Abstract

The new and fast scatterometry method called optical diffraction microscopy is compared with atomic-force microscopy by use of cross-section scanning-electron microscope images as references. The sample is a high-aspect-ratio grating with a period of 1000  nm. To allow the atomic-force microscope to track all parts of the grating profile, the grating is investigated at different tilt angles. The measured quantities of the profile include sidewall angle γ(90°), groove height h(2000  nm), and degree of filling f(40%). The two methods, which respond to quite different material properties, give consistent results within standard uncertainties of u(γ)0.8°, u(h)15  nm, and u(f)1%.

© 2006 Optical Society of America

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References

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  1. E. N. Glytsis, "Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis," J. Opt. Soc. Am. A 19, 702-715 (2002).
    [CrossRef]
  2. D. A. Pommet, M. G. Moharam, and E. B. Grann, "Limits of scalar diffraction theory for diffractive phase elements," J. Opt. Soc. Am. A 11, 1827-1834 (1994).
    [CrossRef]
  3. T. O. Korner, J. T. Sheridan, and J. Schwider, "Interferometric resolution examined by means of electromagnetic theory," J. Opt. Soc. Am. A 12, 752-761 (1995).
    [CrossRef]
  4. H. Hung and F. Terry, Jr., "Spectroscopic ellipsometry and reflectometry from gratings for critical dimension measurements and in situ, real-time process monitoring," Thin Solid Films 455-456, 828-836 (2004).
    [CrossRef]
  5. The optical diffraction microscope is made by LuKa OptoScope, "Method and apparatus for optically measuring the topography of nearly planar periodic structures," Danish patents WO2004008069 and EP1527320 (12 July 2002) (http://www.lukaoptoscope.com).
  6. Y. Martin and H. K. Wickramasinghe, "Methods for imaging sidewalls by atomic force microscopy," Appl. Phys. Lett. 19, 2498-2500 (1994).
    [CrossRef]
  7. A. Meyyappan, M. Klos, and S. Muckenhirn, "Foot (bottom corner) measurement of a structure with SPM," in Metrology, Inspection, and Process Control for Microlithography XV, N.T.Sullivan, ed., Proc. SPIE 4344,733-738 (2001).
  8. J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
    [CrossRef]
  9. J. S. Villarrubia, "Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation," J. Res. Natl. Inst. Stand. Technol. 102, 425-454 (1997).
  10. F. Meli, "Critical dimension (CD) measurements using a metrology AFM," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre Range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 169-174.
    [PubMed]
  11. J. Turunen, "Micro-optics," in Diffraction Theory of Micro-Relief Gratings (Taylor & Francis, 1997), pp. 31-52.
  12. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  13. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995).
    [CrossRef]
  14. L. Li, "Fourier modal methods for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A Pure Appl. Opt. 5, 345-355 (2003).
    [CrossRef]
  15. W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002), pp. 661-712.
  16. Dimension 3100 SPM with metrology AFM head, Digital Instruments (now Veeco).
  17. ISC AFM probe tips, Team Nanotec GmBh, Germany.
  18. J. Garnaes, A. Kühle, L. Nielsen, and F. Borsetto, "True three-dimensional calibration of closed loop scanning probe microscopes," in Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro-and Nanometer Range, G.Wilkening and L.Koenders, eds. (Wiley-VCH, 2005), pp. 193-204.
  19. J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
    [CrossRef]
  20. Scanning probe image processor (SPIP), Image Metrology, Denmark; http://www.imagemet.com.
  21. N. Kofod, J. Garnaes, and J. F. Jørgensen, "Methods for lateral calibration of scanning probe microscopes based on two dimensional transfer standards," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 36-43.
  22. N. Otsu, "A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man Cybern. 9, 62-66 (1979).
    [CrossRef]

2004 (1)

H. Hung and F. Terry, Jr., "Spectroscopic ellipsometry and reflectometry from gratings for critical dimension measurements and in situ, real-time process monitoring," Thin Solid Films 455-456, 828-836 (2004).
[CrossRef]

2003 (3)

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

L. Li, "Fourier modal methods for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A Pure Appl. Opt. 5, 345-355 (2003).
[CrossRef]

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

2002 (1)

1997 (2)

J. S. Villarrubia, "Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation," J. Res. Natl. Inst. Stand. Technol. 102, 425-454 (1997).

