Rigorous Three-Dimensional Time-Domain Finite-Difference Electromagnetic Simulation for Photolithographic Applications

IEEE Transactions on Semiconductor Manufacturing

Volumn 8, Issue 4, 1995, Pages 419-431

  Wong, Alfred K ^a   Neureuther, Andrew R ^b  

^a IMEC   (Belgium)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABERRATIONS; BOUNDARY CONDITIONS; COMPUTER SIMULATION; ELECTROMAGNETIC FIELDS; ELECTROMAGNETIC WAVE DIFFRACTION; ELECTROMAGNETIC WAVE POLARIZATION; ELECTROMAGNETIC WAVE SCATTERING; FINITE DIFFERENCE METHOD; OPTICAL SYSTEMS; PARALLEL PROCESSING SYSTEMS; TIME DOMAIN ANALYSIS;

CONTACT HOLES; PARALLEL IMPLEMENTATION; PROJECTION PRINTING; REFLECTIVE NOTCHING; SIMULATION TIME; SOFTWARE PACKAGE TEMPEST; STEADY-STATE;

PHOTOLITHOGRAPHY;

EID: 0029403880     PISSN: 08946507     EISSN: 15582345     Source Type: Journal    
DOI: 10.1109/66.475184     Document Type: Article

References (50)

