Abstract

A single optical technique is presented that allows direct and selective probing or imaging in the thickness of multilayers. It is based on tunable interferences of polarized light. Adequate vertical resolution is provided with this method.

© 2006 Optical Society of America

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References

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  1. F. J. Milligen, B. Bovard, M. R. Jacobson, J. Mueller, R. Potoff, R. L. Shoemaker, and H. A. Macleod, Appl. Opt. 24, 1799 (1985).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. S. Bosch and F. Monzonis, J. Opt. Soc. Am. A 12, 1375 (1995).
    [CrossRef]
  5. S. Bosch and F. Monzonis, Semicond. Sci. Technol. 10, 1634 (1995).
    [CrossRef]
  6. A. Dubois, K. Grieve, G. Moneron, R. Lecaque, L. Vabre, and C. Boccara, Appl. Opt. 43, 2874 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2005

2004

2002

1995

S. Bosch and F. Monzonis, J. Opt. Soc. Am. A 12, 1375 (1995).
[CrossRef]

S. Bosch and F. Monzonis, Semicond. Sci. Technol. 10, 1634 (1995).
[CrossRef]

1985

Amotchkina, T. V.

Amra, C.

Boccara, C.

Bosch, S.

S. Bosch and F. Monzonis, J. Opt. Soc. Am. A 12, 1375 (1995).
[CrossRef]

S. Bosch and F. Monzonis, Semicond. Sci. Technol. 10, 1634 (1995).
[CrossRef]

Bovard, B.

Deumié, C.

Dubois, A.

Duparré, A.

Gilbert, O.

Grieve, K.

Gunster, S.

Jacobson, M. R.

Kokarev, M. A.

Lecaque, R.

Macleod, H. A.

Messerly, M. J.

Milligen, F. J.

Moneron, G.

Monzonis, F.

S. Bosch and F. Monzonis, Semicond. Sci. Technol. 10, 1634 (1995).
[CrossRef]

S. Bosch and F. Monzonis, J. Opt. Soc. Am. A 12, 1375 (1995).
[CrossRef]

Mueller, J.

Potoff, R.

Quesnel, E.

Ristau, D.

Saxe, S. J.

Shoemaker, R. L.

Tikhonravov, A. V.

Trubetskov, M. K.

Vabre, L.

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Figures (4)

Fig. 1
Fig. 1

Incident polarized plane wave at incidence i on a sample with normal z in the presence of a tunable retardation plate and a rotating analyzer.

Fig. 2
Fig. 2

A spacer layer is arbitrary chosen within a multilayer and allows us to define two submultilayers (bold lines) located at the top (0) and at the back (1) of the figure.

Fig. 3
Fig. 3

Situation similar to that of reflection from a unique top submultilayer (0).

Fig. 4
Fig. 4

Situation where the back submultilayer is probed.

Equations (19)

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E + = E S + + E P + = ( A S + + A P + ) exp ( j k + ρ ) ,
k + = k 0 [ sin ( i ) , 0 , cos ( i ) ] ,
A S + = A S + exp ( j η S ) , A P + = A P + exp ( j η P ) ,
A S + = A S + exp ( j η S * ) , A P + = A P + exp ( j η P * ) ,
A r = r S cos ( ψ ) A S + + r P sin ( ψ ) A P + .
A r = A S + cos ( ψ ) f α ( r ) ,
f α ( r ) = f α ( r S , r P ) = r S + α r P
Δ η = η P η S , Δ η * = η P * η S * .
f α ( r ) = 0 α = α c = r S r P ,
t g ψ c = ( R S R P ) 0.5 , Δ η c * = π Δ η ( δ P δ S ) ,
r S = R S 0.5 exp ( j δ S ) , r P = R P 0.5 exp ( j δ P ) .
r = r 0 + t 0 t 0 r 1 exp ( j 2 κ ) + t 0 t 0 r 0 r 1 2 exp ( j 4 κ ) + = Σ n r n ,
r = r 0 + t 0 t 0 r 1 exp ( j 2 κ ) { 1 [ 1 r 0 r 1 exp ( j 2 κ ) ] } = r 0 + Z ,
κ = ( 2 π λ ) ( ne cos i i ) sp ,
f α ( Σ i r i ) = Σ i f α ( r i ) .
f ( r ) = f ( r 0 ) + f ( Z ) .
f α z ( Z ) = 0 f α z ( r ) = f α z ( r 0 ) .
f ( r ) = Σ n f ( r n ) .
f α [ r t 0 t 0 r 1 exp ( j 2 κ ) ] = 0 f α ( r ) = f [ t 0 t 0 r 1 exp ( j 2 κ ) ] .

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