考虑晶粒尺寸效应的超薄(1050 nm) Cu电阻率模型研究

王宁; 董刚; 杨银堂; 陈斌; 王凤娟; 张岩

doi:10.7498/aps.61.016802

摘要

结合Marom模型与实验数据, 给出了晶粒尺寸与金属薄膜厚度的关系式. 基于已有的理论模型, 针对厚度为1050 nm Cu薄膜, 考虑到表面散射与晶界散射以及电阻率晶粒尺寸效应, 提出一种简化电阻率解析模型. 结果表明, 在1020 nm薄膜厚度范围内, 考虑晶粒尺寸效应后的简化模型与现有实验数据符合得更好. 相对于Lim, Wang与Marom模型, 所提模型的相对标准差分别降低74.24%, 54.85%, 78.29%.

关键词:

Abstract

A relation between grain size and metal film is given by combining the Marom model with experiment data. Based on available theory model, taking into account the surface scattering, boundary scattering and grain size effect, an analytical resistivity model is presented for the 1050 nm thick Cu films. In particular, within a range of 1020 nm, the findings show that the proposed model with consideration of grain size effects is in good agreement with experimental results. Compared with Lim, Wang and Marom' models, the proposed method can reduce the relative standard deviations by 74.24%, 54.85% and 78.29%, respectively.

Keywords:

作者及机构信息

1.
西安电子科技大学微电子所, 宽禁带半导体材料与器件教育部重点实验室, 西安 710071

基金项目: 国家自然科学基金(批准号: 60606006)和国家杰出青年基金(批准号: 60725415)资助的课题.

Authors and contacts

1.
Key Laboratory of Ministry of Education for Wide Band-Gap Semiconductor Materials and Devices, Microelectronics Institute, Xidian University, Xian 710071, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60606006) and the National Science Fund for Distinguished Young Scholars of China (Grant No. 60725415).

