Abstract

Line edge roughness (LER) has been identified as a potential source of uncertainty in optical scatterometry measurements. Characterizing the effect of LER on optical scatterometry signals is required to assess the uncertainty of the measurement. However, rigorous approaches to modeling the structures that are needed to simulate LER can be computationally expensive. In this work, we compare the effect of LER on scatterometry signals computed using an effective medium approximation (EMA) to those computed with realizations of rough interfaces. We find that for correlation lengths much less than the wavelength but greater than the rms roughness, an anisotropic EMA provides a satisfactory approximation in the cases studied.

© 2010 Optical Society of America

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2009 (2)

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

2008 (1)

T. A. Germer, “SCATMECH: Polarized Light Scattering C++ Class Library,” available online at http://physics.nist.gov/scatmech (2008).

2007 (3)

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

B. Yaakobovitz, Y. Cohen, and Y. Tsur, “Line edge roughness detection using deep UV light scatterometry,” Microelectron. Eng. 84, 619–625 (2007).
[CrossRef]

T. A. Germer, “Effect of line and trench profile variation on specular and diffuse reflectance from a periodic structure,” J. Opt. Soc. Am. A 24, 696–701 (2007).
[CrossRef]

2005 (3)

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

G. M. Gallatin, “Resist blur and line edge roughness,” Proc. SPIE 5754, 38–52 (2005).
[CrossRef]

2004 (3)

V. Constantoudis, G. P. Patsis, L. H. A. Leunissen, and E. Gogolides, “Toward a complete description of linewidth roughness: a comparison of different methods for vertical and spatial LER and LWR analysis and CD variation,” Proc. SPIE 5375, 967–977 (2004).
[CrossRef]

K. Huang, B. J. Rice, B. Coombs, and R. Freed, “Methods For evaluating lithographic performance of exposure tools for the 45-nm node: ECD and scatterometry,” Proc. SPIE 5375, 494–502 (2004).
[CrossRef]

V. Constantoudis, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Microlithogr., Microfabr., Microsyst. 3, 429–435 (2004).
[CrossRef]

2003 (5)

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists II: scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B 21, 1019–1026 (2003).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

E. Barouch, and S. L. Knodle, “Scatterometry as a practical in-situ metrology technology,” Proc. SPIE 5038, 559–567 (2003).
[CrossRef]

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

T. G. Makay, “Homogenization of linear and nonlinear complex composite materials,” in Introduction to Complex Mediums for Optics and Electromagnetics, W.S.Weiglhofer, A.Lakhtakia, eds., (SPIE, Bellingham, Washington, 2003), pp. 317–346.
[CrossRef]

1997 (1)

1996 (2)

1995 (3)

1993 (1)

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, 1993).

1980 (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980) pp. 705–708.

1979 (1)

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

1906 (1)

J. C. Maxwell Garnett, “Colours in metal glasses, in metallic films, and in metallic solutions—II,” Proc. R. Soc. London, Ser. A 205, 237–288 (1906).

1897 (1)

L. Rayleigh, “On the incidence of aerial and electric waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and on the passage of electric waves through a circular aperture in a conducting screen,” Philos. Mag. 44, 28–52 (1897).
[CrossRef]

Allgair, J.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Anderson, S. K.

D. Ronnow, S. K. Anderson, and G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4, 815–821 (1995).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Attota, R.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Barnes, B. M.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Barouch, E.

E. Barouch, and S. L. Knodle, “Scatterometry as a practical in-situ metrology technology,” Proc. SPIE 5038, 559–567 (2003).
[CrossRef]

Bischoff, J.

J. Bischoff, E. Drege, and S. Yedur, “Edge Roughness Measurement In Optical Metrology,” US Patent 7,046,375, 16 May 2006.

Boher, P.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980) pp. 705–708.

Bunday, B.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Chaton, P.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Cohen, Y.

B. Yaakobovitz, Y. Cohen, and Y. Tsur, “Line edge roughness detection using deep UV light scatterometry,” Microelectron. Eng. 84, 619–625 (2007).
[CrossRef]

Constantoudis, V.

