Abstract

Periodic micro and nano-structures can be lithographically produced using the Talbot effect. However, the limited depth-of-field of the self-images has effectively prevented its practical use, especially for high-resolution structures with periods less than 1 micrometer. In this article we show that by integrating the diffraction field transmitted by a grating mask over a distance of one Talbot period, one can obtain an effective image that is independent of the absolute distance from the mask. In this way high resolution periodic patterns can be printed without the depth-of-field limitation of Talbot self-images. For one-dimensional patterns the image obtained is shown to be related to the convolution of the mask transmission function with itself. This technique, which we call Displacement Talbot Lithography (DTL), enables high-resolution photolithography without the need for complex and expensive projection optics for the production of periodic structures like diffraction gratings or photonic crystals. Experimental results showing the printing of linear gratings and an array of holes on a hexagonal lattice are presented.

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  1. R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
    [CrossRef] [PubMed]
  2. S. R. J. Brueck, “Optical and interferometric lithography––nanotechnology enablers,” Proc. IEEE 93(10), 1704–1721 (2005).
    [CrossRef]
  3. T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
    [CrossRef]
  4. S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
    [CrossRef]
  5. W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 403–405 (1836).
  6. D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
    [CrossRef] [PubMed]
  7. D. C. Flanders, A. M. Hawryluk, and H. I. Smith, “Spatial period division – a new technique for exposing sub-micrometer linewidth periodic and quasi periodic patterns,” J. Vac. Sci. Technol. 16(6), 1949–1952 (1979).
    [CrossRef]
  8. C. Zanke, M. H. Qi, and H. I. Smith, “Large-area patterning for photonic crystals via coherent diffraction lithography,” J. Vac. Sci. Technol. B 22(6), 3352–3355 (2004).
    [CrossRef]
  9. H. H. Solak and Y. Ekinci, “Achromatic spatial frequency multiplication: a method for production of nanometer-scale periodic structures,” J. Vac. Sci. Technol. B 23(6), 2705–2710 (2005).
    [CrossRef]
  10. H. H. Solak, “A system and a method for generating periodic and/or quasi-periodic pattern on a sample.” Int’l. patent 1810085 (16 March 2011).
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  12. Y. Bourgin, Y. Jourlin, O. Parriaux, A. Talneau, S. Tonchev, C. Veillas, P. Karvinen, N. Passilly, A. R. Md Zain, R. M. De La Rue, J. Van Erps, and D. Troadec, “100 nm period grating by high-index phase-mask immersion lithography,” Opt. Express 18(10), 10557–10566 (2010).
    [CrossRef] [PubMed]
  13. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68(9), 1206–1210 (1978).
    [CrossRef]
  14. D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
    [CrossRef]

2010

2007

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

2005

S. R. J. Brueck, “Optical and interferometric lithography––nanotechnology enablers,” Proc. IEEE 93(10), 1704–1721 (2005).
[CrossRef]

H. H. Solak and Y. Ekinci, “Achromatic spatial frequency multiplication: a method for production of nanometer-scale periodic structures,” J. Vac. Sci. Technol. B 23(6), 2705–2710 (2005).
[CrossRef]

2004

C. Zanke, M. H. Qi, and H. I. Smith, “Large-area patterning for photonic crystals via coherent diffraction lithography,” J. Vac. Sci. Technol. B 22(6), 3352–3355 (2004).
[CrossRef]

1999

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

1996

T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
[CrossRef]

1995

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[CrossRef]

1992

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

1979

D. C. Flanders, A. M. Hawryluk, and H. I. Smith, “Spatial period division – a new technique for exposing sub-micrometer linewidth periodic and quasi periodic patterns,” J. Vac. Sci. Technol. 16(6), 1949–1952 (1979).
[CrossRef]

1978

1836

W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 403–405 (1836).

Bogart, G. R.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Bourgin, Y.

Brueck, S. R. J.

S. R. J. Brueck, “Optical and interferometric lithography––nanotechnology enablers,” Proc. IEEE 93(10), 1704–1721 (2005).
[CrossRef]

Cahill, D. G.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Carter, J. M.

