Abstract

A mechanical design technique for optical coatings that simultaneously controls thermal deformation and optical reflectivity is reported. The method requires measurement of the refractive index and thermal stress of single films prior to the design. Atomic layer deposition was used for deposition because of the high repeatability of the film constants. An Al2O3/HfO2 distributed Bragg reflector was deposited with a predicted peak reflectivity of 87.9% at 542.4 nm and predicted edge deformation of −360 nm/K on a 10 cm silicon substrate. The measured peak reflectivity was 85.7% at 541.7 nm with an edge deformation of −346 nm/K.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. C. H. Hsueh, Thin Solid Films 418, 182 (2002).
    [CrossRef]

2007 (1)

2002 (3)

W. Liu and J. Talghader, Appl. Opt. 41, 3285 (2002).
[CrossRef] [PubMed]

D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, Chem. Mater. 14, 4350 (2002).
[CrossRef]

C. H. Hsueh, Thin Solid Films 418, 182 (2002).
[CrossRef]

1996 (1)

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, Thin Solid Films 289, 250 (1996).
[CrossRef]

1989 (1)

G. S. Higashi and C. G. Fleming, Appl. Phys. Lett. 55, 1963 (1989).
[CrossRef]

1984 (1)

Y. Okada and Y. Tokumaru, J. Appl. Phys. 56, 314 (1984).
[CrossRef]

1983 (1)

Z. Feng and H. Liu, J. Appl. Phys. 54, 83 (1983).
[CrossRef]

1973 (1)

W. A. Brantley, J. Appl. Phys. 44, 534 (1973).
[CrossRef]

1963 (1)

M. Vasudevan and W. Johnson, Appl. Sci. Res., Sect. B 9, 420 (1963).
[CrossRef]

1925 (1)

1909 (1)

G. G. Stoney, Proc. R. Soc. London, Ser. A 82, 172 (1909).
[CrossRef]

Becker, J.

D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, Chem. Mater. 14, 4350 (2002).
[CrossRef]

Brantley, W. A.

W. A. Brantley, J. Appl. Phys. 44, 534 (1973).
[CrossRef]

Feng, Z.

Z. Feng and H. Liu, J. Appl. Phys. 54, 83 (1983).
[CrossRef]

Fleming, C. G.

G. S. Higashi and C. G. Fleming, Appl. Phys. Lett. 55, 1963 (1989).
[CrossRef]

Gabriel, N. T.

Gordon, R. G.

D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, Chem. Mater. 14, 4350 (2002).
[CrossRef]

Hausmann, D. M.

D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, Chem. Mater. 14, 4350 (2002).
[CrossRef]

Higashi, G. S.

G. S. Higashi and C. G. Fleming, Appl. Phys. Lett. 55, 1963 (1989).
[CrossRef]

Hsueh, C. H.

C. H. Hsueh, Thin Solid Films 418, 182 (2002).
[CrossRef]

Johnson, W.

M. Vasudevan and W. Johnson, Appl. Sci. Res., Sect. B 9, 420 (1963).
[CrossRef]

Kim, E.

D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, Chem. Mater. 14, 4350 (2002).
[CrossRef]

Kim, S. S.

Leskelä, M.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, Thin Solid Films 289, 250 (1996).
[CrossRef]

Liu, H.

Z. Feng and H. Liu, J. Appl. Phys. 54, 83 (1983).
[CrossRef]

Liu, W.

Matero, R.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, Thin Solid Films 289, 250 (1996).
[CrossRef]

Okada, Y.

Y. Okada and Y. Tokumaru, J. Appl. Phys. 56, 314 (1984).
[CrossRef]

Riihelä, D.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, Thin Solid Films 289, 250 (1996).
[CrossRef]

Ritala, M.

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, Thin Solid Films 289, 250 (1996).
[CrossRef]

Song, W.

Stoney, G. G.

G. G. Stoney, Proc. R. Soc. London, Ser. A 82, 172 (1909).
[CrossRef]

Talghader, J.

Talghader, J. J.

Timoshenko, S.

Tokumaru, Y.

Y. Okada and Y. Tokumaru, J. Appl. Phys. 56, 314 (1984).
[CrossRef]

Vasudevan, M.

M. Vasudevan and W. Johnson, Appl. Sci. Res., Sect. B 9, 420 (1963).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. S. Higashi and C. G. Fleming, Appl. Phys. Lett. 55, 1963 (1989).
[CrossRef]

Appl. Sci. Res., Sect. B (1)

M. Vasudevan and W. Johnson, Appl. Sci. Res., Sect. B 9, 420 (1963).
[CrossRef]

Chem. Mater. (1)

D. M. Hausmann, E. Kim, J. Becker, and R. G. Gordon, Chem. Mater. 14, 4350 (2002).
[CrossRef]

J. Appl. Phys. (3)

W. A. Brantley, J. Appl. Phys. 44, 534 (1973).
[CrossRef]

Y. Okada and Y. Tokumaru, J. Appl. Phys. 56, 314 (1984).
[CrossRef]

Z. Feng and H. Liu, J. Appl. Phys. 54, 83 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Proc. R. Soc. London, Ser. A (1)

G. G. Stoney, Proc. R. Soc. London, Ser. A 82, 172 (1909).
[CrossRef]

Thin Solid Films (2)

D. Riihelä, M. Ritala, R. Matero, and M. Leskelä, Thin Solid Films 289, 250 (1996).
[CrossRef]

C. H. Hsueh, Thin Solid Films 418, 182 (2002).
[CrossRef]

Other (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

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Figures (4)

Fig. 1
Fig. 1

Parametric fits of the refractive indices of Al 2 O 3 and HfO 2 to VASE measurement data using a modified four-parameter Cauchy model that includes an inverse wavelength term.

Fig. 2
Fig. 2

Measurement of single-film thermal expansion-induced change in curvature with temperature for Al 2 O 3 and HfO 2 on silicon, with a linear fit shown for each.

Fig. 3
Fig. 3

Comparison of simulated and measured reflectivity data for the four-pair multilayer at 15° from normal incidence using s-polarized light.

Fig. 4
Fig. 4

Relative wafer curvature versus temperature for the four-pair design, comparing the simulated prediction to actual measurement (all six heat cycles are shown). The equivalent edge deflection is shown at the right.

Equations (4)

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

n ( λ ) = A + B λ + C λ 2 + D λ 4 .
σ f = E s d s 2 6 d f ρ .
d σ f d T = ( α s α f ) E f .
( α s α f ) E f = E s d s 2 6 d f d ρ d T .

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