Abstract

A new method for the determination of optical constants of absorbing inhomogeneous thin films is proposed. It requires measurements at normal incidence of the reflectance and transmittance of the film. In an inhomogeneous thin film, the optical constants vary along the thickness of the film. It has been reported in the literature that only the spatial integral value of the absorption index needs to be considered if its value is small. Therefore, in the proposed method, the mean value of the absorption index was used. The validity of this assumption was tested. On the other hand, the variation in the refractive index along the thickness of the film was taken into account. The method is discussed along with the nature of the solutions obtained and the effects of various parameters and assumptions. The method is applied successfully to inhomogeneous thin films of zirconium oxide.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Harris, H. A. Macleod, S. Ogura, E. Pelletier, and B. Vidal, "The relationship between optical inhomogeneity and film structure," Thin Solid Films 57, 173-178 (1979).
    [CrossRef]
  2. J. P. Borgogno, B. Lazarides, and E. Pelletier, "Automatic determination of the optical constants of inhomogeneous thin films," Appl. Opt. 21, 4020-4029 (1982).
    [CrossRef] [PubMed]
  3. E. E. Khawaja, S. M. Durrani, and M. A. Daous, "Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques," J. Phys. D 32, 388-394 (1999).
    [CrossRef]
  4. A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and J. A. Dobrowolski, "Influence of small inhomogeneities on the spectral characteristics of single thin films," Appl. Opt. 36, 7188-7198 (1997).
    [CrossRef]
  5. R. E. Klinger and C. K. Carniglia, "Optical and crystalline inhomogeneity in evaporated zirconia films," Appl. Opt. 24, 3184-3187 (1985).
    [CrossRef] [PubMed]
  6. H. K. Pulker, Coatings on Glass (Elsevier, 1984).
  7. D. P. Arndt, R. M. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. T. Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, "Multiple determination of the optical constants of thin-film coating materials," Appl. Opt. 23, 3571-3596 (1984).
    [CrossRef] [PubMed]
  8. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1991).
  9. I. H. Malitson, "Interspecimen comparison of the refractive index of fused silica," J. Opt. Soc. Am. 55, 1205-1209 (1965).
    [CrossRef]
  10. R. A. Synowicki and T. E. Tiwald, "Optical properties of bulk c-ZrO2, c-MgO and a-As2S3 determined by variable angle spectroscopic ellipsometry," Thin Solid Films 455, 248-255 (2004).
    [CrossRef]
  11. B. Kralik, E. K. Chang, and S. G. Louie, "Structural properties and quasiparticle band structure of zirconia," Phys. Rev. B 57, 7027-7036 (1998).
    [CrossRef]
  12. Z. W. Zhao, B. K. Tay, and G. Q. Yu, "Study of the structure and optical properties of nanocrystalline zirconium oxide thin films deposited at low temperatures," J. Phys. D 37, 1701-1705 (2004).
    [CrossRef]

2004

R. A. Synowicki and T. E. Tiwald, "Optical properties of bulk c-ZrO2, c-MgO and a-As2S3 determined by variable angle spectroscopic ellipsometry," Thin Solid Films 455, 248-255 (2004).
[CrossRef]

Z. W. Zhao, B. K. Tay, and G. Q. Yu, "Study of the structure and optical properties of nanocrystalline zirconium oxide thin films deposited at low temperatures," J. Phys. D 37, 1701-1705 (2004).
[CrossRef]

1999

E. E. Khawaja, S. M. Durrani, and M. A. Daous, "Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques," J. Phys. D 32, 388-394 (1999).
[CrossRef]

1998

B. Kralik, E. K. Chang, and S. G. Louie, "Structural properties and quasiparticle band structure of zirconia," Phys. Rev. B 57, 7027-7036 (1998).
[CrossRef]

1997

1985

1984

1982

1979

M. Harris, H. A. Macleod, S. Ogura, E. Pelletier, and B. Vidal, "The relationship between optical inhomogeneity and film structure," Thin Solid Films 57, 173-178 (1979).
[CrossRef]

1965

Arndt, D. P.

Azzam, R. M.

Bennett, J. M.

Borgogno, J. P.

Carniglia, C. K.

Case, W. E.

Chang, E. K.

B. Kralik, E. K. Chang, and S. G. Louie, "Structural properties and quasiparticle band structure of zirconia," Phys. Rev. B 57, 7027-7036 (1998).
[CrossRef]

Daous, M. A.

