Abstract

In the present paper we determine the optical constants and thicknesses of multilayer thin film stacks, in the visible and near infrared ranges. These parameters are derived from the transmittance and reflectance spectra measured by a spectrophotometer, for several angles of incidence. Several examples are studied, from a simple single layer structure up to a 22-layer dielectric filter. We show that the use of a large number of incidence angles is an effective means of reducing the number of mathematical solutions and converging on the correct physical solution when the number of layers increases. More specifically, we provide an in-depth discussion of the approach used to extract the index and thickness of each layer, which is achieved by analysing the various mathematical solutions given by a global optimization procedure, based on as little as 6 and as many as 32 variable parameters. The results show that multiple incidences, lead to the true solution for a filter with a large number of layers. In the present study, a Clustering Global Optimization algorithm is used, and is shown to be efficient even for a high number of variable parameters. Our analysis allows the accuracy of the reverse engineering process to be estimated at approximately 1 nm for the thickness, and 2 10−3 for the index of each layer in a 22-layer filter.

© 2012 OSA

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    [PubMed]

2012

S. Wu, X. Long, K. Yang, and Z. Tan, “A novel determination method of thin film optical parameters with least dependence on photometric measurement systematic errors,” Opt. Laser Technol.44, 771–775 (2012).

A. V. Tikhonravov, T. V. Amotchkina, M. K. Trubetskov, R. J. Francis, V. Janicki, J. Sancho-Parramon, H. Zorc, and V. Pervak, “Optical characterization and reverse engineering based on multiangle spectroscopy,” Appl. Opt.51(2), 245–254 (2012).
[PubMed]

2011

2008

P. A. v. Nijnatten, “Optical analysis of coatings by variable angle spectrophotometry,” Thin Solid Films516, 4553–4557 (2008).

M. Tilsch and K. Hendrix, “Optical Interference Coatings Design Contest 2007: triple bandpass filter and nonpolarizing beam splitter,” Appl. Opt.47(13), C55–C69 (2008).
[PubMed]

2007

F. C. Lai, L. M. Lin, R. Q. Gai, Y. Z. Lin, and Z. G. Huang, “Determination of optical constants and thicknesses of In2O3:Sn films from transmittance data,” Thin Solid Films515, 7387–7392 (2007).

2006

2004

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

2003

A. V. Tikhonravov, M. K. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).

2002

2000

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

1999

D. Poelman, D. Wauters, R. L. V. Meirhaeghe, and F. Cardon, “Intrinsic optical and structural properties of SrS thin films,” Thin Solid Films350, 67–71 (1999).

1998

M. Kildemo, R. Ossikovski, and M. Stchakovsky, “Measurement of absorption edge of thick transparent substrates using incoherent reflection model and spectroscopic UV-visible–near IR ellipsometry,” Thin Solid Films313–314, 108–113 (1998).

1997

1996

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett.69, 371–373 (1996).

1994

1991

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D Appl. Phys.24, 2088–2094 (1991).

1988

T. Csendes, “Nonlinear parameter estimation by global optimization - efficiency and reliability,” Acta Cybernetica8, 361–370 (1988).

1986

1985

1984

1983

1972

R. E. Denton, R. D. Campbell, and S. G. Tomlin, “The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D Appl. Phys.5, 852–863 (1972).

1968

1926

Amotchkina, T. V.

Amra, C.

Arndt, D. P.

Ausserré, D.

Azzam, R. M. A.

Baby, L.

Bartella, J.

Bélanger, P. A.

Bennett, J. M.

Berning, P. H.

Borgogno, J. P.

Boulay, R.

Bovard, B.

Campbell, R. D.

R. E. Denton, R. D. Campbell, and S. G. Tomlin, “The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D Appl. Phys.5, 852–863 (1972).

Cardon, F.

D. Poelman, D. Wauters, R. L. V. Meirhaeghe, and F. Cardon, “Intrinsic optical and structural properties of SrS thin films,” Thin Solid Films350, 67–71 (1999).

Carniglia, C. K.

Case, W. E.

Casparis, E.

Caughman, J. B.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

Chambouleyron, I.

Chu, J. H.

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

Costich, V. R.

Csendes, T.

T. Csendes, “Nonlinear parameter estimation by global optimization - efficiency and reliability,” Acta Cybernetica8, 361–370 (1988).

DeBell, G.

A. V. Tikhonravov, M. K. Trubetskov, and G. DeBell, “On the accuracy of optical thin film parameter determination based on spectrophotometric data,” Proc. SPIE5188, 190–199 (2003).

