Abstract

The preparation and characterization of a reference mirror of protected aluminum (Al) is reported. The mirror is made of 50–60-nm-thick Al film, coated with several-nanometer-thick Al2O3 and 30-nm-thick film of AlN. The mirror characterization is based on reliable and precise reflectance measurements relative to a silicon- (Si-) wafer reference mirror. The simple phenomenological Drude–Lorentz model is applied for modeling the dispersion relations n(λ) and k(λ) of the Al film. The reflection of the protected Al mirror is determined in the 400–800-nm spectral range with accuracy better than 0.01 for p- and s-polarized light at angles of incidence from 0° to 70°. The accuracy has been confirmed with an evaporated thin silver film with known n(λ), k(λ), and d derived by photometric measurements at normal light incidence.

© 2002 Optical Society of America

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References

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  1. T. H. Allen, “Study of Al with combined Auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
    [CrossRef]
  2. V. Panayotov, I. Konstantinov, “Algebraic determination of thin-film optical constants from photometric (T, R, Rf, Rm) and (T, Rb, Rm) measurements,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 1070–1079 (1994).
  3. I. Konstantinov, Tz. Babeva, S. Kitova, “Analysis of errors in thin-film optical parameters derived from spectrophotometric measurements at normal light incidence,” Appl. Opt. 37, 4260–4267 (1998).
    [CrossRef]
  4. H. Liddell, Computer-Aided Techniques for Design of Multilayer Filters (Adam Hilger, Bristol, UK, 1981), p. 134.
  5. SOPRA measurements obtained from http://www.sopra-sa.com .
  6. D. E. Aspnes, A.A. Studna, “Dielectric functions and optical parameters of Si, GaP, GaAs, GaSb, InP, InAs and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
    [CrossRef]
  7. T. Yasuda, D. E. Aspnes, “Optical-standard surfaces of single-crystal silicon for calibrating ellipsometers and reflectometers,” Appl. Opt. 33, 7435–7438 (1994).
    [CrossRef] [PubMed]
  8. A. Rakic, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34, 4755–4767 (1995).
    [CrossRef] [PubMed]
  9. T. F. Coleman, Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM (Soc. Ind. Appl. Math) J. Optimization 6, 418–445 (1996).
    [CrossRef]
  10. D. Smith, E. Shiles, M. Inokuti, Handbook of Optical Constants of Solids, D. Palik, ed. (Academic, San Diego, Calif., 1985), pp. 377–405.
  11. Ref. 4, pp. 9–10.
  12. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific, London, 1955), Chap. 4, pp. 51–53, 69–73.

1998 (1)

1996 (1)

T. F. Coleman, Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM (Soc. Ind. Appl. Math) J. Optimization 6, 418–445 (1996).
[CrossRef]

1995 (1)

1994 (1)

1983 (1)

D. E. Aspnes, A.A. Studna, “Dielectric functions and optical parameters of Si, GaP, GaAs, GaSb, InP, InAs and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

1976 (1)

T. H. Allen, “Study of Al with combined Auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
[CrossRef]

Allen, T. H.

T. H. Allen, “Study of Al with combined Auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
[CrossRef]

Aspnes, D. E.

T. Yasuda, D. E. Aspnes, “Optical-standard surfaces of single-crystal silicon for calibrating ellipsometers and reflectometers,” Appl. Opt. 33, 7435–7438 (1994).
[CrossRef] [PubMed]

D. E. Aspnes, A.A. Studna, “Dielectric functions and optical parameters of Si, GaP, GaAs, GaSb, InP, InAs and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Babeva, Tz.

Coleman, T. F.

T. F. Coleman, Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM (Soc. Ind. Appl. Math) J. Optimization 6, 418–445 (1996).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific, London, 1955), Chap. 4, pp. 51–53, 69–73.

Inokuti, M.

D. Smith, E. Shiles, M. Inokuti, Handbook of Optical Constants of Solids, D. Palik, ed. (Academic, San Diego, Calif., 1985), pp. 377–405.

Kitova, S.

Konstantinov, I.

I. Konstantinov, Tz. Babeva, S. Kitova, “Analysis of errors in thin-film optical parameters derived from spectrophotometric measurements at normal light incidence,” Appl. Opt. 37, 4260–4267 (1998).
[CrossRef]

V. Panayotov, I. Konstantinov, “Algebraic determination of thin-film optical constants from photometric (T, R, Rf, Rm) and (T, Rb, Rm) measurements,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 1070–1079 (1994).

Li, Y.

T. F. Coleman, Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM (Soc. Ind. Appl. Math) J. Optimization 6, 418–445 (1996).
[CrossRef]

Liddell, H.

H. Liddell, Computer-Aided Techniques for Design of Multilayer Filters (Adam Hilger, Bristol, UK, 1981), p. 134.

Panayotov, V.

V. Panayotov, I. Konstantinov, “Algebraic determination of thin-film optical constants from photometric (T, R, Rf, Rm) and (T, Rb, Rm) measurements,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 1070–1079 (1994).

Rakic, A.

Shiles, E.