T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
[CrossRef]

Chou, S. Y.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[CrossRef]

Christodoulou, C. G.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

De La Rue, R. M.

Ekinci, Y.

H. H. Solak and Y. Ekinci, “Achromatic spatial frequency multiplication: a method for production of nanometer-scale periodic structures,” J. Vac. Sci. Technol. B 23(6), 2705–2710 (2005).
[CrossRef]

El-Kady, I. F.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Flanders, D. C.

D. C. Flanders, A. M. Hawryluk, and H. I. Smith, “Spatial period division – a new technique for exposing sub-micrometer linewidth periodic and quasi periodic patterns,” J. Vac. Sci. Technol. 16(6), 1949–1952 (1979).
[CrossRef]

Gnall, R. P.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

Hamza, A. V.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Hawryluk, A. M.

D. C. Flanders, A. M. Hawryluk, and H. I. Smith, “Spatial period division – a new technique for exposing sub-micrometer linewidth periodic and quasi periodic patterns,” J. Vac. Sci. Technol. 16(6), 1949–1952 (1979).
[CrossRef]

Highland, M.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Hong, S. H.

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

Jeon, S.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Jourlin, Y.

Karvinen, P.

Knop, K.

Koch, T. L.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

Krauss, P. R.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[CrossRef]

Liao, H.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Md Zain, A. R.

Mirkin, C. A.

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

Mulgrew, P. P.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

Ostermeyer, F.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

Parriaux, O.

Passilly, N.

Piner, R. D.

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

Qi, M. H.

C. Zanke, M. H. Qi, and H. I. Smith, “Large-area patterning for photonic crystals via coherent diffraction lithography,” J. Vac. Sci. Technol. B 22(6), 3352–3355 (2004).
[CrossRef]

Renstrom, P. J.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[CrossRef]

Rogers, J. A.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Savas, T. A.

T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
[CrossRef]

Schattenburg, M. L.

T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
[CrossRef]

Shir, D. J.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Smith, H. I.

C. Zanke, M. H. Qi, and H. I. Smith, “Large-area patterning for photonic crystals via coherent diffraction lithography,” J. Vac. Sci. Technol. B 22(6), 3352–3355 (2004).
[CrossRef]

T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
[CrossRef]

D. C. Flanders, A. M. Hawryluk, and H. I. Smith, “Spatial period division – a new technique for exposing sub-micrometer linewidth periodic and quasi periodic patterns,” J. Vac. Sci. Technol. 16(6), 1949–1952 (1979).
[CrossRef]

Solak, H. H.

H. H. Solak and Y. Ekinci, “Achromatic spatial frequency multiplication: a method for production of nanometer-scale periodic structures,” J. Vac. Sci. Technol. B 23(6), 2705–2710 (2005).
[CrossRef]

Su, M. F.

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

Talbot, W. H. F.

W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 403–405 (1836).

Talneau, A.

Tennant, D. M.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

Tonchev, S.

Troadec, D.

Van Erps, J.

Veillas, C.

Verdiell, J.-M.

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

Xu, F.

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

Zanke, C.

C. Zanke, M. H. Qi, and H. I. Smith, “Large-area patterning for photonic crystals via coherent diffraction lithography,” J. Vac. Sci. Technol. B 22(6), 3352–3355 (2004).
[CrossRef]

Zhu, J.

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

Appl. Phys. Lett.

S. Y. Chou, P. R. Krauss, and P. J. Renstrom, “Imprint of sub-25nm vias and trenches in polymers,” Appl. Phys. Lett. 67(21), 3114–3116 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem. B

D. J. Shir, S. Jeon, H. Liao, M. Highland, D. G. Cahill, M. F. Su, I. F. El-Kady, C. G. Christodoulou, G. R. Bogart, A. V. Hamza, and J. A. Rogers, “Three-dimensional nanofabrication with elastomeric phase masks,” J. Phys. Chem. B 111(45), 12945–12958 (2007).
[CrossRef] [PubMed]

