12 June 2017 Lithographic stochastics: beyond 3σ
Author Affiliations +
J. of Micro/Nanolithography, MEMS, and MOEMS, 16(2), 023505 (2017). doi:10.1117/1.JMM.16.2.023505
As lithography tools continue their progress in both numerical aperture and wavelength in pursuit of Moore’s law, we have reached the point where the number of features printed in a single pass can now easily surpass one trillion. Statistically, one should not be surprised to see some members of such a population exhibit fluctuations as great as 7σ. But what do these fluctuations look like? We consider the problem in terms of variations in the effective local resist sensitivity caused by feature-to-feature differences in absorbed photons and resist component counts, modeling these as a normal distribution. As the CD versus dose curve is generally nonlinear over large ranges, the normal distribution of the local effective sensitivity then maps to a nonnormal distribution in CD. For the case of individual vias printed near the resolution limit, it results in many more undersized or completely closed vias than one would expect from a normal distribution of the CDs. We show examples of this behavior from both EUV exposures in the fab and ebeam exposures in the lab.
© 2017 Society of Photo-Optical Instrumentation Engineers (SPIE)
Robert L. Bristol, Marie E. Krysak, "Lithographic stochastics: beyond 3σ," Journal of Micro/Nanolithography, MEMS, and MOEMS 16(2), 023505 (12 June 2017). https://doi.org/10.1117/1.JMM.16.2.023505 Submission: Received 24 March 2017; Accepted 25 May 2017
Submission: Received 24 March 2017; Accepted 25 May 2017

Critical dimension metrology

Statistical analysis


Stochastic processes



Extreme ultraviolet


Back to Top