参考文献

[1]	Sun T, Yao B, Warren A P, Barmak K, Toney M F, Peale R E, Coffey K R 2010 Phys. Rev. B 81 155454
[2]	Feldman B, Dunham S T 2009 Appl. Phys. Lett. 95 222101
[3]	Sun T, Yao B, Warren A P, Barmak K, Toney M F, Peale R E, Coffey K R 2009 Phys. Rev. B 79 41402
[4]	Barnat E V, Nagakura D, Wang P I, Lu T M 2002 J. Appl. Phys. 91 1667
[5]	Zhu Z M, Wang D J, Yang Y T 2010 Chin. Phys. B 19 097803
[6]	Bid A, Bora A, Raychaudhuri A K 2006 Phys. Rev. B 74 35426
[7]	Steinh Ogl W, Schindler G U, Steinlesberger G, Engelhardt M 2002 Phys. Rev. B 66 75414
[8]	Feldman B, Deng R, Dunham S T 2008 J. Appl. Phys. 103 113715
[9]	Dong G, Yang Y, Chai C C, Yang Y T 2010 Chin. Phys. B 19 110202
[10]	Dong G, Xue M, Li J W, Yang Y T 2011 Acta Phys. Sin. 60 036601 (in Chinese) [董刚, 薛萌, 李建伟, 杨银堂 2011 60 036601]
[11]	Dong G, Liu J, Xue M, Yang Y T 2011 Acta Phys. Sin. 60 046602 (in Chinese) [董刚, 刘嘉, 薛萌, 杨银堂 2011 60 046602]
[12]	Liu H D, Zhao Y P, Ramanath G, Murarka S P, Wang G C 2001 Thin Solid Films 384 151
[13]	Lim J W, Isshiki M 2006 J. Appl. Phys. 99 94909
[14]	Mayadas A F, Shatzkes M 1970 Phys. Rev. B 1 1382
[15]	Marom H, Eizenberg M 2004 J. Appl. Phys. 96 3319
[16]	Graham R L, Alers G B, Mountsier T, Shamma N, Dhuey S, Cabrini S, Geiss R H, Read D T, Peddeti S 2010 Appl. Phys. Lett. 96 42116
[17]	Wang M, Zhang B, Zhang G P, Yu Q Y, Liu C S 2009 J. Mater. Sci. Technol. 25 699
[18]	Emre Yarimbiyik A, Schafft H A, Allen R A, Vaudin M D, Zaghloul M E 2009 Microelectron. Eng. 49 127
[19]	Mayadas A F, Shatzkes M, Janak J F 1969 Appl. Phys. Lett. 14 345
[20]	Barmak K, Sun T, Coffey K R 2010 AIP Conference Proceedings Stress-induced Phenomena in Metallization: 11th International Workshop Bad Schandau, Germany April 12–14, 2010 p12
[21]	Onuki J, Khoo K, Sasajima Y, Chonan Y, Kimura T 2010 J. Appl. Phys. 108 44302
[22]	Carpenter D T, Rickman J M, Barmak K 1998 J. Appl. Phys. 84 5843
[23]	Marom H, Ritterband M, Eizenberg M 2006 Thin Solid Films 510 62
[24]	Sun T, Yao B, Warren A, Kumar V, Barmak K, Coffey K R 2008 2008 IEEE International Interconnect Technology Conference Burlingame, United States, June 1–4, 2008 p141
[25]	Liu W, Yang Y, Asheghi M 2006 Thermomechanical Phenomena in Electronic Systems -Proceedings of the Intersociety Conference, San Diego, United States, May 30–June 2, 2006 p1171
[26]	Shojaei Zadeh S, Zhang S, Liu W, Yang Y, Sadeghipour S M, Asheghi M, Sverdrup P 2004 Thermomechanical Phenomena in Electronic Systems-Proceedings of the Intersociety Conference Las Vegas, NV United States, June 1–4, 2004 p575
[27]	Fenn M, Akuetey G, Donovan P E 1998 J. Phys.: Condens Matter 10 1707
[28]	Fenn M, Petford Long A K, Donovan P E 1999 J. Magn. Magn. Mater. 198 231
[29]	Marom H, Eizenberg M 2006 J. Appl. Phys. 99 123705
[30]	Rossnagel S M, Kuan T S 2004 J. Vac. Sci. Technol. B 240
[31]	Messaadi S, Medouer H, Daamouche M 2010 J. Alloys Compd. 489 609

