Abstract

High-performance nano-optical elements for application wavelengths in the ultraviolet spectral range often require feature sizes of only a few tens of nanometers where line edge roughness (LER) becomes a critical parameter for the optical performance. In this contribution, we explore the influence of LER on the optical performance of wire grid polarizers (WGP) in the far ultraviolet range. Therefore, we present a method, which uses the finite difference time domain method in combination with a comprehensive spatial frequency dependent LER model. The measured LER of 3.6 nm (standard deviation) reduces the WGP’s extinction ratio by a factor of 3.6 at a wavelength of 248 nm. We identify a critical range of the correlation length, which maximizes the detrimental effect of LER. The presented method and the results provide the basis for future fabrication technology optimization of WGPs and other optical meta-surfaces in the ultraviolet spectral region or at even shorter wavelengths.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (5)

2016 (2)

D. Gkogkou, B. Schreiber, T. Shaykhutdinov, H. K. Ly, U. Kuhlmann, U. Gernert, S. Facsko, P. Hildebrandt, N. Esser, K. Hinrichs, I. M. Weidinger, and T. W. H. Oates, “Polarization- and wavelength-dependent surface-enhanced Raman spectroscopy using optically anisotropic rippled substrates for sensing,” Science 313(5793), 1614– 1616 (2016).

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4(11), 1780–1786 (2016).
[Crossref]

2015 (4)

2014 (7)

2013 (2)

C. A. Mack, “Systematic errors in the measurement of power spectral density,” J. Micro/Nanolithography. MEMS, MOEMS 12(3), 033016 (2013).
[Crossref]

C. A. Mack, “Generating random rough edges, surfaces, and volumes,” Appl. Opt. 52(7), 1472–1480 (2013).
[Crossref] [PubMed]

2012 (4)

E.-B. Kley, H. Schmidt, U. Zeitner, M. Banasch, and B. Schnabel, “Enhanced e-beam pattern writing for nano-optics based on character projection,” Proc. SPIE 8352, 83520M (2012).
[Crossref]

J. S. Cetnar, J. R. Middendorf, and E. R. Brown, “Extraordinary optical transmission and extinction in a terahertz wire-grid polarizer,” Appl. Phys. Lett. 100(23), 231912 (2012).
[Crossref]

T. Weber, T. Käsebier, M. Helgert, E.-B. Kley, and A. Tünnermann, “Tungsten wire grid polarizer for applications in the DUV spectral range,” Appl. Opt. 51(16), 3224–3227 (2012).
[Crossref] [PubMed]

D. Lehr, K. Dietrich, C. Helgert, T. Käsebier, H.-J. Fuchs, A. Tünnermann, and E.-B. Kley, “Plasmonic properties of aluminum nanorings generated by double patterning,” Opt. Lett. 37(2), 157–159 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (2)

2009 (4)

Y. Li, T. X. Wu, and S.-T. Wu, “Design optimization of reflective polarizers for LCD backlight recycling,” J. Disp. Technol. 5(8), 335–340 (2009).
[Crossref]

I. Yamada, K. Takano, M. Hangyo, M. Saito, and W. Watanabe, “Terahertz wire-grid polarizers with micrometer-pitch Al gratings,” Opt. Lett. 34(3), 274–276 (2009).
[Crossref] [PubMed]

A. Lehmuskero, B. Bai, P. Vahimaa, and M. Kuittinen, “Wire-grid polarizers in the volume plasmon region,” Opt. Express 17(7), 5481–5489 (2009).
[Crossref] [PubMed]

P. Zimmerman, “Double patterning lithography: double the trouble or double the fun?” SPIE Newsroom,  2009, 1–3 (2009).

2008 (2)

Z. Ge and S. T. Wu, “Nanowire grid polarizer for energy efficient and wide-view liquid crystal displays,” Appl. Phys. Lett. 93(12), 121104 (2008).
[Crossref]

I. Yamada, K. Kintaka, J. Nishii, S. Akioka, Y. Yamagishi, and M. Saito, “Mid-infrared wire-grid polarizer with silicides,” Opt. Lett. 33(3), 258–260 (2008).
[Crossref] [PubMed]

2007 (3)

