Abstract

A method of measuring thin film thickness is described, based on a previous paper where the authors analyzed a graphical means for grating modulation calculation. Metallic or dielectric films on any substrate may be measured, and precision was shown to be comparable with that achieved ellipsometrically at least in the 300–1500-Å thickness range. The method is non-contact and destructive: the grating is recorded on the film. Measurements are simple, requiring a low-power He–Ne laser and a photodetector, and may be carried out at a distance from the sample. Experimental results are presented for three types of sample, including measurements by reflection and transmission.

© 1984 Optical Society of America

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Corrections

Geraldo F. Meǹdes, Lucila Cescato, and Jaime Frejlich, "Gratings for metrology and process control. 2: Thin film thickness measurement; errata," Appl. Opt. 23, 3517_1-3517 (1984)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-23-20-3517_1

References

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  1. G. F. Mendes, L. Cescato, J. Frejlich, Appl. Opt. 23, 571 (1984).
    [CrossRef] [PubMed]
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 62.
  3. Ellipsometric tables of ellipsometer model L-117 from Gaertner.
  4. See, for example, M. Françon, Progress in Microscopy (Row, Peterson, Elmsford, N.Y., 1961), Chap. 6.
  5. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), p. 119.
  6. Gaertner Bulletin EA-77 reports an accuracy of 2.5–10 Å for the L-117 ellipsometer (Gaertner Scientific Corp., 1201 Wrightwood Ave., Chicago, Ill. 60614).
  7. A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500–Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.
  8. A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500-Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

1984 (1)

1982 (2)

A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500–Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500-Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 62.

Cescato, L.

Françon, M.

See, for example, M. Françon, Progress in Microscopy (Row, Peterson, Elmsford, N.Y., 1961), Chap. 6.

Frejlich, J.

Gauler, A. L.

A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500–Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500-Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), p. 119.

Mendes, G. F.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 62.

Appl. Opt. (1)

Opt. Engl. (2)

A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500–Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

A. L. Gauler, Opt. Engl. 21, 991 (1982) reported a 500-Å accuracy. We think 1/10 of a fringe (300–250 Å) or even somewhat less may be obtained depending on the particular sample. In this paper we report ±150-Å accuracy.

Other (5)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 62.

Ellipsometric tables of ellipsometer model L-117 from Gaertner.

See, for example, M. Françon, Progress in Microscopy (Row, Peterson, Elmsford, N.Y., 1961), Chap. 6.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), p. 119.

Gaertner Bulletin EA-77 reports an accuracy of 2.5–10 Å for the L-117 ellipsometer (Gaertner Scientific Corp., 1201 Wrightwood Ave., Chicago, Ill. 60614).

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Figures (17)

Fig. 1
Fig. 1

Schematic description of a rectangular grating recorded on the full depth of a film of thickness h and complex index n ^ 1, on a substrate of index n ^ 2. Bar and groove widths and period are a, b, and d, respectively.

Fig. 2
Fig. 2

Nomogram for a metallic lamellar reflecting grating in air; a/d is shown vs h for different values of I1/I0, I2/I0, and I3/I0 as the parameters, corresponding to the example depicted in Fig. 6(c). The nomogram is symmetric both through a/d = 0.5 and h = λ/4 = 1582 Å.

Fig. 3
Fig. 3

Schematic description of a nonabsorbing transmitting lamellar grating of groove depth H, substrate thickness Hs, and index n1 with negligible optical interface between them. Parameters a, b, and d are defined in Fig. 1.

Fig. 4
Fig. 4

SiO2 lamellar grating on Si substrate. The refractive indices are n1 = 1.46 for the SiO2 and n ^ 2 = 3.85 + i0.02 for the Si, both for the 6328-Å wavelength. Other dimensions are defined in Fig. 1.

Fig. 5
Fig. 5

Nomogram for SiO2 lamellar grating on Si substrate; a/d is shown vs h for different values of I1/I0, I2/I0, and I3/I0 as the parameters, corresponding to the grating described in Fig. 4 for n0 = 1. As expected, this nomogram is no longer symmetric either through a/d = 0.5 or through h = λ/4.

Fig. 6
Fig. 6

Measurement of a thin aluminum film thickness: (a) a thin aluminum film coated on a Si substrate; (b) for measuring its thickness a lamellar grating is photolithographed on it; (c) the whole is covered again with an evaporated-aluminum film.

Fig. 7
Fig. 7

The sample depicted in Fig. 6(c) is seen in an interferential microscope (Leitz Linnik) in white light (λ = 6000 Å). This picture allows the good quality rectangular sample shape to be checked and the depth of the grating groove to be measured by interferometric-fringe displacement.4

Fig. 8
Fig. 8

Thickness h of the aluminum film in Fig. 6(c) is measured using an interferential microscope (Fig. 7) and our diffraction technique. Both measurements are plotted in this figure. The continuous line represents the ideal result. For large thickness values (h > 2000 Å) experimental points deviate from ideal, presumably because of the stronger influence of grating shape distortion.

