Abstract

We propose a method that uses reflection and transmission photoellipsometry to analyze samples consisting of thin films combined with semitransparent thick layers or substrates in the form of multilayer structures. A thick film or substrate is defined as a layer for which no interference effects can be observed for a given wavelength resolution, and contributions from multiple reflections in the substrate are taken into account in the theoretical treatment. An automatic reflection–transmission spectroscopic ellipsometer was built to test the theory, and satisfactory results have been obtained. Examples corresponding to a strongly absorbing film deposited on a glass substrate and a highly transmitting film also deposited on glass are shown. In both cases a good fit between theory and experiment is found. The photoellipsometric method presented is particularly suited to the analysis of actual samples of energy-efficient coatings for windows.

© 1995 Optical Society of America

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References

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  1. J. B. Theeten, D. E. Aspnes, “Ellipsometry in thin film analysis,” Ann. Rev. Mater. Sci. 11, 97–122 (1981).
    [CrossRef]
  2. D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 799–846.
  3. R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
    [CrossRef]
  4. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).
  5. A. Weissberger, B. W. Rossiter, eds., Physical Methods of Chemistry, (Wiley, New York, 1972), Vol. I, Part III C.
  6. G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection and transmission ellipsometry (RTELL) of multilayer structures on transparent substrates: theory,” GRCMES Rep. 12 (Université de Moncton, New Brunswick, Canada, 1993).
  7. P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
    [CrossRef]
  8. J.-Th. Zettler, L. Schrottke, “Ellipsometric characterization of layers on transparent semiconductor wafers,” Phys. Status Solidi 163, K69–K74 (1991).
    [CrossRef]
  9. I. Hamberg, C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60, R123–R159 (1986).
    [CrossRef]
  10. P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
    [CrossRef]
  11. C. M. Lampert, C. G. Granqvist, eds., Large Area Chromogenics: Materials and Devices for Transmittance Control Vol. IS4 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).

1993 (2)

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

1991 (1)

J.-Th. Zettler, L. Schrottke, “Ellipsometric characterization of layers on transparent semiconductor wafers,” Phys. Status Solidi 163, K69–K74 (1991).
[CrossRef]

1986 (1)

I. Hamberg, C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60, R123–R159 (1986).
[CrossRef]

1981 (1)

J. B. Theeten, D. E. Aspnes, “Ellipsometry in thin film analysis,” Ann. Rev. Mater. Sci. 11, 97–122 (1981).
[CrossRef]

1969 (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Ashrit, P. V.

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection and transmission ellipsometry (RTELL) of multilayer structures on transparent substrates: theory,” GRCMES Rep. 12 (Université de Moncton, New Brunswick, Canada, 1993).

Aspnes, D. E.

J. B. Theeten, D. E. Aspnes, “Ellipsometry in thin film analysis,” Ann. Rev. Mater. Sci. 11, 97–122 (1981).
[CrossRef]

D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 799–846.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Bader, G.

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection and transmission ellipsometry (RTELL) of multilayer structures on transparent substrates: theory,” GRCMES Rep. 12 (Université de Moncton, New Brunswick, Canada, 1993).

Badilescu, S.

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Benaissa, K.

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

Girouard, F. E.

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection and transmission ellipsometry (RTELL) of multilayer structures on transparent substrates: theory,” GRCMES Rep. 12 (Université de Moncton, New Brunswick, Canada, 1993).

Granqvist, C. G.

I. Hamberg, C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60, R123–R159 (1986).
[CrossRef]

Hamberg, I.

I. Hamberg, C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60, R123–R159 (1986).
[CrossRef]

Muller, R. H.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Nguyen, L. Q.

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

Schrottke, L.

J.-Th. Zettler, L. Schrottke, “Ellipsometric characterization of layers on transparent semiconductor wafers,” Phys. Status Solidi 163, K69–K74 (1991).
[CrossRef]

Theeten, J. B.

J. B. Theeten, D. E. Aspnes, “Ellipsometry in thin film analysis,” Ann. Rev. Mater. Sci. 11, 97–122 (1981).
[CrossRef]

Truong, Vo-Van

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection and transmission ellipsometry (RTELL) of multilayer structures on transparent substrates: theory,” GRCMES Rep. 12 (Université de Moncton, New Brunswick, Canada, 1993).

Zettler, J.-Th.

