Abstract

A novel laser scatterometer linewidth measurement tool has been developed for critical dimension metrology of photomasks. Calculation of the linewidth is based on a rigorous theoretical model, thus eliminating the need for calibrations. In addition the effect of the glass substrate on which the photomask grating is placed is explicitly taken into account. The experimental arrangement consists of a chrome photomask diffraction grating that is illuminated with a laser. A rigorous theoretical model is used to provide a lookup table that gives the power in the transmitted zero-order beam as a function of the linewidth for a fixed pitch of the grating. The predicted linewidth values are compared with those that are obtained by using commercial optical linewidth measurement systems, and excellent agreement is obtained.

© 1992 Optical Society of America

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References

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  1. D. Nyyssonen, R. D. Larrabee, “Submicrometer linewidth metrology in the optical microscope,” J. Res. Natl. Bur. Stand. 92, 187–204 (May–June1987).
    [CrossRef]
  2. C-M. Yuan, “Modeling of optical alignment and metrology in VLSI manufacturing,” Ph.D dissertation (Carnegie-Mellon, Pittsburgh, Pa., 1989).
  3. E. Marx, E. C. Teague, “Determination of fields near a silver strip on a glass substrate,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 176–184 (1988).
  4. D. Nyyssonen, “Linewidth measurement with an optical microscope: the effect of operating condition on the image profile,” Appl. Opt. 16, 2223–2230 (1977).
    [CrossRef] [PubMed]
  5. D. Nyyssonen, B. Monteverde, “Linewidth edge detection algorithm for coherent image profiles,” in Integrated Circuit Metrology Inspection and Process Control III, K. M. Manahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1087, 146–152 (1989).
  6. D. Nyyssonen, “Practical method for edge detection and focusing for linewidth measurements on wafers,” Opt. Eng. 26, 81–85 (1987).
    [CrossRef]
  7. H. P. Kleinknecht, H. Meier, “Linewidth measurement on IC masks and wafers by grating test patterns,” Appl. Opt. 19, 525–533 (1980).
    [CrossRef] [PubMed]
  8. T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  9. S. S. H. Naqvi, N. C. Gallagher, “Analysis of a strip grating twist reflector,” J. Opt. Soc. Am. A 7, 1723–1729 (1990).
    [CrossRef]
  10. J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
    [CrossRef]
  11. S. S. H. Naqvi, N. C. Gallagher, “A general solution to the scattering of electromagnetic waves from a strip grating,” J. Mod. Opt. 37, 1629–1643 (1990).
    [CrossRef]
  12. M. G. Moharram, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  13. J. Beard, Prometrix Corporation, 3255 Scott Boulevard, Santa Clara, Calif. 95054 (personal communications, 1991).
  14. W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819–2826 (1987).
    [CrossRef]
  15. G. A. Al-Jumaily, J. J. McNally, J. R. McNeil, “Effect of ion assisted deposition on optical scatter and surface microstructure of thin films,” J. Vac. Sci. Technol. 3, 651–655 (1985).
    [CrossRef]
  16. R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
    [PubMed]
  17. National Institute of Standards and Technology, Standard SRM 473.

1990 (2)

S. S. H. Naqvi, N. C. Gallagher, “Analysis of a strip grating twist reflector,” J. Opt. Soc. Am. A 7, 1723–1729 (1990).
[CrossRef]

S. S. H. Naqvi, N. C. Gallagher, “A general solution to the scattering of electromagnetic waves from a strip grating,” J. Mod. Opt. 37, 1629–1643 (1990).
[CrossRef]

1987 (3)

D. Nyyssonen, R. D. Larrabee, “Submicrometer linewidth metrology in the optical microscope,” J. Res. Natl. Bur. Stand. 92, 187–204 (May–June1987).
[CrossRef]

D. Nyyssonen, “Practical method for edge detection and focusing for linewidth measurements on wafers,” Opt. Eng. 26, 81–85 (1987).
[CrossRef]

W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819–2826 (1987).
[CrossRef]

1985 (2)

G. A. Al-Jumaily, J. J. McNally, J. R. McNeil, “Effect of ion assisted deposition on optical scatter and surface microstructure of thin films,” J. Vac. Sci. Technol. 3, 651–655 (1985).
[CrossRef]

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1982 (1)

1980 (1)

1977 (1)

1975 (1)

J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
[CrossRef]

Al-Jumaily, G. A.

