Nanometrology optical ruler imaging system using diffraction from a quasiperiodic structure

doi:10.1364/OE.18.020827

Nanometrology optical ruler imaging system using diffraction from a quasiperiodic structure

Norimasa Yoshimizu, Amit Lal, and Clifford R. Pollock »View Author Affiliations

Optics Express, Vol. 18, Issue 20, pp. 20827-20838 (2010)
http://dx.doi.org/10.1364/OE.18.020827

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Abstract

This work demonstrates wafer-scale, path-independent, atomically-based long term-stable, position nanometrology. This nanometrology optical ruler imaging system uses the diffraction pattern of an atomically stabilized laser from a microfabricated quasiperiodic aperture array as a two-dimensional optical ruler. Nanometrology is accomplished by cross correlations of image samples of this optical ruler. The quasiperiodic structure generates spatially dense, sharp optical features. This work demonstrates new results showing positioning errors down to 17.2 nm over wafer scales and long term stability below 20 nm over six hours. This work also numerically demonstrates robustness of the optical ruler to variations in the microfabricated aperture array and discretization noise in imagers.

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: August 10, 2010
Revised Manuscript: September 8, 2010
Manuscript Accepted: September 9, 2010
Published: September 16, 2010

Citation
Norimasa Yoshimizu, Amit Lal, and Clifford R. Pollock, "Nanometrology optical ruler imaging system using diffraction from a quasiperiodic structure," Opt. Express 18, 20827-20838 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-20827

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References

N. Yoshimizu, A. Lal, and C. R. Pollock, “MEMS Diffractive Optical Nanoruler Technology for Tip-Based Nanofabrication and Metrology,” in Proceedings of the IEEE MEMS (Institute of Electrical and Electronics Engineers, New York, 2009), pp. 547–550.
N. Yoshimizu, A. Lal, and C. R. Pollock, “Nanometrology Using a Quasiperiodic Pattern Diffraction Optical Ruler,” J. Microelectromech. Syst. 19(4), 865–870 (2010). [CrossRef]
J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, Greenwood Village, CO, 2005).
D. Robinson and P. Milanfar, “Fundamental performance limits in image registration,” IEEE Trans. Image Process. 13(9), 1185–1199 (2004). [CrossRef] [PubMed]
M. Tanibayashi, “Diffraction of light by quasi-periodic gratings,” J. Phys. Soc. Jpn. 61(9), 3139–3145 (1992). [CrossRef]
R. D. Diehl, J. Ledieu, N. Ferralis, A. W. Szmodis, and R. McGrath, “Low-energy electron diffraction from quasicrystal surfaces,” J. Phys. Condens. Matter 15(3), R63–R81 (2003). [CrossRef]
N. Ferralis, A. W. Szmodis, and R. D. Diehl, “Diffraction from one- and two-dimensional quasicrystalline gratings,” Am. J. Phys. 72(9), 1241–1246 (2004). [CrossRef]
R. K. P. Zia and W. J. Dallas, “A Simple Derivation of Quasi-Crystalline Spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985). [CrossRef]
V. Elser, “The Diffraction of Projected Structures,” Acta Crystallogr. A 42(1), 36–43 (1986). [CrossRef]
F. Gähler and J. Rhyner, “Equivalence of the Generalized Grid and Projection Methods for the Construction of Quasiperiodic Tilings,” J. Phys. Math. Gen. 19(2), 267–277 (1986). [CrossRef]
D. Levine and P. J. Steinhardt, “Quasicrystals. I. Definition and structure,” Phys. Rev. B Condens. Matter 34(2), 596–616 (1986). [CrossRef] [PubMed]
J. E. S. Socolar and P. J. Steinhardt, “Quasicrystals. II. Unit-cell configurations,” Phys. Rev. B Condens. Matter 34(2), 617–647 (1986). [CrossRef] [PubMed]
C. Janot, Quasicrystals: A Primer (Cambridge University Press, Oxford, 1997).
M. Senechal, Quasicrystals and Geometry (Cambridge University Press, Oxford, 1995).
N. G. de Bruijn, “Algebraic theory of Penrose’s non-periodic tilings of the plane I & II,” Ned. Akad. Wetensch. Proc. Ser. A 43, 39–66 (1981).