J.-Th. Zettler, L. Schrottke, “Ellipsometric characterization of layers on transparent semiconductor wafers,” Phys. Status Solidi 163, K69–K74 (1991).
[CrossRef]

Ann. Rev. Mater. Sci. (1)

J. B. Theeten, D. E. Aspnes, “Ellipsometry in thin film analysis,” Ann. Rev. Mater. Sci. 11, 97–122 (1981).
[CrossRef]

J. Appl. Phys. (2)

P. V. Ashrit, G. Bader, S. Badilescu, F. E. Girouard, L. Q. Nguyen, Vo-Van Truong, “Dielectric constants of silver particles finely dispersed in a gelatin film,” J. Appl. Phys. 74, 602–606 (1993).
[CrossRef]

I. Hamberg, C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60, R123–R159 (1986).
[CrossRef]

Phys. Status Solidi (1)

J.-Th. Zettler, L. Schrottke, “Ellipsometric characterization of layers on transparent semiconductor wafers,” Phys. Status Solidi 163, K69–K74 (1991).
[CrossRef]

Solid State Ion. (1)

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 45–57 (1993).
[CrossRef]

Surf. Sci. (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Other (5)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

A. Weissberger, B. W. Rossiter, eds., Physical Methods of Chemistry, (Wiley, New York, 1972), Vol. I, Part III C.

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection and transmission ellipsometry (RTELL) of multilayer structures on transparent substrates: theory,” GRCMES Rep. 12 (Université de Moncton, New Brunswick, Canada, 1993).

D. E. Aspnes, “Spectroscopic ellipsometry of solids,” in Optical Properties of Solids: New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), pp. 799–846.

C. M. Lampert, C. G. Granqvist, eds., Large Area Chromogenics: Materials and Devices for Transmittance Control Vol. IS4 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of a multilayer structure that consists of thin and thick layers. Thin films between thick layers (or substrates) can be replaced by a pseudointerface as defined in the text.

Fig. 2
Fig. 2

Schematic representation of the reflection–transmission photoellipsometer: 1, light-input system; 2, beam splitter; 3, reference detector; 4, reflection detector; 5, transmission detector; 6, polarizer; 7, reflection analyzer; 8, transmission analyzer; 9, rotating table; 10, automated sample support.

Fig. 3
Fig. 3

R s , R p , and Re(R ps ) for the absorbing thin gold film described in the text: ♦, R s , experimental; ■, R p , experimental; ▲, Re(R ps ), experimental. The solid curves represent the calculated results.

Fig. 4
Fig. 4

T s , T p , and Re(T ps ) for the absorbing thin gold film described in the text: ♦, T s , experimental; ■, T p , experimental; ▲, Re(T ps ), experimental. The solid curves represent the calculated results.

Fig. 5
Fig. 5

Refractive index N and extinction coefficient K for the absorbing thin gold film described in the text.

Fig. 6
Fig. 6

R s , R p , and Re(R ps ) for the transmitting thin indium tin oxide film described in the text: ♦, R s , experimental; ■, R p , experimental; ▲, Re(R ps ), experimental. The solid curves represent the calculated results.

Fig. 7
Fig. 7

T s , T p , and Re(T ps ) for the transmitting thin indium tin oxide film described in the text: ♦, T s , experimental; ■, T p , experimental; ▲, Re(T ps), experimental. The solid curves represent the calculated results.

Fig. 8
Fig. 8

Refractive index N and extinction coefficient K for the transmitting thin indium tin oxide film described in the text.

Equations (32)