A. Lehmuskero, M. Kuittinen, and P. Vahimaa, “Refractive index and extinction coefficient dependence of thin Al and Ir films on deposition technique and thickness,” Opt. Express 15(17), 10744–10752 (2007).
[Crossref] [PubMed]

J. J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90(6), 061104 (2007).
[Crossref]

S.-K. Kim, “Polarized effects in optical lithography with high NA technology,” J. Korean Phys. Soc. 50(6), 1952 (2007).
[Crossref]

2006 (1)

D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
[Crossref] [PubMed]

2005 (2)

J. M. Benevides, S. A. Overman, and G. J. Thomas, “Raman, polarized Raman and ultraviolet resonance Raman spectroscopy of nucleic acids and their complexes,” J. Raman Spectrosc. 36(4), 279–299 (2005).
[Crossref]

B. Geh, “Polarization effects associated with hyper-numerical-aperture (>1) lithography,” J. Micro/Nanolithography. MEMS, MOEMS 4(3), 31104 (2005).
[Crossref]

2002 (1)

M. Meyer, S. Aloise, and A. N. Grum-Grzhimailo, “Strong, polarized Balmer-α fluorescence after resonant core excitation of HCl,” Phys. Rev. Lett. 88(22), 223001 (2002).
[Crossref] [PubMed]

1993 (1)

G. Palasantzas, “Roughness spectrum and surface width of self-affine fractal surfaces via the K-correlation model,” Phys. Rev. B Condens. Matter 48(19), 14472–14478 (1993).
[Crossref] [PubMed]

1986 (1)

1965 (2)

1960 (1)

1904 (1)

J. C. Maxwell and B. A. Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. Lond. 203A, 385–420 (1904).

Akioka, S.

Aloise, S.

M. Meyer, S. Aloise, and A. N. Grum-Grzhimailo, “Strong, polarized Balmer-α fluorescence after resonant core excitation of HCl,” Phys. Rev. Lett. 88(22), 223001 (2002).
[Crossref] [PubMed]

Artigas, D.

Asano, K.

Bai, B.

Balla, N. K.

Banasch, M.

M. Heusinger, M. Banasch, and U. D. Zeitner, “Rowland ghost suppression in high efficiency spectrometer gratings fabricated by e-beam lithography,” Opt. Express 25(6), 6182–6191 (2017).
[Crossref] [PubMed]

E.-B. Kley, H. Schmidt, U. Zeitner, M. Banasch, and B. Schnabel, “Enhanced e-beam pattern writing for nano-optics based on character projection,” Proc. SPIE 8352, 83520M (2012).
[Crossref]

Bär, M.

H. Gross, S. Heidenreich, M. A. Henn, G. Dai, F. Scholze, and M. Bär, “Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry,” J. Eur. Opt. Soc. 9, 23 (2014).

Baranov, D. G.

Benevides, J. M.

J. M. Benevides, S. A. Overman, and G. J. Thomas, “Raman, polarized Raman and ultraviolet resonance Raman spectroscopy of nucleic acids and their complexes,” J. Raman Spectrosc. 36(4), 279–299 (2005).
[Crossref]

Bergner, B. C.

Bilski, B.

Bird, G. R.

Bourgin, Y.

Brasselet, S.

Brown, E. R.

J. S. Cetnar, J. R. Middendorf, and E. R. Brown, “Extraordinary optical transmission and extinction in a terahertz wire-grid polarizer,” Appl. Phys. Lett. 100(23), 231912 (2012).
[Crossref]

Bruchhausen, A.

D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
[Crossref] [PubMed]

Cantarero, A.

D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
[Crossref] [PubMed]

Cetnar, J. S.

J. S. Cetnar, J. R. Middendorf, and E. R. Brown, “Extraordinary optical transmission and extinction in a terahertz wire-grid polarizer,” Appl. Phys. Lett. 100(23), 231912 (2012).
[Crossref]

Chen, L. Q.

D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
[Crossref] [PubMed]

Chichkov, B. N.

Choi, K. J.

D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
[Crossref] [PubMed]

Choi, S.-W.

Dai, G.

