Abstract

Based on reflective optics at 13.5 nm, extreme-UV lithography is the ultimate top-down technique to define structures below 22 nm but faces several challenges arising from the discrete nature of light and matter. Owing to the short wavelength, mask surface roughness plays a fundamental role in the increase of speckle pattern contrast, compromising the uniformity of the printed features. Herein, we have used a mask with engineered gradient surface roughness to illustrate the impact that speckle has on the resulting photoresist pattern. The speckle increases the photoresist roughness, but surprisingly, only when the mask surface roughness is well above existing manufacturing capabilities.

© 2012 OSA

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2012 (1)

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

2011 (3)

G. M. Gallatin and P. P. Naulleau, “Modeling the transfer of line edge roughness from an EUV mask to the wafer,” Proc. SPIE 7969, 796903, 796903-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

C. A. Mack, J. W. Thackeray, J. J. Biafore, and M. D. Smith, “Stochastic exposure kinetics of EUV photoresists: a simulation study,” J. Micro/Nanolith.  10, 033019 (2011).

2010 (4)

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

A. Vaglio Pret, R. Gronheid, T. Ishimoto, and K. Sekiguchi, “Resist roughness evaluation and frequency analysis: metrological challenges and potential solutions for extreme ultraviolet lithography” J. Micro/Nanolith. 9, 041308 (2010).

Y. Ban, S. Sundareswaran, R. Panda, and D. Z. Pan, “Electrical impact of line-edge roughness on sub-45-nm node standard cells,” J. Micro/Nanolith.  9, 6–10 (2010).

C. Wagner and H. Noreen, “EUV lithography: lithography gets extreme,” Nat. Photonics 4(1), 24–26 (2010).
[Crossref]

2009 (4)

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

G. M. Gallatin, N. Kita, T. Ujike, and B. Partlo, “Residual speckle in a lithographic illumination system,” J. Micro/Nanolith. MEMS MOEMS 8, 043003 (2009).

C. N. Anderson and P. P. Naulleau, “Do not always blame the photons: relationships between deprotection blur, line-edge roughness, and shot noise in extreme ultraviolet photoresists,” J. Vac. Sci. Technol. B 27(2), 665–670 (2009).
[Crossref]

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

2008 (1)

P. P. Naulleau, D. Niakoula, and G. Zhang, “System-level line-edge roughness limits in extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 26(4), 1289–1293 (2008).
[Crossref]

2007 (1)

2006 (2)

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

2004 (2)

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

C. Vassilios, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Micro/Nanolith.  3, 429–435 (2004).

2003 (2)

P. P. Naulleau and G. M. Gallatin, “Line-edge roughness transfer function and its application to determining mask effects in EUV resist characterization,” Appl. Opt. 42(17), 3390–3397 (2003).
[Crossref] [PubMed]

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(3), 1019–1026 (2003).
[Crossref]

Acheta, A.

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

Anderson, C. N.

C. N. Anderson and P. P. Naulleau, “Do not always blame the photons: relationships between deprotection blur, line-edge roughness, and shot noise in extreme ultraviolet photoresists,” J. Vac. Sci. Technol. B 27(2), 665–670 (2009).
[Crossref]

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Anderson, E. H.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

Andrey, T.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Baclea-an, L.-M.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Ban, Y.

Y. Ban, S. Sundareswaran, R. Panda, and D. Z. Pan, “Electrical impact of line-edge roughness on sub-45-nm node standard cells,” J. Micro/Nanolith.  9, 6–10 (2010).

Bengtsson, J.

Biafore, J. J.

C. A. Mack, J. W. Thackeray, J. J. Biafore, and M. D. Smith, “Stochastic exposure kinetics of EUV photoresists: a simulation study,” J. Micro/Nanolith.  10, 033019 (2011).

Blomme, P.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

Chandhok, M.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Choi, C.-J.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Constantoudis, V.

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(3), 1019–1026 (2003).
[Crossref]

Corbalan, M. M.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

Dehaene, W.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

Denham, P.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Du, Y.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Farnsworth, J.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Gallatin, G. M.