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cos θ i = + ( 1 N 0 2 sin 2 θ 0 N i 2 ) 1 / 2 if Im [ ( N i 2 N 0 2 sin 2 θ 0 ) 1 / 2 ] 0 , = ( 1 N 0 2 sin 2 θ 0 N i 2 ) 1 / 2 if Im [ ( N i 2 N 0 2 sin 2 θ 0 ) 1 / 2 ] < 0 ,
β i = 2 π D i λ N i cos θ i ,
I R = k [ R p cos 4 θ a + R s sin 4 θ a + 2 Re ( R p s ) sin 2 θ a cos 2 θ a ] ,
I T = k [ T p cos 4 θ a + T s sin 4 θ a + 2 Re ( T p s ) sin 2 θ a cos 2 θ a ] ,
I R = R p cos 4 θ a + R s sin 4 θ a + 2 Re ( R p s ) sin 2 θ a cos 2 θ a ,
I T = T p cos 4 θ a + T s sin 4 θ a + 2 Re ( T p s ) sin 2 θ a cos 2 θ a .
R p ( s ) = | r p ( s ) | 2 ,
T p ( s ) = | t p ( s ) | 2
R p s = ( r p r s * ) ,
T p s = ( t p t s * )
R p ( s ) = | r p ( s ) | 2 ,
T p ( s ) = | t p ( s ) | 2 ,
R p s = ( r p r s * ) ,
T p s = ( t p t s * )
r = r 0 , 1 + + t 0 , 1 + t 0 , 1 r 1 , 2 + exp ( 2 i β 1 ) 1 r 0 , 1 r 1 , 2 + exp ( 2 i β 1 ) ,
t = t 0 , 1 + t 1 , 2 + exp ( i β 1 ) 1 r 0 , 1 r 1 , 2 + exp ( 2 i β 1 ) .
R p ( s ) = | r p ( s ) | 2 = | r 0 , 1 , p ( s ) + | 2 + | t 0 , 1 , p ( s ) + | 2 | t 0 , 1 , p ( s ) | 2 | r 1 , 2 , p ( s ) + | 2 exp ( 4 Im β 1 ) 1 | r 0 , 1 , p ( s ) | 2 | r 1 , 2 , p ( s ) + | 2 exp ( 4 Im β 1 ) ,
T p ( s ) = | t p ( s ) | 2 = | t 0 , 1 , p ( s ) + | 2 | t 1 , 2 , p ( s ) + | 2 exp ( 2 Im β 1 ) 1 | r 0 , 1 , p ( s ) | 2 | r 1 , 2 , p ( s ) + | 2 exp ( 4 Im β 1 ) .
R p s = ( r p r s * ) = ( r 0 , 1 , p + r 0 , 1 , s * ) + ( t 0 , 1 , p + t 0 , 1 , s + * ) ( t 0 , 1 , p t 0 , 1 , s * ) ( r 1 , 2 , p + r 1 , 2 , s + * ) exp ( 4 Im β 1 ) 1 ( r 0 , 1 , p r 0 , 1 , s * ) ( r 1 , 2 , p + r 1 , 2 , s + * ) exp ( 4 Im β 1 ) ,
T p s = ( t p t s * ) = ( t 0 , 1 , p + t 0 , 1 , s + * ) ( t 1 , 2 , p + t 1 , 2 , s + * ) exp ( 2 Im β 1 ) 1 ( r 0 , 1 , p r 0 , 1 , s * ) ( r 1 , 2 , p + r 1 , 2 , s + * ) exp ( 4 Im β 1 ) .
R ( i 1 , N ) = | r i 1 , i + | 2 + | t i 1 , i + | 2 | t i 1 , i | 2 R ( i , N ) exp ( 4 Im β i ) 1 | r i 1 , i | 2 R ( i , N ) exp ( 4 Im β i ) ,
T ( i 1 , N ) = | t i 1 , i + | 2 T ( i , N ) exp ( 2 Im β i ) 1 | r i 1 , i | 2 R ( i , N ) exp ( 4 Im β i ) ,
R p s ( i 1 , N ) = ( r i 1 , i , p + r i 1 , i , s + ) + ( t i 1 , i , p + t i 1 , i , s + * ) ( t i 1 , i , p t i 1 , i , s * ) R p s ( i , N ) exp ( 4 Im β i ) 1 ( r i 1 , i , p r i 1 , i , s * ) R p s ( i , N ) exp ( 4 Im β i ) ,
T p s ( i 1 , N ) = ( t i 1 , i , p + t i 1 , i , s + * ) T p s ( i , N ) exp ( 2 Im β i ) 1 ( r i 1 , i , p r i 1 , i , s * ) R p s ( i , N ) exp ( 4 Im β i ) .
R p ( s ) = R p ( s ) ( 0 , N ) , T p ( s ) = T p ( s ) ( 0 , N ) , R p s = R p s ( 0 , N ) , T p s = T p s ( 0 , N )
R p ( s ) ( N 1 , N ) = | r N 1 , N , p ( s ) + | 2 , T p ( s ) ( N 1 , N ) = | t N 1 , N , p ( s ) + | 2 , R p s ( N 1 , N ) = ( r N 1 , N , p + r N 1 , N , s + * ) , T p s ( N 1 , N ) = ( t N 1 , N , p + t N 1 , N , s + * ) .
R 1 p ( s ) = R p ( s ) ( N , 0 ) , T 1 p ( s ) = T p ( s ) ( N , 0 ) , R 1 p s = R p s ( N , 0 ) , T 1 p s = T p s ( N , 0 )
R p ( s ) ( 1 , 0 ) = | r 0 , 1 , p ( s ) | 2 , T p ( s ) ( 1 , 0 ) = | t 0 , 1 , p ( s ) | 2 , R p s ( 1 , 0 ) = ( r 0 , 1 , p r 0 , 1 , s * ) , T p s ( 1 , 0 ) = ( t 0 , 1 , p t 0 , 1 , s * )
R ( i , 0 ) = | r i 1 , i | 2 + | t i 1 , i | 2 | t i 1 , i + | 2 R ( i 1 , 0 ) exp ( 4 Im β i 1 ) 1 | r i 1 , i + | 2 R ( i 1 , 0 ) exp ( 4 Im β i 1 ) ,
T ( i , 0 ) = | t i 1 , i | 2 T ( i 1 , 0 ) exp ( 2 Im β i 1 ) 1 | r i 1 , i + | 2 R ( i 1 , 0 ) exp ( 4 Im β i 1 )
R p s ( i , 0 ) = ( r i 1 , i , p r i 1 , i , s ) + ( t i 1 , i , p t i 1 , i , s * ) ( t i 1 , i , p + t i 1 , i , s + * ) R p s ( i 1 , 0 ) exp ( 4 Im β i 1 ) 1 ( r i 1 , i , p + r i 1 , i , s + * ) R p s ( i 1 , 0 ) exp ( 4 Im β i 1 ) ,
T p s ( i , 0 ) = ( t i 1 , i , p t i 1 , i , s * ) T p s ( i 1 , 0 ) exp ( 2 Im β i 1 ) 1 ( r i 1 , i , p + r i 1 , i , s + * ) R p s ( i 1 , 0 ) exp ( 4 Im β i 1 ) .

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