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The diffraction efficiency of freestanding x ray transmission gratings is discussed in relation to the wavelength and grating period using both scalar diffraction theory and rigorous coupled wave analysis, and the grating design is accordingly optimized. A gold freestanding x ray transmission grating with period of 300 nm, line/period ratio of 055, thickness of 200 nm a size of 1 mm ×1 mm and fractional grating area of 65% is fabricated. The absolute diffraction efficiency of the fabricated grating was tested at the National Synchrotron Radiation Laboratory in the wavelength region of 55— 38 nm. The test result shows that the grating has a maximum efficiency of nearly 10%. The grating also shows a stable diffraction efficiency in the wavelength region from 15 nm to 35 nm.
[1] [1]Schattenburg M L, Aucion R J, Fleming R C, Plotnik I, Porter J, Smith H I 1994 Proc. SPIE 2280 181
[2] [2]Leeper R J, Chandler G A, Cooper G W, Derzon M S, et al 1997 Rev. Sci. Instrum. 68 868
[3] [3]Yen A, Anderson E H, Ghanbari R A, Schattenburg M L, Smith H I 1992 Appl. Opt. 31 4540
[4] [4]Solak H H, David C, Gobrecht J, Golovkina V, Cerrina F, Kim S O, Nealey P F 2003 Microelectron. Eng. 67—68 56
[5] [5]Qiu K Q, Xu X D, Liu Y, Hong Y L, Fu S J 2008 Acta Phys. Sin. 57 6329(in Chinese) [邱克强、徐向东、刘颖、洪义麟、傅绍军 2008 57 6329]
[6] [6]Yang J M, Ding Y N, Sun K X, Cheng J X, Jiang S E, Zheng Z J, Zhang W H 2000 Acta Phys. Sin. 49 747 (in Chinese) [杨家敏、丁耀南、孙可煦、成金秀、江少恩、郑志坚、张文海2000 49 747]
[7] [7]Chen B, Zhu P P, Liu J Y, Wang J Y, Yuan Q X, Huang W X, Ming H, Wu Z Y 2008 Acta Phys. Sin. 57 1576 (in Chinese)[陈博、朱佩平、刘宜晋、王寯越、袁清习、黄万霞、明海、吴自玉 2008 57 1576]
[8] [8]Predehl P, Braeuninger H W, Brinkman A C, Dewey D, Drake J J, Flanagan K A, Gunsing T, Hartner G D, Juda J Z, Juda M, Kaastra J S, Marshall H L, Swartz D A 1997 Proc. SPIE 3113 172
[9] [9]Brinkman A C, Gunsing C J T, Kaastra J S, Braeuninger H W, Hartner G D, Predehl P, Drake J J, Juda J Z, Juda M, Dewey D, Flanagan K A, Marshall H L 1997 Proc. SPIE 3113 181
[10] ]Xu X D, Hong Y L, Huo T L, Zhou H J, Tao X M, Fu S J 2001 Opti. Tech. 27 294 (in Chinese) [徐向东、洪义麟、霍同林、周洪军、陶晓明、傅绍军 2001 光学技术 27 294]
[11] ]Xu X D, Hong Y L, Liu Y, Fu S J, Wang Z S 2005 Microfabr. Technol.01 38 (in Chinese) [徐向东、洪义麟、刘颖、傅绍军、王占山2005 微细加工技术 01 38]
[12] ]Qiu K Q 2008 Ph.D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [邱克强 2008 博士学位论文(合肥:中国科技大学)]
[13] ]McMullin D R, Judge D L, Tarrio C, Vest R E, Hanser F 2004 Appl. Opt. 43 3797
[14] ]Xu X D, Hong Y L, Fu S J 2003 Vac. Sci. Technol. 23 362 (in Chinese) [徐向东、洪义麟、傅绍军 2003 真空科学与技术 23 362]
[15] ]Xu X D, Hong Y L, Fu S J 2004 Physics 33 341 (in Chinese) [徐向东、洪义麟、傅绍军 2004 物理 33 340]
[16] ]Schnopper H W, van Speybroeck L P, Delvaille J P, Epstein A, Kllne E, Bachrach R Z, Dijkstra J, Lantward L 1977 Appl. Opt. 16 1088
