OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 5 — May. 1, 2012
  • pp: 748–756

Integral equation analysis and optimization of 2D layered nanolithography masks by complex images Green’s function technique in TM polarization

Mohammad Haghtalab and Reza Faraji-Dana  »View Author Affiliations

JOSA A, Vol. 29, Issue 5, pp. 748-756 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (575 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Analysis and optimization of diffraction effects in nanolithography through multilayered media with a fast and accurate field-theoretical approach is presented. The scattered field through an arbitrary two-dimensional (2D) mask pattern in multilayered media illuminated by a TM-polarized incident wave is determined by using an electric field integral equation formulation. In this formulation the electric field is represented in terms of complex images Green’s functions. The method of moments is then employed to solve the resulting integral equation. In this way an accurate and computationally efficient approximate method is achieved. The accuracy of the proposed method is vindicated through comparison with direct numerical integration results. Moreover, the comparison is made between the results obtained by the proposed method and those obtained by the full-wave finite-element method. The ray tracing method is combined with the proposed method to describe the imaging process in the lithography. The simulated annealing algorithm is then employed to solve the inverse problem, i.e., to design an optimized mask pattern to improve the resolution. Two binary mask patterns under normal incident coherent illumination are designed by this method, where it is shown that the subresolution features improve the critical dimension significantly.

© 2012 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(100.3190) Image processing : Inverse problems
(110.5220) Imaging systems : Photolithography
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(110.4235) Imaging systems : Nanolithography
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

Original Manuscript: November 28, 2011
Revised Manuscript: January 23, 2012
Manuscript Accepted: February 8, 2012
Published: April 19, 2012

Mohammad Haghtalab and Reza Faraji-Dana, "Integral equation analysis and optimization of 2D layered nanolithography masks by complex images Green’s function technique in TM polarization," J. Opt. Soc. Am. A 29, 748-756 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Shao and S. Chen, “Surface plasmon assisted contact scheme nanoscale photolithography using an UV lamp,” J. Vac. Sci. Technol. B 26, 227–231 (2008). [CrossRef]
  2. A. Poonawala and P. Milanfar, “Mask design for optical microlithography—an inverse imaging problem,” IEEE Trans. Image Process. 16, 774–788 (2007). [CrossRef]
  3. M. D. Levenson, N. S. Viswanathan, and R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1828–1836 (1982). [CrossRef]
  4. R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927–929 (2007). [CrossRef]
  5. A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Trans. Antennas Propag. 56, 3159–3165 (2008). [CrossRef]
  6. A. Grbic, R. Merlin, E. M. Thomas, and M. F. Imani, “Near-field plates: metamaterial surfaces/arrays for subwavelength focusing and probing,” Proc. IEEE 99, 1806–1815 (2011). [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  8. J. T. Azpiroz, P. Burchard, and E. Yablonovitch, “Boundary layer model to account for thick mask effects in photolithography,” Proc. SPIE 5040, 1611–1619 (2003). [CrossRef]
  9. K. Adam and A. R. Neureuther, “Domain decomposition methods for the rapid electromagnetic simulation of photomask scattering,” J. Microlith. Microfab. Microsys. 1, 253 (2002). [CrossRef]
  10. F. Schellenberg, K. Adam, L. Sun, J. Matteo, and L. Hesselink, “Polarization effects in plasmonic masks,” Microelectron. Eng. 83, 919–922 (2006). [CrossRef]
  11. M. S. Yeung, “Three-dimensional mask transmission simulation using a single integral equation method,” Proc. SPIE 3334, 704–713 (1998). [CrossRef]
  12. Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microwave Theor. Tech. 39, 588–592 (1991). [CrossRef]
  13. J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microwave Theor. Tech. 40, 595–600 (1992). [CrossRef]
  14. M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antennas Propag. 53, 3644–3653 (2005). [CrossRef]
  15. H. Alaeian and R. Faraji-Dana, “A fast and accurate analysis of 2-D periodic devices using complex images Green’s functions,” J. Lightwave Technol. 27, 2216–2223 (2009). [CrossRef]
  16. Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas Propag. 37, 229–234 (1989). [CrossRef]
  17. A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microwave Theor. Tech. 58, 602–613 (2010). [CrossRef]
  18. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).
  19. T. V. Pistor, “Electromagnetic simulation and modeling with applications in lithography.” Ph.D. thesis (University of California at Berkeley, 2001).
  20. A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the ’simulated annealing’ algorithm,” ACM Trans. Math. Softw. 13, 262–280 (1987). [CrossRef]
  21. E. D. Palik, ed., Handbook of Optical Constants of Solids 11 (Academic, 1991), pp. 374–385.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited