Abstract

In nanolithography using optical near-field sources to push the critical dimension below the diffraction limit, optimization of process parameters is of utmost importance. Herein we present a simple analytic model to predict photoresist profiles with a localized evanescent exposure that decays exponentially in a photoresist of finite contrast. We introduce the concept of nominal developing thickness (NDT) to determine the proper developing process that yields the best topography of the exposure profile fitting to the isointensity contour. Based on this model, we experimentally investigated the NDT and obtained exposure profiles produced by the near-field distribution of a bowtie-shaped nanoaperture. The profiles were properly fit to the calculated results obtained by the finite differential time domain method. Using the threshold exposure dose of a photoresist, we can determine the absolute intensity of the intensity distribution of the near field and analyze the difference in decay rates of the near field distributions obtained via experiment and calculation. For maximum depth of 41 nm, we estimate the uncertainties in the measurements of profile and intensity to be less than 6% and about 1%, respectively. We expect this method will be useful in detecting the absolute value of the near-field distribution produced by nano-scale devices.

© 2011 OSA

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References

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  1. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
    [CrossRef]
  2. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
    [CrossRef]
  3. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
    [CrossRef] [PubMed]
  4. L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006).
    [CrossRef] [PubMed]
  5. X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
    [CrossRef]
  6. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
    [CrossRef] [PubMed]
  7. K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008).
    [CrossRef]
  8. S. A. Campbell, The science and engineering of microelectronic fabrication (Oxford University Press, New York, 1996).
  9. S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996).
    [CrossRef]
  10. R. Guo, E. C. Kinzel, Y. Li, S. M. Uppuluri, A. Raman, and X. Xu, “Three-dimensional mapping of optical near field of a nanoscale bowtie antenna,” Opt. Express 18(5), 4961–4971 (2010).
    [CrossRef] [PubMed]
  11. D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
    [CrossRef] [PubMed]
  12. R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express 13(18), 7198–7208 (2005).
    [CrossRef] [PubMed]
  13. E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008).
    [CrossRef] [PubMed]
  14. E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008).
    [CrossRef]
  15. Y. Kim, S. Kim, H. Jung, E. Lee, and J. W. Hahn, “Plasmonic nano lithography with a high scan speed contact probe,” Opt. Express 17(22), 19476–19485 (2009).
    [CrossRef] [PubMed]
  16. M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
    [CrossRef] [PubMed]
  17. L. Zhou, Q. Gan, F. J. Bartoli, and V. Dierolf, “Direct near-field optical imaging of UV bowtie nanoantennas,” Opt. Express 17(22), 20301–20306 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. MicroChemicals GmbH, “Development of Photoresists” (2007) http://www.microchemicals.eu/technical_information/development_photoresist.pdf
  20. K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992).
    [CrossRef]

2010

2009

2008

J. B. Leen, P. Hansen, Y.-T. Cheng, and L. Hesselink, “Improved focused ion beam fabrication of near-field apertures using a silicon nitride membrane,” Opt. Lett. 33(23), 2827–2829 (2008).
[CrossRef] [PubMed]

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008).
[CrossRef] [PubMed]

E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008).
[CrossRef]

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008).
[CrossRef]

2006

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

L. Wang, E. X. Jin, S. M. Uppuluri, and X. Xu, “Contact optical nanolithography using nanoscale C-shaped apertures,” Opt. Express 14(21), 9902–9908 (2006).
[CrossRef] [PubMed]

2005

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nano-patterning,” Opt. Express 13(18), 7198–7208 (2005).
[CrossRef] [PubMed]

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

2004

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

1999

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

1996

S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996).
[CrossRef]

1992

K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992).
[CrossRef]

Alkaisi, M. M.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

Amarie, D.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

Bartoli, F. J.

Blaikie, R. J.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

Cheng, Y.-T.

Cheung, R.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

Chua, J. K.

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008).
[CrossRef]

Conley, N. R.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Cumming, D. R. S.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

Davy, S.

S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996).
[CrossRef]

Dierolf, V.

