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晶体硅作为一种重要的半导体材料，在集成电路、太阳能电池等方面具有广泛的应用.基于各向异性的刻蚀方法，不同晶面指数的硅都可以在表面形成由{111}晶面族组成的正/倒金字塔.本文基于{111}晶面族与（abc）晶面相交构成类倒金字塔结构的特性，建立了硅的晶面指数（abc）与所形成的类倒金字塔结构的数学模型.将硅的晶面指数（abc）分成0≤a≤bc，0≤ab=c，a=b=c三种情况进行讨论，分别得到不同晶面指数的类倒金字塔结构.实验结果的扫描电子显微镜图证实了理论计算的准确性.晶面指数与类倒金字塔结构具有一一对应的关系，因此可以根据各向异性刻蚀后的类倒金字塔结构，进行硅的晶面指数进行检测.As a kind of important semiconductor material, crystalline silicon has vast applications in many industries, such as integrated circuits and solar cells. With anisotropic etching method, including alkali etching and copper assisted catalytic etching, pyramid or inverted pyramid structure on the surface of silicon can be formed due to different crystal face indices of the silicon wafer, which is especially for multi-crystalline silicon wafers, because there are many different crystal faces on the surface. The proportion of different crystal faces has a high reference value for controlling the quality of multi-crystalline silicon. In this paper, the mathematical model of the inverted pyramid structure is established by making use of the relationship between the silicon crystal indices (abc) and {111} crystal plane. The inverted pyramid structures with different crystal face index (abc) values are divided into three possible cases for discussion, which are 0≤a≤bc, 0≤ab=c, a=b=c. The inverted pyramid structure on which the crystal face index (abc) satisfies 0≤a≤bc is of a pentahedron composed of five points and has a quadrangular cross section. The inverted pyramid structure in which the crystal face index (abc) satisfies 0≤ab=c is of a heptahedron composed of eight points and has a hexagonal cross section. The inverted pyramid structure whose crystal plane index (abc) satisfies a=b=c=1 is also of a heptahedron and has a hexagonal cross section but is composed of nine points. In general, the cross section of the (111) crystal face inverted pyramid is similar to an equilateral triangle because three of the edges are easier to etch away. The scanning electron microscopy image results show that the crystal indices are (100), (110) and (111), thereby demonstrating the correctness of the theoretical calculations. The index of crystal face has a one-to-one correspondence relationship with the inverted pyramid structure. Therefore, according to the inverted pyramid structure after anisotropic etching, we can measure the index of Si crystal face.
[1] Polman A, Knight M, Garnett E C, Ehrler B, Sinke W C 2016 Science 352 307
[2] Yagi T, Uraoka Y, Fuyuki T 2006 Sol. Energy Mater. Sol. Cells 90 2647
[3] Abdullah M F, Alghoul M A, Naser H, Asim N, Ahmadi S, Yatim B, Sopian K 2016 Renew. Sustain. Energy Rev. 66 380
[4] Zha J, Wang T, Pan C, Chen K, Hu F, Pi X, Su X 2017 Appl. Phys. Lett. 110 093901
[5] Zhao J, Wang A, Green M A, Ferrazza F 1998 Appl. Phys. Lett. 73 1991
[6] González-Díaz B, Guerrero-Lemus R, Díaz-Herrera B, Marrero N, Méndez-Ramos J, Borchert D 2017 J. Nanjing Univ. Aeronaut. Aeronaut. 49 744 (in Chinese) [沈鸿烈, 蒋晔 2017 南京航空航天大学学报 49 744]
[7] Park H, Kwon S, Lee J S, Lim H J, Yoon S, Kim D 2009 Sol. Energy Mater. Sol. Cells 93 1773
[8] Zhong S, Wang W, Zhuang Y, Huang Z, Shen W 2016 Adv. Funct. Mater. 26 4768
[9] Wang Y, Yang L, Liu Y, Mei Z, Chen W, Li J, Liang H, Kuznetsov A, Du X 2015 Sci. Rep. 5 10843
