Images of strips on and trenches in substrates
Applied Optics, Vol. 46, Issue 23, pp. 5571-5587 (2007)
http://dx.doi.org/10.1364/AO.46.005571
Enhanced HTML Acrobat PDF (1493 KB)
Abstract
The computation of images of lines or strips on a substrate and trenches in a substrate or a layer above a substrate, all made of dielectric or conducting materials, is presented. The method is based on integral equations, of the single-integral-equation kind, equivalent to Maxwell's equations and on Fourier optics. Examples of computed images illustrating some of the features found in the images are provided. Approximations involved in the model of the actual scatterer and microscope as well as in the theoretical and numerical representations are discussed.
© 2007 Optical Society of America
OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(110.0180) Imaging systems : Microscopy
(110.3960) Imaging systems : Microlithography
(290.3700) Scattering : Linewidth
ToC Category:
Scattering
History
Original Manuscript: August 11, 2006
Revised Manuscript: January 11, 2007
Manuscript Accepted: March 23, 2007
Published: August 7, 2007
Citation
Egon Marx, "Images of strips on and trenches in substrates," Appl. Opt. 46, 5571-5587 (2007)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-23-5571
Sort: Year | Journal | Reset
References
- R. M. Silver, R. Attota, M. Stocker, M. Bishop, J. Jun, E. Marx, M. Davidson, and R. Larrabee, "High-resolution optical overlay metrology," in Metrology, Inspection, and Process Control for Microlithography XVIII, Proc. SPIE 5375, 78-95 (2004). [CrossRef]
- R. Attota, R. M. Silver, M. Bishop, E. Marx, J. Jun, M. Stocker, M. Davidson, and R. Larrabee, "Evaluation of new in-chip and arrayed line overlay target designs," in Metrology, Inspection, and Process Control for Microlithography XVIII, Proc. SPIE 5375, 395-402 (2004). [CrossRef]
- D. Nyyssonen, "Theory of optical edge detection and imaging of thick layers," J. Opt. Soc. Am. 72, 1425-1436 (1982).
- 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 5, 1270-1280 (1988).
- M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).
- M. Davidson, "Developments in optical modeling methods for metrology," in Metrology, Inspection, and Process Control XIII, Proc. SPIE 3677, 866-875 (1999). [CrossRef]
- J. T. Sheridan and C. J. R. Shepard, "Coherent imaging of periodic thick fine isolated structures," J. Opt. Soc. Am. A 10, 614-632 (1993).
- J. F. Aguilar and E. R. Méndez, "Imaging optically thick objects in scanning microscopy: perfectly conducting surfaces," J. Opt. Soc. Am. A 11, 155-167 (1994).
- J. F. Aguilar, E. R. Méndez, and A. A. Maradudin, "Imaging thick objects in optical scanning microscopy: penetrable surfaces and patterned-layer structures," J. Opt. Technol. 69, 422-427 (2002).
- D. Maystre, "Integral equations," in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer, 1980).
- E. Marx, "Fields scattered by a dielectric strip on a dielectric half-space," in 1987 Digest of the IEEE Antennas and Propagation Society International Symposium (IEEE, 1987), pp. 1138-1141.
- E. Marx, "Scattering by an arbitrary cylinder at a plane interface: broadside incidence," IEEE Trans. Antennas Propag. 37, 619-628 (1989). [CrossRef]
- E. Marx, "Scattering by an arbitrary cylinder at a plane interface," in Radar Cross Sections of Complex Objects, W. R. Stone, ed. (IEEE, 1990), pp. 356-370.
- E. Marx, "Integral equation for scattering by a dielectric," IEEE Trans. Antennas Propag. 32, 166-172 (1984). [CrossRef]
- A. W. Glisson, "An integral equation for electromagnetic scattering from homogeneous dielectric bodies," IEEE Trans. Antennas Propag. 32, 173-175 (1984). [CrossRef]
- E. Marx, "Extinction coefficients for dielectric and conducting doublets of spheres," in1998 Digest of the IEEE Antennas and Propagation Society International Symposium (IEEE, 1998), pp. 2198-2201.
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
- R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961).