[17] ]Markert T H, Dewey D, Davis J E, Flanagan K A, Graessle D E, Bauer J M, Nelson C S 1995 Proc. SPIE 2518 424
[18] ]Yang J M, Yi R Q, Chen Z L, Sun K X, Ding Y N, Zheng Z J, Li C G, Cui M Q, Zhu P P, Cui C W 1998 Acta Phys. Sin. 47 613 (in Chinese) [杨家敏、易荣清、陈正林、孙可煦、丁耀南、郑志坚、李朝光、崔明启、朱佩平、崔聪悟 1998 47 613]
[19] ]Born M, Wolf E 1980 Principle of Optics (London: Pergamon) p450
[20] ]Moharam M G, Grann E B, Prommet D A, Gaylord T K 1995 J. Opt. Soc. Am. A 12 1068
[21] ]Moharam M G, Prommet D A, Grann E B, Gaylord T K 1995 J. Opt. Soc. Am. A 12 1077
[22] ]Zhu W Z, Wu Y Q, Guo Z, Zhu X L, Ma J, Xie C Q, Shi P X, Zhou H J, Huo T L, Tai R Z, Xu H J 2008 Acta Phys. Sin. 57 6386 (in Chinese)[朱伟忠、吴衍青、郭智、朱效立、马杰、谢常青、史沛熊、周洪军、霍同林、邰仁忠、徐洪杰 2008 57 6386]
[23] ]Kong W J, Yun M J, Sun X, Liu J H, Fan Z X, Shao J D 2008 Acta Phys. Sin. 57 4904 (in Chinese) [孔伟金、云茂金、孙欣、刘均海、范正修、邵建达 2008 57 4904]
[24] ]Zhou C H, Wang L, Wang Z H 2001 Acta Phys. Sin. 50 1046 (in Chinese) [周传宏、王磊、王植恒 2001 50 1046]
[25] ]Zhou C H, Wang L, Nie Y, Wang Z H 2002 Acta Phys. Sin. 51 68 (in Chinese) [周传宏、王磊、聂娅、王植恒 2002 51 68]
[26] ]Schattenburg M L, Anderson E H, Smith H I 1990 Phys. Script. 41 13
[27] ]Zhu X L, Xie C Q, Ye T C, Zhao M, Ma J, Jiang J, Niu J B, Liu M 2008 Proc. SPIE 6832 68320V
[28] ]Zhu X L, Ma J, Cao L F, Yang J M, Xie C Q, Liu M, Chen B Q, Niu J B, Zhang Q Z, Jiang J, Zhao M, Ye T C 2007 Chin. J. Semiconduct. 28 91 (in Chinese) [朱效立、马杰、曹磊峰、杨家敏、谢长青、刘明、陈宝钦、牛洁斌、张庆钊、姜骥、赵珉、叶甜春 2007 半导体学报 28 91]
[29] ]Zhu X L, Ma J, Xie C Q, Ye T C, Liu M, Cao L F, Yang J M, Zhang W H 2008 Acta Opt. Sin. 28 1026 (in Chinese)[朱效立、马杰、谢长青、叶甜春、刘明、曹磊峰、杨家敏、张文海 2008 光学学报28 1026]
[30] ]Attwood D T 2003 Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Beijing: Science Press) p119(in Chinese) [Attwood D T(中译本) 2003 软X射线与极紫外辐射的原理和应用(北京:科学出版社) 第119页]
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[1] [1]Schattenburg M L, Aucion R J, Fleming R C, Plotnik I, Porter J, Smith H I 1994 Proc. SPIE 2280 181
[2] [2]Leeper R J, Chandler G A, Cooper G W, Derzon M S, et al 1997 Rev. Sci. Instrum. 68 868
[3] [3]Yen A, Anderson E H, Ghanbari R A, Schattenburg M L, Smith H I 1992 Appl. Opt. 31 4540
[4] [4]Solak H H, David C, Gobrecht J, Golovkina V, Cerrina F, Kim S O, Nealey P F 2003 Microelectron. Eng. 67—68 56
[5] [5]Qiu K Q, Xu X D, Liu Y, Hong Y L, Fu S J 2008 Acta Phys. Sin. 57 6329(in Chinese) [邱克强、徐向东、刘颖、洪义麟、傅绍军 2008 57 6329]
[6] [6]Yang J M, Ding Y N, Sun K X, Cheng J X, Jiang S E, Zheng Z J, Zhang W H 2000 Acta Phys. Sin. 49 747 (in Chinese) [杨家敏、丁耀南、孙可煦、成金秀、江少恩、郑志坚、张文海2000 49 747]
[7] [7]Chen B, Zhu P P, Liu J Y, Wang J Y, Yuan Q X, Huang W X, Ming H, Wu Z Y 2008 Acta Phys. Sin. 57 1576 (in Chinese)[陈博、朱佩平、刘宜晋、王寯越、袁清习、黄万霞、明海、吴自玉 2008 57 1576]
[8] [8]Predehl P, Braeuninger H W, Brinkman A C, Dewey D, Drake J J, Flanagan K A, Gunsing T, Hartner G D, Juda J Z, Juda M, Kaastra J S, Marshall H L, Swartz D A 1997 Proc. SPIE 3113 172
