Abstract

Binary optics processing methods were applied to a silicon substrate to generate an array of small pillars in order to enhance transmission. The volume fraction of the silicon in the pillars was chosen to simulate a single homogeneous antireflection layer, and the pillar height was targeted to be a quarter-wave thickness. A mask was generated, using a graphics computer-aided design system; reactive-ion etching was used to generate the pillars. An improvement in long-wavelength infrared transmission is observed, with diffraction and scattering dominating at shorter wavelengths.

© 1992 Optical Society of America

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References

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  1. M. J. Minot, “Single-layer, gradient index antireflective films effective from 0.35 μm to 2.5 μm,” J. Opt. Soc. Am. 66, 515–519 (1976).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. C. G. Bernhard, “Adaptation in a visual system,” Endeavour 26, 79–84 (1967).
  6. S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
    [CrossRef]
  7. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854 (Lincoln Laboratory, MIT, Lexington, Mass., 1989).
  8. W. H. Southwell, “Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces,” J. Opt. Soc. Am. A 8, 549–553 (1991).
    [CrossRef]
  9. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), p. 73.
  10. W. H. Southwell, “Gradient-index antireflection coatings,” Opt. Lett. 8, 584–586 (1983).
    [CrossRef] [PubMed]

1991 (1)

1987 (1)

1986 (1)

1983 (2)

1982 (1)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

1976 (1)

1967 (1)

C. G. Bernhard, “Adaptation in a visual system,” Endeavour 26, 79–84 (1967).

Baird, W. E.

Bernhard, C. G.

C. G. Bernhard, “Adaptation in a visual system,” Endeavour 26, 79–84 (1967).

Case, S. K.

Enger, R. C.

Gaylord, T. K.

Glytsis, E. N.

Hutley, M. C.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), p. 73.

Minot, M. J.

Moharam, M. G.

Southwell, W. H.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854 (Lincoln Laboratory, MIT, Lexington, Mass., 1989).

Wilson, S. J.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Appl. Opt. (3)

Endeavour (1)

C. G. Bernhard, “Adaptation in a visual system,” Endeavour 26, 79–84 (1967).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Opt. Lett. (1)

Other (2)

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), p. 73.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854 (Lincoln Laboratory, MIT, Lexington, Mass., 1989).

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Figures (10)

Fig. 1
Fig. 1

Predicted refractive index from various surface structures: a, for rectangular grooves with an incident field parallel to the grooves, shown in Eq. (1); b, for rectangular grooves with an incident field perpendicular to the grooves, shown in Eq. (2); and c, for a polarization-independent pillar structure, shown in Eq. (3).

Fig. 2
Fig. 2

Geometry of the pillar array produced by etching the substrate. This array approximates a single quarter-wave antireflection layer.

Fig. 3
Fig. 3

Flow chart for producing antireflection surfaces by very-large-scale-integrated processes: CAD, computer-aided design; LITH, lithography; CARL SUSS MJB, deep UV mask aligner; EBL, electron beam lithography.

Fig. 4
Fig. 4

Surface structure demonstrating anisotropic etch profile.

Fig. 5
Fig. 5

Surface structure demonstrating isotropic etch profile.

Fig. 6
Fig. 6

SEM photomicrograph of a pillar array in silicon that closely approximates the desired profile.

Fig. 7
Fig. 7

Calculated refractive-index profile produced by the tapered pillars observed in Fig. 6 using refractive-index expressions from Eq. (3).

Fig. 8
Fig. 8

Measured transmittance of a, the etched silicon pillar array shown in Fig. 6, and b, a bare silicon wafer.

Fig. 9
Fig. 9

The absorptance function D = exp(−αd) as determined from the bare silicon transmittance measurement.

Fig. 10
Fig. 10

Surface transmittance of the etched silicon pillar structure: a, as determined from the measured transmittance after the effects of absorption and backside reflection have been removed. Also shown is the transmittance for an ideal unetched silicon surface, b, and c, that predicted based on the graded antireflection layer model using Eq. (3).

Equations (14)

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n = ( 1 - f + f n s 2 ) 1 / 2 ,
n = ( 1 - f + f / n s 2 ) 1 / 2 ,
n = | [ 1 - f + f n s 2 ] [ f + ( 1 - f ) n s 2 ] + n s 2 2 [ f + ( 1 - f ) n s 2 ] | 1 / 2 ,
n = n s
t = λ / ( 4 n ) ,
f = a 2 / b 2 .
b < λ / n s .
x = 0.65 + 0.289 y ,
a = b - 2 x ,
T = T a T b D 1 - ( 1 - T a ) ( 1 - T b ) D 2 ,
D = exp ( - α d ) ,
T b = 4 n s ( 1 + n s ) 2 .
D = { [ T b 4 + 4 ( 1 - T b ) 2 T 0 2 ] } 1 / 2 - T b 2 2 ( 1 - T b ) 2 T 0 .
T a = [ 1 - ( 1 - T b ) D 2 ] T [ T b D - ( 1 - T b ) D 2 T ] .

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