G. A. Al-Jumaily, J. J. McNally, J. R. McNeil, “Effect of ion assisted deposition on optical scatter and surface microstructure of thin films,” J. Vac. Sci. Technol. 3, 651–655 (1985).
[CrossRef]

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

Beard, J.

J. Beard, Prometrix Corporation, 3255 Scott Boulevard, Santa Clara, Calif. 95054 (personal communications, 1991).

Bennett, J. M.

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

Gallagher, N. C.

S. S. H. Naqvi, N. C. Gallagher, “Analysis of a strip grating twist reflector,” J. Opt. Soc. Am. A 7, 1723–1729 (1990).
[CrossRef]

S. S. H. Naqvi, N. C. Gallagher, “A general solution to the scattering of electromagnetic waves from a strip grating,” J. Mod. Opt. 37, 1629–1643 (1990).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

M. G. Moharram, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

Jacobson, R. D.

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

Kleinknecht, H. P.

Larrabee, R. D.

D. Nyyssonen, R. D. Larrabee, “Submicrometer linewidth metrology in the optical microscope,” J. Res. Natl. Bur. Stand. 92, 187–204 (May–June1987).
[CrossRef]

Marx, E.

E. Marx, E. C. Teague, “Determination of fields near a silver strip on a glass substrate,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 176–184 (1988).

Mattsson, L.

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

McNally, J. J.

G. A. Al-Jumaily, J. J. McNally, J. R. McNeil, “Effect of ion assisted deposition on optical scatter and surface microstructure of thin films,” J. Vac. Sci. Technol. 3, 651–655 (1985).
[CrossRef]

McNeil, J. R.

G. A. Al-Jumaily, J. J. McNally, J. R. McNeil, “Effect of ion assisted deposition on optical scatter and surface microstructure of thin films,” J. Vac. Sci. Technol. 3, 651–655 (1985).
[CrossRef]

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

Meier, H.

Moharram, M. G.

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

M. G. Moharram, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

Monteverde, B.

D. Nyyssonen, B. Monteverde, “Linewidth edge detection algorithm for coherent image profiles,” in Integrated Circuit Metrology Inspection and Process Control III, K. M. Manahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1087, 146–152 (1989).

Montgomery, J. P.

J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
[CrossRef]

Naqvi, S. S. H.

S. S. H. Naqvi, N. C. Gallagher, “Analysis of a strip grating twist reflector,” J. Opt. Soc. Am. A 7, 1723–1729 (1990).
[CrossRef]

S. S. H. Naqvi, N. C. Gallagher, “A general solution to the scattering of electromagnetic waves from a strip grating,” J. Mod. Opt. 37, 1629–1643 (1990).
[CrossRef]

Nyyssonen, D.

D. Nyyssonen, R. D. Larrabee, “Submicrometer linewidth metrology in the optical microscope,” J. Res. Natl. Bur. Stand. 92, 187–204 (May–June1987).
[CrossRef]

D. Nyyssonen, “Practical method for edge detection and focusing for linewidth measurements on wafers,” Opt. Eng. 26, 81–85 (1987).
[CrossRef]

D. Nyyssonen, “Linewidth measurement with an optical microscope: the effect of operating condition on the image profile,” Appl. Opt. 16, 2223–2230 (1977).
[CrossRef] [PubMed]

D. Nyyssonen, B. Monteverde, “Linewidth edge detection algorithm for coherent image profiles,” in Integrated Circuit Metrology Inspection and Process Control III, K. M. Manahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1087, 146–152 (1989).

Pliskin, W. A.

W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819–2826 (1987).
[CrossRef]

Teague, E. C.