- R. F. Harrington, Field Computations by Moment Methods (Krieger, 1982).
- C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer, 1969), p. 260.
- A. J. Poggio and E. K. Miller, "Integral equation solutions of three-dimensional problems," in Computer Techniques for Electromagnetics, R. Mittra, ed. (Pergamon, 1973).
- A. Mendoza-Suárez and E. R. Méndez, "Light scattering by a re-entrant fractal surface," Appl. Opt. 36, 3521-3531 (1997).
- D. R. Swatek and I. R. Ciric, "A recursive single-source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies," IEEE Trans. Antennas Propag. 48, 1175-1185 (2000). [CrossRef]
- R. E. Kleinman and P. A. Martin, "On single integral equations for the transmission problem of acoustics," SIAM J. Appl. Math. 48, 307-325 (1988). [CrossRef]
- J. Meixner, "The behavior of electromagnetic fields at edges," IEEE Trans. Antennas Propag. 20, 442-446 (1972). [CrossRef]
- E. Marx, "Scattering of an arbitrary plane wave by a dielectric wedge: Integral equations and fields near the edge," Radio Sci. (in press).
- E. Marx, "Electromagnetic scattering from a dielectric wedge and the single hypersingular integral equation," IEEE Trans. Antennas Propag. 41, 1001-1008 (1993). [CrossRef]
- E. Marx and J. Potzick, "Simulation of optical microscope images for photomask feature size measurements," in 2005 Digest of the IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), pp. 2116-2119.
- P. J. Evennett, "Köhler illumination centenary: a collection of papers detailing Köhler illumination" (Royal Microscopical Society, 1994), pp. 1-30.
- T. A. Germer and E. Marx, "Simulations of optical microscope images of line gratings," in Metrology, Inspection, and Process Control for Microlithography XX, Proc. SPIE 6152, 61520I (2006).
- E. Marx, "Scattering by a finite grating on a substrate," in PIERS 2006: Progress in Electromagnetics Research Symposium Proceedings, 66-70 (Electromagnetics Academy, 2006), pp. 66-70.
- R. Attota, R. M. Silver, T. A. Germer, M. Bishop, R. Larrabee, M. T. Stocker, and L. Howard, "Application of through-focus focus-metric analysis in high resolution optical metrology," in Metrology, Inspection, and Process Control for Microlithography XIX, Proc. SPIE 5752, 1441-1449 (2005). [CrossRef]
- G. L. Wojcik, J. Mould, Jr., E. Marx, and M. P. Davidson, "Standard reference models for optical metrology simulation," in IC Metrology, Inspection, and Process Control VI, Proc. SPIE 1673, 70-82 (1992). [CrossRef]
- R. Silver, R. Attota, M. Stocker, J. Jun, E. Marx, R. Larrabee, B. Russo, and M. Davidson, "Comparison of measured optical image profiles of silicon lines with two different theoretical models," in Metrology, Inspection, and Process Control for Microlithography XVI, Proc. SPIE 4689, 409-429 (2002). [CrossRef]
- J. Potzick, E. Marx, and M. Davidson, "Parametric uncertainties in optical image modeling," in Photomask Technology 2006, Proc. SPIE 6349, 63494U (2006).
- J. Potzick, E. Marx, and M. Davidson, "Accuracy in optical image modeling," in Metrology, Inspection, and Process Control Conference for Microlithography XXI, Proc. SPIE 6518, 651814 (2007).
- U.S. Guide to the Expression of uncertainty in measurement, ANSI/NCSL standard Z540-2-1997 (the U.S. version of guide to the expression of uncertainty in measurement, ISO, 1995, ISBN 92-67-10188-9); International Vocabulary of Basic and General Terms in Metrology, ISO, 1993, ISBN 92-67-01075-1.
- R. M. Silver, T. Germer, R. Attota, B. Barnes, B. Bunday, J. A. Allgair, E. Marx, and J. Jun, "Fundamental limits of optical critical dimension metrology: A simulation study," in Inspection, and Process Control Conference for Microlithography XXI, Proc. SPIE 6518, 65180U (2007). [CrossRef]
- A. Sommerfeld, Optics (Academic, 1964), pp. 40-50.
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.