Ivanova T.V., Zhadin A.V. "Simulated annealing" algorithm for light source parametric optimization in photolithography. Scientific and Technical Journal of Information Technologies, Mechanics and Optics
, 2017, vol. 17, no. 2, pp. 242–248 (in Russian). doi: 10.17586/2226-1494-2017-17-2-242-248
Subject of Research. The paper deals with methods of resolution enhancement, as well as stability and repeatability of photolithographic process with the use of complex shape light source. Possibilities of source shapeoptimization to be used with specific patterns or pattern groups are shown. Methods. We applied "Simulated annealing" stochastic algorithm for source optimization for periodic patterns with a various pitch. The periodic patterns contrast with a various pitch (including "forbidden" pitch) was used as a merit function, as well as the area of elliptical process window for photolithographic setup. Research was carried out with the aid of Sentaurus Lithography program (Synopsys Inc). Main Results. Optimization of periodic patterns with 150-300 nm pitch, 193 nmwavelength and optical system numerical aperture equal to 0.93 is shown as an example. The case of optimization algorithmwith focus-expose matrix is considered. It is shown, that proposedsource optimization with the use of the algorithm allows increasing image contrast for various pitches, as well as the area of process windowforphotolithographic setup. The convergence study shows that 100 iterations are enough for the source optimization for 600-800 nm mask pitch and further increasing of iteration number has no impact to the contrast. Practical Relevance.The studied algorithm can be used as a replacement for more complex algorithms of source optimization for reducing the minimum element size and the process stability enhancement. The algorithm has high convergence.
photolithography, complex shape light source, light source optimization, "simulated annealing" algorithm, process window for photolithographic setup References
1. Mack С.A. Fundamental Principles of Optical Lithography: The Science of Microfabrication. Bellingham, USA, Wiley, 2008, 534 p.
2. Levenson M.D., Viswanathan N.S., Simpson R.A. Improving resolution in photolithography with a phase-shifting mask. IEEE Transactions on Electron Devices
, 1982, vol. 29, no. 12, pp. 1828–1836. doi: 10.1109/T-ED.1982.21037
3. De Bisschop P. How to make lithography patterns print: the role of OPC and pattern layout. Advanced Optical Technologies
, 2015, vol. 4, no. 4, pp. 253–284. doi: 10.1515/aot-2015-0023
4. Shi X., Hsu S., Chen F., Hsu M., Socha R.J. Dusa M. Understanding the forbidden pitch phenomenon and assist feature placement. Proceedings of SPIE
, 2002, vol. 4689, pp. 985–996. doi: 10.1117/12.473427
5. Moh L.L., Gek S.C., Qunying L., Cho J.T., Chenggen Q. Customized illumination shapes for 193nm immersion lithography. SPIE Advanced Lithography. Proceedings of SPIE
, 2008, vol. 6924, art. 692435. doi: 10.1117/12.772441
6. Leonard J., Carriere, J., Stack, J., Jones, R., Himel, M., Childers, J., Welch, K. An improved process for manufacturing diffractive optical elements (DOEs) for off-axis illumination systems. Proceedings of SPIE
, 2008, vol. 6924, art. 69242O. doi: 10.1117/12.774666
7. Bekaert J., Van Look L., D’have K., Laenens B., Vandenberghe G., van Adrichem P., Shao W., Ghan J., Schreel K., Neumann J.T. Scanner matching for standard and freeform illumination shapes using FlexRay. Proceedings of SPIE
, 2011, vol. 7973, art. 79731I. doi: 10.1117/12.881607
8. Mulder M., Engelen A., Noordman O., Streutker G., van Drieenhuizen B. et. al. Performance of FlexRay: a fully programmable illumination system for generation of freeform sources on high NA immersion systems. Proceedings of SPIE
, 2010, vol. 7640, art. 845984. doi: 10.1117/12.845984
9. Granik Y. Source optimization for image fidelity and throughput. Journal of Microlithography, Microfabrication and Microsystems
, 2004, vol. 3, no. 4, pp. 509–522. doi: 10.1117/1.1794708
10. Socha R., Shi X., LeHoty D. Simultaneous source mask optimization (SMO). Proceedings of SPIE
, 2005, vol. 5853 part I, pp. 180–193. doi: 10.1117/12.617431
11. Rosenbluth A.E., Melville D.O., Tian K., Bagheri S., Azpiroz J.T. et al. Intensive optimization of masks and sources for 22nm lithography. Proceedings of SPIE
, 2009, vol. 7274, art. 727409. doi: 10.1117/12.814844
12. Bertsimas D., Tsitsiklis J. Simulated annealing. Statistical Science
, 1993, vol. 8, no. 1, pp. 10–15. doi: 10.1214/ss/1177011077
13. Jiang H., Xing T., Du M. Source optimization using simulated annealing algorithm. Proceedings of SPIE
, 2014, vol. 9282, art. 928239. doi: 10.1117/12.2069398
14. Hopkins H.H. On the diffraction theory of optical images. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1953, vol. 217, no. 1130.
15. Ivanova T.V., Zueva L.Yu. Study of methods for discretizing a source when modelling a photolithographic image. Journal of Optical Technology, 2012, vol. 79, no. 5, pp. 295–298.
16. Sentaurus Lithography. Predictive Modeling of Lithographic Processes. Available at: https://www.synopsys.com/silicon/mask-synthesis/sentaurus-lithography.html (accessed: 23.01.2017).
17. Smith B.W. Forbidden pitch or duty-free: revealing the causes of across-pitch imaging differences. Proceedings of SPIE
, 2003, vol. 5040 I, pp. 399–407. doi: 10.1117/12.485490