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

V. Constantoudis, G. P. Patsis, L. H. A. Leunissen, and E. Gogolides, “Toward a complete description of linewidth roughness: a comparison of different methods for vertical and spatial LER and LWR analysis and CD variation,” Proc. SPIE 5375, 967–977 (2004).
[CrossRef]

V. Constantoudis, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Microlithogr., Microfabr., Microsyst. 3, 429–435 (2004).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists II: scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B 21, 1019–1026 (2003).
[CrossRef]

Coombs, B.

K. Huang, B. J. Rice, B. Coombs, and R. Freed, “Methods For evaluating lithographic performance of exposure tools for the 45-nm node: ECD and scatterometry,” Proc. SPIE 5375, 494–502 (2004).
[CrossRef]

Desieres, Y.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Drege, E.

J. Bischoff, E. Drege, and S. Yedur, “Edge Roughness Measurement In Optical Metrology,” US Patent 7,046,375, 16 May 2006.

Elazami, A.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Fernand, C.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Foucher, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Freed, R.

K. Huang, B. J. Rice, B. Coombs, and R. Freed, “Methods For evaluating lithographic performance of exposure tools for the 45-nm node: ECD and scatterometry,” Proc. SPIE 5375, 494–502 (2004).
[CrossRef]

Frenner, K.

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

Gallatin, G. M.

G. M. Gallatin, “Resist blur and line edge roughness,” Proc. SPIE 5754, 38–52 (2005).
[CrossRef]

Gaylord, T. K.

Germer, T.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Germer, T. A.

T. A. Germer, “SCATMECH: Polarized Light Scattering C++ Class Library,” available online at http://physics.nist.gov/scatmech (2008).

T. A. Germer, “Effect of line and trench profile variation on specular and diffuse reflectance from a periodic structure,” J. Opt. Soc. Am. A 24, 696–701 (2007).
[CrossRef]

K. A. Michalski and T. A. Germer, available from the author at thomas.germer@nist.gov.

Gogolides, E.

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

V. Constantoudis, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Microlithogr., Microfabr., Microsyst. 3, 429–435 (2004).
[CrossRef]

V. Constantoudis, G. P. Patsis, L. H. A. Leunissen, and E. Gogolides, “Toward a complete description of linewidth roughness: a comparison of different methods for vertical and spatial LER and LWR analysis and CD variation,” Proc. SPIE 5375, 967–977 (2004).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists II: scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B 21, 1019–1026 (2003).
[CrossRef]

Grann, E. B.

Grozev, G.

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

Guevremont, M.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Hazart, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Henry, D.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Herisson, D.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Hottier, F.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Huang, K.

K. Huang, B. J. Rice, B. Coombs, and R. Freed, “Methods For evaluating lithographic performance of exposure tools for the 45-nm node: ECD and scatterometry,” Proc. SPIE 5375, 494–502 (2004).
[CrossRef]

Joubert, O.

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Jun, J.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Knodle, S. L.

E. Barouch, and S. L. Knodle, “Scatterometry as a practical in-situ metrology technology,” Proc. SPIE 5038, 559–567 (2003).
[CrossRef]

Kokkoris, G.

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

Kremer, S.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Lalanne, P.

Landis, S.

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Leroux, T.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Leunissen, L. H. A.

V. Constantoudis, G. P. Patsis, L. H. A. Leunissen, and E. Gogolides, “Toward a complete description of linewidth roughness: a comparison of different methods for vertical and spatial LER and LWR analysis and CD variation,” Proc. SPIE 5375, 967–977 (2004).
[CrossRef]

Li, L. F.

Makay, T. G.

T. G. Makay, “Homogenization of linear and nonlinear complex composite materials,” in Introduction to Complex Mediums for Optics and Electromagnetics, W.S.Weiglhofer, A.Lakhtakia, eds., (SPIE, Bellingham, Washington, 2003), pp. 317–346.
[CrossRef]

Martin, M.

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

Marx, E.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses, in metallic films, and in metallic solutions—II,” Proc. R. Soc. London, Ser. A 205, 237–288 (1906).

Michalski, K. A.

K. A. Michalski and T. A. Germer, available from the author at thomas.germer@nist.gov.

Moharam, M. G.

Morris, G. M.