Denton, R. E.

R. E. Denton, R. D. Campbell, and S. G. Tomlin, “The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D Appl. Phys.5, 852–863 (1972).

Dobrowolski, J. A.

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(28), 7188–7198 (1997).
[PubMed]

J. A. Dobrowolski, F. C. Ho, L. Baby, R. Boulay, B. Drouin, R. Gagnon, and P. A. Bélanger, “Use of the inverse synthesis method for the determination of the optical constants of paper in the far infrared,” Appl. Opt.25(16), 2681–2687 (1986).
[PubMed]

J. Bartella, P. H. Berning, B. Bovard, C. K. Carniglia, E. Casparis, V. R. Costich, J. A. Dobrowolski, U. J. Gibson, R. Herrmann, F. C. Ho, M. R. Jacobson, R. E. Klinger, J. A. Leavitt, H.-G. Lotz, H. A. Macleod, M. J. Messerly, D. F. Mitchell, W. D. Muenz, K. W. Nebesny, R. Pfefferkorn, S. G. Saxe, D. Y. Song, P. Swab, R. M. Swenson, W. Thoeni, F. V. Milligen, S. Vincent, and A. Waldorf, “Multiple analysis of an unknown optical multilayer coating,” Appl. Opt.24(16), 2625–2646 (1985).
[PubMed]

D. P. Arndt, R. M. A. 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(20), 3571–3596 (1984).
[PubMed]

J. A. Dobrowolski, F. C. Ho, and A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt.22(20), 3191–3200 (1983).
[PubMed]

Drouin, B.

Eres, G.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

Francis, R. J.

Gagnon, R.

Gai, R. Q.

F. C. Lai, L. M. Lin, R. Q. Gai, Y. Z. Lin, and Z. G. Huang, “Determination of optical constants and thicknesses of In2O3:Sn films from transmittance data,” Thin Solid Films515, 7387–7392 (2007).

Gao, L.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films520, 501–509 (2011).

Geohegan, D. B.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

Gibson, U. J.

Hart, T. T.

Hendrix, K.

Hendrix, K. D.

Herrmann, R.

Ho, F. C.

Hodgkin, V. A.

Hopfe, V.

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D Appl. Phys.24, 2088–2094 (1991).

Hu, S. H.

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

Hu, Z. G.

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

Huang, Z. G.

F. C. Lai, L. M. Lin, R. Q. Gai, Y. Z. Lin, and Z. G. Huang, “Determination of optical constants and thicknesses of In2O3:Sn films from transmittance data,” Thin Solid Films515, 7387–7392 (2007).

Huang, Z. M.

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

Ikonen, E.

Jacobson, M. R.

Janicki, V.

Jellison, G. E.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett.69, 371–373 (1996).

Kildemo, M.

M. Kildemo, R. Ossikovski, and M. Stchakovsky, “Measurement of absorption edge of thick transparent substrates using incoherent reflection model and spectroscopic UV-visible–near IR ellipsometry,” Thin Solid Films313–314, 108–113 (1998).

Klapp, W. P.

Klinger, R. E.

Klobes, P.

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D Appl. Phys.24, 2088–2094 (1991).

Kronig, R. D. L.

Lai, F. C.

F. C. Lai, L. M. Lin, R. Q. Gai, Y. Z. Lin, and Z. G. Huang, “Determination of optical constants and thicknesses of In2O3:Sn films from transmittance data,” Thin Solid Films515, 7387–7392 (2007).

Lamminpää, A.

Leavitt, J. A.

Lemarchand, F.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films520, 501–509 (2011).

C. Ndiaye, F. Lemarchand, M. Zerrad, D. Ausserré, and C. Amra, “Optimal design for 100% absorption and maximum field enhancement in thin-film multilayers at resonances under total reflection,” Appl. Opt.50(9), C382–C387 (2011).
[PubMed]

Lequime, M.

L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films520, 501–509 (2011).

Lin, L. M.

F. C. Lai, L. M. Lin, R. Q. Gai, Y. Z. Lin, and Z. G. Huang, “Determination of optical constants and thicknesses of In2O3:Sn films from transmittance data,” Thin Solid Films515, 7387–7392 (2007).

Lin, Y. Z.

F. C. Lai, L. M. Lin, R. Q. Gai, Y. Z. Lin, and Z. G. Huang, “Determination of optical constants and thicknesses of In2O3:Sn films from transmittance data,” Thin Solid Films515, 7387–7392 (2007).

