Abstract

Traditional optical methods for locating an edge are based on light intensity variation with respect to a reference triggering level. Since the intensity variation is subject to stray light, the intensity variation of the light source, and the triggering level variation, the exact position of the edge cannot be determined. We describe a method for edge location that uses a phase variation in a modified differential interferometer. The maximal point of the slope of the phase variation across an edge is determined exactly by the relative position between the focused beam spot and the detected edge if the initial intensity ratio of the two single-frequency interference beams is kept unchanged. Therefore the phase variation can be used to locate the edge with high resolution and accuracy. To make practical use of the phase variation, the second derivative of the phase was used as a monotonic zero-crossing signal across the edge. The theoretical and the experimental verification have been conducted in detail. The results of the experiment show the feasibility of edge location when phase variation is used. The scheme is not affected by stray light and the intensity variation of the light source.

© 2000 Optical Society of America

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References

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  1. K. Creath, “Submicron linewidth measurement using an interferometric optical profiler,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 474–483 (1991).
  2. K. Phan, J. Nistler, B. Singh, “Metrology issues associated with submicron linewidths,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 424–437 (1991).
  3. V. M. Dusa, H. E. Rauch, “Sub-halfmicron lithography mask metrology: matching of the optical and mask system,” in Photomask and X-Ray Mask Technology, H. Yoshihara, ed., Proc. SPIE2254, 338–348 (1994).
    [CrossRef]
  4. A. Sicignano, M. V. Iravani, “Quantitative linewidth measurement using in situ differential SEM techniques,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1261, 2–8 (1987).
  5. M. Lagerquist, W. Bither, R. Brouillette, “Improving SEM linewidth metrology by two-dimensional scanning force microscopy,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 494–503 (1996).
    [CrossRef]
  6. K. H. Hart, “A laser-source photoelectric microscope for sensing moving scale lines,” Metrologia 13, 63–66 (1977).
    [CrossRef]
  7. H. Noguchi, M. Sawabe, T. Makino, “Development of an interferometer for measurement of linear grating and index scales,” J. Jpn. Soc. Precis. Eng. 58, 1497–1502 (1992).
    [CrossRef]
  8. Q. Yang, C. Butler, “3-D noncontact trigger probe for coordinate measuring machines,” Measurement 17, 39–44 (1996).
    [CrossRef]
  9. Y. Li, “Design of zero reference marks for grating measurement systems: a new method,” Meas. Sci. Technol. 1, 848–851 (1990).
    [CrossRef]
  10. K. C. Pohlmann, The Compact Disc Handbook, 2nd ed. (A-R Editions, Madison, Wis., 1992), pp. 47–166.
  11. N. D. Zhu, R. Probst, “Ein interferentielles Kantenfinder-Messverfahren zur Positionierung von Mikrostrukturen,” PTB-Mitt. 97, 384–390 (1987).
  12. W. D. Zhou, L. Cai, “A phase jump phenomenon in interferometry,” Appl. Phys. Lett. 73, 3339–3341 (1998).
    [CrossRef]
  13. W. D. Zhou, L. Cai, “Investigation on phase jump in a differential interferometer,” J. Appl. Phys. 85, 6295–6302 (1999).
    [CrossRef]
  14. W. Zhou, L. Cai, “Method for edge detection based on phase jump in a differential interferometer,” Appl. Opt. 38, 152–159 (1999).
    [CrossRef]
  15. E. Hecht, Optics, 3rd ed. (Addison-Wesley Longman, Reading, Mass., 1998), pp. 286–287.