G. M. Gallatin and P. P. Naulleau, “Modeling the transfer of line edge roughness from an EUV mask to the wafer,” Proc. SPIE 7969, 796903, 796903-10 (2011).
[Crossref]

G. M. Gallatin, N. Kita, T. Ujike, and B. Partlo, “Residual speckle in a lithographic illumination system,” J. Micro/Nanolith. MEMS MOEMS 8, 043003 (2009).

P. P. Naulleau and G. M. Gallatin, “Line-edge roughness transfer function and its application to determining mask effects in EUV resist characterization,” Appl. Opt. 42(17), 3390–3397 (2003).
[Crossref] [PubMed]

Gary, P.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

George, S.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

George, S. A.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

Gogolides, E.

C. Vassilios, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Micro/Nanolith.  3, 429–435 (2004).

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(3), 1019–1026 (2003).
[Crossref]

Goldberg, K. A.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Goldstein, M.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Gronheid, R.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

A. Vaglio Pret, R. Gronheid, T. Ishimoto, and K. Sekiguchi, “Resist roughness evaluation and frequency analysis: metrological challenges and potential solutions for extreme ultraviolet lithography” J. Micro/Nanolith. 9, 041308 (2010).

Gullikson, E. M.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

Hayashi, H.

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

Hoef, B.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Hsia, K.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Hudyma, R.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Ishimoto, T.

A. Vaglio Pret, R. Gronheid, T. Ishimoto, and K. Sekiguchi, “Resist roughness evaluation and frequency analysis: metrological challenges and potential solutions for extreme ultraviolet lithography” J. Micro/Nanolith. 9, 041308 (2010).

James, T.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Jan, B.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Jones, G.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Kawata, M.

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

Kikugawa, S.

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

Kita, N.

G. M. Gallatin, N. Kita, T. Ujike, and B. Partlo, “Residual speckle in a lithographic illumination system,” J. Micro/Nanolith. MEMS MOEMS 8, 043003 (2009).

Koh, C.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

La Fontaine, B.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

La Fontaine, B. M.

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

Lalovic, I.

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

Lanzendorf, E. J.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Leeson, M. J.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Levinson, H. J.

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

Liang, T.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Mack, C. A.

C. A. Mack, J. W. Thackeray, J. J. Biafore, and M. D. Smith, “Stochastic exposure kinetics of EUV photoresists: a simulation study,” J. Micro/Nanolith.  10, 033019 (2011).

Manfred, M.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

McClinton, B.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Michael, P.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Miyakawa, R. H.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Mochi, I.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

Montgomery, W.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Naulleau, P. P.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

G. M. Gallatin and P. P. Naulleau, “Modeling the transfer of line edge roughness from an EUV mask to the wafer,” Proc. SPIE 7969, 796903, 796903-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

C. N. Anderson and P. P. Naulleau, “Do not always blame the photons: relationships between deprotection blur, line-edge roughness, and shot noise in extreme ultraviolet photoresists,” J. Vac. Sci. Technol. B 27(2), 665–670 (2009).
[Crossref]

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

P. P. Naulleau, D. Niakoula, and G. Zhang, “System-level line-edge roughness limits in extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 26(4), 1289–1293 (2008).
[Crossref]

P. P. Naulleau and G. M. Gallatin, “Line-edge roughness transfer function and its application to determining mask effects in EUV resist characterization,” Appl. Opt. 42(17), 3390–3397 (2003).
[Crossref] [PubMed]

Niakoula, D.

P. P. Naulleau, D. Niakoula, and G. Zhang, “System-level line-edge roughness limits in extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 26(4), 1289–1293 (2008).
[Crossref]

Noordman, O.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Noreen, H.

C. Wagner and H. Noreen, “EUV lithography: lithography gets extreme,” Nat. Photonics 4(1), 24–26 (2010).
[Crossref]

Pan, D. Z.

Y. Ban, S. Sundareswaran, R. Panda, and D. Z. Pan, “Electrical impact of line-edge roughness on sub-45-nm node standard cells,” J. Micro/Nanolith.  9, 6–10 (2010).