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

1995 (2)

1994 (2)

D. A. Pommet, M. G. Moharam, and E. B. Grann, "Limits of scalar diffraction theory for diffractive phase elements," J. Opt. Soc. Am. A 11, 1827-1834 (1994).
[CrossRef]

Y. Martin and H. K. Wickramasinghe, "Methods for imaging sidewalls by atomic force microscopy," Appl. Phys. Lett. 19, 2498-2500 (1994).
[CrossRef]

1979 (1)

N. Otsu, "A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man Cybern. 9, 62-66 (1979).
[CrossRef]

Abeles, J. H.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Adesida, I.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Bae, J. W.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Blunt, L.

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

Borsetto, F.

J. Garnaes, A. Kühle, L. Nielsen, and F. Borsetto, "True three-dimensional calibration of closed loop scanning probe microscopes," in Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro-and Nanometer Range, G.Wilkening and L.Koenders, eds. (Wiley-VCH, 2005), pp. 193-204.

Dirscherl, K.

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

Flannery, B. P.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002), pp. 661-712.

Garnaes, J.

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

J. Garnaes, A. Kühle, L. Nielsen, and F. Borsetto, "True three-dimensional calibration of closed loop scanning probe microscopes," in Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro-and Nanometer Range, G.Wilkening and L.Koenders, eds. (Wiley-VCH, 2005), pp. 193-204.

N. Kofod, J. Garnaes, and J. F. Jørgensen, "Methods for lateral calibration of scanning probe microscopes based on two dimensional transfer standards," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 36-43.

Gaylord, T. K.

Glytsis, E. N.

Grann, E. B.

Hung, H.

H. Hung and F. Terry, Jr., "Spectroscopic ellipsometry and reflectometry from gratings for critical dimension measurements and in situ, real-time process monitoring," Thin Solid Films 455-456, 828-836 (2004).
[CrossRef]

Jang, J. H.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Jørgensen, J. F.

N. Kofod, J. Garnaes, and J. F. Jørgensen, "Methods for lateral calibration of scanning probe microscopes based on two dimensional transfer standards," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 36-43.

Klos, M.

A. Meyyappan, M. Klos, and S. Muckenhirn, "Foot (bottom corner) measurement of a structure with SPM," in Metrology, Inspection, and Process Control for Microlithography XV, N.T.Sullivan, ed., Proc. SPIE 4344,733-738 (2001).

Kofod, N.

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

N. Kofod, J. Garnaes, and J. F. Jørgensen, "Methods for lateral calibration of scanning probe microscopes based on two dimensional transfer standards," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 36-43.

Korner, T. O.

Kühle, A.

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

J. Garnaes, A. Kühle, L. Nielsen, and F. Borsetto, "True three-dimensional calibration of closed loop scanning probe microscopes," in Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro-and Nanometer Range, G.Wilkening and L.Koenders, eds. (Wiley-VCH, 2005), pp. 193-204.

Kwakernaak, M.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Lepore, A.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Li, L.

L. Li, "Fourier modal methods for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A Pure Appl. Opt. 5, 345-355 (2003).
[CrossRef]

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

Martin, Y.

Y. Martin and H. K. Wickramasinghe, "Methods for imaging sidewalls by atomic force microscopy," Appl. Phys. Lett. 19, 2498-2500 (1994).
[CrossRef]

Meli, F.

F. Meli, "Critical dimension (CD) measurements using a metrology AFM," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre Range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 169-174.
[PubMed]

Meyyappan, A.

A. Meyyappan, M. Klos, and S. Muckenhirn, "Foot (bottom corner) measurement of a structure with SPM," in Metrology, Inspection, and Process Control for Microlithography XV, N.T.Sullivan, ed., Proc. SPIE 4344,733-738 (2001).

Moharam, M. G.

Muckenhirn, S.

A. Meyyappan, M. Klos, and S. Muckenhirn, "Foot (bottom corner) measurement of a structure with SPM," in Metrology, Inspection, and Process Control for Microlithography XV, N.T.Sullivan, ed., Proc. SPIE 4344,733-738 (2001).