Neira, D.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Niklasson, G. A.

D. Ronnow, S. K. Anderson, and G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4, 815–821 (1995).
[CrossRef]

Osten, W.

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

Pargon, E.

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

Patsis, G. P.

V. Constantoudis, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Microlithogr., Microfabr., Microsyst. 3, 429–435 (2004).
[CrossRef]

V. Constantoudis, G. P. Patsis, L. H. A. Leunissen, and E. Gogolides, “Toward a complete description of linewidth roughness: a comparison of different methods for vertical and spatial LER and LWR analysis and CD variation,” Proc. SPIE 5375, 967–977 (2004).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists II: scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B 21, 1019–1026 (2003).
[CrossRef]

Pauliac, S.

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Paz, V. F.

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

Petit, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Polli, M.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Pommet, D. A.

Rafler, S.

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

Rayleigh, L.

L. Rayleigh, “On the incidence of aerial and electric waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and on the passage of electric waves through a circular aperture in a conducting screen,” Philos. Mag. 44, 28–52 (1897).
[CrossRef]

Rice, B. J.

K. Huang, B. J. Rice, B. Coombs, and R. Freed, “Methods For evaluating lithographic performance of exposure tools for the 45-nm node: ECD and scatterometry,” Proc. SPIE 5375, 494–502 (2004).
[CrossRef]

Ronnow, D.

D. Ronnow, S. K. Anderson, and G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4, 815–821 (1995).
[CrossRef]

Schuster, T.

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

Silver, R.

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Thiault, J.

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Thony, P.

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

Tompkins, H. G.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, 1993).

Tortai, J. H.

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Tserepi, A.

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists II: scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B 21, 1019–1026 (2003).
[CrossRef]

Tsur, Y.

B. Yaakobovitz, Y. Cohen, and Y. Tsur, “Line edge roughness detection using deep UV light scatterometry,” Microelectron. Eng. 84, 619–625 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980) pp. 705–708.

Xydi, P.

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

Yaakobovitz, B.

B. Yaakobovitz, Y. Cohen, and Y. Tsur, “Line edge roughness detection using deep UV light scatterometry,” Microelectron. Eng. 84, 619–625 (2007).
[CrossRef]

Yedur, S.

J. Bischoff, E. Drege, and S. Yedur, “Edge Roughness Measurement In Optical Metrology,” US Patent 7,046,375, 16 May 2006.

J. Microlithogr., Microfabr., Microsyst. (1)

V. Constantoudis, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Microlithogr., Microfabr., Microsyst. 3, 429–435 (2004).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Vac. Sci. Technol. B (3)

V. Constantoudis, G. P. Patsis, A. Tserepi, and E. Gogolides, “Quantification of line-edge roughness of photoresists II: scaling and fractal analysis and the best roughness descriptors,” J. Vac. Sci. Technol. B 21, 1019–1026 (2003).
[CrossRef]

G. P. Patsis, V. Constantoudis, A. Tserepi, E. Gogolides, and G. Grozev, “Quantification of line-edge roughness of photoresists. I. a comparison between off-line and on-line analysis of top-down scanning electron microscopy images,” J. Vac. Sci. Technol. B 21, 1008–1018 (2003).
[CrossRef]

J. Thiault, J. Foucher, J. H. Tortai, O. Joubert, S. Landis, and S. Pauliac, “Line edge roughness characterization with a three-dimensional atomic force microscope: transfer during gate patterning processes,” J. Vac. Sci. Technol. B 23, 3075–3079 (2005).
[CrossRef]

Med. Instrum. (1)

T. Schuster, S. Rafler, V. F. Paz, K. Frenner, and W. Osten, “Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Med. Instrum. 86, 1029–1032 (2009).