Panda, R.

Y. Ban, S. Sundareswaran, R. Panda, and D. Z. Pan, “Electrical impact of line-edge roughness on sub-45-nm node standard cells,” J. Micro/Nanolith.  9, 6–10 (2010).

Park, S.-

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Partlo, B.

G. M. Gallatin, N. Kita, T. Ujike, and B. Partlo, “Residual speckle in a lithographic illumination system,” J. Micro/Nanolith. MEMS MOEMS 8, 043003 (2009).

Patsis, G. P.

C. Vassilios, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Micro/Nanolith.  3, 429–435 (2004).

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(3), 1019–1026 (2003).
[Crossref]

Pawloski, A. R.

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

Poliakov, P.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

Roller, J.

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Rydberg, C.

Salmassi, F.

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

Sanchez, P.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Sandström, T.

Sekiguchi, K.

A. Vaglio Pret, R. Gronheid, T. Ishimoto, and K. Sekiguchi, “Resist roughness evaluation and frequency analysis: metrological challenges and potential solutions for extreme ultraviolet lithography” J. Micro/Nanolith. 9, 041308 (2010).

Shu, E. Y.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Smith, M. D.

C. A. Mack, J. W. Thackeray, J. J. Biafore, and M. D. Smith, “Stochastic exposure kinetics of EUV photoresists: a simulation study,” J. Micro/Nanolith.  10, 033019 (2011).

Stivers, A. R.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Sugimoto, N.

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

Sundareswaran, S.

Y. Ban, S. Sundareswaran, R. Panda, and D. Z. Pan, “Electrical impact of line-edge roughness on sub-45-nm node standard cells,” J. Micro/Nanolith.  9, 6–10 (2010).

Takada, A.

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

Thackeray, J. W.

C. A. Mack, J. W. Thackeray, J. J. Biafore, and M. D. Smith, “Stochastic exposure kinetics of EUV photoresists: a simulation study,” J. Micro/Nanolith.  10, 033019 (2011).

Tserepi, A.

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(3), 1019–1026 (2003).
[Crossref]

Ujike, T.

G. M. Gallatin, N. Kita, T. Ujike, and B. Partlo, “Residual speckle in a lithographic illumination system,” J. Micro/Nanolith. MEMS MOEMS 8, 043003 (2009).

Vaglio Pret, A.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

A. Vaglio Pret, R. Gronheid, T. Ishimoto, and K. Sekiguchi, “Resist roughness evaluation and frequency analysis: metrological challenges and potential solutions for extreme ultraviolet lithography” J. Micro/Nanolith. 9, 041308 (2010).

Van Houdt, J.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

Vandentop, G.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Vassilios, C.

C. Vassilios, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Micro/Nanolith.  3, 429–435 (2004).

Verkest, D.

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

Vladan, B.

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Wagner, C.

C. Wagner and H. Noreen, “EUV lithography: lithography gets extreme,” Nat. Photonics 4(1), 24–26 (2010).
[Crossref]

Wurm, T. W. S

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

Yan, P.-Y.

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Zhang, G.

P. P. Naulleau, D. Niakoula, and G. Zhang, “System-level line-edge roughness limits in extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 26(4), 1289–1293 (2008).
[Crossref]

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

Appl. Opt. (1)

IEEE Electron Device Lett. (1)

P. Poliakov, P. Blomme, A. Vaglio Pret, M. M. Corbalan, R. Gronheid, D. Verkest, J. Van Houdt, and W. Dehaene, “Induced variability of cell-to-cell interference by line edge roughness in NAND flash arrays,” IEEE Electron Device Lett. 33(2), 164–166 (2012).
[Crossref]

J. Micro/Nanolith (2)

C. A. Mack, J. W. Thackeray, J. J. Biafore, and M. D. Smith, “Stochastic exposure kinetics of EUV photoresists: a simulation study,” J. Micro/Nanolith.  10, 033019 (2011).

C. Vassilios, G. P. Patsis, and E. Gogolides, “Photoresist line-edge roughness analysis using scaling concepts,” J. Micro/Nanolith.  3, 429–435 (2004).

