Abstract

Precise three dimensional (3D) profile measurements of vertical sidewalls of concave micro-structures are impossible by conventional profiling techniques. This paper introduces a simple technique which can obtain 3D sidewall geometry by means of laser fluorescent confocal microscopy and an intensity gradient algorithm. The measurement principle is: when a concave micro-structure is filled up with fluorescent solution, the position where the maximum intensity variation lays represents the profile of the micro-structure in the fluorescent 3D volume image. The physical essence behind this measurement principle is analyzed in this paper in detail. The strengths and limitations of this technique are studied by experiments or by illustrations. The factors that are able to improve the measurement accuracy are discussed. This technique has demonstrated the capability for measuring of 3D geometry of various concave features, such as vertical, buried and other micro channels with sub-µm (RMS) measurement accuracy and repeatability.

©2008 Optical Society of America

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References

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  1. T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001).
    [Crossref]
  2. B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
    [Crossref]
  3. C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007).
    [Crossref]
  4. K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004).
    [Crossref]
  5. Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001).
    [Crossref]
  6. http://www.zeiss.com/4125681f004ca025/Contents-Frame/f5445011b5a0a89f852571d200714c4d.
  7. http://www.olympusconfocal.com/applications/index.html.
  8. D. L. Hitt, “Optical Considerations for Accurate Volumetric Reconstructions from 3-D Confocal Imaging,” in Science, Technology & Education of Microscopy: an Overview, Vol. II, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2004).
  9. D. L. Hitt, “Confocal Imaging of Fluidic Interfaces in Microchannel Geometries,” in Science, Technology & Education of Microscopy: an Overview, Vol.1, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2003).
  10. D. L. Hitt and N. Macken, “A simplified model for determining interfacial position in convergent microchannel flows,” J. Fluids Eng. 126, 758–767 (2004).
    [Crossref]
  11. LSM 510 and LSM 510 META Laser Scanning Microscopes, Operating Manual, Carl Zeiss, 2002
  12. http://www.hi.helsinki.fi/amu/AMU%20Cf_tut/cf_tut_part1-5.htm.
  13. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 8th ed., (Addison-Wesley, 1992) 328.
    [PubMed]

2007 (1)

C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007).
[Crossref]

2005 (1)

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

2004 (2)

K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004).
[Crossref]

D. L. Hitt and N. Macken, “A simplified model for determining interfacial position in convergent microchannel flows,” J. Fluids Eng. 126, 758–767 (2004).
[Crossref]

2001 (2)

Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001).
[Crossref]

T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001).
[Crossref]

Ayres, S. F.

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

Buhr, E.

C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007).
[Crossref]

Bushman, S. G.

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

Celii, F. G.

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

Dawson, D.

K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004).
[Crossref]

Dirscherl, K.

C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007).
[Crossref]

Dror, O.

T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001).
[Crossref]

Eytan, G.

T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001).
[Crossref]

Finney, R. L.

G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 8th ed., (Addison-Wesley, 1992) 328.
[PubMed]

Frase, C. G.

C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007).
[Crossref]

Geiszler, V.

K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004).
[Crossref]

Hitt, D. L.

D. L. Hitt and N. Macken, “A simplified model for determining interfacial position in convergent microchannel flows,” J. Fluids Eng. 126, 758–767 (2004).
[Crossref]

D. L. Hitt, “Confocal Imaging of Fluidic Interfaces in Microchannel Geometries,” in Science, Technology & Education of Microscopy: an Overview, Vol.1, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2003).

D. L. Hitt, “Optical Considerations for Accurate Volumetric Reconstructions from 3-D Confocal Imaging,” in Science, Technology & Education of Microscopy: an Overview, Vol. II, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2004).

Klos, M.

Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001).
[Crossref]

Kris, R.

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

Macken, N.

D. L. Hitt and N. Macken, “A simplified model for determining interfacial position in convergent microchannel flows,” J. Fluids Eng. 126, 758–767 (2004).
[Crossref]

Marschner, T.

T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001).
[Crossref]

Meyyappan,

Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001).
[Crossref]

Miller, K.

K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004).
[Crossref]

Muckenhirn, S.

Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001).
[Crossref]

Rathsack, B. M.

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

Thomas, G. B.

G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 8th ed., (Addison-Wesley, 1992) 328.
[PubMed]

J. Fluids Eng. (1)

D. L. Hitt and N. Macken, “A simplified model for determining interfacial position in convergent microchannel flows,” J. Fluids Eng. 126, 758–767 (2004).
[Crossref]

Meas. Sci. Technol. (1)

C. G. Frase, E. Buhr, and K. Dirscherl, “CD characterization of nanostructures in SEM metrology,” Meas. Sci. Technol. 18, 510–519 (2007).
[Crossref]

Proc. SPIE (4)

K. Miller, V. Geiszler, and D. Dawson, “Characterization and control of sub-100-nm etch and lithography processes using atomic force metrology,” Proc. SPIE 5375, 1325–1330 (2004).
[Crossref]

Meyyappan, M. Klos, and S. Muckenhirn, “Foot (bottom corner) measurement of a structure with SPM,” Proc. SPIE 4344, 733–738 (2001).
[Crossref]

T. Marschner, G. Eytan, and O. Dror, “Determination of best focus and exposure dose using CD-SEM side-wall imaging,” Proc. SPIE 4344, 355–365 (2001).
[Crossref]

B. M. Rathsack, S. G. Bushman, F. G. Celii, S. F. Ayres, and R. Kris, “Inline Sidewall Angle Monitoring of Memory Capacitor Profiles,” Proc. SPIE 5752, 1237–1247 (2005).
[Crossref]

Other (7)

http://www.zeiss.com/4125681f004ca025/Contents-Frame/f5445011b5a0a89f852571d200714c4d.

http://www.olympusconfocal.com/applications/index.html.

