandwidth of the instrument [1], [2]. The measured PSD distribution can be presented as a product of the squared MTF and the ideal PSD distribution inherent for the System Under Test (SUT). Therefore, the instrumental MTF can be evaluated by comparing a measured PSD distribution of a known test surface with the corresponding ideal numerically simulated PSD. The square root of the ratio of the measured and simulated PSD distributions gives the MTF of the instrument. In previous work [5], [6] 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 two-dimensional (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 protocols. 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 prescription [7] initially used for x-ray and gamma ray astronomy applications. The URA's superior imaging capability originates from the fact that its cyclical autocorrelation function very closely approximates a delta function, which produces a flat PSD. Three different size BPR array patterns were fabricated by electron beam lithography and ICP etching of silicon. The basic size unit was 200 nm, 400 nm, and 600 nm. Two different etch processes were used, CF{sub 4}/Ar and HBr, which resulted in undercut and vertical sidewall profiles, respectively. The 2D BPR arrays were used as standard test surfaces for MTF calibration of the MicroMap{trademark}-570 interferometric microscope using all available objectives. The HBr etched two-dimensional BPR arrays have proven to be a very effective calibration standard making possible direct calibration corrections without the need of additional calculation considerations, while departures from the ideal vertical sidewall require an additional correction term for the CF{sub 4}/Ar etched samples. [8] Initial surface roughness of low cost 'prime' wafers limits low magnification calibration but should not be a limitation if better polished samples are used.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- Materials Sciences Division
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 962663
- Report Number(s):
- LBNL-2016E; TRN: US200916%%308
- Journal Information:
- Journal of Vacuum Science and Technology B, Journal Name: Journal of Vacuum Science and Technology B
- Country of Publication:
- United States
- Language:
- English
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Development of pseudo-random binary gratings and arrays for calibration of surface profile metrology tools
Binary Pseudo-Random Gratings and Arrays for Calibration of Modulation Transfer Functions of Surface Profilometers
Related Subjects
ASTRONOMY
CALIBRATION
CALIBRATION STANDARDS
COMMUNICATIONS
DELTA FUNCTION
DISTRIBUTION
ELECTRON BEAMS
ETCHING
FREQUENCY RANGE
MICROSCOPES
MODULATION
ROUGHNESS
SCATTERING
SILICON
SPECTRAL DENSITY
THREE-DIMENSIONAL CALCULATIONS
TRANSFER FUNCTIONS
WAVELENGTHS
Pseudorandom binary arrays
metrology tools