Microelectron. Eng. (1)

B. Yaakobovitz, Y. Cohen, and Y. Tsur, “Line edge roughness detection using deep UV light scatterometry,” Microelectron. Eng. 84, 619–625 (2007).
[CrossRef]

Opt. Mater. (1)

D. Ronnow, S. K. Anderson, and G. A. Niklasson, “Surface roughness effects in ellipsometry: comparison of truncated sphere and effective medium models,” Opt. Mater. 4, 815–821 (1995).
[CrossRef]

Philos. Mag. (1)

L. Rayleigh, “On the incidence of aerial and electric waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and on the passage of electric waves through a circular aperture in a conducting screen,” Philos. Mag. 44, 28–52 (1897).
[CrossRef]

Phys. Rev. B (1)

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–3302 (1979).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

J. C. Maxwell Garnett, “Colours in metal glasses, in metallic films, and in metallic solutions—II,” Proc. R. Soc. London, Ser. A 205, 237–288 (1906).

Proc. SPIE (8)

G. M. Gallatin, “Resist blur and line edge roughness,” Proc. SPIE 5754, 38–52 (2005).
[CrossRef]

V. Constantoudis, G. P. Patsis, L. H. A. Leunissen, and E. Gogolides, “Toward a complete description of linewidth roughness: a comparison of different methods for vertical and spatial LER and LWR analysis and CD variation,” Proc. SPIE 5375, 967–977 (2004).
[CrossRef]

V. Constantoudis, G. Kokkoris, P. Xydi, E. Gogolides, E. Pargon, and M. Martin, “Line edge roughness transfer during plasma etching: modeling approaches and comparison with experimental results,” Proc. SPIE 7273, 72732J (2009).
[CrossRef]

K. Huang, B. J. Rice, B. Coombs, and R. Freed, “Methods For evaluating lithographic performance of exposure tools for the 45-nm node: ECD and scatterometry,” Proc. SPIE 5375, 494–502 (2004).
[CrossRef]

E. Barouch, and S. L. Knodle, “Scatterometry as a practical in-situ metrology technology,” Proc. SPIE 5038, 559–567 (2003).
[CrossRef]

D. Herisson, D. Neira, C. Fernand, P. Thony, D. Henry, S. Kremer, M. Polli, M. Guevremont, and A. Elazami, “Spectroscopic ellipsometry for lithography front-end level CD control: a complete analysis for production integration,”Proc. SPIE 5038, 264–273 (2003).
[CrossRef]

R. Silver, T. Germer, R. Attota, B. M. Barnes, B. Bunday, J. Allgair, E. Marx, and J. Jun, “Fundamental limits of optical critical dimension metrology: a simulation study,” Proc. SPIE 6518, 65180U (2007).
[CrossRef]

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desieres, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203 (2005).
[CrossRef]

Other (6)

T. G. Makay, “Homogenization of linear and nonlinear complex composite materials,” in Introduction to Complex Mediums for Optics and Electromagnetics, W.S.Weiglhofer, A.Lakhtakia, eds., (SPIE, Bellingham, Washington, 2003), pp. 317–346.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980) pp. 705–708.

J. Bischoff, E. Drege, and S. Yedur, “Edge Roughness Measurement In Optical Metrology,” US Patent 7,046,375, 16 May 2006.

K. A. Michalski and T. A. Germer, available from the author at thomas.germer@nist.gov.

T. A. Germer, “SCATMECH: Polarized Light Scattering C++ Class Library,” available online at http://physics.nist.gov/scatmech (2008).

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, 1993).

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Figures (9)

Fig. 1
Fig. 1

Schematic representations of the structures used in the simulations. The figures show (a) the nominal profile, (b) a 2D periodic profile used to directly calculate the effect of LER using a 2DRCW algorithm, and (c) a 1D periodic profile used to approximate the effect of the LER with an effective medium layer. The magnitudes of the roughness are exaggerated and the figure is not to scale.

Fig. 2
Fig. 2

Reflectance from a silicon grating with P x = 200 nm , w = 100 nm , and h = 200 nm simulated for wavelength λ = 632.8 nm . The curves represent (solid curve) s-polarization and (dashed curve) p-polarization for the nominal grating with LER defined by a self-affine function with σ = 2.5 nm , ξ = 20 nm , and α = 0.5 .

Fig. 3
Fig. 3

Examples of line edge profiles used in the simulations: (a) self-affine profile with ξ = 20 nm and α = 0.5 , (b) self-affine profile with ξ = 20 nm and α = 1.0 , (c) self-affine profile with ξ = 100 nm and α = 0.5 , (d) self-affine profile with ξ = 20 nm and α = 0.75 , (e) sinusoidal profile with P y = 20 nm , and (f) rectangular profile with P y = 20 nm . The rms roughness values are 5 nm and the sides of the square boxes are 200 nm .

