Abstract

We describe a novel method for measuring the unconstrained flatness error of thin, plane-parallel precision optics. Test parts are floated on high-density aqueous metatungstate solutions while measuring the flatness error with an interferometer. The support of the flat optics by the uniform hydrostatic pressure at the submerged face of the flat optic eliminates flatness errors caused by mounting forces. A small, well characterized flatness error results from the bending of the floating flat by the hydrostatic pressure gradient at the edges. An equation describing the bending of thin, flat plates floating on a liquid is derived, which can be used to correct the flatness measurements of arbitrarily shaped plates. The method can be used to measure flatness errors of both nontransparent and transparent parts, and it is illustrated with flatness measurements of photomask blanks and substrates for extreme ultraviolet lithography. The refractive index of a saturated aqueous lithium metatungstate solution was measured at 632.8nm and was found to be close to the refractive indices of several low thermal expansion optical materials.

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  1. J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
    [CrossRef]
  2. M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
    [CrossRef]
  3. U. Griesmann, Q. Wang, and J. A. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 093601 (2007).
    [CrossRef]
  4. “SEMI Standard specification for extreme ultraviolet lithography mask substrates,” SEMI P37-1102 (Semiconductor Equipment and Materials International, 2002).
  5. V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
    [CrossRef]
  6. C. J. Evans, B. Truax, and C. Smith, “Chuck induced deformations in euv mask substrate metrology,” presented at ASPE Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, USA,7-8 April 2008.
  7. N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd ed. (Butterworth-Heinemann, 1997).
  8. S. T. Krukowski, “Sodium metatungstate; a new heavy-mineral separation medium for the extraction of conodonts from insoluble residues,” J. Paleontol. 62, 314-316 (1988).
  9. W. P. C. Duyvesteyn, H. Liu, N. L. Labaso, and P. L. Shrestha, “Lithium metatungstate,” U.S. patent 5,178,848 (1993).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, 1959).
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    [CrossRef] [PubMed]
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    [CrossRef]
  19. J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (1)

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

2007 (3)

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
[CrossRef]

U. Griesmann, Q. Wang, and J. A. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 093601 (2007).
[CrossRef]

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet,” Appl. Opt. 46, 3811-3820 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

J. H. Burnett and S. G. Kaplan, “Measurement of the refractive index and thermo-optic coefficient of water near 193 nm,” J. Microlithogr. Microfabrication Microsyst. 3, 68-72(2004).
[CrossRef]

2001 (1)

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
[CrossRef]

2000 (2)

1998 (1)

P. D. Fuqua and J. D. Barrie, “Optical properties and corrosion resistance of durable silver coatings,” Mater. Res. Soc. Proc. 555, 85-90 (1998).
[CrossRef]

1997 (1)

1992 (1)

1988 (1)

S. T. Krukowski, “Sodium metatungstate; a new heavy-mineral separation medium for the extraction of conodonts from insoluble residues,” J. Paleontol. 62, 314-316 (1988).

1967 (2)

J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
[CrossRef]

P. Clapham and G. Dew, “Surface-coated reference flats for testing fully aluminized surfaces by means of a Fizeau interferometer,” J. Sci. Instrum. 44, 899-902 (1967).
[CrossRef]

1965 (1)

Barrie, J. D.

Battula, V. S.

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Burke, J.

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
[CrossRef]

Burnett, J. H.

J. H. Burnett and S. G. Kaplan, “Measurement of the refractive index and thermo-optic coefficient of water near 193 nm,” J. Microlithogr. Microfabrication Microsyst. 3, 68-72(2004).
[CrossRef]

Chu, C.-T.

Clapham, P.

P. Clapham and G. Dew, “Surface-coated reference flats for testing fully aluminized surfaces by means of a Fizeau interferometer,” J. Sci. Instrum. 44, 899-902 (1967).
[CrossRef]

Daimon, M.

de Groot, P.

Dew, G.

P. Clapham and G. Dew, “Surface-coated reference flats for testing fully aluminized surfaces by means of a Fizeau interferometer,” J. Sci. Instrum. 44, 899-902 (1967).
[CrossRef]

Duyvesteyn, W. P. C.

W. P. C. Duyvesteyn, H. Liu, N. L. Labaso, and P. L. Shrestha, “Lithium metatungstate,” U.S. patent 5,178,848 (1993).

Earnshaw, A.

N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd ed. (Butterworth-Heinemann, 1997).

Engelstad, R. L.