Dragnea, B.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Fromm, D. P.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Gan, Q.

Guo, R.

Hahn, J. W.

Y. Kim, S. Kim, H. Jung, E. Lee, and J. W. Hahn, “Plasmonic nano lithography with a high scan speed contact probe,” Opt. Express 17(22), 19476–19485 (2009).
[CrossRef] [PubMed]

E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008).
[CrossRef] [PubMed]

E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008).
[CrossRef]

Hansen, P.

Hesselink, L.

Ishihara, T.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

Jacobson, S. C.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

Jin, E. X.

Johnson, E. G.

Jones, A. C.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Jung, H.

Kawamura, E.

K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992).
[CrossRef]

Kim, S.

Kim, Y.

Kino, G. S.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Kinzel, E. C.

Lee, E.

Y. Kim, S. Kim, H. Jung, E. Lee, and J. W. Hahn, “Plasmonic nano lithography with a high scan speed contact probe,” Opt. Express 17(22), 19476–19485 (2009).
[CrossRef] [PubMed]

E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008).
[CrossRef]

E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008).
[CrossRef] [PubMed]

Leen, J. B.

Li, Y.

Li, Z.-Y.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Liu, Z. W.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Luo, X.

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

McNab, S. J.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

Moerner, W. E.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Morisaki, K.

K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992).
[CrossRef]

Murukeshan, V. M.

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008).
[CrossRef]

Raman, A.

Rang, M.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Raschke, M. B.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Rawlinson, N. D.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

Rumpf, R. C.

Schaich, W. L.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

Schuck, P. J.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Spajer, M.

S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996).
[CrossRef]

Sreekanth, K. V.

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008).
[CrossRef]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Sun, C.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Sundaramurthy, A.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Uppuluri, S. M.

Wang, L.

Wei, Q. H.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

Wiley, B. J.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Xia, Y.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Xu, X.

Zhang, X.

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Zhou, F.

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Zhou, L.

Appl. Phys. Lett.

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, R. Cheung, and D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75(22), 3560–3562 (1999).
[CrossRef]

X. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

K. V. Sreekanth, V. M. Murukeshan, and J. K. Chua, “A planar layer configuration for surface plasmon interference nanoscale lithography,” Appl. Phys. Lett. 93(9), 093103 (2008).
[CrossRef]

S. Davy and M. Spajer, “Near field optics: Snapshot of the field emitted by a nanosource using a photosensitive polymer,” Appl. Phys. Lett. 69(22), 3306–3308 (1996).
[CrossRef]

J. Appl. Phys.

E. Lee and J. W. Hahn, “The effect of photoresist contrast on the exposure profiles obtained with evanescent fields of nanoapertures,” J. Appl. Phys. 103(8), 083550 (2008).
[CrossRef]

Microelectron. Eng.

K. Morisaki and E. Kawamura, “Lithography process control system,” Microelectron. Eng. 17(1-4), 435–438 (1992).
[CrossRef]

Nano Lett.

D. Amarie, N. D. Rawlinson, W. L. Schaich, B. Dragnea, and S. C. Jacobson, “Three-dimensional mapping of the light intensity transmitted through nanoapertures,” Nano Lett. 5(7), 1227–1230 (2005).
[CrossRef] [PubMed]

M. Rang, A. C. Jones, F. Zhou, Z.-Y. Li, B. J. Wiley, Y. Xia, and M. B. Raschke, “Optical near-field mapping of plasmonic nanoprisms,” Nano Lett. 8(10), 3357–3363 (2008).
[CrossRef] [PubMed]

Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
[CrossRef] [PubMed]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006).
[CrossRef] [PubMed]

Nanotechnology

E. Lee and J. W. Hahn, “Modeling of three-dimensional photoresist profiles exposed by localized fields of high-transmission nano-apertures,” Nanotechnology 19(27), 275303 (2008).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Other

MicroChemicals GmbH, “Development of Photoresists” (2007) http://www.microchemicals.eu/technical_information/development_photoresist.pdf

S. A. Campbell, The science and engineering of microelectronic fabrication (Oxford University Press, New York, 1996).

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Figures (6)

Fig. 1
Fig. 1

Cross-sectional topography of a photoresist exposed with several different peak doses and developed for the same NDT of 50 nm. (a) Exposure dose distributions on the top surface of the photoresist. The dashed lines represent the levels of the threshold (lower) and clearing (upper) doses. (b) Photoresist profiles with far-field exposures assuming no attenuation along the depth. Near-field-exposed profiles obtained from (c) the previous model by E. Lee et al. [13] and (d) the analytic formula in this paper.

