Abstract

The effective parallel and perpendicular dielectric constants for a multilayer metal–insulator stack are obtained from numerical simulations and compared with analytical homogenization results as a function of wavelength and number of periods. The influence of inevitable film surface roughness on the homogenized dielectric constants, determined from numerical scattered field calculations, is evaluated as a function of roughness. The impact of this roughness on resolution in a subwavelength imaging application gives smoothness guidelines for material deposition.

© 2012 Optical Society of America

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  1. E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
    [CrossRef]
  2. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
    [CrossRef]
  3. K. J. Webb and M. Yang, Opt. Lett. 31, 2130 (2006).
    [CrossRef]
  4. H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 33, 2568 (2008).
  5. H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 34, 2243 (2009).
  6. M. Scholer and R. J. Blaikie, J. Opt. A 11, 105503 (2009).
    [CrossRef]
  7. T. Stefaniuk, G. Nowak, and R. Kotynski, Proc. SPIE 8070, 807010 (2011).
    [CrossRef]
  8. K. J. Webb and J. Li, Phys. Rev. A 78, 015803 (2008).
    [CrossRef]
  9. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).
  10. W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
    [CrossRef]
  11. A. Ludwig and K. J. Webb, Opt. Lett. 36, 106 (2011).
    [CrossRef]
  12. Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
    [CrossRef]
  13. V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
    [CrossRef]
  14. Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
    [CrossRef]
  15. S. M. Durbin, University of Purdue, West Lafayette, Indiana, “AFM roughness data for Ag and ZnO films” (personal communication, 2008).
  16. N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
    [CrossRef]

2011 (3)

T. Stefaniuk, G. Nowak, and R. Kotynski, Proc. SPIE 8070, 807010 (2011).
[CrossRef]

A. Ludwig and K. J. Webb, Opt. Lett. 36, 106 (2011).
[CrossRef]

Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
[CrossRef]

2009 (3)

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 34, 2243 (2009).

M. Scholer and R. J. Blaikie, J. Opt. A 11, 105503 (2009).
[CrossRef]

2008 (2)

K. J. Webb and J. Li, Phys. Rev. A 78, 015803 (2008).
[CrossRef]

H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 33, 2568 (2008).

2006 (1)

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

2003 (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
[CrossRef]

2001 (1)

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

1997 (1)

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

1965 (1)

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
[CrossRef]

Bagnall, D.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Blaikie, R. J.

M. Scholer and R. J. Blaikie, J. Opt. A 11, 105503 (2009).
[CrossRef]

Bond, W. L.

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
[CrossRef]

Bossard, J. A.

Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
[CrossRef]

Chaturvedi, P.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Chen, Y.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Durbin, S. M.

S. M. Durbin, University of Purdue, West Lafayette, Indiana, “AFM roughness data for Ag and ZnO films” (personal communication, 2008).

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Fang, N. X.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Goto, T.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Hiraga, K.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Islam, M. S.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Jiang, Z. H.

Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
[CrossRef]

Kalinin, V.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Kobayashi, N. P.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Kotynski, R.

T. Stefaniuk, G. Nowak, and R. Kotynski, Proc. SPIE 8070, 807010 (2011).
[CrossRef]

Koyama, S.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Li, J.

K. J. Webb and J. Li, Phys. Rev. A 78, 015803 (2008).
[CrossRef]

Liu, H.

Logeeswaran, V. J.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Ludwig, A.

Nowak, G.

T. Stefaniuk, G. Nowak, and R. Kotynski, Proc. SPIE 8070, 807010 (2011).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

Park, K.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
[CrossRef]

Ringhofer, K.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Scholer, M.

M. Scholer and R. J. Blaikie, J. Opt. A 11, 105503 (2009).
[CrossRef]

Sekiuchi, T.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Shamonina, E.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Shen, M.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Shivanand,

Solymar, L.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Stefaniuk, T.

T. Stefaniuk, G. Nowak, and R. Kotynski, Proc. SPIE 8070, 807010 (2011).
[CrossRef]

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Wang, S. Y.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Wang, X.

Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
[CrossRef]

Webb, K. J.

Werner, D. H.

Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
[CrossRef]

Williams, R. S.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
[CrossRef]

Wu, W.

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Yang, M.

Yao, T.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Zhu, Z.