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Evans, C. J.

C. J. Evans, B. Truax, and C. Smith, “Chuck induced deformations in euv mask substrate metrology,” presented at ASPE Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, USA,7-8 April 2008.

Fuqua, P. D.

Greenwood, N. N.

N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd ed. (Butterworth-Heinemann, 1997).

Griesmann, U.

U. Griesmann, Q. Wang, and J. A. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 093601 (2007).
[CrossRef]

Hanayama, R.

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
[CrossRef]

Hibino, K.

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
[CrossRef]

Kaplan, S. G.

J. H. Burnett and S. G. Kaplan, “Measurement of the refractive index and thermo-optic coefficient of water near 193 nm,” J. Microlithogr. Microfabrication Microsyst. 3, 68-72(2004).
[CrossRef]

Krukowski, S. T.

S. T. Krukowski, “Sodium metatungstate; a new heavy-mineral separation medium for the extraction of conodonts from insoluble residues,” J. Paleontol. 62, 314-316 (1988).

Küchel, M. F.

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
[CrossRef]

Labaso, N. L.

W. P. C. Duyvesteyn, H. Liu, N. L. Labaso, and P. L. Shrestha, “Lithium metatungstate,” U.S. patent 5,178,848 (1993).

Larkin, K. G.

Liu, H.

W. P. C. Duyvesteyn, H. Liu, N. L. Labaso, and P. L. Shrestha, “Lithium metatungstate,” U.S. patent 5,178,848 (1993).

Malitson, I. H.

Masumura, A.

Mikkelson, A. R.

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Oreb, B. F.

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
[CrossRef]

K. G. Larkin and B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740-1748 (1992).
[CrossRef]

Peski, C. K. V.

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Schwider, J.

J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
[CrossRef]

Shrestha, P. L.

W. P. C. Duyvesteyn, H. Liu, N. L. Labaso, and P. L. Shrestha, “Lithium metatungstate,” U.S. patent 5,178,848 (1993).

Smith, C.

C. J. Evans, B. Truax, and C. Smith, “Chuck induced deformations in euv mask substrate metrology,” presented at ASPE Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, USA,7-8 April 2008.

Soons, J. A.

U. Griesmann, Q. Wang, and J. A. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 093601 (2007).
[CrossRef]

Surrel, Y.

Timoshenko, S. P.

S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, 1959).

Truax, B.

C. J. Evans, B. Truax, and C. Smith, “Chuck induced deformations in euv mask substrate metrology,” presented at ASPE Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, USA,7-8 April 2008.

Vukkadala, P.

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Wang, Q.

U. Griesmann, Q. Wang, and J. A. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 093601 (2007).
[CrossRef]

Woinowsky-Krieger, S.

S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, 1959).

Zeuske, J. R.

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Appl. Opt. (4)

J. Microlithogr. Microfabrication Microsyst. (1)

J. H. Burnett and S. G. Kaplan, “Measurement of the refractive index and thermo-optic coefficient of water near 193 nm,” J. Microlithogr. Microfabrication Microsyst. 3, 68-72(2004).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Paleontol. (1)

S. T. Krukowski, “Sodium metatungstate; a new heavy-mineral separation medium for the extraction of conodonts from insoluble residues,” J. Paleontol. 62, 314-316 (1988).

J. Sci. Instrum. (1)

P. Clapham and G. Dew, “Surface-coated reference flats for testing fully aluminized surfaces by means of a Fizeau interferometer,” J. Sci. Instrum. 44, 899-902 (1967).
[CrossRef]

Mater. Res. Soc. Proc. (1)

P. D. Fuqua and J. D. Barrie, “Optical properties and corrosion resistance of durable silver coatings,” Mater. Res. Soc. Proc. 555, 85-90 (1998).
[CrossRef]

Opt. Acta (1)

J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
[CrossRef]

Opt. Eng. (1)

U. Griesmann, Q. Wang, and J. A. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 093601 (2007).
[CrossRef]

Opt. Lasers Eng. (1)

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tuneable phase-shifting method,” Opt. Lasers Eng. 45, 326-341 (2007).
[CrossRef]

Optik (Jena) (1)

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
[CrossRef]

Proc. SPIE (1)

V. S. Battula, J. R. Zeuske, R. L. Engelstad, P. Vukkadala, A. R. Mikkelson, and C. K. V. Peski, “Mounting methodologies to measure EUV reticle nonflatness,” Proc. SPIE 7470, 747014(2009).
[CrossRef]

Topics Appl. Phys. (1)

Y. Surrel, “Fringe analysis,” Topics Appl. Phys. 77, 52-102(2000).

Other (5)

C. J. Evans, B. Truax, and C. Smith, “Chuck induced deformations in euv mask substrate metrology,” presented at ASPE Topical Meeting on Precision Mechanical Design and Mechatronics for Sub-50 nm Semiconductor Equipment, Berkeley, California, USA,7-8 April 2008.