[9] [9]Brinkman A C, Gunsing C J T, Kaastra J S, Braeuninger H W, Hartner G D, Predehl P, Drake J J, Juda J Z, Juda M, Dewey D, Flanagan K A, Marshall H L 1997 Proc. SPIE 3113 181
[10] ]Xu X D, Hong Y L, Huo T L, Zhou H J, Tao X M, Fu S J 2001 Opti. Tech. 27 294 (in Chinese) [徐向东、洪义麟、霍同林、周洪军、陶晓明、傅绍军 2001 光学技术 27 294]
[11] ]Xu X D, Hong Y L, Liu Y, Fu S J, Wang Z S 2005 Microfabr. Technol.01 38 (in Chinese) [徐向东、洪义麟、刘颖、傅绍军、王占山2005 微细加工技术 01 38]
[12] ]Qiu K Q 2008 Ph.D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese) [邱克强 2008 博士学位论文(合肥:中国科技大学)]
[13] ]McMullin D R, Judge D L, Tarrio C, Vest R E, Hanser F 2004 Appl. Opt. 43 3797
[14] ]Xu X D, Hong Y L, Fu S J 2003 Vac. Sci. Technol. 23 362 (in Chinese) [徐向东、洪义麟、傅绍军 2003 真空科学与技术 23 362]
[15] ]Xu X D, Hong Y L, Fu S J 2004 Physics 33 341 (in Chinese) [徐向东、洪义麟、傅绍军 2004 物理 33 340]
[16] ]Schnopper H W, van Speybroeck L P, Delvaille J P, Epstein A, Kllne E, Bachrach R Z, Dijkstra J, Lantward L 1977 Appl. Opt. 16 1088
[17] ]Markert T H, Dewey D, Davis J E, Flanagan K A, Graessle D E, Bauer J M, Nelson C S 1995 Proc. SPIE 2518 424
[18] ]Yang J M, Yi R Q, Chen Z L, Sun K X, Ding Y N, Zheng Z J, Li C G, Cui M Q, Zhu P P, Cui C W 1998 Acta Phys. Sin. 47 613 (in Chinese) [杨家敏、易荣清、陈正林、孙可煦、丁耀南、郑志坚、李朝光、崔明启、朱佩平、崔聪悟 1998 47 613]
[19] ]Born M, Wolf E 1980 Principle of Optics (London: Pergamon) p450
[20] ]Moharam M G, Grann E B, Prommet D A, Gaylord T K 1995 J. Opt. Soc. Am. A 12 1068
[21] ]Moharam M G, Prommet D A, Grann E B, Gaylord T K 1995 J. Opt. Soc. Am. A 12 1077
[22] ]Zhu W Z, Wu Y Q, Guo Z, Zhu X L, Ma J, Xie C Q, Shi P X, Zhou H J, Huo T L, Tai R Z, Xu H J 2008 Acta Phys. Sin. 57 6386 (in Chinese)[朱伟忠、吴衍青、郭智、朱效立、马杰、谢常青、史沛熊、周洪军、霍同林、邰仁忠、徐洪杰 2008 57 6386]
[23] ]Kong W J, Yun M J, Sun X, Liu J H, Fan Z X, Shao J D 2008 Acta Phys. Sin. 57 4904 (in Chinese) [孔伟金、云茂金、孙欣、刘均海、范正修、邵建达 2008 57 4904]
[24] ]Zhou C H, Wang L, Wang Z H 2001 Acta Phys. Sin. 50 1046 (in Chinese) [周传宏、王磊、王植恒 2001 50 1046]
[25] ]Zhou C H, Wang L, Nie Y, Wang Z H 2002 Acta Phys. Sin. 51 68 (in Chinese) [周传宏、王磊、聂娅、王植恒 2002 51 68]
[26] ]Schattenburg M L, Anderson E H, Smith H I 1990 Phys. Script. 41 13
[27] ]Zhu X L, Xie C Q, Ye T C, Zhao M, Ma J, Jiang J, Niu J B, Liu M 2008 Proc. SPIE 6832 68320V
[28] ]Zhu X L, Ma J, Cao L F, Yang J M, Xie C Q, Liu M, Chen B Q, Niu J B, Zhang Q Z, Jiang J, Zhao M, Ye T C 2007 Chin. J. Semiconduct. 28 91 (in Chinese) [朱效立、马杰、曹磊峰、杨家敏、谢长青、刘明、陈宝钦、牛洁斌、张庆钊、姜骥、赵珉、叶甜春 2007 半导体学报 28 91]
[29] ]Zhu X L, Ma J, Xie C Q, Ye T C, Liu M, Cao L F, Yang J M, Zhang W H 2008 Acta Opt. Sin. 28 1026 (in Chinese)[朱效立、马杰、谢长青、叶甜春、刘明、曹磊峰、杨家敏、张文海 2008 光学学报28 1026]
[30] ]Attwood D T 2003 Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Beijing: Science Press) p119(in Chinese) [Attwood D T(中译本) 2003 软X射线与极紫外辐射的原理和应用(北京:科学出版社) 第119页]
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