Long, X.

S. Wu, X. Long, K. Yang, and Z. Tan, “A novel determination method of thin film optical parameters with least dependence on photometric measurement systematic errors,” Opt. Laser Technol.44, 771–775 (2012).

Lotz, H.-G.

Lowndes, D. H.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

Ma, J. H.

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

Macleod, H. A.

Manoocheri, F.

Martínez, J. M.

Meirhaeghe, R. L. V.

D. Poelman, D. Wauters, R. L. V. Meirhaeghe, and F. Cardon, “Intrinsic optical and structural properties of SrS thin films,” Thin Solid Films350, 67–71 (1999).

Merkulov, V. I.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

Messerly, M. J.

Milligen, F. V.

Mitchell, D. F.

Modine, F. A.

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett.69, 371–373 (1996).

Moretti, A. C.

Muenz, W. D.

Mulato, M.

Ndiaye, C.

Nebesny, K. W.

Nevas, S.

Nijnatten, P. A. v.

P. A. v. Nijnatten, “Optical analysis of coatings by variable angle spectrophotometry,” Thin Solid Films516, 4553–4557 (2008).

Nilsson, P. O.

Oliver, J.

Ossikovski, R.

M. Kildemo, R. Ossikovski, and M. Stchakovsky, “Measurement of absorption edge of thick transparent substrates using incoherent reflection model and spectroscopic UV-visible–near IR ellipsometry,” Thin Solid Films313–314, 108–113 (1998).

Paulick, T. C.

Pelletier, E.

Pervak, V.

Pfefferkorn, R.

Poelman, D.

D. Poelman, D. Wauters, R. L. V. Meirhaeghe, and F. Cardon, “Intrinsic optical and structural properties of SrS thin films,” Thin Solid Films350, 67–71 (1999).

Puretzky, A. A.

G. E. Jellison, V. I. Merkulov, A. A. Puretzky, D. B. Geohegan, G. Eres, D. H. Lowndes, and J. B. Caughman, “Characterization of thin film amorphous semiconductors using spectroscopic ellipsometry,” Thin Solid Films377–378, 68–73 (2000).

Purvis, M. K.

Quinn, D. M.

Sancho-Parramon, J.

Saxe, S. G.

Song, D. Y.

Stchakovsky, M.

M. Kildemo, R. Ossikovski, and M. Stchakovsky, “Measurement of absorption edge of thick transparent substrates using incoherent reflection model and spectroscopic UV-visible–near IR ellipsometry,” Thin Solid Films313–314, 108–113 (1998).

Stenzel, O.

O. Stenzel, V. Hopfe, and P. Klobes, “Determination of optical parameters for amorphous thin film materials on semitransparent substrates from transmittance and reflectance measurements,” J. Phys. D Appl. Phys.24, 2088–2094 (1991).

Strome, D. H.

Sullivan, B. T.

Swab, P.

Swenson, R.

Swenson, R. M.

Tan, Z.

S. Wu, X. Long, K. Yang, and Z. Tan, “A novel determination method of thin film optical parameters with least dependence on photometric measurement systematic errors,” Opt. Laser Technol.44, 771–775 (2012).

Temple, P. A.

Thoeni, W.

Thonn, T. F.

Tikhonravov, A. V.

Tilsch, M.

Tomlin, S. G.

R. E. Denton, R. D. Campbell, and S. G. Tomlin, “The determination of the optical constants of thin films from measurements of reflectance and transmittance at normal incidence,” J. Phys. D Appl. Phys.5, 852–863 (1972).

Tonova, D.

Trubetskov, M. K.

Ullmann, J.

Verly, P.

Vincent, S.

von Blanckenhagen, B.

Waldorf, A.

Wang, G. S.

Z. G. Hu, Z. M. Huang, Y. N. Wu, S. H. Hu, G. S. Wang, J. H. Ma, and J. H. Chu, “Optical characterization of ferroelectric Bi3.25La0.75Ti3O12 thin films,” Eur. Phys. J. B38, 431–436 (2004).

Wang, H.

Wauters, D.

D. Poelman, D. Wauters, R. L. V. Meirhaeghe, and F. Cardon, “Intrinsic optical and structural properties of SrS thin films,” Thin Solid Films350, 67–71 (1999).

Wu, S.