H. Gross, S. Heidenreich, M. A. Henn, G. Dai, F. Scholze, and M. Bär, “Modelling line edge roughness in periodic line-space structures by Fourier optics to improve scatterometry,” J. Eur. Opt. Soc. 9, 23 (2014).

Deng, X.

J. J. Wang, F. Walters, X. Liu, P. Sciortino, and X. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90(6), 061104 (2007).
[Crossref]

Dietrich, K.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4(11), 1780–1786 (2016).
[Crossref]

D. Lehr, K. Dietrich, C. Helgert, T. Käsebier, H.-J. Fuchs, A. Tünnermann, and E.-B. Kley, “Plasmonic properties of aluminum nanorings generated by double patterning,” Opt. Lett. 37(2), 157–159 (2012).
[Crossref] [PubMed]

Eom, C. B.

D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
[Crossref] [PubMed]

Esser, N.

D. Gkogkou, B. Schreiber, T. Shaykhutdinov, H. K. Ly, U. Kuhlmann, U. Gernert, S. Facsko, P. Hildebrandt, N. Esser, K. Hinrichs, I. M. Weidinger, and T. W. H. Oates, “Polarization- and wavelength-dependent surface-enhanced Raman spectroscopy using optically anisotropic rippled substrates for sensing,” Science 313(5793), 1614– 1616 (2016).

Evlyukhin, A. B.

Facsko, S.

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D. Gkogkou, B. Schreiber, T. Shaykhutdinov, H. K. Ly, U. Kuhlmann, U. Gernert, S. Facsko, P. Hildebrandt, N. Esser, K. Hinrichs, I. M. Weidinger, and T. W. H. Oates, “Polarization- and wavelength-dependent surface-enhanced Raman spectroscopy using optically anisotropic rippled substrates for sensing,” Science 313(5793), 1614– 1616 (2016).

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D. Gkogkou, B. Schreiber, T. Shaykhutdinov, H. K. Ly, U. Kuhlmann, U. Gernert, S. Facsko, P. Hildebrandt, N. Esser, K. Hinrichs, I. M. Weidinger, and T. W. H. Oates, “Polarization- and wavelength-dependent surface-enhanced Raman spectroscopy using optically anisotropic rippled substrates for sensing,” Science 313(5793), 1614– 1616 (2016).

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D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
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D. A. Tenne, A. Bruchhausen, N. D. Lanzillotti-Kimura, A. Fainstein, R. S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J. H. Haeni, W. Tian, D. G. Schlom, K. J. Choi, D. M. Kim, C. B. Eom, H. P. Sun, X. Q. Pan, Y. L. Li, L. Q. Chen, Q. X. Jia, S. M. Nakhmanson, K. M. Rabe, and X. X. Xi, “Probing nanoscale ferroelectricity by ultraviolet raman spectroscopy,” Science 313(5793), 1614–1616 (2006).
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Liu, X.

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Ly, H. K.

D. Gkogkou, B. Schreiber, T. Shaykhutdinov, H. K. Ly, U. Kuhlmann, U. Gernert, S. Facsko, P. Hildebrandt, N. Esser, K. Hinrichs, I. M. Weidinger, and T. W. H. Oates, “Polarization- and wavelength-dependent surface-enhanced Raman spectroscopy using optically anisotropic rippled substrates for sensing,” Science 313(5793), 1614– 1616 (2016).

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Merino, D.

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M. Meyer, S. Aloise, and A. N. Grum-Grzhimailo, “Strong, polarized Balmer-α fluorescence after resonant core excitation of HCl,” Phys. Rev. Lett. 88(22), 223001 (2002).
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Figures (17)

