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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.
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Keywords:
- surface scattering /
- boundary scattering /
- grain size effects /
- mean free path
[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
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[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
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