J. Micro/Nanolith. (3)

A. Vaglio Pret, R. Gronheid, T. Ishimoto, and K. Sekiguchi, “Resist roughness evaluation and frequency analysis: metrological challenges and potential solutions for extreme ultraviolet lithography” J. Micro/Nanolith. 9, 041308 (2010).

O. Noordman, T. Andrey, B. Jan, T. James, P. Gary, P. Michael, B. Vladan, and M. Manfred, “Speckle in optical lithography and the influence on line width roughness,” J. Micro/Nanolith. 8, 043002 (2009).

Y. Ban, S. Sundareswaran, R. Panda, and D. Z. Pan, “Electrical impact of line-edge roughness on sub-45-nm node standard cells,” J. Micro/Nanolith.  9, 6–10 (2010).

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (4)

C. N. Anderson and P. P. Naulleau, “Do not always blame the photons: relationships between deprotection blur, line-edge roughness, and shot noise in extreme ultraviolet photoresists,” J. Vac. Sci. Technol. B 27(2), 665–670 (2009).
[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(3), 1019–1026 (2003).
[Crossref]

S. A. George, P. P. Naulleau, F. Salmassi, I. Mochi, E. M. Gullikson, K. A. Goldberg, and E. H. Anderson, “Extreme ultraviolet mask substrate surface roughness effects on lithographic patterning,” J. Vac. Sci. Technol. B 28, C6E23–C6E30 (2010).

P. P. Naulleau, D. Niakoula, and G. Zhang, “System-level line-edge roughness limits in extreme ultraviolet lithography,” J. Vac. Sci. Technol. B 26(4), 1289–1293 (2008).
[Crossref]

MEMS MOEMS (1)

G. M. Gallatin, N. Kita, T. Ujike, and B. Partlo, “Residual speckle in a lithographic illumination system,” J. Micro/Nanolith. MEMS MOEMS 8, 043003 (2009).

Nat. Photonics (1)

C. Wagner and H. Noreen, “EUV lithography: lithography gets extreme,” Nat. Photonics 4(1), 24–26 (2010).
[Crossref]

Proc. SPIE (6)

M. Kawata, A. Takada, H. Hayashi, N. Sugimoto, and S. Kikugawa, “Novel low thermal expansion material for EUV application,” Proc. SPIE 6151, 368–374 (2006).

G. Zhang, P.-Y. Yan, T. Liang, Y. Du, P. Sanchez, S.- Park, E. J. Lanzendorf, C.-J. Choi, E. Y. Shu, A. R. Stivers, J. Farnsworth, K. Hsia, M. Chandhok, M. J. Leeson, and G. Vandentop, “EUV Mask process development and integration,” Proc. SPIE 6283, 62830G, 62830G-10 (2006).
[Crossref]

P. P. Naulleau, C. N. Anderson, L.-M. Baclea-an, P. Denham, S. George, K. A. Goldberg, M. Goldstein, B. Hoef, R. Hudyma, G. Jones, C. Koh, B. La Fontaine, B. McClinton, R. H. Miyakawa, W. Montgomery, J. Roller, and T. W. S Wurm, “The SEMATECH Berkeley microfield exposure tool: learning at the 22-nm node and beyond,” Proc. SPIE 7271, 7271W (2009).

G. M. Gallatin and P. P. Naulleau, “Modeling the transfer of line edge roughness from an EUV mask to the wafer,” Proc. SPIE 7969, 796903, 796903-10 (2011).
[Crossref]

S. A. George, P. P. Naulleau, E. M. Gullikson, I. Mochi, F. Salmassi, K. A. Goldberg, and E. H. Anderson, “Replicated mask surface roughness effects on EUV lithographic patterning and line edge roughness,” Proc. SPIE 7969, 79690E, 79690E-10 (2011).
[Crossref]

A. R. Pawloski, A. Acheta, I. Lalovic, B. M. La Fontaine, and H. J. Levinson, “Characterization of line-edge roughness in photoresist using an image fading technique,” Proc. SPIE 5376, 414–425 (2004).
[Crossref]

Other (10)

A. K. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, 2001), Chaps. 2–4.

H.-J. Mann, “Six-mirror EUV projection system with low incidence angles,” U.S. patent 7,973,908 (July 5, 2011). http://www.google.com/patents/US20090079952 .