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

Electron. Lett. (1)

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

J. Appl. Phys. (2)

W. L. Bond, J. Appl. Phys. 36, 1674 (1965).
[CrossRef]

Z. H. Jiang, J. A. Bossard, X. Wang, and D. H. Werner, J. Appl. Phys. 109, 013515 (2011).
[CrossRef]

J. Cryst. Growth (1)

Y. Chen, D. Bagnall, Z. Zhu, T. Sekiuchi, K. Park, K. Hiraga, T. Yao, S. Koyama, M. Shen, and T. Goto, J. Cryst. Growth 181, 165 (1997).
[CrossRef]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
[CrossRef]

J. Opt. A (1)

M. Scholer and R. J. Blaikie, J. Opt. A 11, 105503 (2009).
[CrossRef]

Nano Lett. (1)

V. J. Logeeswaran, N. P. Kobayashi, M. S. Islam, W. Wu, P. Chaturvedi, N. X. Fang, S. Y. Wang, and R. S. Williams, Nano Lett. 9, 178 (2009).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

K. J. Webb and J. Li, Phys. Rev. A 78, 015803 (2008).
[CrossRef]

Proc. SPIE (1)

T. Stefaniuk, G. Nowak, and R. Kotynski, Proc. SPIE 8070, 807010 (2011).
[CrossRef]

Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Other (2)

S. M. Durbin, University of Purdue, West Lafayette, Indiana, “AFM roughness data for Ag and ZnO films” (personal communication, 2008).

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Geometry considered for the numerical extraction of the effective dielectric constants of the multilayer slab. (b) Multilayer stack is composed of alternate layers of metal (yellow) and insulator (blue), with Gaussian-distributed surface roughness in each layer.

Fig. 2.
Fig. 2.

Effective dielectric constants for different numbers of periods with smooth surfaces. The Ag/ZnO multilayer slab has a total thickness of 0.2 μm. The analytical results shown in green were obtained using (5) and (6), while the others were obtained from the FEM simulation and using (1) and (2).

Fig. 3.
Fig. 3.

Difference between the effective dielectric constants obtained numerically [from FEM simulations and using (1) and (2)] and analytically [using (5) and (6)] for the 0.2 μm Ag/ZnO multilayer slab having 10 periods and different standard deviations of the surface roughness, σ . The lines and the error bars show the mean and the standard deviation, respectively, for the differential dielectric constants.

Fig. 4.
Fig. 4.

(a) Geometry for numerical study of the influence of surface roughness in an anisotropic lens: a 50 nm thick chromium (Cr) mask with two 10 nm slits and 30 nm center-to-center distance; Ag/ZnO multilayer stack with 10 nm thick layers and a surface roughness with standard deviation σ . Photoresist and silica are shown in pink and white, respectively. (b) Normalized | E | obtained at the image plane (right edge of the stack) for three stacks having different σ at λ = 0.405 μm . (c) Standard deviation (error bars) and mean (lines) of normalized | E | calculated over the incident wavelength range of 0.4–0.41 μm for the same stacks used to obtain | E | in (b). (d) Normalized | E | showing the statistical influence of random film roughness on the resolution in this double slit imaging arrangement. The mean (lines) and standard deviation (error bars) in | E | are calculated from the normalized | E | obtained for several different stacks having random roughness for the incident wavelength λ = 0.405 μm .

Equations (6)

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

ϵ = β i ¯ ω 0 ϵ 0 Z i ¯ , i = 1 , 2 ,
ϵ = ω 0 μ 0 ( sin 2 θ 2 sin 2 θ 1 ) β 1 ¯ Z 1 ¯ β 2 ¯ Z 2 ¯ ,
Z i ¯ = μ 0 ϵ 0 ( 1 + S 11 , i ) 2 S 21 , i 2 ( 1 S 11 , i ) 2 S 21 , i 2 cos θ i , i = 1 , 2
β i ¯ = 1 d arccos [ 1 S 11 , i 2 + S 21 , i 2 2 S 21 , i ] , i = 1 , 2
ϵ h = ϵ Ag D + ϵ ZnO ( 1 D ) ,
ϵ h = ϵ Ag ϵ ZnO ϵ Ag ( 1 D ) + ϵ ZnO D .

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