Nielsen, C.

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

Nielsen, L.

J. Garnaes, A. Kühle, L. Nielsen, and F. Borsetto, "True three-dimensional calibration of closed loop scanning probe microscopes," in Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro-and Nanometer Range, G.Wilkening and L.Koenders, eds. (Wiley-VCH, 2005), pp. 193-204.

Otsu, N.

N. Otsu, "A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man Cybern. 9, 62-66 (1979).
[CrossRef]

Pommet, D. A.

Press, W. H.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002), pp. 661-712.

Rommel, S. L.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Schwider, J.

Selvanthan, D.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Sheridan, J. T.

Terry, F.

H. Hung and F. Terry, Jr., "Spectroscopic ellipsometry and reflectometry from gratings for critical dimension measurements and in situ, real-time process monitoring," Thin Solid Films 455-456, 828-836 (2004).
[CrossRef]

Teukolsky, S. A.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002), pp. 661-712.

Turunen, J.

J. Turunen, "Micro-optics," in Diffraction Theory of Micro-Relief Gratings (Taylor & Francis, 1997), pp. 31-52.

Vetterling, W. T.

W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002), pp. 661-712.

Villarrubia, J. S.

J. S. Villarrubia, "Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation," J. Res. Natl. Inst. Stand. Technol. 102, 425-454 (1997).

Wickramasinghe, H. K.

Y. Martin and H. K. Wickramasinghe, "Methods for imaging sidewalls by atomic force microscopy," Appl. Phys. Lett. 19, 2498-2500 (1994).
[CrossRef]

Zhao, W.

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

J. H. Jang, W. Zhao, J. W. Bae, D. Selvanthan, S. L. Rommel, I. Adesida, A. Lepore, M. Kwakernaak, and J. H. Abeles, "Direct measurement of sidewall roughness of optical waveguides using an atomic force microscopy," Appl. Phys. Lett. 83, 4116-4118 (2003).
[CrossRef]

Y. Martin and H. K. Wickramasinghe, "Methods for imaging sidewalls by atomic force microscopy," Appl. Phys. Lett. 19, 2498-2500 (1994).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

N. Otsu, "A threshold selection method from gray-level histograms," IEEE Trans. Syst. Man Cybern. 9, 62-66 (1979).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

L. Li, "Fourier modal methods for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A Pure Appl. Opt. 5, 345-355 (2003).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Res. Natl. Inst. Stand. Technol. (1)

J. S. Villarrubia, "Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation," J. Res. Natl. Inst. Stand. Technol. 102, 425-454 (1997).

Precis. Eng. (1)

J. Garnaes, N. Kofod, A. Kühle, C. Nielsen, K. Dirscherl, and L. Blunt, "Calibration of step heights and roughness measurements with atomic force microscopes," Precis. Eng. 27, 91-98 (2003).
[CrossRef]

Thin Solid Films (1)

H. Hung and F. Terry, Jr., "Spectroscopic ellipsometry and reflectometry from gratings for critical dimension measurements and in situ, real-time process monitoring," Thin Solid Films 455-456, 828-836 (2004).
[CrossRef]

Other (10)

The optical diffraction microscope is made by LuKa OptoScope, "Method and apparatus for optically measuring the topography of nearly planar periodic structures," Danish patents WO2004008069 and EP1527320 (12 July 2002) (http://www.lukaoptoscope.com).

F. Meli, "Critical dimension (CD) measurements using a metrology AFM," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre Range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 169-174.
[PubMed]

J. Turunen, "Micro-optics," in Diffraction Theory of Micro-Relief Gratings (Taylor & Francis, 1997), pp. 31-52.

A. Meyyappan, M. Klos, and S. Muckenhirn, "Foot (bottom corner) measurement of a structure with SPM," in Metrology, Inspection, and Process Control for Microlithography XV, N.T.Sullivan, ed., Proc. SPIE 4344,733-738 (2001).

W. H. Press, W. T. Vetterling, S. A. Teukolsky, and B. P. Flannery, Numerical Recipes in C++ (Cambridge U. Press, 2002), pp. 661-712.

Dimension 3100 SPM with metrology AFM head, Digital Instruments (now Veeco).