1999

W. D. Zhou, L. Cai, “Investigation on phase jump in a differential interferometer,” J. Appl. Phys. 85, 6295–6302 (1999).
[CrossRef]

W. Zhou, L. Cai, “Method for edge detection based on phase jump in a differential interferometer,” Appl. Opt. 38, 152–159 (1999).
[CrossRef]

1998

W. D. Zhou, L. Cai, “A phase jump phenomenon in interferometry,” Appl. Phys. Lett. 73, 3339–3341 (1998).
[CrossRef]

1996

Q. Yang, C. Butler, “3-D noncontact trigger probe for coordinate measuring machines,” Measurement 17, 39–44 (1996).
[CrossRef]

1992

H. Noguchi, M. Sawabe, T. Makino, “Development of an interferometer for measurement of linear grating and index scales,” J. Jpn. Soc. Precis. Eng. 58, 1497–1502 (1992).
[CrossRef]

1990

Y. Li, “Design of zero reference marks for grating measurement systems: a new method,” Meas. Sci. Technol. 1, 848–851 (1990).
[CrossRef]

1987

N. D. Zhu, R. Probst, “Ein interferentielles Kantenfinder-Messverfahren zur Positionierung von Mikrostrukturen,” PTB-Mitt. 97, 384–390 (1987).

1977

K. H. Hart, “A laser-source photoelectric microscope for sensing moving scale lines,” Metrologia 13, 63–66 (1977).
[CrossRef]

Bither, W.

M. Lagerquist, W. Bither, R. Brouillette, “Improving SEM linewidth metrology by two-dimensional scanning force microscopy,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 494–503 (1996).
[CrossRef]

Brouillette, R.

M. Lagerquist, W. Bither, R. Brouillette, “Improving SEM linewidth metrology by two-dimensional scanning force microscopy,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 494–503 (1996).
[CrossRef]

Butler, C.

Q. Yang, C. Butler, “3-D noncontact trigger probe for coordinate measuring machines,” Measurement 17, 39–44 (1996).
[CrossRef]

Cai, L.

W. Zhou, L. Cai, “Method for edge detection based on phase jump in a differential interferometer,” Appl. Opt. 38, 152–159 (1999).
[CrossRef]

W. D. Zhou, L. Cai, “Investigation on phase jump in a differential interferometer,” J. Appl. Phys. 85, 6295–6302 (1999).
[CrossRef]

W. D. Zhou, L. Cai, “A phase jump phenomenon in interferometry,” Appl. Phys. Lett. 73, 3339–3341 (1998).
[CrossRef]

Creath, K.

K. Creath, “Submicron linewidth measurement using an interferometric optical profiler,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 474–483 (1991).

Dusa, V. M.

V. M. Dusa, H. E. Rauch, “Sub-halfmicron lithography mask metrology: matching of the optical and mask system,” in Photomask and X-Ray Mask Technology, H. Yoshihara, ed., Proc. SPIE2254, 338–348 (1994).
[CrossRef]

Hart, K. H.

K. H. Hart, “A laser-source photoelectric microscope for sensing moving scale lines,” Metrologia 13, 63–66 (1977).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley Longman, Reading, Mass., 1998), pp. 286–287.

Iravani, M. V.

A. Sicignano, M. V. Iravani, “Quantitative linewidth measurement using in situ differential SEM techniques,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1261, 2–8 (1987).

Lagerquist, M.

M. Lagerquist, W. Bither, R. Brouillette, “Improving SEM linewidth metrology by two-dimensional scanning force microscopy,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 494–503 (1996).
[CrossRef]

Li, Y.

Y. Li, “Design of zero reference marks for grating measurement systems: a new method,” Meas. Sci. Technol. 1, 848–851 (1990).
[CrossRef]

Makino, T.

H. Noguchi, M. Sawabe, T. Makino, “Development of an interferometer for measurement of linear grating and index scales,” J. Jpn. Soc. Precis. Eng. 58, 1497–1502 (1992).
[CrossRef]

Nistler, J.

K. Phan, J. Nistler, B. Singh, “Metrology issues associated with submicron linewidths,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 424–437 (1991).

Noguchi, H.

H. Noguchi, M. Sawabe, T. Makino, “Development of an interferometer for measurement of linear grating and index scales,” J. Jpn. Soc. Precis. Eng. 58, 1497–1502 (1992).
[CrossRef]

Phan, K.

