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In order to get a better understanding of etching mechanism and provide optimization guidance for manufacturing process, a three-dimensional (3D) profile evolution simulator based on cellular model is developed to investigate the surface evolution of etching process, and discuss emphatically the effect of ions on the surface evolution. According to the solving problem for angle of ion incidence, a component fitting-based dimension reduction method is presented to convert a 3D surface fitting problem into a two-dimensional (2D) curve fitting problem, and achieve fast solution for the surface normal vector of the incident point. Compared with least squares polynomial fitting method, this method improves computational accuracy and efficiency of the ion incidence angle. The improvement on the accuracy of fitting is achieved by improving the selection method of surface cellular for fitting. The fitting method is applied to 3D simulation of silicon etching process, and the simulation results verify the simulated surface by comparing with relevant experimental results.
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Keywords:
- etching /
- three-dimensional cellular model /
- surface evolution algorithm /
- component fitting-based dimension reduction method
[1] Wang Y Y, Wu G Y, Hao Y L, Zhang D C, Xiao Z X, Li T, Zhang G B, Zhang J W 2002 Chin. J. Electron. 30 1577 (in Chinese) [王阳元, 武国英, 郝一龙, 张大成, 肖志雄, 李婷, 张国炳, 张锦文 2002 电子学报 30 1577]
[2] Dai Z L, Mao M, Wang Y N 2006 Physics 35 693 (in Chinese) [戴忠玲, 毛明, 王友年 2006 物理 35 693]
[3] Zhou Z F, Huang Q A, Li W H, Lu W 2007 Sci. China 37 32 (in Chinese) [周再发, 黄庆安, 李伟华, 卢伟 2007 中国科学 37 32]
[4] Toh K K H, Neureuther A R, Scheckler E W 1994 IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 13 616
[5] Zhang J, Qi H C, Xu D L, Hu Z W 2011 Chin. J. Electron. 39 1869 (in Chinese) [张鉴, 戚昊琛, 徐栋梁, 胡智文 2011 电子学报 39 1869]
[6] Jewett R E, Hagouel P I, Neureuther A R, van Duzer T 1977 Polym. Eng. Sci. 17 381
[7] Osher S, Sethian J A 1988 J. Comput. Phys. 79 12
[8] Osher S, Fedkiw R P 2001 J. Comput. Phys. 169 463
[9] Kawai H 2008 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[10] Zhou Z F 2009 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese) [周再发 2009 博士学位论文 (南京: 东南大学)]
[11] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477 (in Chinese) [李强, 李殿中, 钱百年 2004 物理学报 53 3477]
[12] Xue Y, Dong L Y, Dai S Q 2001 Acta Phys. Sin. 50 445 (in Chinese) [薛郁, 董力耘, 戴世强 2001 物理学报 5 445]
[13] Saussac J, Margot J, Chaker M 2009 J. Vac. Sci. Technol. A 27 130
[14] Dai Z L, Yue G, Wang Y N 2011 Curr. Appl. Phys. 11 S121
[15] Guo W, Sawin H H 2009 J. Phys. D: Appl. Phys. 42 194014
[16] Chang J P, Arnold J C, Zau G C H, Shin H S, Sawin H H 1997 J. Vac. Sci. Technol. A 15 1853
[17] Chang J P, Mahorowala A P, Sawin H H 1998 J. Vac. Sci. Technol. A 16 217
[18] Osano Y, Ono K 2005 Jpn. J. Appl. Phys. 44 8650
[19] Vitale S A, Chae H, Sawin H H 2001 J. Vac. Sci. Technol. A 19 2197
[20] Chang J P, Sawin H H 1997 J. Vac. Sci. Technol. A 15 610
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[1] Wang Y Y, Wu G Y, Hao Y L, Zhang D C, Xiao Z X, Li T, Zhang G B, Zhang J W 2002 Chin. J. Electron. 30 1577 (in Chinese) [王阳元, 武国英, 郝一龙, 张大成, 肖志雄, 李婷, 张国炳, 张锦文 2002 电子学报 30 1577]
[2] Dai Z L, Mao M, Wang Y N 2006 Physics 35 693 (in Chinese) [戴忠玲, 毛明, 王友年 2006 物理 35 693]
[3] Zhou Z F, Huang Q A, Li W H, Lu W 2007 Sci. China 37 32 (in Chinese) [周再发, 黄庆安, 李伟华, 卢伟 2007 中国科学 37 32]
[4] Toh K K H, Neureuther A R, Scheckler E W 1994 IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 13 616
[5] Zhang J, Qi H C, Xu D L, Hu Z W 2011 Chin. J. Electron. 39 1869 (in Chinese) [张鉴, 戚昊琛, 徐栋梁, 胡智文 2011 电子学报 39 1869]
[6] Jewett R E, Hagouel P I, Neureuther A R, van Duzer T 1977 Polym. Eng. Sci. 17 381
[7] Osher S, Sethian J A 1988 J. Comput. Phys. 79 12
[8] Osher S, Fedkiw R P 2001 J. Comput. Phys. 169 463
[9] Kawai H 2008 Ph. D. Dissertation (Cambridge: Massachusetts Institute of Technology)
[10] Zhou Z F 2009 Ph. D. Dissertation (Nanjing: Southeast University) (in Chinese) [周再发 2009 博士学位论文 (南京: 东南大学)]
[11] Li Q, Li D Z, Qian B N 2004 Acta Phys. Sin. 53 3477 (in Chinese) [李强, 李殿中, 钱百年 2004 物理学报 53 3477]
[12] Xue Y, Dong L Y, Dai S Q 2001 Acta Phys. Sin. 50 445 (in Chinese) [薛郁, 董力耘, 戴世强 2001 物理学报 5 445]
[13] Saussac J, Margot J, Chaker M 2009 J. Vac. Sci. Technol. A 27 130
[14] Dai Z L, Yue G, Wang Y N 2011 Curr. Appl. Phys. 11 S121
[15] Guo W, Sawin H H 2009 J. Phys. D: Appl. Phys. 42 194014
[16] Chang J P, Arnold J C, Zau G C H, Shin H S, Sawin H H 1997 J. Vac. Sci. Technol. A 15 1853
[17] Chang J P, Mahorowala A P, Sawin H H 1998 J. Vac. Sci. Technol. A 16 217
[18] Osano Y, Ono K 2005 Jpn. J. Appl. Phys. 44 8650
[19] Vitale S A, Chae H, Sawin H H 2001 J. Vac. Sci. Technol. A 19 2197
[20] Chang J P, Sawin H H 1997 J. Vac. Sci. Technol. A 15 610
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