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(12) United States Patent ao) Patent No.: us 6,608,690 B2
Niu et al. (45) Date of Patent: Aug. 19,2003
(54) OPTICAL PROFILOMETRY OF
ADDITIONAL-MATERIAL DEVIATIONS IN A
(75) Inventors: Xinhui Niu, Los Altos, CA (US);
Nickhil Jakatdar, Los Altos, CA (US)
(73) Assignee: Timbre Technologies, Inc., Santa Clara, CA (US)
( * ) Notice: Subject to any disclaimer, the term of this patent is extended or adjusted under 35 U.S.C. 154(b) by 0 days.
N. W. Ashcroft et al., "Solid State Physics", Saunders College, Philadelphia, 1976, pp. 133-134.
Azzam et al., "Ellipsometry and Polarized Light", North Holland library, Amsterdam, 1987, book.
Ch. M. Bishop, "Neural Networks for Pattern Recognition", Clarendon Press-Oxford, 1995, Ch. 4„ pp. 116-163.
G. Granet et al., "Efficient implementation of the coupled-wave method for metallic lamellar in TM polarization", J. Opt. Soc. Am. vol. 13, No. 5, May 1996, pp. 1019-1023.
Disclosed is a method and system for measurement of periodic gratings which have deviations which result in more than two materials occurring along at least one line in the periodic direction. A periodic grating is divided into a plurality of hypothetical layers, each hypothetical layer having a normal vector orthogonal to the direction of periodicity, each hypothetical layer having a single material within any line parallel to the normal vector, and at least one of the hypothetical layers having at least three materials along a line in the direction of periodicity. A harmonic expansion of the permittivity e or inverse permittivity 1/e is performed along the direction of periodicity for each of the layers including the layer which includes the first, second and third materials. Fourier space electromagnetic equations are then set up in each of the layers using the harmonic expansion of the permittivity e or inverse permittivity 1/e, and Fourier components of electric and magnetic fields in each layer. The Fourier space electromagnetic equations are then coupled based on boundary conditions between the layers, and solved to provide the calculated diffraction spectrum.
60 Claims, 13 Drawing Sheets
Divide Target Periodic Grating Into
Subdivide Hypothetical Layers into Slabs I | Corresponding to Layer/Mate rial Intersections
Generate Hypothetical Layer Data
Determine Permittivity e((x)
for each Hypothetical Layer
Complete Fourier Transformation of
Permittivity Function by Summing Term
over Boundaries Between Materials
in the Periodic Direction
Define Permittivity Harmonics Matrix
Including the Harmonic components
of the Fourier expansion of the
Couple Fourier Spcce Equations
using Boundary Conditions Betwee
i the Coupled Fourier Space Equc
for the Diffracted Reflectivity
Set up Fourier Space
Electromagnetic Field Equations
P. Lalanne et al., "Highly improved convergence of the
coupled-wave method for TM polarization", J. Opt. Soc.
Am. vol. 13, No. 4, Apr. 1996, pp. 779-784.
L. Li et al., "Convergence of the coupled-wave method for
metallic lamellar diffraction gratings", J. Opt. Soc. Am. vol.
10, No. 6, Jun. 1993, pp. 1184-1189.
M. G. Moharam et al., "Rigorous coupled-wave analysis of
planar-grating diffraction", J. Opt. Soc. Am. vol. 71, No.
7/Jul. 1981, pp. 811-818.
M. G. Moharam et al., "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings", J. Opt. Soc. Am. vol. 12, No. 5, May 1995, pp. 1068-1076.
Moharam et al., "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach", J. Opt. Soc. Am. vol. 12, No. 5, May 1995, pp. 1077-1086.
X. Niu, "Specular Spectroscopic Scatterometry in DUV Lithography", IEEE Trans, on Semiconductor Manuf. vol. 14, No. 2, May 2001, 10 pgs.
J. A. Rice, "Mathematical Statistics and Data Analysis" sec. ed., ch. 14, Duxbury Press, 1995, pp. 507-570.
W. H. Press et al., "Numerical Recipes", Cambridge University Press, 1986, pp. 444-455.
* cited by examiner