E. E. Khawaja, S. M. Durrani, and M. A. Daous, "Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques," J. Phys. D 32, 388-394 (1999).
[CrossRef]

Dobrowolski, J. A.

Durrani, S. M.

E. E. Khawaja, S. M. Durrani, and M. A. Daous, "Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques," J. Phys. D 32, 388-394 (1999).
[CrossRef]

Gibson, U. J.

Harris, M.

M. Harris, H. A. Macleod, S. Ogura, E. Pelletier, and B. Vidal, "The relationship between optical inhomogeneity and film structure," Thin Solid Films 57, 173-178 (1979).
[CrossRef]

Hart, T. T.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1991).

Ho, F. C.

Hodgkin, V. A.

Khawaja, E. E.

E. E. Khawaja, S. M. Durrani, and M. A. Daous, "Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques," J. Phys. D 32, 388-394 (1999).
[CrossRef]

Klapp, W. P.

Klinger, R. E.

Kralik, B.

B. Kralik, E. K. Chang, and S. G. Louie, "Structural properties and quasiparticle band structure of zirconia," Phys. Rev. B 57, 7027-7036 (1998).
[CrossRef]

Lazarides, B.

Louie, S. G.

B. Kralik, E. K. Chang, and S. G. Louie, "Structural properties and quasiparticle band structure of zirconia," Phys. Rev. B 57, 7027-7036 (1998).
[CrossRef]

Macleod, H. A.

Malitson, I. H.

Ogura, S.

M. Harris, H. A. Macleod, S. Ogura, E. Pelletier, and B. Vidal, "The relationship between optical inhomogeneity and film structure," Thin Solid Films 57, 173-178 (1979).
[CrossRef]

Pelletier, E.

Pulker, H. K.

H. K. Pulker, Coatings on Glass (Elsevier, 1984).

Purvis, M. K.

Quinn, D. M.

Strome, D. H.

Sullivan, B. T.

Swenson, R.

Synowicki, R. A.

R. A. Synowicki and T. E. Tiwald, "Optical properties of bulk c-ZrO2, c-MgO and a-As2S3 determined by variable angle spectroscopic ellipsometry," Thin Solid Films 455, 248-255 (2004).
[CrossRef]

Tay, B. K.

Z. W. Zhao, B. K. Tay, and G. Q. Yu, "Study of the structure and optical properties of nanocrystalline zirconium oxide thin films deposited at low temperatures," J. Phys. D 37, 1701-1705 (2004).
[CrossRef]

Temple, P. A.

Thonn, T. F.

Tikhonravov, A. V.

Tiwald, T. E.

R. A. Synowicki and T. E. Tiwald, "Optical properties of bulk c-ZrO2, c-MgO and a-As2S3 determined by variable angle spectroscopic ellipsometry," Thin Solid Films 455, 248-255 (2004).
[CrossRef]

Trubetskov, M. K.

Vidal, B.

M. Harris, H. A. Macleod, S. Ogura, E. Pelletier, and B. Vidal, "The relationship between optical inhomogeneity and film structure," Thin Solid Films 57, 173-178 (1979).
[CrossRef]

Yu, G. Q.

Z. W. Zhao, B. K. Tay, and G. Q. Yu, "Study of the structure and optical properties of nanocrystalline zirconium oxide thin films deposited at low temperatures," J. Phys. D 37, 1701-1705 (2004).
[CrossRef]

Zhao, Z. W.

Z. W. Zhao, B. K. Tay, and G. Q. Yu, "Study of the structure and optical properties of nanocrystalline zirconium oxide thin films deposited at low temperatures," J. Phys. D 37, 1701-1705 (2004).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Phys. D

E. E. Khawaja, S. M. Durrani, and M. A. Daous, "Depth profiling of inhomogeneous zirconia films by optical and Rutherford backscattering spectrometric techniques," J. Phys. D 32, 388-394 (1999).
[CrossRef]

Z. W. Zhao, B. K. Tay, and G. Q. Yu, "Study of the structure and optical properties of nanocrystalline zirconium oxide thin films deposited at low temperatures," J. Phys. D 37, 1701-1705 (2004).
[CrossRef]