K. Phan, J. Nistler, B. Singh, “Metrology issues associated with submicron linewidths,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 424–437 (1991).

Pohlmann, K. C.

K. C. Pohlmann, The Compact Disc Handbook, 2nd ed. (A-R Editions, Madison, Wis., 1992), pp. 47–166.

Probst, R.

N. D. Zhu, R. Probst, “Ein interferentielles Kantenfinder-Messverfahren zur Positionierung von Mikrostrukturen,” PTB-Mitt. 97, 384–390 (1987).

Rauch, H. E.

V. M. Dusa, H. E. Rauch, “Sub-halfmicron lithography mask metrology: matching of the optical and mask system,” in Photomask and X-Ray Mask Technology, H. Yoshihara, ed., Proc. SPIE2254, 338–348 (1994).
[CrossRef]

Sawabe, M.

H. Noguchi, M. Sawabe, T. Makino, “Development of an interferometer for measurement of linear grating and index scales,” J. Jpn. Soc. Precis. Eng. 58, 1497–1502 (1992).
[CrossRef]

Sicignano, A.

A. Sicignano, M. V. Iravani, “Quantitative linewidth measurement using in situ differential SEM techniques,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1261, 2–8 (1987).

Singh, B.

K. Phan, J. Nistler, B. Singh, “Metrology issues associated with submicron linewidths,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 424–437 (1991).

Yang, Q.

Q. Yang, C. Butler, “3-D noncontact trigger probe for coordinate measuring machines,” Measurement 17, 39–44 (1996).
[CrossRef]

Zhou, W.

Zhou, W. D.

W. D. Zhou, L. Cai, “Investigation on phase jump in a differential interferometer,” J. Appl. Phys. 85, 6295–6302 (1999).
[CrossRef]

W. D. Zhou, L. Cai, “A phase jump phenomenon in interferometry,” Appl. Phys. Lett. 73, 3339–3341 (1998).
[CrossRef]

Zhu, N. D.

N. D. Zhu, R. Probst, “Ein interferentielles Kantenfinder-Messverfahren zur Positionierung von Mikrostrukturen,” PTB-Mitt. 97, 384–390 (1987).

Appl. Opt.

Appl. Phys. Lett.

W. D. Zhou, L. Cai, “A phase jump phenomenon in interferometry,” Appl. Phys. Lett. 73, 3339–3341 (1998).
[CrossRef]

J. Appl. Phys.

W. D. Zhou, L. Cai, “Investigation on phase jump in a differential interferometer,” J. Appl. Phys. 85, 6295–6302 (1999).
[CrossRef]

J. Jpn. Soc. Precis. Eng.

H. Noguchi, M. Sawabe, T. Makino, “Development of an interferometer for measurement of linear grating and index scales,” J. Jpn. Soc. Precis. Eng. 58, 1497–1502 (1992).
[CrossRef]

Meas. Sci. Technol.

Y. Li, “Design of zero reference marks for grating measurement systems: a new method,” Meas. Sci. Technol. 1, 848–851 (1990).
[CrossRef]

Measurement

Q. Yang, C. Butler, “3-D noncontact trigger probe for coordinate measuring machines,” Measurement 17, 39–44 (1996).
[CrossRef]

Metrologia

K. H. Hart, “A laser-source photoelectric microscope for sensing moving scale lines,” Metrologia 13, 63–66 (1977).
[CrossRef]

PTB-Mitt.

N. D. Zhu, R. Probst, “Ein interferentielles Kantenfinder-Messverfahren zur Positionierung von Mikrostrukturen,” PTB-Mitt. 97, 384–390 (1987).

Other

E. Hecht, Optics, 3rd ed. (Addison-Wesley Longman, Reading, Mass., 1998), pp. 286–287.

K. C. Pohlmann, The Compact Disc Handbook, 2nd ed. (A-R Editions, Madison, Wis., 1992), pp. 47–166.

K. Creath, “Submicron linewidth measurement using an interferometric optical profiler,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 474–483 (1991).