[10] Yang L, Liu Y, Wang Y, Chen W, Chen Q, Wu J, Kuznetsov A, Du X 2017 Sol. Energy Mater. Sol. Cells 166 121
[11] Zhao J, Wang A, Altermatt P, Green M A 1995 Appl. Phys. Lett. 66 3636
[12] Jiang Y, Shen H, Pu T, Zheng C, Tang Q, Gao K, Wu J, Rui C, Li Y, Liu Y 2017 Sol. Energy 142 91
[13] Shen H L, Jiang Y 2017 J. Nanjing Univ. Aeronaut. Aeronaut. 49 744 (in Chinese) [沈鸿烈, 蒋晔 2017 南京航空航天大学学报 49 744]
[14] Geng C, Zhen Y, Zhang Y Z, Yan H 2016 Acta Phys. Sin. 65 070201 (in Chinese) [耿超, 郑义, 张永哲, 严辉 2016 物理学报 65 070201]
[15] Wang K X, Feng S M, Xu H T, Tian J T, Yang S Q, Huang J H, Pei J 2012 Sci. Sin.: Technol. 42 643 (in Chinese) [王坤霞, 冯仕猛, 徐华天, 田嘉彤, 杨树泉, 黄建华, 裴骏 2012 中国科学: 技术科学 42 643]
[16] Tang Q, Shen H, Yao H, Gao K, Jiang Y, Yang W, Liu Y 2018 Sol. Energy 170 263
[17] Wang P, Xiao S, Jia R, Sun H, Dai X, Su G, Tao K 2018 Sol. Energy 169 153
[18] Campbell P, Wenham S R, Green M A 1993 Sol. Energy Mater. Sol. Cells 31 133
[19] Chen W, Liu Y, Yang L, Wu J, Chen Q, Zhao Y, Wang Y, Du X 2018 Sci. Rep. 8 3408
[20] Wu J, Liu Y, Chen Q, Chen W, Yang L, Wang Y, He M, Du X 2018 Sol. Energy 171 675
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[1] Polman A, Knight M, Garnett E C, Ehrler B, Sinke W C 2016 Science 352 307
[2] Yagi T, Uraoka Y, Fuyuki T 2006 Sol. Energy Mater. Sol. Cells 90 2647
[3] Abdullah M F, Alghoul M A, Naser H, Asim N, Ahmadi S, Yatim B, Sopian K 2016 Renew. Sustain. Energy Rev. 66 380
[4] Zha J, Wang T, Pan C, Chen K, Hu F, Pi X, Su X 2017 Appl. Phys. Lett. 110 093901
[5] Zhao J, Wang A, Green M A, Ferrazza F 1998 Appl. Phys. Lett. 73 1991
[6] González-Díaz B, Guerrero-Lemus R, Díaz-Herrera B, Marrero N, Méndez-Ramos J, Borchert D 2017 J. Nanjing Univ. Aeronaut. Aeronaut. 49 744 (in Chinese) [沈鸿烈, 蒋晔 2017 南京航空航天大学学报 49 744]
[7] Park H, Kwon S, Lee J S, Lim H J, Yoon S, Kim D 2009 Sol. Energy Mater. Sol. Cells 93 1773
[8] Zhong S, Wang W, Zhuang Y, Huang Z, Shen W 2016 Adv. Funct. Mater. 26 4768
[9] Wang Y, Yang L, Liu Y, Mei Z, Chen W, Li J, Liang H, Kuznetsov A, Du X 2015 Sci. Rep. 5 10843
[10] Yang L, Liu Y, Wang Y, Chen W, Chen Q, Wu J, Kuznetsov A, Du X 2017 Sol. Energy Mater. Sol. Cells 166 121
[11] Zhao J, Wang A, Altermatt P, Green M A 1995 Appl. Phys. Lett. 66 3636
[12] Jiang Y, Shen H, Pu T, Zheng C, Tang Q, Gao K, Wu J, Rui C, Li Y, Liu Y 2017 Sol. Energy 142 91
[13] Shen H L, Jiang Y 2017 J. Nanjing Univ. Aeronaut. Aeronaut. 49 744 (in Chinese) [沈鸿烈, 蒋晔 2017 南京航空航天大学学报 49 744]
[14] Geng C, Zhen Y, Zhang Y Z, Yan H 2016 Acta Phys. Sin. 65 070201 (in Chinese) [耿超, 郑义, 张永哲, 严辉 2016 物理学报 65 070201]
[15] Wang K X, Feng S M, Xu H T, Tian J T, Yang S Q, Huang J H, Pei J 2012 Sci. Sin.: Technol. 42 643 (in Chinese) [王坤霞, 冯仕猛, 徐华天, 田嘉彤, 杨树泉, 黄建华, 裴骏 2012 中国科学: 技术科学 42 643]
[16] Tang Q, Shen H, Yao H, Gao K, Jiang Y, Yang W, Liu Y 2018 Sol. Energy 170 263
[17] Wang P, Xiao S, Jia R, Sun H, Dai X, Su G, Tao K 2018 Sol. Energy 169 153
[18] Campbell P, Wenham S R, Green M A 1993 Sol. Energy Mater. Sol. Cells 31 133
[19] Chen W, Liu Y, Yang L, Wu J, Chen Q, Zhao Y, Wang Y, Du X 2018 Sci. Rep. 8 3408
[20] Wu J, Liu Y, Chen Q, Chen W, Yang L, Wang Y, He M, Du X 2018 Sol. Energy 171 675
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