J. Vac. Sci. Technol.

D. C. Flanders, A. M. Hawryluk, and H. I. Smith, “Spatial period division – a new technique for exposing sub-micrometer linewidth periodic and quasi periodic patterns,” J. Vac. Sci. Technol. 16(6), 1949–1952 (1979).
[CrossRef]

J. Vac. Sci. Technol. B

C. Zanke, M. H. Qi, and H. I. Smith, “Large-area patterning for photonic crystals via coherent diffraction lithography,” J. Vac. Sci. Technol. B 22(6), 3352–3355 (2004).
[CrossRef]

H. H. Solak and Y. Ekinci, “Achromatic spatial frequency multiplication: a method for production of nanometer-scale periodic structures,” J. Vac. Sci. Technol. B 23(6), 2705–2710 (2005).
[CrossRef]

D. M. Tennant, T. L. Koch, P. P. Mulgrew, R. P. Gnall, F. Ostermeyer, and J.-M. Verdiell, “Characterization of near field holography grating masks for optoelectronics fabricated by electron beam lithography,” J. Vac. Sci. Technol. B 10(6), 2530–2535 (1992).
[CrossRef]

T. A. Savas, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Large‐area achromatic interferometric lithography for 100 nm period gratings and grids,” J. Vac. Sci. Technol. B 14(6), 4167–4170 (1996).
[CrossRef]

Opt. Express

Philos. Mag.

W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 403–405 (1836).

Proc. IEEE

S. R. J. Brueck, “Optical and interferometric lithography––nanotechnology enablers,” Proc. IEEE 93(10), 1704–1721 (2005).
[CrossRef]

Science

R. D. Piner, J. Zhu, F. Xu, S. H. Hong, and C. A. Mirkin, ““Dip-Pen” nanolithography, ” Science 283(5402), 661–663 (1999).
[CrossRef] [PubMed]

Other

H. H. Solak, “A system and a method for generating periodic and/or quasi-periodic pattern on a sample.” Int’l. patent 1810085 (16 March 2011).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., 1968), p. 48.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic diagram illustrating the new DTL method. The photoresist-coated substrate is moved towards the mask by one Talbot period during the exposure. (b) Calculated intensity distribution after a linear grating. Two self images are marked with dashed lines at distances 0.9 μm and 2.7 μm from the grating. The dotted horizontal line below marks the position of a Talbot sub-image, with twice the frequency of the original grating.

Fig. 2
Fig. 2

SEM images of high-resolution linear grating patterns fabricated in photoresist using the DTL method. The periods of the patterns shown in (a)-(c) are 250 nm, 300 nm and 350 nm, whereas the periods of the respective patterns in the mask were 500 nm, 600 nm and 700 nm. The DTL exposure therefore produces a frequency multiplication. The scale bar is 500 nm long.

Fig. 3
Fig. 3

Application of the DTL method to a periodic pattern with hexagonal symmetry. (a) Schematic view of the mask pattern which consists of clear circular apertures in a thin opaque layer. (b) SEM image of a pattern of 300 nm-diameter holes with 600 nm period obtained by a DTL exposure and transferred into a silicon wafer by reactive ion etching. (c) Photograph of the photonic crystal pattern printed in photoresist on a 4” Si wafer.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

T ( x ) = m A m exp ( i 2 m π p x ) ,
E ( x , z ) = m A m exp ( i 2 m π p x ) exp ( i 2 π λ z 1 λ 2 m 2 p 2 ) .
I ( x , z ) = m , n A m A n * exp ( i 2 π p ( m n ) x ) exp ( i 2 π τ z ( m 2 n 2 ) ) ,
D ( x ) = m , n A m A n * exp ( i 2 π p ( m n ) x ) z 0 z 0 + τ exp ( i 2 π τ z ( m 2 n 2 ) ) d z .
D ( x ) = τ m | A m | 2 τ | A 0 | 2 + τ S ( 2 x ) ,
S ( x ) = m A m A m * exp ( i 2 π m x p ) ,
S ( x ) = p / 2 p / 2 T ( x ' ) T * ( x x ' ) d x ' .

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