page_title: Extreme ultraviolet lithography
section_title: Shot noise: the statistical resolution limit
hierarchical_section_title: Extreme ultraviolet lithography / Throughput-scaling limits / Shot noise: the statistical resolution limit
caption_attribution_description: English: The isolated or semi-isolated via CD is highly sensitive to reductions of dose such as from shot noise. A 10% dose reduction leads to greater than 10% reduction of CD. In the extreme case, the via fails to print. Ref.: R. L. Bristol and M. E. Krysak, Proc. SPIE vol. 10143, 101430Z (2017).
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: With the natural Poisson distribution due to the random arrival and absorption times of the photons, there is an expected natural dose (photon number) variation of at least several percent 3 sigma, making the exposure process susceptible to stochastic variations. The dose variation leads to a variation of the feature edge position, effectively becoming a blur component. Unlike the hard resolution limit imposed by diffraction, shot noise imposes a softer limit, with the main guideline being the ITRS line width roughness (LWR) spec of 8% (3s) of linewidth. Increasing the dose will reduce the shot noise, but this also requires higher source power.
  A 10 nm wide, 10 nm long assist feature region, at a target non-printing dose of 15 mJ/cm², with 10% absorption, is defined by just over 100 photons, which leads to a 6s noise of 59%, corresponding to a stochastic dose range of 6 to 24 mJ/cm², which could affect the printability.
  A 2017 study by Intel showed that for semi-isolated vias (whose Airy disk can be approximated by a Gaussian), the sensitivity of CD to dose was particularly strong, strong enough that a reduction of dose could nonlinearly lead to failure to print the via.
  Minimum dose to restrain shot noise for process variation tolerance areas:
  + A process variation tolerance area is the largest region over which process variation is allowed.
  The two issues of shot noise and EUV-released electrons point out two constraining factors: 1) keeping dose high enough to reduce shot noise to tolerable levels, but also 2) avoiding too high a dose due to the increased contribution of EUV-released photoelectrons and secondary electrons to the resist exposure process, increasing the edge blur and thereby limiting the resolution. Aside from the resolution impact, higher dose also increases outgassing and limits throughput, and crosslinking occurs at very high dose levels. For chemically amplified resists, higher dose exposure also increases line edge roughness due to acid generator decomposition.
  As mentioned earlier, a more absorbing resist actually leads to less vertical dose uniformity. This also means shot noise is worse toward the bottom of a highly absorbing EUV resist layer.
  Even with higher absorption, EUV has a larger shot noise concern than the ArF (193 nm) wavelength, mainly because it is applied to smaller dimensions and current dose targets are lower due to currently available source power levels.
  As can be seen above, at the target incident dose levels, significantly fewer EUV photons are absorbed in EUV resists compared to ArF photons in ArF resists. Despite greater transparency of the resist, the incident photon flux is about 14 times larger (193/13.5) for the same energy dose per unit area. The resist thickness is limited by transparency as well as resist collapse and resist strip considerations.
caption: Via printing failure from noise-induced dose reduction. Shot noise-induced dose reduction could in extreme cases lead to via printing failure (CD->0).
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