Abstract

When a thin film that is prepared in a step form on a substrate and coated uniformly with a reflective material is illuminated by a parallel coherent beam of monochromatic light, the Fresnel diffraction fringes are formed on a screen perpendicular to the reflected beam. The visibility of the fringes depends on film thickness, angle of incidence, and light wavelength. Measuring visibility versus incident angle provides the film thickness with an accuracy of a few nanometers. The technique is easily applicable and it covers a wide range of thicknesses with highly reliable results.

© 2009 Optical Society of America

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References

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  1. K. L. Chopra, Thin Film Phenomena (McGraw-Hill, 1969).
  2. H. K. Pulker, “Film thickness,” in Coating On Glass, H. K. Pulker, ed. (Elsevier, 1984), pp. 287-340.
  3. W. A. Pliskin and S. J. Zanin, “Film thickness and composition,” in Handbook of Thin Film Technology, L. I. Maissel and R. Glang, eds. (McGraw-Hill, 1970), pp. 11:1-11:54.
  4. “Film thickness,” in Semiconductor Measurements and Instrumentation, W. R. Runyan and T. J. Shaffner, eds. (McGraw-Hill, 1998), pp. 177-199.
  5. D. M. Mattox, “Non-elemental characterization of films and coatings,” in Handbook of Deposition Technologies for Films and Coatings, R. F. Bunshah, ed. (Noyes, 1994).
  6. L. Eckertová, Physics of Thin Films (SNTL, 1986).
  7. S. Tolansky, Multiple Beam Interferometries (Clarendon, 1948).
  8. C. Weaver and P. Benjamin, “Measurement of the thickness of thin films by multiple-beam interference,” Nature 177, 1030-1031 (1956).
    [CrossRef]
  9. O. S. Heavens, “Measurement of the thickness of thin films by multiple-beam interferometry,” Proc. Phys. Soc. B 64, 419-425(1951).
    [CrossRef]
  10. C. Weaver and P. Benjamin, “Errors in the measurement of film thickness by multiple-beam interferometry,” Nature 182, 1149-1150 (1958).
    [CrossRef]
  11. K. Seung-Woo and K. Gee-Hong, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968-5973 (1999).
    [CrossRef]
  12. P. Hlubina, J. Lunacek, and D. Ciprian, “White-light spectral interferometry and reflectometry to measure thickness of thin films,” Proc. SPIE 7389, 738926 (2009).
    [CrossRef]
  13. A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
    [CrossRef]
  14. M. T. Tavassoly, M. Amiri, A. Darudi, R. Alipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540-547 (2009).
    [CrossRef]
  15. M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes,” Opt. Commun. 272, 349-361 (2007).
    [CrossRef]

2009 (2)

P. Hlubina, J. Lunacek, and D. Ciprian, “White-light spectral interferometry and reflectometry to measure thickness of thin films,” Proc. SPIE 7389, 738926 (2009).
[CrossRef]

M. T. Tavassoly, M. Amiri, A. Darudi, R. Alipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540-547 (2009).
[CrossRef]

2007 (1)

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes,” Opt. Commun. 272, 349-361 (2007).
[CrossRef]

2001 (1)

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

1999 (1)

1958 (1)

C. Weaver and P. Benjamin, “Errors in the measurement of film thickness by multiple-beam interferometry,” Nature 182, 1149-1150 (1958).
[CrossRef]

1956 (1)

C. Weaver and P. Benjamin, “Measurement of the thickness of thin films by multiple-beam interference,” Nature 177, 1030-1031 (1956).
[CrossRef]

1951 (1)

O. S. Heavens, “Measurement of the thickness of thin films by multiple-beam interferometry,” Proc. Phys. Soc. B 64, 419-425(1951).
[CrossRef]

Alipour, R.

Amiri, M.

M. T. Tavassoly, M. Amiri, A. Darudi, R. Alipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540-547 (2009).
[CrossRef]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes,” Opt. Commun. 272, 349-361 (2007).
[CrossRef]

Benjamin, P.

C. Weaver and P. Benjamin, “Errors in the measurement of film thickness by multiple-beam interferometry,” Nature 182, 1149-1150 (1958).
[CrossRef]

C. Weaver and P. Benjamin, “Measurement of the thickness of thin films by multiple-beam interference,” Nature 177, 1030-1031 (1956).
[CrossRef]

Chopra, K. L.

