page_title: Extreme ultraviolet lithography
section_title: EUV stochastic issues
hierarchical_section_title: Extreme ultraviolet lithography / EUV stochastic issues
caption_attribution_description: A missing feature defect can result from stochastic underexposure (red) while a bridging defect can result from stochastic overexposure (green). These stochastic deviations from the nominal exposure arise from photon shot noise. Following exposure, various physical and chemical mechanisms (e.g., secondary electrons, acid diffusion, flare, aberrations, heating) "blur" the image. Ref.: https://www.linkedin.com/pulse/from-shot-noise-stochastic-defects-dose-dependent-gaussian-chen/
context_page_description: Extreme ultraviolet lithography is a lithography technology using a range of extreme ultraviolet wavelengths, roughly spanning a 2% FWHM bandwidth about 13.5 nm.
  While EUV technology is available for mass production, 53 machines worldwide capable of producing wafers using the technique were delivered since Q1 2018, while 201 immersion lithography systems were delivered during the same period. Issues that make EUV adoption difficult are tool costs, tool uptime and stochastic phenomena. The latest NXE:3400 tools have been equipped with lower pupil fill capability for better imaging, but this leads to lower productivity due to limited use of the exposure field.
context_section_description: EUV lithography is particularly sensitive to stochastic effects. In a large population of features printed by EUV, although the overwhelming majority are resolved, some suffer complete failure to print, e.g. missing holes or bridging lines. A known significant contribution to this effect is the dose used to print. This is related to shot noise , to be discussed further below. Due to the stochastic variations in arriving photon numbers, some areas designated to print actually fail to reach the threshold to print, leaving unexposed defect regions. Some areas may be overexposed, leading to excessive resist loss or crosslinking. The probability of stochastic failure increases exponentially as feature size decreases, and for the same feature size, increasing distance between features also significantly increases the probability. Line cuts which are relatively widely spaced are a significant issue. Yield requires detection of stochastic failures down to below 1e-12.
  The tendency to stochastic defects is worse when the image consists of photons from different patterns, such as from a large-area pattern or from defocus over a large pupil fill.
  Multiple failure modes may exist for the same population. For example, besides bridging of trenches, the lines separating the trenches may be broken. This can be attributed to stochastic resist loss, from secondary electrons.
  The coexistence of stochastically underexposed and overexposed defect regions leads to a loss of dose window at a certain post-etch defect level between the low-dose and high-dose patterning cliffs. Hence, the resolution benefit from shorter wavelength is lost.
  The resist underlayer also plays an important role. This could be due to the secondary electrons generated by the underlayer. Secondary electrons may remove over 10 nm of resist from the exposed edge.
  The defect level is on the order of 1K/mm².
  Photon shot noise can be linked to stochastic defects through the presence of dose-dependent blur (modeled as Gaussian).
caption: Stochastic defects arise from dose-dependent blur. Dose-dependent blur aggravates photon shot noise, causing features to fail to print (red) or bridge the gap to the neighboring features (green).
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