Fig. 2
Fig. 2

Cross-sectional profiles of a photoresist developed for several different processing times corresponding to NDTs of (a) 15 nm, (b) 25 nm, (c) 35 nm, (d) 50 nm, (e) 70 nm, and (f) 90 nm. The profiles based on our analytic model are represented by blue lines, whereas those obtained by the previous model and the non-decaying far-field model are represented by red and green lines, respectively. Dashed lines in each panel indicate isoexposure contours at the threshold dose (lower curve) and the clearing dose (upper curve).

Fig. 3
Fig. 3

Pattern profile (solid lines) as a function of (a) peak exposure dose and (b) photoresist contrast for several different NDTs indicated in the legend. The expectations of the previous model (fine dashed-lines) are also plotted as dotted lines in each graph. The depth at threshold dose and clearing dose are also plotted as bold dashed line and bold black dot-dashed line, respectively.

Fig. 6
Fig. 6

Cross-section of the developed pattern profile (under-filled black solid lines) and FDTD calculation results (dotted-lines) for the (a) xz-plane and (b) yz-plane. A scanning electron micrograph of bowtie-shaped nano aperture in experiment is shown in (c).

Fig. 4
Fig. 4

Developed photoresist maximum depth with respect to NDT. As NDT increases, the pattern depth increases until reaching the contour of threshold dose (S th). In this experiment the maximum depth of S E was expected to approach the 48.7 nm (red dotted-line). Above a NDT of 145 nm (dashed arrow), the pattern depth was expected to be similar to that of isoexposure at the threshold dose with a tolerance less than 1%.

Fig. 5
Fig. 5

(a) – (c) AFM measured three-dimensional profiles of developed patterns for different exposure times. From left (a) to right (c) in the upper row, the exposure time was 20, 30, and 50 ms, respectively, while the laser power was set at 60 nW. The isointensity surfaces from the three-dimensional near-field distribution using FDTD calculation are plotted in the bottom row (d) - (f), and the corresponding intensity was normalized to the intensity of the input plane. The intensity level of (d) - (f) are correspond to the peak intensity at the depth of 6.5, 21, and 41 nm, indicated in the inset of (a) - (c), respectively. The shape of the bowtie aperture is illustrated with white dotted lines, and white arrows indicate the polarization axis of illumination. The visualized space is 500 nm × 500 nm × 50 nm in x-y-z space.

Equations (8)

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E ex ( x , y ; z ) = E 0 ( x , y ) exp ( z β ) = E p exp [ 2 ( ρ w ) 2 ] exp ( z β ) ,
Γ = 1 log 10 ( E cl / E th ) ,
η ( E e x ) = { 0 , for E ex < E th , Γ log 10 ( E ex / E th ) , for E th E ex < E cl , and 1 , for E cl E ex .
τ D = 0 S E 1 η ( E ex ) v cl d z ,
T 0 = 0 S E 1 η ( E ex ) d z .
S E ( E 0 ) = { 0 , for E 0 < E th , β ln ( E 0 / E th ) [ 1 exp ( γ T 0 / β ) ] , for E th E 0 < E cl , β ln ( E 0 / E th ) β [ ( E 0 / E th ) γ / e γ ] exp ( γ T 0 / β ) , for E cl E 0 , and T 0 , for E cl e T 0 / β E 0 .
T o ( β / γ ) ln f res 1
T o β (     1 γ ln ( 1 f res )     + ln ( E p E th )     1 γ { ln [ ln ( E p E th ) ] + ln γ + 1 } ) ,

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