施引文献

[1]	Sun T, Yao B, Warren A P, Barmak K, Toney M F, Peale R E, Coffey K R 2010 Phys. Rev. B 81 155454
[2]	Feldman B, Dunham S T 2009 Appl. Phys. Lett. 95 222101
[3]	Sun T, Yao B, Warren A P, Barmak K, Toney M F, Peale R E, Coffey K R 2009 Phys. Rev. B 79 41402
[4]	Barnat E V, Nagakura D, Wang P I, Lu T M 2002 J. Appl. Phys. 91 1667
[5]	Zhu Z M, Wang D J, Yang Y T 2010 Chin. Phys. B 19 097803
[6]	Bid A, Bora A, Raychaudhuri A K 2006 Phys. Rev. B 74 35426
[7]	Steinh Ogl W, Schindler G U, Steinlesberger G, Engelhardt M 2002 Phys. Rev. B 66 75414
[8]	Feldman B, Deng R, Dunham S T 2008 J. Appl. Phys. 103 113715
[9]	Dong G, Yang Y, Chai C C, Yang Y T 2010 Chin. Phys. B 19 110202
[10]	Dong G, Xue M, Li J W, Yang Y T 2011 Acta Phys. Sin. 60 036601 (in Chinese) [董刚, 薛萌, 李建伟, 杨银堂 2011 60 036601]
[11]	Dong G, Liu J, Xue M, Yang Y T 2011 Acta Phys. Sin. 60 046602 (in Chinese) [董刚, 刘嘉, 薛萌, 杨银堂 2011 60 046602]
[12]	Liu H D, Zhao Y P, Ramanath G, Murarka S P, Wang G C 2001 Thin Solid Films 384 151
[13]	Lim J W, Isshiki M 2006 J. Appl. Phys. 99 94909
[14]	Mayadas A F, Shatzkes M 1970 Phys. Rev. B 1 1382
[15]	Marom H, Eizenberg M 2004 J. Appl. Phys. 96 3319
[16]	Graham R L, Alers G B, Mountsier T, Shamma N, Dhuey S, Cabrini S, Geiss R H, Read D T, Peddeti S 2010 Appl. Phys. Lett. 96 42116
[17]	Wang M, Zhang B, Zhang G P, Yu Q Y, Liu C S 2009 J. Mater. Sci. Technol. 25 699
[18]	Emre Yarimbiyik A, Schafft H A, Allen R A, Vaudin M D, Zaghloul M E 2009 Microelectron. Eng. 49 127
[19]	Mayadas A F, Shatzkes M, Janak J F 1969 Appl. Phys. Lett. 14 345
[20]	Barmak K, Sun T, Coffey K R 2010 AIP Conference Proceedings Stress-induced Phenomena in Metallization: 11th International Workshop Bad Schandau, Germany April 12–14, 2010 p12
[21]	Onuki J, Khoo K, Sasajima Y, Chonan Y, Kimura T 2010 J. Appl. Phys. 108 44302
[22]	Carpenter D T, Rickman J M, Barmak K 1998 J. Appl. Phys. 84 5843
[23]	Marom H, Ritterband M, Eizenberg M 2006 Thin Solid Films 510 62
[24]	Sun T, Yao B, Warren A, Kumar V, Barmak K, Coffey K R 2008 2008 IEEE International Interconnect Technology Conference Burlingame, United States, June 1–4, 2008 p141
[25]	Liu W, Yang Y, Asheghi M 2006 Thermomechanical Phenomena in Electronic Systems -Proceedings of the Intersociety Conference, San Diego, United States, May 30–June 2, 2006 p1171
[26]	Shojaei Zadeh S, Zhang S, Liu W, Yang Y, Sadeghipour S M, Asheghi M, Sverdrup P 2004 Thermomechanical Phenomena in Electronic Systems-Proceedings of the Intersociety Conference Las Vegas, NV United States, June 1–4, 2004 p575
[27]	Fenn M, Akuetey G, Donovan P E 1998 J. Phys.: Condens Matter 10 1707
[28]	Fenn M, Petford Long A K, Donovan P E 1999 J. Magn. Magn. Mater. 198 231
[29]	Marom H, Eizenberg M 2006 J. Appl. Phys. 99 123705
[30]	Rossnagel S M, Kuan T S 2004 J. Vac. Sci. Technol. B 240
[31]	Messaadi S, Medouer H, Daamouche M 2010 J. Alloys Compd. 489 609