D. L. Hitt, “Optical Considerations for Accurate Volumetric Reconstructions from 3-D Confocal Imaging,” in Science, Technology & Education of Microscopy: an Overview, Vol. II, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2004).

D. L. Hitt, “Confocal Imaging of Fluidic Interfaces in Microchannel Geometries,” in Science, Technology & Education of Microscopy: an Overview, Vol.1, A. Mendez-Vilas, ed. (Formatex, Badajoz, Spain, 2003).

LSM 510 and LSM 510 META Laser Scanning Microscopes, Operating Manual, Carl Zeiss, 2002

http://www.hi.helsinki.fi/amu/AMU%20Cf_tut/cf_tut_part1-5.htm.

G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 8th ed., (Addison-Wesley, 1992) 328.
[PubMed]

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Figures (14)

Fig. 1.
Fig. 1. Plan view of the surface profile of a “┛” shaped elliptical microchannel obtained with optical interferometry (Model: Veeco NT3000). Color represents height value. Unit: µm. The inset is the schematic of the cross section of the microchannel

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Fig. 2.
Fig. 2. Cross sectional profile comparison at A-A in Fig.5 conducted between the adaptive threshold method in this paper and the fixed threshold method in the commercial laser confocal microscope.

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Fig. 3.
Fig. 3. Model of signal intensity variation when laser spot scans through a profiled surface with laser fluorescent confocal microscopy

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Fig. 4.
Fig. 4. Normalized signal intensity I and intensity variation over one scanning step ΔI (dI in plots) varied with laser point position l when (a) t = 2b, (b) t = 1.5b, and (c) t = 0.5b. l is normalized with the depth resolution of the objective, b. Position “1” represents the profiled surface position. The intensity gradually decreases from the maximum intensity to the minimum in Fig. 4(a). The profiled surface is at the ΔI min position plus half of step interval. The intensity cannot reach the peak during scanning in Fig. 4(b), however the profiled surface still can be found with the same rule in Fig. 4(a). There is no fixed relationship between the profiled surface and ΔI min position in Fig. 4(c).

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Fig. 5.
Fig. 5. (a) The fluorescent image of a “T” shaped elliptical channel. Color represents the signal intensity value. A-A is the cross sectional position in Fig. 2, and Fig. 5 (b, c, e, f). (b) Cross sectional image of the 3D image stack. (c) Cross section of the 3D differentiation stack nx ×ny ×(nz -1). (d) Extracted 3D profile of the microchannel. (e) Comparison between the cross sectional curve of the extracted profile with the reference cross section. (f) Cross sectional curves measured for 5 times for the same feature.

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Fig. 6.
Fig. 6. (a) Cross section of the 3D volume image of a trapezoid channel. (b) 3D profile of the right sidewall of the microchannel. (c) Comparison of the extracted sidewall profile with the cross sectional curve obtained after the sample was cut. (d) 3D profile of the microchannel when the differentiation was conducted along the z direction.

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Fig. 7.
Fig. 7. (a) Cross section of the 3D volume image of an edge whose sidewall angle >90°. (b) Extracted sidewall profile

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Fig. 8.
Fig. 8. The enclosed volume between the cover slip and the microchanel in Fig. 5

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Fig. 9.
Fig. 9. Comparison before and after image contrast adjustment for the microchannel in Fig. 6 (a)

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Fig. 10.
Fig. 10. Comparison before and after the background noise is removed for the microchannel in Fig. 5

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Fig. 11.
Fig. 11. Illustration on signal intensity variation when the scanning direction tilts to the profiled surface

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Fig. 12.
Fig. 12. Profile comparison when using different N.A. objectives

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Fig. 13.
Fig. 13. Variation of |ΔI|max with the differentiation step interval

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Fig. 14.
Fig. 14. Measured cross sectional profiles of a triangular microchannel when choosing different differentiation intervals. The data points inside the channel profile are noise points.

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Tables (1)

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Table 1. Detailed algorithm to extract sidewall profile

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Equations (6)

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I = ρ ∫ b − h b π a 2 ( 1 − x 2 b 2 ) dx = π ρ a 2 h 2 b ( 1 − h 3 b )
Δ I = π ρ a 2 ( h − d ) 2 b ( 1 − ( h − d ) 3 b ) − π ρ a 2 h 2 b ( 1 − h 3 b )
l max = 2 b − h max = b − d 2
Δ I min = − π ρ a 2 d b ( b − d 2 12 b )
I ′ = π ρ a 2 h 2 b ( 1 − h 3 b ) − π ρ a 2 h ′ 2 b ( 1 − h ′ 3 b )
∣ Δ I ∣ max ≤ 3 I sat 4 b ( d − d 3 12 b 2 )

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