ISC AFM probe tips, Team Nanotec GmBh, Germany.

J. Garnaes, A. Kühle, L. Nielsen, and F. Borsetto, "True three-dimensional calibration of closed loop scanning probe microscopes," in Nanoscale Calibration Standards and Methods: Dimensional and Related Measurements in the Micro-and Nanometer Range, G.Wilkening and L.Koenders, eds. (Wiley-VCH, 2005), pp. 193-204.

Scanning probe image processor (SPIP), Image Metrology, Denmark; http://www.imagemet.com.

N. Kofod, J. Garnaes, and J. F. Jørgensen, "Methods for lateral calibration of scanning probe microscopes based on two dimensional transfer standards," in Proceedings of the 4th Seminar on Quantitative Microscopy QM 2000 Dimensional Measurements in the Micro-and Nanometre range, K.Hasche, W.Mirandé, and G.Wilkening, eds. (PTB-Bericht, 2000), pp. 36-43.

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Figures (8)

Fig. 1
Fig. 1

(a) Shape and parameters that describe the profile of the grating measured. (b) Definitions of the material part of the grating, marked M, and the void part of the grating, marked V. SEM, scanning-electron microscopy.

Fig. 2
Fig. 2

(a) Experimental setup for ODM measurements. Light from a broadband light source passes through a collimating lens, a polarizer, and a pinhole with a diameter of 0.5 mm before it is incident onto the grating. The diffracted beams are collected by an achromatic error-free reflector-based system that focuses the light onto two fibers with the help of two lenses mounted in front of the fibers. An identical lens focuses the zero-order beam onto a third fiber. The three fibers are connected to an optical switch and a spectrometer. (b) Schematic showing how zero and nonzero diffracted orders are collected. One can make reflection measurement by moving the input optics to the reflection position and replacing the illumination fiber with a bifurcated fiber that can be used for illumination and zero-order signal detection.

Fig. 3
Fig. 3

Diffraction efficiencies from the grating structure found by approximating the grating profile with slabs of width wqi , height hi , displacement xqi , dielectrical constant εqi and then calculating the diffraction efficiencies for this approximation.

Fig. 4
Fig. 4

(a) For scanning with the tip normal to the surface we show the relationship among observed profile po (x) traced by vertex V of the tip, (true) profile p(x) of the grating, profile of the tip t(x′) relative to coordinate system (x′, z′) with (moving) origin in V, observed width of the groove wo at chosen apparent depth po (XV ), and contact point between the tip's flank and the left side of the groove CL and a similar contact point between the tip's flank and the right side of the groove CR. Also shown is (true) depth p(XC ) of the contact point, radius of curvature of the tip rt , angle of the tip's flanks α t , and vertical distance XVC between vertex V of the tip and closest contact point CR when the vertex of the tip is in the chosen depth of po (XV ). For the tip tilted relative to the surface, (b) shows observed profile pt (xt ) traced by vertex Vt of the tilted tip, contact point between the tips at the rounded end and at the right-hand side of the groove CR , and angle of the sidewall γ r.

Fig. 5
Fig. 5

AFM profiles observed with the grating in lying flat (lighter curves) and in a 12° tilted orientation (darker curves). The relative orientation and shape of the tip used are also drawn. The profiles are averaged from the images in Fig. 6. and are recorded at two different spots on the grating. The dashed parts of the profiles are where only the side of the tip has touched the corner of the upper part of the surface. The observed profile of the steep sidewalls found by the tilted tip (solid darker curves) is different from the profile of the sidewall observed by the vertical tip (lighter curve).

Fig. 6
Fig. 6

(a) AFM pictures of the grating. The image is a top view of the nontilted grating with a scan area of 4.0 μm × 0.25 μm. (b) Three-dimensional 4.0 μm × 0.5 μm image recorded with the sample tilted approximately 12°. The small bumps on the top of ridges and the structures along the left-hand sidewalls of the ridges are traced easily by the tip. The end of the tip, however, does not trace the right-hand sidewalls of the ridges, and the angle of these sidewalls reflects only the angle of the sidewall of the tip. The dark solid line indicates the left part of the two trapezoids used to model the grating.

