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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

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
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  • 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%.
    • 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.
    [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 物理学报 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 物理学报 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]

    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 物理学报 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 物理学报 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

  • 引用本文:
    Citation:
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出版历程
  • 收稿日期:  2011-05-07
  • 修回日期:  2011-07-01
  • 刊出日期:  2012-01-05

考虑晶粒尺寸效应的超薄(1050 nm) Cu电阻率模型研究

  • 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.

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%.

English Abstract

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