Phys. Rev. B

B. Kralik, E. K. Chang, and S. G. Louie, "Structural properties and quasiparticle band structure of zirconia," Phys. Rev. B 57, 7027-7036 (1998).
[CrossRef]

Thin Solid Films

M. Harris, H. A. Macleod, S. Ogura, E. Pelletier, and B. Vidal, "The relationship between optical inhomogeneity and film structure," Thin Solid Films 57, 173-178 (1979).
[CrossRef]

R. A. Synowicki and T. E. Tiwald, "Optical properties of bulk c-ZrO2, c-MgO and a-As2S3 determined by variable angle spectroscopic ellipsometry," Thin Solid Films 455, 248-255 (2004).
[CrossRef]

Other

H. K. Pulker, Coatings on Glass (Elsevier, 1984).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Transmittance T as function of ka for a multilayer system with na = 2.2, Δn = 0.2, ns = 1.45, d = 200 nm, λ = 500 nm, and N = 10. (b) Transmittance T and reflectance R as functions of na for a multilayer system calculated with ka = 0.02, Δn = 0.2, ns = 1.45, d = 200 nm, λ = 500 nm, and N = 10.

Fig. 2
Fig. 2

Calculated ΔR as a function of d∕λ. The values of ka are given on the curves. The parameters used are (a) na = 2.0, Δn = 0.1na , Δk = 0.1ka , (b) na = 2.0, Δn = 0.15na , Δk = 0.15ka , and (c) na = 2.4, Δn = 0.1na , Δk = 0.1ka.

Fig. 3
Fig. 3

Dispersion curves of the hypothetical film described in Subsection 2.D [Eqs. (11) and (12) with d = 220 nm and Δn = 0.10na ]. (a) Δk = 0.10ka , (b) Δk = 0.

Fig. 4
Fig. 4

(a) The dispersion curve of the hypothetical film described in Subsection 2.D. The continuous curve was obtained using the actual variation of k along the depth of the film (that is, Δk = 0.1ka ), and the dots correspond to solutions obtained with Δk = 0. (b) Same as (a), but for the absorption index.

Fig. 5
Fig. 5

Percentage deviation in na from the actual value due to the use of the approximation (Δk = 0) as a function of ka.

Fig. 6
Fig. 6

Dispersion curves for a hypothetical inhomogeneous film of thickness d = 220 nm and Δn = 0.1na. (a) Solutions calculated with exact d (=220 nm) and Δn (=0.1na ); (b)–(i) solutions calculated when d and Δn (either or both) were increased or decreased as indicated.

Fig. 7
Fig. 7

Measured reflectance R and transmittance T of a ZrO2 film with a thickness of 205 nm. Rs and Ts refer to the reflectance and transmittance of the substrate, respectively.

Fig. 8
Fig. 8

(a) The dispersion curve for a ZrO2 film derived from the data of Fig. 7, with d = 205 nm and Δn = 0.12na. (b) Same as (a) but for the absorption index.

Fig. 9
Fig. 9

(kE2 )1∕2 versus E plot for the ZrO2 film whose data are shown in Fig. 8.

Equations (14)

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

n ˜ ( y , λ ) = n ( y , λ ) i k ( y , λ ) ,
n ( z ) = n a + Δ n ( z 1 / 2 ) ,
n ˜ ( z , λ ) = n a ( λ ) + Δ n ( z 1 / 2 ) i k a ( λ ) .
n ( m ) = n a + Δ n [ 2 m ( N + 1 ) 2 N ] .
T = F 1 ( n a , k a , n s , Δ n , λ , d ) ,
R = F 2 ( n a , k a , n s , Δ n , λ , d ) ,
f 1 ( n a , k a ) T F 1 = 0 ,
f 2 ( n a , k a ) R F 2 = 0.
n a ( λ ) = 2.0 + ( 6.0 × 10 4 / λ 2 ) for   300 λ 1000   nm ,
k a ( λ ) = 0.55 + ( 1.2 × 10 5 / λ 2 ) for   λ < 470   nm, k a = 0 for   λ 470   nm .
n ( m , λ ) = n a ( λ ) + Δ n [ 2 m ( N + 1 ) 2 N ] ,
k ( m , λ ) = k a ( λ ) + Δ k [ 2 m ( N + 1 ) 2 N ] ,
α E ( E E g ) η ,
k E 2 ( E E g ) η .

Metrics