D. Smith, E. Shiles, M. Inokuti, Handbook of Optical Constants of Solids, D. Palik, ed. (Academic, San Diego, Calif., 1985), pp. 377–405.

Smith, D.

D. Smith, E. Shiles, M. Inokuti, Handbook of Optical Constants of Solids, D. Palik, ed. (Academic, San Diego, Calif., 1985), pp. 377–405.

Studna, A.A.

D. E. Aspnes, A.A. Studna, “Dielectric functions and optical parameters of Si, GaP, GaAs, GaSb, InP, InAs and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

Yasuda, T.

Appl. Opt. (3)

J. Vac. Sci. Technol. (1)

T. H. Allen, “Study of Al with combined Auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976).
[CrossRef]

Phys. Rev. B (1)

D. E. Aspnes, A.A. Studna, “Dielectric functions and optical parameters of Si, GaP, GaAs, GaSb, InP, InAs and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985–1009 (1983).
[CrossRef]

SIAM (Soc. Ind. Appl. Math) J. Optimization (1)

T. F. Coleman, Y. Li, “An interior, trust region approach for nonlinear minimization subject to bounds,” SIAM (Soc. Ind. Appl. Math) J. Optimization 6, 418–445 (1996).
[CrossRef]

Other (6)

D. Smith, E. Shiles, M. Inokuti, Handbook of Optical Constants of Solids, D. Palik, ed. (Academic, San Diego, Calif., 1985), pp. 377–405.

Ref. 4, pp. 9–10.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths Scientific, London, 1955), Chap. 4, pp. 51–53, 69–73.

V. Panayotov, I. Konstantinov, “Algebraic determination of thin-film optical constants from photometric (T, R, Rf, Rm) and (T, Rb, Rm) measurements,” in Optical Interference Coatings, F. Abelès, ed., Proc. SPIE2253, 1070–1079 (1994).

H. Liddell, Computer-Aided Techniques for Design of Multilayer Filters (Adam Hilger, Bristol, UK, 1981), p. 134.

SOPRA measurements obtained from http://www.sopra-sa.com .

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Figures (9)

Fig. 1
Fig. 1

Dispersion curves of n derived by spectrophotometric measurements at normal incidence (points) and fitted with the dispersion formula of Selmeier (curve) for AlN film with d = 30±1.2 nm.

Fig. 2
Fig. 2

Reflections of eight Si wafers measured at normal incidence after the first and the second cleaning (solid curve includes 16 experimental curves) and calculated (dashed curve) with the optical constants taken from the literature.6

Fig. 3
Fig. 3

Contours of the error ratio ΔR Si θR Si with indicated values in the θ−λ plane, calculated for a Si wafer at Δn = 0.03 and Δk = 0.02. ΔR Si and ΔR Si θ were calculated from Eq. (3) at normal and obliquely incident s-polarized light, respectively.

Fig. 4
Fig. 4

Error ΔR sp θ as a function of the ratio R sp θ/R st θ, calculated from Eq. (7) for the denoted values of Z.

Fig. 5
Fig. 5

Reflection of protected Al mirror, calculated by the matrix method (points) and measured (curves) with a reference mirror of Si wafer at angles of incidence θ = 30°, 50°, and 70° of s-polarized light as well as at normal light incidence.

Fig. 6
Fig. 6

Dispersion curves of n Al and k Al obtained with the initial and the fitted parameters from Table 1, as well as data from the literature for Al deposited in ultrahigh vacuum.10

Fig. 7
Fig. 7

Contours of the reflection of s- and p-polarized light (a and b, respectively) with denoted values in the θ−λ plane for the protected Al mirror.

Fig. 8
Fig. 8

Dispersion curves of n and k of 36-nm-thick Ag film obtained by photometric measurements at normal light incidence.

Fig. 9
Fig. 9

Reflections of Ag film. Points are R s θ and R p θ values measured at θ = 30°, 50°, and 70° with the reference Al mirror. Solid curves are the values calculated by the Fresnel equations with n(λ), k(λ), and d = 36 nm, determined by the photometric measurements at normal light incidence.

Tables (1)

Tables Icon

Table 1 Initial and Fitted Values of the Drude- and Oscillator-Model Parameters and the Thicknesses of AlN and AlO Films

Equations (13)

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n=1+ A1-B/λ21/2.
F=q=1Mj=1NRq, jcalc-Rq, jmeas2,
ΔRSiθ= RSiθnΔn+ RSiθkΔk.
Rspθ= R2θR1θ Rstθ,
R1θ=ZRstθ,R2θ=ZRspθ,
ΔRspθ2=RspθR1θ ΔR1θ2+RspθR2θ ΔR2θ2+RspθRstθ ΔRstθ2.
ΔRspθ2= RspθRstθ ΔRstθ2+ΔRθZ21+RspθRstθ2.
ΔRθ2= ΔRinstrθ2+Rθθ Δθ2.
Rsp30Rst30= RAl30RSi302.
¯=¯Drω+¯Lorω.
¯Drω=1- Ωp2ω2+iω/τ.
¯Lorω=-j=1Kfjωp2ω2-ωj2+iωΓj,
nAl=0.5r+r2+i21/2, kAl=0.5-r+r2+i21/2.

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