Abstract

We describe a new method for edge detection that uses polarization mixing in a differential heterodyne interferometer. When one of the focused beams of the interferometer scans across an edge, a phase jump of 180° takes place in the very small region of the edge if certain conditions are satisfied. We call this phenomenon phase jump. The conditions in which phase jump can occur are given. The theoretical analysis shows that the slope of a phase jump is infinite and is not affected by step height, the vibration of the sample, or the intensity variation of the light source. Therefore phase jump can be used as the precise index for edge detection. The experimental results show good agreement with the theoretical analysis.

© 1999 Optical Society of America

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  1. K. H. Hart, “A laser-source photoelectric microscope for sensing moving scale lines,” Metrologia 13, 63–66 (1977).
    [CrossRef]
  2. 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]
  3. Q. Yang, C. Butler, “3-D noncontact trigger probe for coordinate measuring machines,” Measurement 17, 39–44 (1996).
    [CrossRef]
  4. 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).
    [CrossRef]
  5. 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).
    [CrossRef]
  6. 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]
  7. 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).
  8. 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]
  9. W. Zhou, Z. Zhou, G. Chi, “Investigation of common-path interference interferometry,” Opt. Eng. 36, 3172–3175 (1997).
    [CrossRef]
  10. G. E. Sommargren, “Optical heterodyne profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  11. T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging System (Academic, San Diego, Calif., 1996), pp. 248–250.
  12. E. Hecht, Optics, 3rd. ed. (Addison Wesley Longman, Reading, Mass., 1998), pp. 286–287.

1997

W. Zhou, Z. Zhou, G. Chi, “Investigation of common-path interference interferometry,” Opt. Eng. 36, 3172–3175 (1997).
[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]

1981

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]

Chi, G.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common-path interference interferometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Corle, T. R.

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging System (Academic, San Diego, Calif., 1996), pp. 248–250.

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).
[CrossRef]

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).

Kino, G. S.

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging System (Academic, San Diego, Calif., 1996), pp. 248–250.

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]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Sommargren, G. E.

Yang, Q.

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

Zhou, W.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common-path interference interferometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Zhou, Z.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common-path interference interferometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Appl. Opt.

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]

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]

Opt. Eng.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common-path interference interferometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Other

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging System (Academic, San Diego, Calif., 1996), pp. 248–250.

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

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).
[CrossRef]

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).
[CrossRef]

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 (12)

Fig. 1
Fig. 1

Heterodyne differential interferometer.

Fig. 2
Fig. 2

Schematic diagram of two focused beams on a sample.

Fig. 3
Fig. 3

Addition of φ2A and φ2B when δ2 = π.

Fig. 4
Fig. 4

Experimental setup for edge detection.

Fig. 5
Fig. 5

Experimental setup for edge detection.

Fig. 6
Fig. 6

Phase change with a chromium step of 100 nm when δ2 < π.

Fig. 7
Fig. 7

Amplitude change with a chromium step of 100 nm when δ2 < π.

Fig. 8
Fig. 8

Phase jump with a chromium step of 100 nm.

Fig. 9
Fig. 9

Amplitude change corresponding to the phase jump of Fig. 8.

Fig. 10
Fig. 10

Phase jump with a chromium step of 150 nm.

Fig. 11
Fig. 11

Phase jump with a silver step of 100 nm.

Fig. 12
Fig. 12

Details of Fig. 8.

Equations (36)

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E1=expiφ10-ω1t,
E2=expiφ20-ω2t.
E=RαE1E2=EAEB=E1 cos α+E2 sin α-E1 sin α+E2 cos α,
Rα=cos αsin α-sin αcos α.
Eo=TrEAEB,
Tr=rA00rB
Eo=TPEo,
TP=1-1-1-1.
I=EoEo=|E1A+E2A+E1B+E2B|2,
E1A=rA cos α expiφ1AP+φ1AW-ω1t=rA cos α expiφ1A-ω1t, E2A=rA sin α expiφ2AP+φ2AW-ω2t=rA sin α expiφ2A-ω2t, E1B=-rB sin α expiφ1BP+φ1BW-ω1t=-rB sin α expiφ1B-ω1t, E2B=rB cos α expiφ2BP+φ2BW-ω2t=rB cos α expiφ2B-ω2t,
Eo=r1 cos αE1-r1η1 sin αE1-r2η2 sin αE1+r1 sin αE2r1η1 cos αE2+r2η2 cos αE2.
I=EoEo=|E1A+E2A+E1B+E2B+E1B+E2B|2,
E1A=r1 cos α expiφ1A-ω1t, E2A=r1 sin α expiφ2A-ω2t, E1B=-r1η1 sin α expiφ1B-ω1t, E2B=r1η1 cos α expiφ2B-ω2t, E1B=-r2η2 sin α expiφ1B-ω1t, E2B=r2η2 cos α expiφ2B-ω2t.
I=|E1A+E2A+E1B+E2B|2=|E1AB+E2AB|2,
E1AB=E1A+E1B=M1 expiφ1-ω1t, E2AB=E2A+E2B=M2 expiφ2-ω2t,
S|E1AB+E2AB|2=M1M21+cosω2-ω1t-φ2-φ1.
φ=φ2-φ1.
E2A=r1 sin α cosω2t-φ2A,
E2B=r1η1 cos α cosω2t-φ2B,
E2AB=M2 cosω2t-φ2.
M2 cos φ2=r1 cos φ2A+r1η1 cos φ2B,
M2 sin φ2=r1 sin φ2A+r1η1 sin φ2B,
cos φ2dM2dη1-M2 sin φ2dφ2dη1=r1 cos α cos φ2B,
sin φ2dM2dη1+M2 cos φ2dφ2dη1=r1 cos α sin φ2B.
dM2dη12+M22dφ2dη12=r12 cos2 α.
dφ2dη12=r12 cos2 α-dM2dη12M22.
M2=r12 sin2 α+r12η1 cos2 α+2r12η1 sin α cos α cosφ2A-φ2B.
2M2dM2dη1=2r12η1 cos2 α+2r12 sin α cos α cosφ2A-φ2B.
η1=-tan α cos δ2,
M2 min2=r12 sin2 α sin2 δ2.
dφ2dη12max=1tan2 α sin2 δ2.
η1=-cos δ1tan α,
M1 min2=r12 cos2 α sin2 δ1,
dφ1dη12max=tan2 αsin2 δ1,
δ1=π,
η1=1tan α.

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