Fig. 9
Fig. 9

(a) A thin Shipley AZ-1350B photoresist coated on a glass substrate. Refractive indices were measured to be 1.64 and 1.51, respectively, for λ = 6328 Å. (b) A lamellar grating is photolithographed on the resist film, which may be considered as an approach to the transmission grating in Fig. 3. Diffraction by transmission is measured on these samples and H is calculated in the text. If the photoresist film thickness is to be measured the grating must be etched to the full depth of the film (i.e., H should be the actual film thickness).

Fig. 10
Fig. 10

Interferometric picture of the sample in Fig. 9(b) but covered with aluminum (see Fig. 7 for comments).

Fig. 11
Fig. 11

Interferometric vs reflection diffraction measurements of samples shown in Fig. 10. The continuous line shows the expected ideal result.

Fig. 12
Fig. 12

Transmission vs reflection diffraction measurements of the thickness of the samples in Fig. 9(b). For reflection measurements, the samples were covered with an evaporated-aluminum film. Good agreement can be observed between both sets of measurements.

Fig. 13
Fig. 13

Interferometric picture of a lamellar grating etched on a glass substrate (as shown in Fig. 3) and later covered with aluminum and measured as described in Fig. 7.

Fig. 14
Fig. 14

Interferometric vs diffraction grating modulation measurements for the gratings described in Fig. 13.

Fig. 15
Fig. 15

Transmission vs reflection diffraction measurements for the samples in Fig. 13 before and after being evaporated aluminum covered, respectively.

Fig. 16
Fig. 16

Interferometric picture of a lamellar grating of SiO2 over a Si substrate as described in Fig. 4 and covered with aluminum (see Fig. 7 for comments).

Fig. 17
Fig. 17

Ellipsometric vs diffraction thickness measurements for SiO2 films coated on Si substrates. Ellipsometric measurements (Gaertner model L-117 ellipsometer) were carried out for the SiO2 film on the Si substrate before the gratings were etched on the samples. The crosses represent the diffraction measured once the lamellar gratings were etched on the samples (Fig. 4); the circles show the same measurements carried out on the samples after being evaporated-aluminum covered.

Equations (13)

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I N / I 0 = r ^ a - r ^ b 2 ( a / d ) 2 r ^ b + ( r ^ a - r ^ b ) ( a / d ) 2 sinc 2 ( N a / d ) ,
r ^ a = r ^ 1 + r ^ 2 exp ( i 2 β ) 1 + r ^ 1 r ^ 2 exp ( i 2 β ) , where 2 β 4 π h n ^ 1 / λ , r ^ b = r ^ 3 exp ( i 2 γ ) , where 2 γ 4 π h n 0 / λ . }
r ^ 1 = ( n 0 - n ^ 1 ) / ( n 0 + n ^ 1 ) , r ^ 2 = ( n ^ 1 - n ^ 2 ) / ( n ^ 1 + n ^ 2 ) , r ^ 3 = ( n 0 - n ^ 2 ) / ( n 0 + n ^ 2 ) . }
r ^ a = r ^ 1 r ^ b = r 1 exp ( i 2 γ ) where 2 γ = 4 π h / λ } ,
cos ( 2 γ ) = 1 - I N / I 0 2 ( a / d ) 2 sinc 2 ( N a / d ) + ( I N / I 0 ) 2 ( 1 - a / d ) a / d .
2 γ = K 2 π ± 2 γ 0 or h = K λ / 2 ± h 0 with K an integer } .
I N / I 0 = t ^ a - t ^ b 2 ( a / d ) 2 t ^ b + ( t ^ a - t ^ b ) a / d 2 sinc 2 ( N a / d ) .
t ^ a = t 01 t 10 exp ( i β ) 1 + r 01 r 10 exp ( i 2 β ) with β 2 π ( H + H s ) n 1 / λ , t ^ b = t 01 t 10 exp ( i γ ) 1 + r 01 r 10 exp ( i 2 γ ) with γ 2 π ( H s n 1 + H n 0 ) / λ , }
cos ( β - γ ) = 1 - I N / I 0 2 ( a / d ) 2 sinc 2 ( N a / d ) + 2 I N / I 0 ( 1 - a / d ) a / d .
H = h 2 n 0 / ( n 1 - n 0 ) .
r 1 = - 0.1870 , r ^ 2 = - 0.4501 - i 0.0021 , r ^ 3 = - 0.5876 - i 0.0017. }
r ^ a = - 0.1870 - 0.4501 exp [ i ( 2 β + 0.0047 ) ] 1 + 0.0842 exp [ i ( 2 β + 0.0046 ) ] , r ^ b = - 0.5876 exp [ i ( 2 γ + 0.0029 ) ] . }
r ^ a - 0.1870 - 0.4501 exp ( i 2 β ) 1 + 0.0842 exp ( i 2 β ) , r ^ b - 0.5876 exp ( i 2 γ ) , }

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