1. E. Barouch, B. Bradie, G. Karniadakis, and S. Orszag, “Comprehensive 3D simulator with nonplanar substrates,” in Proc. SPIE, Optical/Laser Microlithography II I, 1990, 334-342.
2. N. Bobroff and A. Rosenbluth, “Alignment errors from resist coating topography,” J. Vac. Sci. Technol., B, vol. 6, no. 1, pp. 403-408, Jan./Feb. 1988.
3. M. Born and E. Wolf, Principles of Optics. New York: Pergamon, 1989, pp. 526-532.
4. F. H. Dill, A. R. Neureuther, J. A. Tuttle, and E. J. Walker, “Modeling projection printing of positive photoresist,” IEEE Trans. Electron Devices, vol. ED-22, no. 7, pp. 456-464, July 1975.
5. T. Doi, K. Tadros, B. Kuyel, and A. R. Neureuther, “Edge-profile, materials and protective coating effects on image quality,” in Proc. SPIE, Integrated Circuit Metrology, Inspection, and Process Control V, 1991, pp. 336-345.
6. B. Engquist and A. Majda, “Radiation boundary conditions for acoustic and elastic wave calculations,” Commun. Pure Appl. Math., vol. 32, pp. 313-357, 1979.
7. G. M. Gallatin, J. C. Wedster, E. C. Kintner, and F. Wu, “Modeling the images of alignment marks under photoresist,” in Proc. SPIE, Optical Microlithography VI, 1987, 193-201.
8. J. Gamelin, “Simulation of topography scattering for optical lithography with the connection machine,” M.S. thesis, University of California, Memorandum no. UCB/ERL 1989.
9. R. Guerrieri, K. H. Tadros, J. Gamelin, and A. Neureuther, “Massively parallel algorithms for scattering in optical lithography,” IEEE Trans. Computer-Aided Design, vol. 10, no. 9, pp. 1091-1100, Sept. 1991.
10. S. G. Hansen, OCG R&D, East Providence, personal communication.
11. W. Henke, D. Mewes, M. Weiss, G. Czech, and R. Schiessl-Hoyler, “Simulation of defects in 3-dimensional resist profiles in optical lithography,” Microelectronic Eng., vol. 13, pp. 497-501, 1991.
12. D. Kershaw, “The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations,” J. Comp. Phys., vol. 26, pp. 43-65, 1978.
13. C. P. Kirk, “Theoretical models for the optical alignment of wafer steppers,” in Proc. SPIE, Optical Microlithography VI, 1987, pp. 134-141.
14. Z. Krivokapic, personal discussions, Feb. 1994.
15. M. E. Law and R. W. Dutton, “Verification of analytic point defect models using SUPREM-IV,” IEEE Trans. Computer-Aided Design, vol. CAD-7, pp. 181-190, Feb. 1988.
16. K. Lucas, A. Strojwas, K. K. Low, and C. Yuan, “Intensity optimization for phase shifting masks,” in Proc. SPIE Optical/Laser Microlithography VI, 1993, pp. 438-449.
17. R. J. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma,” IEEE Trans. Antenn. Propagat., vol. 39, no. 1, pp. 29-34, Jan. 1991.
18. T. Matsuzawa, A. Moniwa, Norio Hasegawa, and H. Sunami, “Two-dimensional simulation of photolithography on reflective stepped substrate,” IEEE Trans. Computer-Aided Design, vol. CAD-6, no. 3, pp. 446-451, May 1987.
19. K. K. Mei, A. Cangellaris, and D. J. Angelakos, “Conformal time domain finite difference method,” Radio Science, vol. 19, no. 5, pp. 1145-1147, Sept./Oct. 1984.
20. L. W. Nagel, “SPICE2—A computer program to simulate semiconductor circuits,” M.S. thesis, University of California, Berkeley, Memorandum no. ERL-M520, May 1975.
21. K. Nguyen, T. Nguyen, A. Wong, A. Neureuther, and D. Attwood, “Areal images of EUV projection lithography masks with defects in reflective coatings: Electromagnetic simulation,” in OSA Proc. Soft X-Ray Projection Lithography, 1993, pp. 47-53.
22. D. Nyyssonen, “Theory of optical edge detection and imaging of thick layers,” J. Opt. Soc. Am., vol. 72, no. 10, pp. 1425-1436, Oct. 1982.
23. D. Nyyssonen and C. P. Kirk, “Optical microscope imaging of lines patterned in thick layers with variable edge geometry: Theory,” J. Opt. Soc. Am., A, vol. 5, no. 8, pp. 1270-1280, Aug. 1988.
24. W. G. Oldham, S. N. Nandgaonkar, A. R. Neureuther, and M. M. O Toole, “A general simulator for VLSI lithography and etching processes: Part I—Application to projection lithography,” IEEE Trans. Electron Devices, vol. ED-26, no. 4, pp. 717-722, Apr. 1979.
25. E. D. Palik, Ed., Handbook of Optical Constants of Solids II. New York: Academic, 1991, pp. 374-385.
26. C. Pierrat, A. Wong, and S. Vaidya, “Phase-shifting mask topography effects on lithographic image quality,” in IEDM Tech. Digest, 1992, pp. 53-56.
27. M. R. Pinto, C. S. Rafferty, and R. W. Dutton, “PISCES-II—Poisson and continuity equation solver,” Stanford University, Stanford Electronics Laboratory Tech. Rep., Sept. 1984.
28. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, A, vol. 79, pp. 399-416, 1907.
29. Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput., vol. 7, no. 3, pp. 856-869, July 1986.
30. S. Selberherr, A. Schütz, and H. W. Pvtzl, “MINIMOS—A two-dimensional MOS transistor analyzer,” IEEE Trans. Electron Devices, vol. ED-27, pp. 1540-1550, 1980.
31. R. Socha, A. Wong, M. Cagan, Z. Krivokapic, and A. Neureuther, “Effects of wafer topography on the formation of polysilicon gates,” in Proc. SPIE, Optical/Laser Microlithography VIII, 1995.
32. K. Tadros, A. R. Neureuther, and R. Guerrieri, “Understanding metrology of polysilicon gates through reflectance measurements and simulation,” in Proc. SPIE, Integrated Circuit Metrology, Inspection and Process Control V, 1991, pp. 177-186.
33. A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time dependent Maxwell's equations,” IEEE Trans. Microwave Theory Technol., vol. MTT-23, pp. 623-630, Aug. 1975.
34. DEPICT-2. Palo Alto, CA: Technology Modeling Associates, 1990.
35. K. Toh, “Two-dimensional images with effects of lens aberrations in optical lithography,” M.S. thesis, Memorandum No. UCB/ERL M88/30, of 1988.
36. H. P. Urbach and D. A. Bernard, “Modeling latent image formation in photolithography using the Helmholtz equation,” in Proc. SPIE, Optical/Laser Microlithography III, 1990, pp. 278-293.
37. A. J. Warnecke and P. J. Lopresti, “Refractive index dispersion in semiconductor-related thin films,” IBM J. Res. Develop., pp. 256-262, May 1973.
38. G. Wojcik, D. Vaughn, and L. Galbriath, “Calculation of light scatter from structures on silicon surfaces,” in Proc. SPIE, Optical/Laser Microlithography, 1987, pp. 21-31.
39. G. L. Wojcik, D. K. Vaughan, J. Mould, F. Leon, Q.-D. Qian, and M. A. Lutz, “Laser alignment modeling using rigorous numerical simulations,” in Proc. SPIE, Optical/Laser Microlithography IV, 1991, pp. 292-303.
40. G. L. Wojcik, J. Mould, R. J. Monteverde, J. J. Prochazka, and J. R. Frank, “Numerical simulation of thick line width measurements by reflected light,” in Proc. SPIE, Integrated Circuit Metrology, Inspection, and Process Control V, 1991, pp. 187-203.
41. G. Wojcik, J. Mould, R. Ferguson, R. Martino, and K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Proc. SPIE, Optical/Laser Microlithography VII, 1994, pp. 455-465.
42. A. Wong, T. Doi, D. Dunn, and A. R. Neureuther, “Experimental and simulation studies of alignment marks,” in Proc. SPIE, Optical/Laser Microlithography IV, 1991, pp. 315-323.
43. A. K. Wong and A. Neureuther, “Polarization effects in mask transmission,” in Proc. SPIE, Optical/Laser Microlithography V, 1992, pp. 315-323.
44. A. K. Wong, “Two-dimensional electromagnetic simulation of topography scattering and diffraction for optical lithography,” M.S. thesis, University of California, Berkeley, Memorandum no. UCB/ERL M92/115, Oct. 1992.
45. A. K. Wong, R. Guerrieri, and A. R. Neureuther, “Massively parallel electromagnetic simulation for photolithographic applications,” IEEE Trans. Computer-Aided Design, to be published.
46. A. K. Wong and A. R. Neureuther, “A novel numerical boundary condition for time-domain electromagnetic simulation,” IEEE Trans. Antenn. Propagat., to be published.
47. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propagat., vol. 14, pp. 302-307, May 1966.
48. M. Yeung, SCOE Review Presentation, University of California, Berkeley, May 1994.
49. C.-M. Yuan, “Calculation of one-dimensional lithographic aerial images using the vector theory,” IEEE Trans. Electron Devices, vol. 40, no. 9, pp. 1604-1613, Sept. 1993.
50. S. S. Zivanovic, K. S. Yee, and K. K. Mei, “A subgridding method for the time-domain finite-difference method to solve Maxwell's equations,” IEEE Trans. Microwave Theory Technol., vol. 39, no. 3, pp. 471-479, Mar. 1991.