K. L. Chopra, Thin Film Phenomena (McGraw-Hill, 1969).

Ciprian, D.

P. Hlubina, J. Lunacek, and D. Ciprian, “White-light spectral interferometry and reflectometry to measure thickness of thin films,” Proc. SPIE 7389, 738926 (2009).
[CrossRef]

Darudi, A.

De Laet, J.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Eckertová, L.

L. Eckertová, Physics of Thin Films (SNTL, 1986).

Franquet, A.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Gee-Hong, K.

Heavens, O. S.

O. S. Heavens, “Measurement of the thickness of thin films by multiple-beam interferometry,” Proc. Phys. Soc. B 64, 419-425(1951).
[CrossRef]

Hlubina, P.

P. Hlubina, J. Lunacek, and D. Ciprian, “White-light spectral interferometry and reflectometry to measure thickness of thin films,” Proc. SPIE 7389, 738926 (2009).
[CrossRef]

Lunacek, J.

P. Hlubina, J. Lunacek, and D. Ciprian, “White-light spectral interferometry and reflectometry to measure thickness of thin films,” Proc. SPIE 7389, 738926 (2009).
[CrossRef]

Mattox, D. M.

D. M. Mattox, “Non-elemental characterization of films and coatings,” in Handbook of Deposition Technologies for Films and Coatings, R. F. Bunshah, ed. (Noyes, 1994).

Moradi, A.-R.

Pliskin, W. A.

W. A. Pliskin and S. J. Zanin, “Film thickness and composition,” in Handbook of Thin Film Technology, L. I. Maissel and R. Glang, eds. (McGraw-Hill, 1970), pp. 11:1-11:54.

Pulker, H. K.

H. K. Pulker, “Film thickness,” in Coating On Glass, H. K. Pulker, ed. (Elsevier, 1984), pp. 287-340.

Saber, A.

Schram, T.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Seung-Woo, K.

Subramanian, V.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Tavassoly, M. T.

M. T. Tavassoly, M. Amiri, A. Darudi, R. Alipour, A. Saber, and A.-R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540-547 (2009).
[CrossRef]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes,” Opt. Commun. 272, 349-361 (2007).
[CrossRef]

Terryn, H.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Tolansky, S.

S. Tolansky, Multiple Beam Interferometries (Clarendon, 1948).

van Ooij, W. J.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Vereecken, J.

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Weaver, C.

C. Weaver and P. Benjamin, “Errors in the measurement of film thickness by multiple-beam interferometry,” Nature 182, 1149-1150 (1958).
[CrossRef]

C. Weaver and P. Benjamin, “Measurement of the thickness of thin films by multiple-beam interference,” Nature 177, 1030-1031 (1956).
[CrossRef]

Zanin, S. J.

W. A. Pliskin and S. J. Zanin, “Film thickness and composition,” in Handbook of Thin Film Technology, L. I. Maissel and R. Glang, eds. (McGraw-Hill, 1970), pp. 11:1-11:54.

Appl. Opt. (1)

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

Nature (2)

C. Weaver and P. Benjamin, “Measurement of the thickness of thin films by multiple-beam interference,” Nature 177, 1030-1031 (1956).
[CrossRef]

C. Weaver and P. Benjamin, “Errors in the measurement of film thickness by multiple-beam interferometry,” Nature 182, 1149-1150 (1958).
[CrossRef]

Opt. Commun. (1)

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes,” Opt. Commun. 272, 349-361 (2007).
[CrossRef]

Proc. Phys. Soc. B (1)

O. S. Heavens, “Measurement of the thickness of thin films by multiple-beam interferometry,” Proc. Phys. Soc. B 64, 419-425(1951).
[CrossRef]

Proc. SPIE (1)

P. Hlubina, J. Lunacek, and D. Ciprian, “White-light spectral interferometry and reflectometry to measure thickness of thin films,” Proc. SPIE 7389, 738926 (2009).
[CrossRef]

Thin Solid Films (1)

