doi: 10.17586/2226-1494-2015-15-2-196-201


E. A. Nikulina, V. A. Zverev

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Article in Russian

For citation: Nikulina E.A., Zverev V.A. Study of birefringence influence on image quality of photolithography systems in view of partially-coherent light source. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol.15, no. 2, pp. 196–201. (in Russian)

Subject of study. A vector model for conversion of electromagnetic radiation in optical systems is considered, taking into account the influence of birefringence, as well as partially coherent illumination.
Model. The proposed model is based on the representation of the complex amplitude of the monochromatic field through thesuperposition of basic plane waves. Transmitted light image with partially coherent illumination is performed by the sourceintegration method.
Main results. The results of simulation for the point spread function are demonstrating the level of the birefringence influence on the image quality. In the presence of the wave aberration about 0.098 of the wavelength, the wave energy loss in the center of the Airy disk with an average birefringence of 4 nm/cm was 8%, and at 16 nm/cm it reached 30%. The calculation of the point spread function for a real sample of fluorite is given. The central peak of the PSF without birefringence was 0.722, with regard to birefringence it was equal to 0.701.
Practical significance. The findings can be used in the development of photolithographic lenses, as well as for the manufacturing of any other optical systems that require consideration of the polarization properties of the materials. 

Keywords: birefringence, polarization, aberration, point spread function.

1. Kirillovsky V.K., Tuan L.Z. Opticheskie Izmereniya Ch. 6. Innovatsionnye Napravleniya v Opticheskikh Izmereniyakh i Issledovaniyakh Opticheskikh Sistem [Optical Measurements Part 6. Innovative Trends in Optical Measurement and Analysis of Optical Systems]. St. Petersburg, SPbSU ITMO Publ., 2008, 128 p.
2. Unno Y., Suzuki A. Analyses of imaging performance degradation caused by birefringence residual in lens materials. Proceedings of SPIE - The International Society for Optical Engineering, 2001, vol. 4346, no. 2, pp. 1306–1317. doi: 10.1117/12.435667
3. Hlubina P., Ciprian D. Absolute phase birefringence dispersion in polarization-maintaining fiber or birefringent crystal retrieved from a channeled spectrum. Optics Letters, 2010, vol. 35, no. 10, pp. 1566–
1568. doi: 10.1364/OL.35.001566
4. Safrani A., Abdulhalim I. Spectropolarimetric method for optic axis, retardation, and birefringence dispersion measurement. Optical Engineering, 2009, vol. 48, no. 5, art. 053601. doi: 10.1117/1.3126628
5. Bailey G.E., Adam K. Polarization influences through the optical path. Proceedings of SPIE - The International Society for Optical Engineering, 2005, vol. 5754, pp. 1102–1113. doi: 10.1117/12.600660
6. Seisyan R.P. Extreme ultraviolet nanolithography for ULSI: a review. Technical Physics. The Russian Journal of Applied Physics, 2005, vol. 75, no. 5, pp. 535–545. doi: 10.1134/1.1927207
7. Kirillovsky V.K., Gavrilov E.V., Zhevlakov A.P. Primenenie komp'yuternoi izofotometrii pri kontrole ob"ektiva dlya nanolitografa [Application of computer isophotometry for checking of objective for nanolithography]. Izv. vuzov. Priborostroenie, 2011, vol. 54, no. 1, pp. 66–73.
8. Jia Y., Li Y., Liu L., Han C., Liu X. Polarization aberration compensation method by adjusting illumination partial coherent factors in immersion lithography. Proceedings of SPIE - The International Society for Optical Engineering, 2014, vol. 9277, art. 92770Z. doi: 10.1117/12.2087529
9. Kye J., McIntyre G., Yamamoto N., Levinson H.J. Polarization aberration analysis in optical lithography systems. Proceedings of SPIE - The International Society for Optical Engineering, 2006, vol. 6154, art. 61540E. doi: 10.1117/12.656864
10. Kim S.-K. Polarized effects in optical lithography with high NA technology. Journal of the Korean Physical Society, 2007, vol. 50, no. 6, pp. 1952–1958.
11. Li Y., Guo X., Liu X., Liu L. A technique for extracting and analyzing the polarization aberration of hypernumerical aperture image optics. Proceedings of SPIE - The International Society for Optical Engineering, 2013, vol. 9042, art. 904204. doi: 10.1117/12.2038176
12. Domnenko V.M., Bursov M.V., Ivanova T.V. Modelirovanie Formirovaniya Opticheskogo Izobrazheniya [Simulation of Optical Image Formation]. St. Petersburg, NIU ITMO Publ., 2011, 141 p.
13. Landsberg G.S. Optika [Optics]. Moscow, Fizmatlit Publ., 2003, 848 p.
14. Ivanova T.V., Zueva L.V. Study of methods for discretizing a source when modelling a photolithographic image. Journal of Optical Technology (A Translation of Opticheskii Zhurnal), 2012, vol. 79, no. 5, pp. 295–298.
15. Mozharov G.A. Teoriya Aberratsii Opticheskikh System [Theory of Aberrations of Optical Systems]. St. Petersburg, Lan' Publ., 2013, 288 p.

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