[1]	刘雨, 田强, 王新艳, 关雪飞. 基于单向测量超声背散射系数的晶粒尺寸评价高效方法. , 2024, 73(7): 074301. doi: 10.7498/aps.73.20231959
[2]	厉桂华, 张梦雅, 马慧, 田悦, 焦安欣, 郑林启, 王畅, 陈明, 刘向东, 李爽, 崔清强, 李冠华. 低温促进表面等离激元共振效应及肌酐的超灵敏表面增强拉曼散射探测. , 2022, 71(14): 146101. doi: 10.7498/aps.71.20220151
[3]	刘亦轩, 李昭, 汤浩正, 逯景桐, 李敬锋, 龚文, 王轲. 晶粒尺寸对钙钛矿型压电陶瓷压电性能的影响. , 2020, 69(21): 217704. doi: 10.7498/aps.69.20201079
[4]	程自强, 石海泉, 余萍, 刘志敏. 银纳米颗粒阵列的表面增强拉曼散射效应研究. , 2018, 67(19): 197302. doi: 10.7498/aps.67.20180650
[5]	刘英光, 张士兵, 韩中合, 赵豫晋. 纳晶铜晶粒尺寸对热导率的影响. , 2016, 65(10): 104401. doi: 10.7498/aps.65.104401
[6]	周旺, 牛书通, 闫学文, 白雄飞, 韩承志, 张鹛枭, 周利华, 杨爱香, 潘鹏, 邵剑雄, 陈熙萌. 100-keV质子在聚碳酸酯微孔膜中传输的动态演化过程. , 2016, 65(10): 103401. doi: 10.7498/aps.65.103401
[7]	叶通, 高云, 尹彦. 利用聚碳酸酯模板制备的金纳米棒的表面增强Raman散射效应研究. , 2013, 62(12): 127801. doi: 10.7498/aps.62.127801
[8]	李静, 冯妍卉, 张欣欣, 黄丛亮, 杨穆. 考虑界面散射的金属纳米线热导率修正. , 2013, 62(18): 186501. doi: 10.7498/aps.62.186501
[9]	杨卫明, 刘海顺, 敦超超, 赵玉成, 窦林名. Fe基纳米晶合金晶粒尺寸反常变化的物理机制. , 2012, 61(10): 106802. doi: 10.7498/aps.61.106802
[10]	黄茜, 熊绍珍, 赵颖, 张晓丹. 表面等离子激元非线性表面增强拉曼散射效应. , 2012, 61(15): 157801. doi: 10.7498/aps.61.157801
[11]	侯海虹, 孙喜莲, 田光磊, 吴师岗, 马小凤, 邵建达, 范正修. 利用总积分散射仪对光学薄膜表面散射特性的研究. , 2009, 58(9): 6425-6429. doi: 10.7498/aps.58.6425
[12]	刘玮书, 张波萍, 李敬锋, 张海龙, 赵立东. Co1-xNixSb3-ySey热电输运中晶界和点缺陷的耦合散射效应. , 2008, 57(6): 3791-3797. doi: 10.7498/aps.57.3791
[13]	陈雷, 楼祺洪, 王之江, 董景星, 魏运荣. 纳米ZnO粉末中随机激光现象. , 2006, 55(2): 920-922. doi: 10.7498/aps.55.920
[14]	王英龙, 周阳, 褚立志, 傅广生, 彭英才. Ar环境气压对脉冲激光烧蚀制备纳米Si晶粒平均尺寸的影响. , 2005, 54(4): 1683-1686. doi: 10.7498/aps.54.1683
[15]	董正超. 多层金属圆柱线中量子输运的表面和界面散射效应. , 1999, 48(1): 127-133. doi: 10.7498/aps.48.127
[16]	董正超, 盛利, 邢定钰, 董锦明. 金属双层膜中量子输运的表面和界面散射效应. , 1996, 45(2): 249-257. doi: 10.7498/aps.45.249
[17]	郑海荣, 苟增光, 莫育俊. CI~-对铜表面上表面增强喇曼散射效应的影响. , 1995, 44(2): 287-291. doi: 10.7498/aps.44.287
[18]	傅石友, 张鹏翔, 李秀英. 氯离子对银胶中表面增强喇曼散射效应的影响. , 1991, 40(12): 1915-1921. doi: 10.7498/aps.40.1915
[19]	刘慕仁, 孔令江, 江峰. Frish-Hasslecher-Pomeau流体力学模型的平均自由程. , 1991, 40(11): 1736-1740. doi: 10.7498/aps.40.1736
[20]	施建青, 李国强, 高琴. 核子平均自由程温度效应的自洽半经典研究. , 1990, 39(1): 24-29. doi: 10.7498/aps.39.24

计量

文章访问数: 7425
PDF下载量: 493
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板