A. Franquet, J. De Laet, T. Schram, H. Terryn, V. Subramanian, W. J. van Ooij, and J. Vereecken, “Determination of the thickness of thin silane films on aluminium surfaces by means of spectroscopic ellipsometry,” Thin Solid Films 384, 37-45(2001).
[CrossRef]

Other (7)

K. L. Chopra, Thin Film Phenomena (McGraw-Hill, 1969).

H. K. Pulker, “Film thickness,” in Coating On Glass, H. K. Pulker, ed. (Elsevier, 1984), pp. 287-340.

W. A. Pliskin and S. J. Zanin, “Film thickness and composition,” in Handbook of Thin Film Technology, L. I. Maissel and R. Glang, eds. (McGraw-Hill, 1970), pp. 11:1-11:54.

“Film thickness,” in Semiconductor Measurements and Instrumentation, W. R. Runyan and T. J. Shaffner, eds. (McGraw-Hill, 1998), pp. 177-199.

D. M. Mattox, “Non-elemental characterization of films and coatings,” in Handbook of Deposition Technologies for Films and Coatings, R. F. Bunshah, ed. (Noyes, 1994).

L. Eckertová, Physics of Thin Films (SNTL, 1986).

S. Tolansky, Multiple Beam Interferometries (Clarendon, 1948).

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Figures (7)

Fig. 1
Fig. 1

Geometry used to show the Fresnel diffraction from a one-dimensional (1D) step.

Fig. 2
Fig. 2

Calculated normalized intensity distribution on the diffraction patterns of lights diffracted from a 1D step of height (a)  λ / 12 , (b)  λ / 4 , and (c)  3 λ / 7 .

Fig. 3
Fig. 3

Calculated visibility of the three central diffraction fringes formed by the light diffracted from a 1D step, versus the optical path difference divided by the wavelength, Δ / λ . The visibilities under 0.7 lie on the linear parts of the visibility curve.

Fig. 4
Fig. 4

Sketch of the experimental setup. L, NF, L1, L2, TF, CCD, and PC stand for laser, neutral filter, lenses 1 and 2, thin film with step, intensity detector, and personal computer, respectively.

Fig. 5
Fig. 5

Typical experimental diffraction patterns and intensity profiles of lights diffracted from a step formed by a thin film of thickness 446 nm at incident angles (a)  56 ° , (b)  68 ° , and (c)  77 ° . The dots are experimental values averaged over the lines parallel to the step edge. The light wavelength was λ = 632.8 nm .

Fig. 6
Fig. 6

Experimental visibilities, Δ, versus the cosine of incident angle for the three central diffraction fringes of light diffracted from a step formed by a thin film of thickness 446 nm . The solid curve is the calculated visibility.

Fig. 7
Fig. 7

Circles and triangles are experimental visibilities for the incident light wavelengths λ = 532 nm and λ = 633 nm , respectively, versus the cosine of incident angle in the linear part of the visibility curve for film thicknesses of (a)  57 nm and (b)  462 nm . The solid lines are the best fitted visibility lines.

Tables (2)

Tables Icon

Table 1 Six Film Thicknesses Measured Using Fresnel Diffraction of Light from Steps Formed by the Thin Films Using Two Different Wavelengths

Tables Icon

Table 2 Comparison between the Thicknesses Measured by Fitting Data on Visibility Line (FVL) and the Thicknesses Obtained from Zero Visibility Point (ZVP)

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I L = I 0 r L r R [ cos 2 ( φ / 2 ) + 2 ( C 0 2 + S 0 2 ) sin 2 ( φ / 2 ) ( C 0 S 0 ) sin φ ] + I 0 2 [ ( 1 / 2 + C 0 2 + S 0 2 ) ( r L r R ) 2 + ( C 0 + S 0 ) ( r L 2 r R 2 ) ] ,
I n = [ cos 2 ( φ / 2 ) + 2 ( C 0 2 + S 0 2 ) sin 2 ( φ / 2 ) ( C 0 S 0 ) sin φ ] .
V = I max L + I max R 2 I min I max L + I max R 2 + I min ,
tan α = ( V 2 V 1 ) λ 2 h ( cos θ 2 cos θ 1 ) ,
h = s λ 5.54 .
h = λ 2 ( cos θ 1 cos θ 2 ) .

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