S. Wu, X. Long, K. Yang, and Z. Tan, “A novel determination method of thin film optical parameters with least dependence on photometric measurement systematic errors,” Opt. Laser Technol.44, 771–775 (2012).

Wu, Y. N.

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Figures (14)

Fig. 1
Fig. 1

Notations and design of a thin film filter.

Fig. 2
Fig. 2

CGO flowchart.

Fig. 3
Fig. 3

Optimized error function for the Ta2O5 single-layer at different S.I.θ and M.I.

Fig. 4
Fig. 4

Distances between the nominal (M.I.) and S.I.θ solutions, for the Ta2O5 single-layer. The nominal thickness of the layer is d = 403.4 nm.

Fig. 5
Fig. 5

(a) Experimental and M.I. optimized spectra for the Ta2O5 single-layer as a function of wavelength. The dots correspond to values measured by the spectrophotometer (a reduced number of dots has been plotted to improve visibility). The continuous curves correspond to the M.I. optimized values. Rs, Rp and T are plotted using different colours, at different incidence angles. (b) M.I. optimized refractive index (n) and extinction coefficient (k) for the Ta2O5 single-layer as a function of wavelength.

Fig. 6
Fig. 6

Experimental and calculated transmittance (red) at S.I.0°, and experimental and calculated (from the solution for S.I.0°) reflectance (green), at pol s at S.I.45°, for the Ta2O5/SiO2 7-layer filter as a function of wavelength.

Fig. 7
Fig. 7

Optimized Error function for the Ta2O5/SiO2 7-layer filter at different S.I.θ, and M.I.

Fig. 8
Fig. 8

Distances between the nominal (M.I.) and S.I.θ solutions, for the Ta2O5/SiO2 7-layer filter, (nH, kH for the high index Ta2O5 layer, and nL, kL for the low index SiO2 layer).

Fig. 9
Fig. 9

(a) Experimental and M.I. optimized spectra for the Ta2O5/SiO2 7-layer filter, as a function of wavelength. (b) M.I. optimized refractive indices (nH for the high index Ta2O5 layer, and nL for the low index SiO2 layer) as a function of wavelength, and thicknesses (d) as a function of layer, for the Ta2O5/SiO2 7-layer filter.

Fig. 10
Fig. 10

Experimental and calculated transmittance for 2 solutions of the Ta2O5/SiO2 22-layer filter at S.I.0°, as a function of wavelength.

Fig. 11
Fig. 11

Distances between solution 1 and the other 9 solutions found with M.I. optimization, for the Ta2O5/SiO2 22-layer filter, (nH for the high index Ta2O5 layer, and nL for the low index SiO2 layer).

Fig. 12
Fig. 12

(a) Experimental and M.I. optimized spectra for the Ta2O5/SiO2 22-layer filter as a function of wavelength. (b) M.I. optimized refractive indices (nH for the high index Ta2O5 layer, and nL for the low index SiO2 layer) as a function of wavelength, and thicknesses (d) as a function of layer, for the Ta2O5/SiO2 22-layer filter.

Fig. 13
Fig. 13

Ta2O5/SiO2 22-layer filter: distances between the nominal (M.I. solution) and other configurations, (nH for the high index Ta2O5 layer, and nL for the low index SiO2 layer).

Fig. 14
Fig. 14

Distances between the M.I. optimized index of Ta2O5 layer for the single-layer, Ta2O5/SiO2 7-layer and Ta2O5/SiO2 22-layer filters.

Equations (6)

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ε 2 ( E )= A E 0 C ( E E g ) 2 ( E 2 E 0 2 ) 2 + C 2 E 2 1 E ,(E> E g ) =0,(E E g ),
E= hc λ ,
ε 1 i ε 2 = ( nik ) 2 ,
EF(θ,pol,S)= 1 N w j=1 N w ( S j,cal (X,d) S j,exp Δ S j ) 2 ,
E F 0° =EF( 0°,a,T ) E F 8° = 1 2 [ EF( 8°,a,R )+EF( 8,a,T ) ] E F θ = 1 2 [ EF( θ,s,R )+EF( θ,p,R ) ] E F mi = 1 N θ +2 [ E F 0° +E F 8° + i=1 N θ E F θ i ],
distance(n)= 1 N w j=1 N w | n(sol1,j)n(sol2,j) | 2 distance(k)= 1 N w j=1 N w | k(sol1,j)k(sol2,j) | 2 distance(d)= 1 N d p=1 N d | d p (sol1) d p (sol2) | 2 ,

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