E. Marx, E. C. Teague, “Determination of fields near a silver strip on a glass substrate,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 176–184 (1988).

Wilson, S. R.

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

Yuan, C-M.

C-M. Yuan, “Modeling of optical alignment and metrology in VLSI manufacturing,” Ph.D dissertation (Carnegie-Mellon, Pittsburgh, Pa., 1989).

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

J. P. Montgomery, “Scattering by an infinite periodic array of thin conductors on a dielectric sheet,” IEEE Trans. Antennas Propag. AP-23, 70–75 (1975).
[CrossRef]

J. Electrochem. Soc. (1)

W. A. Pliskin, “Refractive index dispersion of dielectric films used in the semiconductor industry,” J. Electrochem. Soc. 134, 2819–2826 (1987).
[CrossRef]

J. Mod. Opt. (1)

S. S. H. Naqvi, N. C. Gallagher, “A general solution to the scattering of electromagnetic waves from a strip grating,” J. Mod. Opt. 37, 1629–1643 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Res. Natl. Bur. Stand. (1)

D. Nyyssonen, R. D. Larrabee, “Submicrometer linewidth metrology in the optical microscope,” J. Res. Natl. Bur. Stand. 92, 187–204 (May–June1987).
[CrossRef]

J. Vac. Sci. Technol. (1)

G. A. Al-Jumaily, J. J. McNally, J. R. McNeil, “Effect of ion assisted deposition on optical scatter and surface microstructure of thin films,” J. Vac. Sci. Technol. 3, 651–655 (1985).
[CrossRef]

Opt. Eng. (1)

D. Nyyssonen, “Practical method for edge detection and focusing for linewidth measurements on wafers,” Opt. Eng. 26, 81–85 (1987).
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Other (6)

J. Beard, Prometrix Corporation, 3255 Scott Boulevard, Santa Clara, Calif. 95054 (personal communications, 1991).

R. D. Jacobson, S. R. Wilson, G. A. Al-Jumaily, J. R. McNeil, J. M. Bennett, L. Mattsson, “Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques,” submitted to Appl. Opt.
[PubMed]

National Institute of Standards and Technology, Standard SRM 473.

C-M. Yuan, “Modeling of optical alignment and metrology in VLSI manufacturing,” Ph.D dissertation (Carnegie-Mellon, Pittsburgh, Pa., 1989).

E. Marx, E. C. Teague, “Determination of fields near a silver strip on a glass substrate,” in Scanning Microscopy Technologies and Applications, E. C. Teague, ed., Proc. Soc. Photo-Opt. Instrum. Eng.897, 176–184 (1988).

D. Nyyssonen, B. Monteverde, “Linewidth edge detection algorithm for coherent image profiles,” in Integrated Circuit Metrology Inspection and Process Control III, K. M. Manahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1087, 146–152 (1989).

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Figures (11)

Fig. 1
Fig. 1

Photomask grating structure.

Fig. 2
Fig. 2

Theoretical structure to be modeled for perfectly conducting diffraction analysis.

Fig. 3
Fig. 3

Theoretical plot of the fraction of power that is diffracted into the transmitted zero-order beam.

Fig. 4
Fig. 4

Comparison of theoretically modeled reflectivity from the photomask with experimental reflectivity, which is obtained by using a Perkin Elmer (Model 330) spectrophotometer.

Fig. 5
Fig. 5

Comparison of transmitted zero-order powers for TE polarization, which is obtained by using rigorous coupled-wave analysis and the infinitely conducting diffraction analysis.

Fig. 6
Fig. 6

Experimental arrangement of the scatterometer.

Fig. 7
Fig. 7

Plot of experimentally measured scatter power as a function of the scatter angle.

Fig. 8
Fig. 8

Plot of the CD measurement as a function of spot size on the sample for each grating on mask SF010.

Fig. 9
Fig. 9

CD measurements for various positions on each grating on mask SF010.

Fig. 10
Fig. 10

Plot of the CD measurement that was obtained by using TE and TM polarization for each grating on mask SF010.

Fig. 11
Fig. 11

CD measurement for different wavelengths on each grating of mask SF010.

