Abstract

The fundamentals of a new high contrast technique for optical microscopy, named “Surface Enhanced Ellipsometric Contrast” (SEEC), are presented. The technique is based on the association of enhancing contrast surfaces as sample stages and microscope observation between cross polarizers. The surfaces are designed to become anti-reflecting when used in these conditions. They are defined by the simple equation rp + rs = 0 between their two Fresnel coefficients. Most often, this equation can be met by covering a solid surface with a single λ/4 layer with a well defined refractive index. A higher flexibility is obtained with multilayer stacks. Solutions with an arbitrary number of all-dielectric λ/4 layers are derived.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. J. T. Cox and G. Hass "Antireflection coatings for optical and infrared materials," in Physics of Thin Films, G. Hass and R.E. Thun, eds., (Academic Press, New York, 1968), Vol. 2 p. 239.
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    [CrossRef]

2006 (1)

D. Ausserré, and M.-P. Valignat, "Wide field optical imaging of surface nanostructures," Nano Lett. 6,1384-1388 (2006).
[CrossRef] [PubMed]

1986 (1)

D. Ausserré, A.-M. Picart and L. Léger, "Existence and role of the precursor film in the spreading of polymer liquids," Phys. Rev. Lett. 57,2671-2674 (1986).
[CrossRef] [PubMed]

1985 (1)

1954 (1)

L. G. Parratt, "Surface studies of solids by total reflection of X-Rays," Phys. Rev. 95, 359-369 (1954).
[CrossRef]

1833 (1)

G. B. Airy, Phil. Mag. 2, 20 (1833).

Appl. Opt. (1)

Nano Lett. (1)

D. Ausserré, and M.-P. Valignat, "Wide field optical imaging of surface nanostructures," Nano Lett. 6,1384-1388 (2006).
[CrossRef] [PubMed]

Phil. Mag. (1)

G. B. Airy, Phil. Mag. 2, 20 (1833).

Phys. Rev. (1)

L. G. Parratt, "Surface studies of solids by total reflection of X-Rays," Phys. Rev. 95, 359-369 (1954).
[CrossRef]

Phys. Rev. Lett. (1)

D. Ausserré, A.-M. Picart and L. Léger, "Existence and role of the precursor film in the spreading of polymer liquids," Phys. Rev. Lett. 57,2671-2674 (1986).
[CrossRef] [PubMed]

Other (3)

A. Musset and A. Thelen, "Multilayer antireflection coating," in Progress in Optics, E. Wolf, ed., (North Holland Publ. Co., Amsterdam, 1970) Vol. 8 p. 201-237.
[CrossRef]

J. T. Cox and G. Hass "Antireflection coatings for optical and infrared materials," in Physics of Thin Films, G. Hass and R.E. Thun, eds., (Academic Press, New York, 1968), Vol. 2 p. 239.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (Elsevier, Amsterdam 1987).

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Figures (4)

Fig. 1.
Fig. 1.

Objective and sample illumination. Symbols, signs and conventions. Left: incident beam: (a) side view; (b) top view. Right: reflected beam (c) side view; (d) top view. The dashed area in top views underlines the sample surface section and the double arrow figures the objective lens. The (p,s,k) triedra drawn in (b) and (d) are taken above the objective lens.

Fig. 2.
Fig. 2.

Imaging contrast with respect to bare substrate of a 0.1 nm thick layer as a function of intermediate layer thickness (λ=540 nm); a) blue line: single incidence θ0 = 15°; b) green line: θmin = 12° and θmax = 17°; c) red line: θmin = 0° and θmax = 20°

Fig. 3.
Fig. 3.

Imaging contrast of a sample layer as a function of its thickness for a fixed optimal intermediate layer thickness (λ= 540 nm); (a) blue line: single incidence θ0 = 15°; (b) green line: θmin = 12° and θmax = 17°; c) red line: θmin = 0° and θmax = 20°

Fig. 4.
Fig. 4.

Computed imaging contrast of a sample layer as a function of its thickness on a silicon substrate bearing two quarterwave layers (at λ= 540 nm). (a) stacking scheme: n0=1.33, e1 = 930 nm, n1= 1.47, e2=636 nm, n2= 2.15, n3=3.88 ; (b) step contrast versus step thickness when θmin = 0° and θmax=20°.

Equations (41)

