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The term “shot effect” (schroteffekt) was coined in 1918 when Walter Schottky studied electrical noise in vacuum tubes. Earlier still, the foundations of shot noise theory go back to Einstein, who in 1905 explained the photoelectric effect as caused by discrete “particles” of light and Brownian motion as caused by discrete particles of matter. When the numbers of particles that affect observable outcomes are large, shot noise effects (variability in number as a fraction of the mean number) become small, and the continuum approximation (energy and matter are continuous) becomes accurate. For most of the history of semiconductor lithography, the continuum approximation has served well. But at small dimensional scales, where the number of discrete particles or events is small, the counting statistics of shot noise can dominate. The 100-year history of shot noise in science and engineering is today playing a role in our understanding of shot noise in lithography.
Due to the high energy of extreme ultraviolet (EUV) photons, stochastic effects become more important at a constant dose when compared with deep ultraviolet exposures. Photoresists are used to transfer information from the aerial image into physical features and play an important role in the transduction of these stochastic effects. Recently, metal-oxide-based nonchemically amplified resists (non-CARs) have attracted a lot of attention. We study how the properties of these non-CARs impact the local critical dimension uniformity (LCDU) of a regular contact hole array printed with EUV lithography using Monte Carlo simulations and an analytical model. We benchmark both the simulations and the analytical model to experimental data, and then use the flexibility of both methods to systematically investigate the role of microscopic resist properties in the final LCDU. It is found that metal-oxide clusters should be <1 nm in diameter, otherwise granularity will have a significant contribution to LCDU. When varying resist properties to change the resist dose-to-size, we find that the LCDU scaling with dose depends on how the resist is modified. After performing an overall sensitivity analysis to identify the optimum scaling of LCDU with dose, we find a scaling of dose − 0.5 when the development threshold is modified, and a scaling of dose − 0.33 when core radius or the quantum efficiency is changed.