Tables (1)

Tables Icon

Table I Measured Linewidths (Micrometers) on Mask SF016

Equations (33)

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sin θ n = sin θ i + n λ d , n = 0 , ± 1 , ± 2 , .
E 1 ( x , y , z ) = exp ( i k 1 · r ) + n = R n exp ( i k 1 n · r ) .
E 3 ( x , y , z ) = n = T n exp ( i k 3 n · r ) exp ( i k 3 n · z ˆ w ) ,
E 2 ( x , y , z ) = n = [ X n exp ( i k 2 n · z z ˆ ) + Y n exp ( i k 2 n · z z ˆ ) ] × exp [ i ( k 2 n · x x ˆ + k 2 n · y y ˆ ) ] .
k p n · x ˆ = k p · x ˆ n 2 π d ,
k p 2 = ( k p · x ˆ ) 2 + ( k p · z ˆ ) 2 .
D n = exp ( j 2 k 2 n · z ˆ w ) ( k 2 n · z ˆ + k 3 n · z ˆ k 2 n · z ˆ k 3 n · z ˆ ) .
E 1 ( x ) = exp ( i k 1 · x x ˆ ) n = ( R n + δ n , 0 ) exp ( i n 2 π d x ) ,
J y ( x ) = exp ( i k 1 · x x ˆ ) n = C n exp ( i n 2 π d x ) .
C n = B n R n + ν δ n , 0 ,
B n = i ωμ [ i k 1 n · z ˆ i k 2 n · z ˆ ( D n 1 D n + 1 ) ] ,
ν = i ωμ [ i k 10 · z ˆ i k 20 · z ˆ ( D 0 1 D 0 + 1 ) ] .
S ( x ) = { 0 in gap 1 everywhere else ,
J ( x ) = S ( x ) J ( x ) ,
E ( x , 0 ) = E ( x , 0 ) [ 1 S ( x ) ] .
S n = { 1 i 2 π n [ exp ( i 2 π d c n ) 1 . 0 ] for n 0 d c d for n = 0 ,
C n = p = C p S n p ,
R m + δ m , 0 = n = ( R n + δ n , 0 ) ( δ m n , 0 S m n ) .
R m = S m + n = 1 B n ( C n ν δ n , 0 ) ( δ m n , 0 S m n ) .
R m = S m + n = 1 B n [ p = ( B p R p + ν δ p , 0 ) S n p ν δ n , 0 ] × ( δ m n , 0 S m n ) .
[ I ¯ Q ¯ ] R = P d ,
Q ¯ = A ¯ 2 B ¯ 1 A ¯ 1 B ¯ ,
P d = A ¯ 2 B ¯ 1 ( A ¯ 1 I ¯ ) Y + P .
R [ m ] = R m , Y [ m ] = ν δ m , 0 ,
B ¯ [ m , n ] = B n δ m , n , B ¯ 1 [ m , n ] = 1 B n δ m , n ,
A ¯ 1 [ m , n ] = S m n , A ¯ 2 [ m , n ] = δ m n , 0 S m n ,
P [ m ] = S m .
T n = [ D n exp ( i k 2 n · z ˆ w ) + exp ( i k 2 n · z ˆ w ) ] ( 1 1 + D n ) ( R n + δ n , 0 ) .
n = n 1 + n 2 λ + n 3 λ 2 + n 4 λ 3 ,
( n 1 , n 2 , n 3 , n 4 ) = ( 3 . 832 , 2 . 299 × 10 3 , 2 . 726 × 10 7 , 1 . 1397 × 10 11 ) ,
( k 1 , k 2 , k 3 , k 4 ) = ( 6 . 9365 , 4 . 8723 × 10 3 , 8 . 5732 × 10 7 , 4 . 9645 × 10 11 )
n = n 1 + n 2 λ 2 + n 3 λ 4 ,
( n 1 , n 2 , n 3 , n 4 ) = ( 0 . 3249 , 1 . 014 × 10 8 , 9 . 44 × 10 14 ) .

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