Recent studies [1-3] have increased awareness of stochastic effects in EUV lithography. These effects have in fact been brought up years earlier [4-6] as the manifestation of shot noise. The general idea is that photons used in lithography arrive randomly from the source, within the printed area. As the area shrinks, there are fewer photons for the same dose. This leads to a necessary trend of increasing dose to compensate. This will be clarified below.

From the Poisson statistics, the natural variation in the photon number is measured by the standard deviation in the photon number, which is the square root of the average photon number. Since chips these days contain many billions of features, we easily need +/- 6 standard deviations of coverage; this already leaves out ~2 parts per billion of the feature population; Intel in fact is even stricter, going for 7 standard deviations [3]. In any case, the natural feature dose variation over the whole chip exceeds 6*sqrt(N)/N = 6/sqrt(N), where N is the average photon number in the printing area for the given dose. For example, if the number of absorbed EUV photons is 1800, 6 standard deviations corresponds to 14%. If the photon number is fixed, the incident dose is inversely proportional to the reference exposed area.

The trend is clear:

1. P. de Bisschop, J. Van de Kerkhove, J. Mailfert, A. Vaglio Pret, J. Biafore, “Impact of Stochastic effects on EUV printability limits,” Proc. of SPIE vol. 9048, 904809 (2014).

2. S. Hsu, R. Howell, J. Jia, H-Y. Liu, K. Gronlund, S. Hansen, J. Zimmermann, “EUV Resolution Enhancement Techniques (RETs) for k1 0.4 and below,” Proc. of SPIE vol, 9422, 94221I (2015).

3. A. Lio, “EUV Resists: What’s Next?,” Proc. of SPIE vol. 9776, 97760V (2015).

4. Z-Y. Pan, C-K. Chen, T-S. Gau, and B. J. Lin, “Influence of Shot Noise on CDU with DUV, EUV and E-Beam,” Proc. of SPIE vol. 6924, 69241K (2008).

5. S. H. Lee, R. Bristol, and J. Bjorkholm, “Shot noise and process window study for printing small contact holes using EUV Lithography,” Proc. of SPIE vol. 5013, 890-899 (2003).

6. F. T. Chen, W-S. Chen, M-J. Tsai, and T-K. Ku, “Complementary polarity exposures for cost-effective line-cutting in multiple patterning lithography,” Proc. of SPIE vol. 8326, 82362L (2012).

7. A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J-W. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. of SPIE vol. 9776, 97760A (2015).

8. N. Felix, D. Corliss, K. Petrillo, N. Saulnier, Y. Xu, L. Meli, H. Tang, A. De Silva, B. Hamieh, M. Burkhardt, Y. Mignot, R. Johnson, C. Robinson, M. Breton, I. Seshadri, D. Dunn, S. Sieg, E. Miller, G. Beique, A. Labonte, L. Sun, G. Han, E. Verduijn, E. Han, B. C. Kim, J. Kim, K. Hontake, L. Huli, C. Lemley, D. Hetzer, S. Kawakami, and K. Matsunaga, “EUV Patterning Successes and Frontiers,” Proc. of SPIE vol. 9776, 97761O (2015).

From the Poisson statistics, the natural variation in the photon number is measured by the standard deviation in the photon number, which is the square root of the average photon number. Since chips these days contain many billions of features, we easily need +/- 6 standard deviations of coverage; this already leaves out ~2 parts per billion of the feature population; Intel in fact is even stricter, going for 7 standard deviations [3]. In any case, the natural feature dose variation over the whole chip exceeds 6*sqrt(N)/N = 6/sqrt(N), where N is the average photon number in the printing area for the given dose. For example, if the number of absorbed EUV photons is 1800, 6 standard deviations corresponds to 14%. If the photon number is fixed, the incident dose is inversely proportional to the reference exposed area.

The trend is clear:

__each successive 0.7x scaled node is expected to require double the minimum EUV dose__[6]. A higher dose requires proportionally higher power or else slower scan, i.e., lower throughput. Clearly, EUV source power and resists and pellicles sufficient to enable/tolerate these increasing doses at satisfactory throughput are the primary issues.**Note**: Only a fraction of the incident photons are absorbed. For example, for 20 nm thick resist with absorption of 20/um, e.g., Inpria resist, about a third of the dose is absorbed. While a larger fraction of EUV photons are absorbed by resists compared to DUV, this is offset by the much smaller exposed areas targeted by EUV.**Update:**I have updated the discussion of this issue at this site: The Stochastic Behavior of Optical Images and their Impact on Resolution An example figure from that article is posted below.**References:**

1. P. de Bisschop, J. Van de Kerkhove, J. Mailfert, A. Vaglio Pret, J. Biafore, “Impact of Stochastic effects on EUV printability limits,” Proc. of SPIE vol. 9048, 904809 (2014).

2. S. Hsu, R. Howell, J. Jia, H-Y. Liu, K. Gronlund, S. Hansen, J. Zimmermann, “EUV Resolution Enhancement Techniques (RETs) for k1 0.4 and below,” Proc. of SPIE vol, 9422, 94221I (2015).

3. A. Lio, “EUV Resists: What’s Next?,” Proc. of SPIE vol. 9776, 97760V (2015).

4. Z-Y. Pan, C-K. Chen, T-S. Gau, and B. J. Lin, “Influence of Shot Noise on CDU with DUV, EUV and E-Beam,” Proc. of SPIE vol. 6924, 69241K (2008).

5. S. H. Lee, R. Bristol, and J. Bjorkholm, “Shot noise and process window study for printing small contact holes using EUV Lithography,” Proc. of SPIE vol. 5013, 890-899 (2003).

6. F. T. Chen, W-S. Chen, M-J. Tsai, and T-K. Ku, “Complementary polarity exposures for cost-effective line-cutting in multiple patterning lithography,” Proc. of SPIE vol. 8326, 82362L (2012).

7. A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J-W. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. of SPIE vol. 9776, 97760A (2015).

8. N. Felix, D. Corliss, K. Petrillo, N. Saulnier, Y. Xu, L. Meli, H. Tang, A. De Silva, B. Hamieh, M. Burkhardt, Y. Mignot, R. Johnson, C. Robinson, M. Breton, I. Seshadri, D. Dunn, S. Sieg, E. Miller, G. Beique, A. Labonte, L. Sun, G. Han, E. Verduijn, E. Han, B. C. Kim, J. Kim, K. Hontake, L. Huli, C. Lemley, D. Hetzer, S. Kawakami, and K. Matsunaga, “EUV Patterning Successes and Frontiers,” Proc. of SPIE vol. 9776, 97761O (2015).

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