ITRS website. http://www.itrs.net/ .

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004), Chap. 6.

J. W. Goodman, Speckle Phenomena in Optics (Roberts and Company Publishers, 2010), Chaps. 1–3, 6, 8.

R. Hudyma and U. Mann, “Projection system for EUV lithography,” U.S. patent 7,355,678 (April 8, 2008). http://spie.org/samples/PM178.pdf

C. A. Mack, Fundamental Principles of Optical Lithography (Wiley & Sons, 2007), Chaps. 5–7.

Y. Wei and R. L. Brainard, Line-Edge Roughness of Resist Patterns in Advanced Processes for 193-Nm Immersion Lithography (SPIE Press, 2009), Chap. 10.

T.-S. Gau and C.-C. Hsia, “Illumination aperture filter design using superposition,” U.S. patent 6,361,909 (March 26, 2002). http://www.google.com/patents/US6361909 .

K. Jain, C. G. Willson, B. J. Lin, and B. J, “Fine-line high-speed excimer laser lithography,” Symposium on VLSI Technology, Digest of Technical Papers (1982), pp. 92–93.

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Figures (5)

Fig. 1
Fig. 1

(a) Cartoon of an EUV mask representing the absorber stack, the Mo/Si multilayer, the Cr layer for surface roughness variation, the LTEM substrate, and the EUV light path. (b) Mask layout used for speckle evaluation: the red area represents the Cr layer deposited to increase the surface roughness (labeled from A to H), the white rectangles represent the locations of the mask gratings (54 nm line/space, 1:1 duty cycle), the red dots are the top-down SEM picture locations on wafer, and the green dashed lines indicate the reference modules (no Cr deposited, I site). On the left, AFM images for high, mid and low surface roughness are reported.

Fig. 2
Fig. 2

Sketch of the Conventional (a) and Dipole-60 (b) illuminations used for the exposures. In the cartoons, the + 1 diffraction orders are represented for f = fcut-off. c) Aerial image contrast of Conventional (blue) and Dipole-60 (red) illumination for 54 nm line/space exposure.

Fig. 3
Fig. 3

(a) Exposure energies and (b) LER upon mask surface roughness for Conventional (blue) and Dipole-60 (red) illumination. Below, top-down SEM micrographs for 54 nm line/space gratings exposed with (c) Conventional and (d) Dipole-60 illumination at different mask surface roughness. On the right, the speckle patterns are also shown [18].

Fig. 4
Fig. 4

PSD analysis of line edge roughness for 54 nm line/space gratings exposed with (a) Conventional and (b) Dipole-60 illuminations. The black line correspond to the reference modules (AFM = 60 pm), the other mask surface roughness conditions are represented following the roygbiv color code from violet (low rms) to red (high rms). The dashed grey lines represent the fcut-off for each illumination condition.

Fig. 5
Fig. 5

LER variations upon exposure energy variation normalized on the reference case for Conventional (blue) and Dipole-60 (red) illumination. The solid lines represent a linear fitting of the data. In the graph, fitting equation and R2 values are also reported.

Tables (1)

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Table 1 AFM MSR and mask reflectivity measurements along the mask area where Cr is deposited to aggravate the resulting surface roughness. Measurements errors are respectively 20 pm and 0.08%.

Equations (5)

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Speckle pattern contrast 1 N p λ 2 G + τ c T τ c = 1 2πc λ 2 Δλ
f cutoff ( Conventional )= NA λ ( 1+ σ out )=34μ m 1
{ y=mx+q x 2 + y 2 =1
q= ( m 2 +1 ) q= 5 2 f cutoff ( Dipole )=q NA λ =20.7μ m 1
f cutoff ( Conventional )=34μ m 1 f cutoff ( Dipole60 )=20.7μ m 1

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