K. Phan, J. Nistler, B. Singh, “Metrology issues associated with submicron linewidths,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1464, 424–437 (1991).

V. M. Dusa, H. E. Rauch, “Sub-halfmicron lithography mask metrology: matching of the optical and mask system,” in Photomask and X-Ray Mask Technology, H. Yoshihara, ed., Proc. SPIE2254, 338–348 (1994).
[CrossRef]

A. Sicignano, M. V. Iravani, “Quantitative linewidth measurement using in situ differential SEM techniques,” in Integrated Circuit Metrology, Inspection, and Process Control, W. H. Arnold, ed., Proc. SPIE1261, 2–8 (1987).

M. Lagerquist, W. Bither, R. Brouillette, “Improving SEM linewidth metrology by two-dimensional scanning force microscopy,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 494–503 (1996).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Vector diagram of phase variation.

Fig. 2
Fig. 2

Theoretical curves of phase jump and phase variation.

Fig. 3
Fig. 3

Amplitude change with phase variation.

Fig. 4
Fig. 4

Curves of dφ/dη versus η with a phase difference of 175°.

Fig. 5
Fig. 5

Curves of d2φ/dη2 versus η with a phase difference of 175°.

Fig. 6
Fig. 6

Edge location for linewidth measurement.

Fig. 7
Fig. 7

Experimental setup for edge location by using phase variation: BS, beam splitter.

Fig. 8
Fig. 8

Schematic diagram of two focused beams on a sample.

Fig. 9
Fig. 9

Experimental curve of phase versus displacement.

Fig. 10
Fig. 10

Second differentiating circuit: P 1, P 2, phase signals; C1–C4, capacitors; R1–R13, resistances; A1–A4, amplifiers.

Fig. 11
Fig. 11

Experimental curve of the derivative of phase versus displacement.

Fig. 12
Fig. 12

Experimental curve of the second derivative of phase versus displacement.

Fig. 13
Fig. 13

Curves of five repeated experiments on the second phase derivative versus displacement.

Equations (26)

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y1=M1 cosωt-φ1,
y2=ηM2 cosωt-φ2,
y=y1+y2=M cosωt-φ.
M cos φ=M1 cos φ1+ηM2 cos φ2,
M sin φ=M1 sin φ1+ηM2 sin φ2.
dφdη2=M22-dMdη2M2.
M2=M12+η2M22+2ηM1M2 cosφ2-φ1.
η=-M1M2 cos δ,
Mmin2=M12 sin2 δ.
dφdη2max=M22M12 sin2 δ.
d2φdη2=dMdηM-d2Mdη2-dφdη2M2dφdη.
E1=cosω1t-ϕ1,
E2=cosω2t-ϕ2.
A: E1A=cos α cosω1t-ϕ1AE2A=sin α cosω2t-ϕ2A,
B: E1B=sin α cosω1t-ϕ1BE2B=cos α cosω2t-ϕ2B.
A: E1A=rc cos α cosω1t-ϕ1AE2A=rc sin α cosω2t-ϕ2A,
B: E1B=rcκ sin α cosω1t-ϕ1BE2B=rcκ cos α cosω2t-ϕ2B.
I=|E1A+E2A+E1B+E2B|2=|E1AB+E2AB|2,
E1AB=E1A+E1B=G1 cosω1t-ϕ1,
E2AB=E2A+E2B=G2 cosω2t-ϕ2,
SmG1G21+cosω2-ω1t-ϕ2-ϕ1.
ϕ=ϕ2-ϕ1.
G2min2 =rc2 sin2 α sin2 δ2,
dϕ2dt2max =dκdt2tan2 α sin2 δ2;
G1min2=rc2 cos2 α sin2 δ1,
dϕ1dt2max=tan2 αsin2 δ1dκdt2,

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