Fig. 7
Fig. 7

SEM image of a focused ion beam cut through the grating under investigation (voltage, 3 kV; magnification, 50,000×). The dark silhouette is the material part of the grating (fused silica), and the light area is the void grooves covered by gold–platinum; solid lines indicate the trapezoidal shape of the profile. The small dark areas in the middle of the grooves are voids not filled completely by gold–platinum. The SEM image was kindly provided by the Danish Technological Institute.

Fig. 8
Fig. 8

Picture of an ODM measurement. Top, zero-order diffraction efficiency; bottom, ratio between negative and positive diffracted orders.

Tables (2)

Tables Icon

Table 1 Results from the Profile a

Tables Icon

Table 2 Results from Trapezoid Fit a

Equations (28)

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

I grating T ( x m , y ) = { ξ lens 2 ξ pol η 0 T I s T ( x , y ) m = 0 ξ lens 2 ξ mir ξ pol η m T I s T ( x , y )   otherwise  ,
I grating R ( x m , y ) = { ξ lens 2 ξ pol 2 η 0 R I s R ( x , y ) m = 0 ξ lens 2 ξ mir ξ pol η m R I s R ( x , y )   otherwise  ,
η 0 = { η 0 T = I grating T I background T I ref T I background T     Transmission η 0 R = R I grating R I background R I ref R I background R     Reflection ,
η ratio = { η ratio T = m > 0 I grating T I background T m < 0 I grating T I background T = I grating T , + I background T I grating T , I background T       Transmission η ratio R = m > 0 I grating R I background R m < 0 I grating R I background R = I grating R , + I background R I grating R , I background R       Reflection .
χ 2 = 1 N i = 1 N [ η ( λ i ) η theory ( Ω i , α ) σ ( λ i ) ] 2 ,
σ 0 ( λ i ) = { I grating ( λ i ) + η 0 2 ( λ i ) I ref ( λ i ) + I background ( λ i ) [ I ref ( λ i ) I grating ( λ i ) I ref ( λ i ) I background ( λ i ) ] 2 [ I r e f ( λ i ) I b a c k g r o u n d ( λ i ) ] 2 } 1 / 2 ,
σ ratio ( λ i ) = { [ I grating + ( λ i ) + I background ( λ i ) ] + [ I grating ( λ i ) + I background ( λ i ) ] η ratio 2 ( λ i ) [ I grating ( λ i ) I background ( λ i ) ] 2 } 1 / 2 .
η theory ( Ω i , α ) η theory ( Ω i , α 0 ) + η theory ( Ω i , α 0 ) α Δ α ,
χ 2 1 N ( η η theory η theory α Δ α ) 2 ,
η = { η 1 σ 1 , , η N σ N } ,
η theory = [ η theory ( Ω 1 , α 0 ) σ 1 , , η theory ( Ω N , α 0 ) σ N ] ,
η theory α = [ η theory ( Ω 1 , α 0 ) α | | η theory ( Ω N , α 0 ) α ] .
( η theory α ) T ( η theory α ) Δ α = ( η theory α ) T ( η η theory ) .
p ( x ) = p o ( x V ) + t ( x V C ) ,
d p ( x ) d x = d t ( x V C ) d x V C .
d p o ( x V ) d x V ( 1 d x V C d x ) = d t ( x V C ) d x V C ( 1 d x V C d x ) .
d p o ( x V ) d x V = d t ( x V C ) d x V C .
C R = [ X C , p ( X C ) ]
d p ( X C ) d x = tan ( π 2 α t ) ,
w C = w o + 2 X V C ,
X V C = r t + [ p ( X C ) p o ( X V ) r t ] tan α t .
d p t ( X V t ) d x t = tan ( π 2 α t ) ,
p ( x ) p t ( x t ) , p t ( x t ) < p t ( X V t ) ,
p ( x ) p o ( x V ) , p o ( x V ) > p t ( X V t ) ,
w = w c δ ( γ r ) δ ( γ r ) ,
w = w o + 2 { [ p ( X C ) p o ( X V ) r t ] tan α t + r t [ h 2 p ( X C ) ] cot γ r + cot γ l 2 } ,
d p t ( X V t ) d x = tan ( π 2 α t ) .
f = 100 × M / ( M + V ) % .

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