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E A E i 0 = ( u A v A ) ( 1 0 0 0 ) ( cos β sin β sin β cos β ) ( r p 0 0 r s ) ( cos φ sin φ sin φ cos φ ) 2 2 ( 1 0 )
E A E i 0 = u A 2 2 ( r p cos β cos φ + r s sin β sin φ )
E A E i 0 = u A 2 2 [ ( r p r s ) cos φ + ( r p + r s ) cos ( φ 2 ϕ ) ]
I N = I I 0 = 1 8 ( r p 2 + r p 2 ) + 1 16 r p r s 2 cos 2 ϕ
I NX = I I 0 = 1 16 r p + r s 2
σ r p + r s = 0
I NX ( θ min , θ max ) = 1 16 ( 1 cos θ min cos θ max ) θ min θ max r p + r s 2 sin θ d θ
{ r p ( i 1 , i ) = n i cos θ i 1 n i 1 cos θ i n i cos θ i 1 + n i 1 cos θ i r s ( i 1 , i ) = n i 1 cos θ i 1 n i cos θ i n i 1 cos θ i 1 + n i cos θ i }
σ ( i 1 , i ) = r p ( i 1 , i ) + r s ( i 1 , i )
π ( i 1 , i ) = r p ( i 1 , i ) * r s ( i 1 , i )
σ i 1 , i 1 + π i 1 , i = ( c i 1 2 c i 2 ) ( c i 1 2 + c i 2 )
r 0,2 = r 0,1 + r 1,2 e 2 j β 1 1 + r 0,1 · r 1,2 e 2 j β 1
σ 0,2 = σ 0,1 ( 1 + π 1,2 e 4 j β 1 ) + σ 1,2 ( 1 + π 0,1 ) e 2 j β 1 ( 1 + r p ( 0,1 ) r p ( 1,2 ) e 2 j β 1 ) ( 1 + r s ( 0,1 ) r s ( 1,2 ) e 2 j β 1 )
2 β 1 = ( 2 k + 1 ) π
2 β 1 = 2 k π
n 1 e 1 cos θ 1 = λ 4 + k λ 2
n 1 e 1 cos θ 1 = k λ 2
σ 0,1 ( 1 + π 1,2 ) σ 1,2 ( 1 + π 0,1 ) = 0
σ 0,1 ( 1 + π 1,2 ) + σ 1,2 ( 1 + π 0,1 ) = 0
c 0 c 2 = c 1 2
2 n 0 2 n 2 2 n 1 2 ( n 0 2 + n 2 2 ) = ( n 0 2 n 2 2 n 1 4 ) sin 2 θ 1
n 1 2 = n 0 2 n 2 2 + n 2 2 cos 2 θ 0 ( n 2 2 n 0 2 sin 2 θ 0 ) n 2 2 + n 0 2 cos 2 θ 0
2 n 1 2 = 1 n 0 2 + 1 n 2 2
r i 1 , n + 1 = r i 1 , i + r i , n + 1 e 2 j β i 1 + r i 1 , i · r i , n + 1 e 2 j β i
σ i 1 , n + 1 r p ( i 1 , n + 1 ) + r s ( i 1 , n + 1 )
π i 1 , n + 1 r p ( i 1 , n + 1 ) r s ( i 1 , n + 1 )
ξ i 1 , n + 1 = σ i 1 , n + 1 1 + π i 1 , n + 1
{ σ i 1 , n + 1 = σ i 1 , i ( 1 + π i , n + 1 ) σ i , n + 1 ( 1 + π i 1 , i ) ( ( 1 r p ( i 1 , i ) r p ( i , n + 1 ) ) ( 1 r s ( i 1 , i ) r s ( i , n + 1 ) ) ) 1 + π i 1 , n + 1 = 1 + π i 1 , i + π i , n + 1 + π i 1 , π i , n + 1 σ i 1 , i σ i , n + 1 ( ( 1 r p ( i 1 , i ) r p ( i , n + 1 ) ) ( 1 r s ( i 1 , i ) r s ( i , n + 1 ) ) ) }
ξ i 1 , n + 1 = ξ i 1 , i ξ i , n + 1 1 ξ i 1 , i ξ i , n + 1
{ A ( i 1 , n + 1 ) = c i 1 2 p = 1 n i + 1 2 c 2 ( p + i 1 ) 3 B ( i 1 , n + 1 ) = c n + 1 2 p = 1 n + 1 i 2 c 2 ( p + i 1 ) 1 4 } when ( n i + 1 ) is even
{ A ( i 1 , n + 1 ) = c i 1 2 c n + 1 2 p = 1 n i 2 c 2 ( p + i 1 ) 4 B ( i 1 , n + 1 ) = p = 1 n i 2 + 1 c 2 ( p + i 1 ) 1 4 } when ( n i + 1 ) is odd
ξ i , n + 1 = A ( i , n + 1 ) B ( i , n + 1 ) A ( i , n + 1 ) + B ( i , n + 1 )
ξ i 2 , n + 1 = A ( i 2 , n + 1 ) B ( i 2 , n + 1 ) A ( i 2 , n + 1 ) + B ( i 2 , n + 1 )
ξ i 1 , n + 1 = c i 1 2 ( 1 ξ i , n + 1 ) c i 2 ( 1 + ξ i , n + 1 ) c i 1 2 ( 1 ξ i , n + 1 ) + c i 2 ( 1 + ξ i , n + 1 )
ξ i 1 , n + 1 = σ i 1 , i ( 1 + π i , n + 1 ) σ i , n + 1 ( 1 + π i 1 , i ) 1 + π i 1 , i + π i , i + 1 + π i 1 , i π i , i + 1 σ i 1 , i σ i , i + 1
c 0 2 p = 1 n 2 c 2 p 4 = c n + 1 2 p = 1 n 2 c 2 p 1 4 if n is even
c 0 2 c n + 1 2 p = 1 n 1 2 c 2 p 4 = p = 1 n + 1 2 c 2 p 1 4 if n is odd
1 n 0 2 = 2 p = 1 n 2 1 n 2 p 2 + 2 p = 1 n 2 1 n 2 p 1 2 + 1 n n + 1 2 = 0 if n is even , and
1 n 0 2 2 p = 1 n 1 2 1 n 2 p 2 + 2 p = 1 n + 1 2 1 n 2 p 1 2 1 n n + 1 2 = 0 if n is odd
i = 0 n ( 1 ) i ( 1 n i 2 1 n i + 1 2 ) = 0
( 1 n 0 2 2 n 1 2 + 2 n 2 2 1 n 3 2 ) = 0

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