Fig. 4
Fig. 4

Change in reflectance between the nominal grating with P x = 200 nm , w = 100 nm , and h = 200 nm and that (solid curve) with random LER defined by ξ = 20 nm and α = 0.5 , that (dashed curve) with a rectangular roughness profile with P y = 20 nm , and that (dotted curve) with a sinusoidal roughness profile having P y = 20 nm . The rms roughness was 2.5 nm for all three curves.  

Fig. 5
Fig. 5

Rms change in reflectance calculated by 2DRCW as a function of rms amplitude σ, correlation length ξ, and roughness exponent α as described in the text. For each graph the roughness parameters that are not varied are fixed at α = 0.5 , ξ = 20 nm , and σ = 2.5 nm . The data are for s-polarization (filled squares) and p-polarization (open squares).

Fig. 6
Fig. 6

Change in reflectance between the nominal grating and (solid squares) the grating with LWR defined by σ = 2.5 nm , ξ = 20 nm , α = 0.5 calculated using a 2DRCW algorithm; (solid curve) the reflectance calculated using a 1DRCW algorithm and an EMA with ( L x , L y , L z ) = ( 0 , 1 , 0 ) ; (dotted curve) the reflectance calculated using a 1DRCW algorithm and an EMA with ( L x , L y , L z ) = ( 0.5 , 0.5 , 0 ) ; (long-dashed curve) the reflectance calculated using a 1DRCW algorithm and an EMA with ( L x , L y , L z ) = ( 1 3 , 1 3 , 1 3 ) ; and (short-dashed curve) the reflectance calculated using a 1DRCW algorithm and an EMA with ( L x , L y , L z ) = ( 0.7 , 0.3 , 0 ) . The nominal grating has P x = 200 nm , w = 100 nm , and h = 200 nm . The fill factor was f = 0.50 and the thickness of the effective medium layer was t = 2 σ in all cases.

Fig. 7
Fig. 7

Best fit EMA parameters L x (filled squares), L y (open squares), and L z (triangles) as functions of roughness correlation length.

Fig. 8
Fig. 8

Wavelength dependent specular reflectance differences for an incident angle of 65° and the nominal grating with P x = 200 nm , w = 100 nm , and h = 200 nm (filled squares) for the grating with LER defined by σ = 2.5 nm , ξ = 20 nm , α = 0.5 calculated using a 2DRCW algorithm and (solid curves) for the grating with an effective medium layer defined by ( L x , L y , L z ) = ( 0.7 , 0.3 , 0 ) , f = 50 % , and t = 2 σ . Top curves are for s-polarization, bottom for p-polarization.

Fig. 9
Fig. 9

Objective functions ( S s and S p ) for various gratings with LER defined by σ = 2.5 nm , ξ = 20 nm , α = 0.5 . All the gratings have P x = 200 nm .

Equations (9)

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A ( ρ ) = exp [ ( ρ ξ ) 2 α ] ,
P ( k ) = A ( ρ ) exp ( i k ρ ) d ρ .
Δ x ( y ) = a [ P ( k ) ] 1 2 exp [ i φ ( k ) i k y ] d k ,
ε eff ε 0 ε 0 + L ( ε eff ε 0 ) = i = 1 M f i ε i ε 0 ε 0 + L ( ε i ε 0 ) ,
ε eff = ε 1 ( f 1 L ) + ε 2 ( f 2 L ) ± [ ε 1 ( f 1 L ) + ε 2 ( f 2 L ) ] 2 4 ε 1 ε 2 L ( L 1 ) 2 ( 1 L ) .
ε x = ε z = ( 1 f ) ε 0 + f ε 1
ε y = [ ( 1 f ) ε 0 1 + f ε 1 1 ] 1 .
S s , p = 1 N i = 1 N [ R s , p EMA ( θ i ) R s , p 2 DRCW ( θ i ) ] 2 ,
S = S s 2 + S p 2 ,

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