Simulation Research on the Thermal Effects in Dipolar Illuminated Lithography

Yao, Changcheng;Gong, Yan

  • Received : 2016.01.11
  • Accepted : 2016.03.18
  • Published : 2016.04.25


The prediction of thermal effects in lithography projection objective plays a significant role in the real-time dynamic compensation of thermal aberrations. For the illuminated lithography projection objective, this paper applies finite element analysis to get the temperature distribution, surface deformation and stress data. To improve the efficiency, a temperature distribution function model is proposed to use for the simulation of thermal aberrations with the help of optical analysis software CODE V. SigFit is approved integrated optomechanical analysis software with the feature of calculating OPD effects due to temperature change, and it is utilized to prove the validation of the temperature distribution function. Results show that the impact of surface deformation and stress is negligible compared with the refractive index change; astigmatisms and 4-foil aberrations dominate in the thermal aberration, about 1.7 λ and 0.45 λ. The system takes about one hour to reach thermal equilibrium and the contrast of the imaging of dense lines get worse as time goes on.


Thermal aberrations;Lithography;Integrated optomechanical analysis


  1. C. Liu, W. Huang, Z. Shi, and W. Xu, “Wavefront aberration compensation of projection lens using clocking lens elements,” Appl. Opt. 52, 5398-5401 (2013).
  2. M. Y. Ni and Y. Gong, “Design and analysis of kinematic lens positioning structure in lithographic projection objective,” Chinese Optics 5, 476-484 (2012).
  3. Y. Uehara, T. Matsuyama, T. Nakashima, Y. Ohmura, T. Ogata, and K. Suzuki, “Thermal aberration control for low-k1 lithography,” Proc. SPIE 6520, 65202V-1~65202V-11 (2007).
  4. L. Zhao and Y. Gong, “Design and analysis for high-precision lens support structure of objective lens for lithography,” Acta Optica Sinica 9, 217-222 (2012).
  5. T. Nakashima, Y. Ohmura, T. Ogata, Y. Uehara, H. Nishinaga, and T. Matsuyama, “Thermal aberration control in projection lens,” Proc. SPIE 6924, 69241V-1~69241V-9 (2008).
  6. X. F. Yu, M. Y. Ni, W. Zhang, Y. X. Sui, and S. Qin, “Analysis and experiments of the thermal-optical performance for a kinematically mounted lens element,” Appl. Opt. 53, 4079-4084 (2014).
  7. H. Chen, H. J. Yang, X. F. Yu, and Z. G. Shi, “Simulated and experimental study of laser-beam-induced thermal aberrations in precision optical systems,” Appl. Opt. 52, 4370-4376 (2013).
  8. K. Fukuhara, A. Mimotogi, T. Kono, H. Aoyama, T. Ogata, and N. Kita, “Solutions with precise prediction for thermal aberration error in low-k1 immersion lithography,” Proc. SPIE 8683, 86830U-1~86830U-7 (2013).
  9. W. L. Shang, J. M. Yang, Y. Zhao, T. Zhu, and G. Xiong, “General model of transmission grating diffraction efficiency,” Acta Physica Sinica 60, 392-397 (2011).
  10. S. Qin, Y. Gong, W. Q. Yuan, and H. J. Yang, “High precision temperature control for projection lens with long time thermal response constant,” Optics and Precision Engineering 21, 108-114 (2013).
  11. Y. P. Shen, “A dissertation submitted in partial fulfillment of the requirements for the degree of doctor of philosophy in engineering (in Chinese),” Huazhong University of Science and Technology, 39 (2014).
  12. HPFS Fused Silica Standard Grade Semiconductor Optics, Corning Inc..
  13. SigFit Reference Manual, Version 2012R1d, Sigmadyne Inc., p. 127.
  14. K. B. Doyle, V. L Genberg, and G. J. Michels, “Numerical methods to compute optical errors due to stress birefringence,” Proc. SPIE 34, 34-42 (2002).

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