Dallas, W. J.
de Bruijn, N. G.
Diehl, R. D.
Elser, V.
Ferralis, N.
Gähler, F.
Lal, A.
Ledieu, J.
Levine, D.
McGrath, R.
Milanfar, P.
Pollock, C. R.
Rhyner, J.
Robinson, D.
Socolar, J. E. S.
Steinhardt, P. J.
Szmodis, A. W.
Tanibayashi, M.
Yoshimizu, N.
Zia, R. K. P.

Acta Crystallogr. A

V. Elser, “The Diffraction of Projected Structures,” Acta Crystallogr. A 42(1), 36–43 (1986). [CrossRef]

Am. J. Phys.

N. Ferralis, A. W. Szmodis, and R. D. Diehl, “Diffraction from one- and two-dimensional quasicrystalline gratings,” Am. J. Phys. 72(9), 1241–1246 (2004). [CrossRef]

IEEE Trans. Image Process.

D. Robinson and P. Milanfar, “Fundamental performance limits in image registration,” IEEE Trans. Image Process. 13(9), 1185–1199 (2004). [CrossRef] [PubMed]

J. Microelectromech. Syst.

N. Yoshimizu, A. Lal, and C. R. Pollock, “Nanometrology Using a Quasiperiodic Pattern Diffraction Optical Ruler,” J. Microelectromech. Syst. 19(4), 865–870 (2010). [CrossRef]

J. Phys. Condens. Matter

R. D. Diehl, J. Ledieu, N. Ferralis, A. W. Szmodis, and R. McGrath, “Low-energy electron diffraction from quasicrystal surfaces,” J. Phys. Condens. Matter 15(3), R63–R81 (2003). [CrossRef]

J. Phys. Math. Gen.

R. K. P. Zia and W. J. Dallas, “A Simple Derivation of Quasi-Crystalline Spectra,” J. Phys. Math. Gen. 18(7), L341–L345 (1985). [CrossRef]
F. Gähler and J. Rhyner, “Equivalence of the Generalized Grid and Projection Methods for the Construction of Quasiperiodic Tilings,” J. Phys. Math. Gen. 19(2), 267–277 (1986). [CrossRef]

J. Phys. Soc. Jpn.

M. Tanibayashi, “Diffraction of light by quasi-periodic gratings,” J. Phys. Soc. Jpn. 61(9), 3139–3145 (1992). [CrossRef]

Ned. Akad. Wetensch. Proc. Ser. A

N. G. de Bruijn, “Algebraic theory of Penrose’s non-periodic tilings of the plane I & II,” Ned. Akad. Wetensch. Proc. Ser. A 43, 39–66 (1981).

Phys. Rev. B Condens. Matter

D. Levine and P. J. Steinhardt, “Quasicrystals. I. Definition and structure,” Phys. Rev. B Condens. Matter 34(2), 596–616 (1986). [CrossRef] [PubMed]
J. E. S. Socolar and P. J. Steinhardt, “Quasicrystals. II. Unit-cell configurations,” Phys. Rev. B Condens. Matter 34(2), 617–647 (1986). [CrossRef] [PubMed]

Other

C. Janot, Quasicrystals: A Primer (Cambridge University Press, Oxford, 1997).
M. Senechal, Quasicrystals and Geometry (Cambridge University Press, Oxford, 1995).
J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, Greenwood Village, CO, 2005).
N. Yoshimizu, A. Lal, and C. R. Pollock, “MEMS Diffractive Optical Nanoruler Technology for Tip-Based Nanofabrication and Metrology,” in Proceedings of the IEEE MEMS (Institute of Electrical and Electronics Engineers, New York, 2009), pp. 547–550.

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