N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd ed. (Butterworth-Heinemann, 1997).

W. P. C. Duyvesteyn, H. Liu, N. L. Labaso, and P. L. Shrestha, “Lithium metatungstate,” U.S. patent 5,178,848 (1993).

“SEMI Standard specification for extreme ultraviolet lithography mask substrates,” SEMI P37-1102 (Semiconductor Equipment and Materials International, 2002).

S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. (McGraw-Hill, 1959).

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Figures (13)

Fig. 1
Fig. 1

Dimensions of an EUVL photomask substrate and coatings on an EUVL photomask blank.

Fig. 2
Fig. 2

Schematic of the XCALIBIR setup for photomask blank and substrate measurements. The inset photograph shows the actual setup of fold mirror and reference flat.

Fig. 3
Fig. 3

Flatness error of the reference flat shown in Fig. 2. The black square indicates the approximate size and location of the photomask blanks and substrates in the field of view of the interferometer.

Fig. 4
Fig. 4

EUVL photomask blank floating on a lithium metatungstate (LMT) solution.

Fig. 5
Fig. 5

Mechanical parameters of a thin plate floating on a liquid. The pressure gradient due to hydrostatic pressure at the edge of the plate is indicated in red.

Fig. 6
Fig. 6

Repeatability map (standard deviation) of the blank flatness error calculated from 10 repeated measurements of the photomask blank flatness.

Fig. 7
Fig. 7

Interferometer fringes of a photomask blank floating on a heavy liquid.

Fig. 8
Fig. 8

Phase response (red) and normalized sensitivity (blue) of the 13-sample phase shifting algorithm with 60 ° sampling steps used for the photomask blank measurements. F a ( ν ) and F b ( ν ) are the real and imaginary spectral transfer functions of the phase shifting algorithm.

Fig. 9
Fig. 9

Flatness error of the photomask blank (reference error removed).

Fig. 10
Fig. 10

Difference of two measurements of the photomask blank of Fig. 7 made three weeks apart.

Fig. 11
Fig. 11

Frequencies observed in wavelength shifting during photomask substrate measurements.

Fig. 12
Fig. 12

Phase response (red) and normalized sensitivity (blue) of the seven-sample phase shifting algorithm with 60 ° sampling steps used for the photomask substrate measurements.

Fig. 13
Fig. 13

Flatness error of the top surface of a photomask substrate floating on a lithium metatungstate solution (LMT).

Tables (3)

Tables Icon

Table 1 Properties of Aqueous Tungstate Solutions at Room Temperature

Tables Icon

Table 2 Densities and Refractive Indices of Several Low Thermal Expansion Materials at 632.8 nm

Tables Icon

Table 3 Coefficients of Phase Shifting Algorithms for Blank and Substrate Flatness Measurements

Equations (13)

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

Δ λ = λ 2 2 n t ,
z l = t ( ρ g ρ l 1 2 ) .
p ( z ) = { 0 if    z z l ρ l g ( z l z ) if    z < z l ,
M = t / 2 t / 2 p ( z ) z d z = t / 2 z l ρ l g ( z l z ) z d z = g t 3 ρ g ( ρ g 2 6 ρ l 2 ρ g 4 ρ l ) .
w ( x , y ) = M 2 D ( 1 + ν ) ( x 2 + y 2 ) ,
D = E t 3 12 ( 1 ν 2 ) ,
w ( x , y ) = 6 ( 1 ν ) g ρ g E ( ρ g 2 6 ρ l 2 ρ g 4 ρ l ) ( x 2 + y 2 ) .
w m = 3 ( 1 ν ) g ρ g E ( ρ g 4 ρ l ρ g 2 6 ρ l 2 ) L 2 .
w m = 6 ( 1 ν ) g ρ g E ( ρ g 4 ρ l ρ g 2 6 ρ l 2 ) R 2 .
Δ l = l α w d T d z .
Δ l = w l R .
1 R = α d T d z .
s L 2 2 1 2 R = 1 4 L 2 α d T d z .

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