Fig. 1
Fig. 1 Schematic wire grid polarizer and coordinate system.
Fig. 2
Fig. 2 Simulated optical performance of a tungsten WGP with a period of 100 nm, a ridge width of 23 nm and a ridge height of 150 nm. For the simulation the material data by Palik [39] were used.
Fig. 3
Fig. 3 Schematic fabrication process for a WGP consisting of a) patterning of the electron beam resist on the initial layer stack, b) etching of the template grating, c) coating of the ridge material and d) removing the horizontal surfaces and the template structure by ion beam etching to achieve the final WGP structure.
Fig. 4
Fig. 4 a) SEM top view and cross section of a tungsten WGP. b) Measured transmittance and extinction ratio [17].
Fig. 5
Fig. 5 a) Template grating with rough edges. b) The deposited tungsten layer resamples the roughness of the template grating. c) After removal of the template grating the position of the template edges resembles the original rough edge.
Fig. 6
Fig. 6 Illustration of the roughness parameters’ influence on the power spectral density. To enable a comparison, the bold curves and right sketches (red color) of a rough edge always have the same parameters σ = 10 nm, ξ = 10 nm and H = 0.7. a) Influence of the standard deviation σ. b) Influence of the correlation length ξ and c) Influence of the Hurst exponent H.
Fig. 7
Fig. 7 a) SEM image of the patterned electron beam resist with a resolution of 1280 px by 980 px and a pixel size of 1.24 nm. b) PSD of the measured edge profiles and fit retrieved from 32 SEM images. The fit parameters are shown in Table 1.
Fig. 8
Fig. 8 Magnification of a random rough edge achieved by the algorithm of Thorsos. The gray shaded area illustrates the ridge.
Fig. 9
Fig. 9 Dependence of the extinction ration and transmittance (TM) on the standard deviation σ for ξ=10 nm and H=0.7.
Fig. 10
Fig. 10 PSD according the measured values (see Table 1) where the inverse wavelength of incident light, the region of macroscopic disturbances and the region for effective media are indicated.
Fig. 11
Fig. 11 a) Simulated TM transmittance and extinction ratio in dependence of the displacement. b) Normalized electrical field distribution for TE- and TM-polarized light with a ridge displaced by 5 nm.
Fig. 12
Fig. 12 Angle resolved scattering of the transmitted light normalized to the intensities of the zero order transmittances for a) TE and b) TM polarized incident light, respectively. The simulation was performed with the roughness parameters: �� = 2.5 nm, �� = 10 nm, H = 0.7.
Fig. 13
Fig. 13 a) Volume fraction δw and absolute effective permittivity | ε eff |  for half a unit cell in dependence of the position along the ridge. The gray area resembles a rough edge viewed from top with the roughness parameters σ=2.5 nm, ξ=10 nm and H=0.7 and b) simulated dependency of the TM transmittance and extinction ratio on the width of an ideal ridge without roughness.
Fig. 14
Fig. 14 Variation of the correlation length ξ for σ=2.5 nm and H=0.7.
Fig. 15
Fig. 15 Variation of the Hurst exponent H for σ=2.5 nm and  ξ =10nm.
Fig. 16
Fig. 16 Wavelength dependence of T TM and Er for σ=2.5 nm, ξ=10 nm and H=1 in comparison to the simulated values for an ideal WGP structure.
Fig. 17
Fig. 17 Ratio of the simulated TM transmittance and extinction ratio of rough WGP structures to ideal ridges. The calculations were performed for σ = 2.5 nm, ξ = 10 nm and H = 0.7.

Tables (1)

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Table 1 Roughness parameters of the electron beam resist acquired by fitting of the measured PSD.

Equations (11)

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Λ< λ n sub +sinφ .
PSD(f)= 2 σ 2 ξ π Γ(H+ 1 2 ) Γ(H) / [ 1+( 2πfξ ) 2 ) ] H+ 1 2 .
PSD(f)=L×|FFT(d(x)) | 2 .
d( x n )= 1 L N/2 N/21 F( f j ) e i2π f j x n ,
F( f j )= L*PSD( f j ) { ( η 1 +i η 2 )/ 2, η 1, j0,±N/2 j=0,±N/2 .
Δ x opt = πξ N 1/(1+2H) .
< σ data >σ 12( Γ(H+3/2 π Γ(H+1) )( 1 N 2H/(1+2H) ) .
ΔEr Er =| Δ T TE < T TE > |+| Δ T TM < T TM > |.
ε eff = ε air 2 δ W ( ε W ε air )+ ε W +2 ε air 2 ε air + ε W + δ W ( ε air ε W ) .
δ W (y)= 1 L 0 L ρ(x,y)dx .
ρ(x,y)={ 1 0 y<s/2+d(x) ys/2+d(x) .

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