Based on vector electromagnetic theory and the Waveguide Model, the vector Hopkins model is deduced. The model contains the vector Hopkins formula and the resist profile model of fast Optical Proximity Correction. The vector Hopkins formula considers incidence angles and azimuth angles of off-axis illumination, which differs from the traditional scalar Hopkins formula. The resist profile model is employed to analyze the effect of the photoresist diffusion under off-axis illumination by using self-adaptive Gaussian filter with scale adjustable, and a new transmission cross coefficient is obtained. The projection system parameters are introduced simultaneously, such as incidence angles, azimuth angles of off-axis illumination and diffusion parameters of photoresist. By simulating the aerial image of 3D mask in the actual lithography process, the optimal angular range of oblique incidence is studied; the image quality by impact with the oblique incidence angle is discussed as well.
2. Pistor, T. V., A. R. Neureuther, and R. J. Socha, "Modeling oblique incidence efffects in phoromasks," Proc. of SPIE on Optical Microlithography XIII, Vol. 4000, 228, Santa Clara, CA, USA, 2000.
3. Born, M. and E. Wolf, Principles of Optics,, Pergamon Press, 1980.
4. Saied, M., F. Foussadier, and J. Belledent, "3D mask modeling with oblique incidence and mask corner rounding effects for the 32nm mode," Proc. of SPIE on Photomask Technology, Vol. 6730, Monterey, CA, USA, 2007.
5. Liu, P., Y. Cao, and L. Chen, "Fast and accurate 3D mask model for full-chip OPC and verification," Proc. of SPIE on Optical Microlithography XX, Vol. 6520, San Jose, CA, USA, 2007.
6. Inui, H. and T. Ohta, "A practical 3D lithography simulation system," SPIE, Vol. 3051, 522-528, 1997.
7. Stratton, J., Electromagnetic Theory, McGraw-Hill Book Company, 1941.
8. Guo, L., Y. Wang, R. Wang, and Z.-S. Wu, "Investigation on the electromagnetic scattering of plane wave/Gaussian beam by adjacent multi-particles," Progress In Electromagnetics Research B, Vol. 14, 219-245, 2009.
9. Giampaolo, Di, E. and F. Bardati, "A projective approach to electromagnetic propagation in complex environments," Progress In Electromagnetics Research B, Vol. 13, 357, 2009.
10. Ayub, M., A. B. Mann, M. Ramzan, and M. H. Tiwana, "Diffraction of plane waves by a slit in an infinite soft-hard plane," Progress In Electromagnetics Research B, Vol. 11, 103-131, 2009.
11. Molinet, F. A., "Plane wave diffraction by a strongly elongated object illuminated in the paraxial diretion," Progress In Electromagnetics Research B, Vol. 6, 135-151, 2008.
12. Yuan, C. M., "Efficient light scattering modeling for alignment, metrology, and resist exposure in photolithography," J. Opt. Soc. Amer., Vol. 8, 778, 1991.
13. Rahim, T., M. J. Mughal, Q. A. Naqvi, and M. Faryad, "Field around the focal region of a paraboloidal reflector placed in isotropic chiral medium," Progress In Electromagnetics Research B, Vol. 15, No. 57, 2009.
14. Yeung, M. S. and D. Lee, "Extension of the Hopkins theory of partially coherent imaging to include thin-film interference effects," Proc. of SPIE on Optical/Laser Microlithography, Vol. 1927, 452-463, San Jose, CA, USA, 1993.
15. McCartin, B. J., L. J. Bahrmasel, and G. Meltz, "Application of the control region approximation to two-dimensional election of the control region approximation to two-dimensional electromagnetic scattering," Progress In Electromagnetics Research, Vol. 02, 175-21, 1990.
16. Yeung, M. S., "Modelling high numerical aperture optical lithography," Proc. SPIE, Vol. 922, 149-167, 1988.
17. Wolf, E., "Electromagnetic diffraction in optical system I. An integral representation of the image field," Proc. Roc. Soc. A, Vol. 253, 349-357, 1959.
18. Hatamzadeh-Varmazyar, S. and M. Naser-Moghadasi, "An integral equation modeling of electromagnetic scattering from the surfaces of arbitrary resistance distribution," Progress In Electromagnetics Research B, Vol. 3, 157-172, 2008.
19. Cornsweet, T. N. and J. I. Yellott, "Intensity dependent spatial summation," Journal of Optical Society of America A, Vol. 2, No. 10, 1769-1786, 1985.
20. Golub, G. H. and C. F. Van Loan, Matrix Computations, JHU Press, 1996.
21. Dhillon, I., "A new O(n2) algorithm for the symmetric tri-diagonal eigenvalue/eigenvector problem,", University of California Report, Berkeley, 1997.
22. Holland, J. H., Adaptation in Nature and Artificial Systems, The University of Michigan Press, 1975.
23. Raymer, M. L. and W. F. Punch, "Dimensionality reduction using genetic algorithms," IEEE Transactions on Evolutionary Computation, Vol. 4, 164-171, 2000.
24. Bruge, S., "Rigorous simulation of 3D masks," Proc. SPIE on 26th Annual BACUS Symposium on Photomask Technology, Vol. 6349, Monterey, CA, USA, 2006.
25. Wang, Y. J., W. J. Koh, and C. K. Lee, "Electromagnetic coupling analysis of transient signal through slots or apertures perforated in a shielding metallic enclosure using FDTD methodology," Progress In Electromagnetics Research, Vol. 36, 247-264, 2002.
26. Bruge, S., "Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation," Proc. SPIE on 25th Annual BACUS Symposium on Photomask Technology, Monterey, Vol. 5992, CA, USA, 2005.