13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Table 3. Threshold values of current density jth [MA/cm2] obtained from simulations Sample type 1: none 2:+- 3:- 4:+ Short 0.76 0.82 0.71 Reservoir length Long 0.77 0.76 0.88 0.67 5. Conclusions The numerical simulation technique was applied to evaluation of reservoir structure and AFD* gen -based evaluation of jth was carried out. We found that if a reservoir is located only on the cathode via, the threshold current density of EM damage is increased. And it was concluded that this phenomenon is caused by the change in atomic density distribution among a metal line. Acknowledgments This work was partly supported by JSPS under Grant-in-Aid for Scientific Research (B) 21360046. References [1] C. S. Hau-Riege, An introduction to Cu electromigration. Microelectronics Reliability, 44 (2004) 195-205. [2] H. Abé, K. Sasagawa, M. Saka, Electromigration failure of metal lines. International Journal of Fracture, 138 (2006) 219-240. [3] K. Sasagawa, T. Abo, Evaluation of threshold current density of electromigration damage in interconnect tree with angled Cu lines. Proc. of 12th EMAP (2010) Paper ID:230, 110-116. [4] M. H. Lin, K. P. Chang, K. C. Su, T. Wang, Effects of width scaling and layout variation on dual damascene copper interconnect electromigration. Microelectronics Reliability, 47 (2007) 2100-2108. [5] C. -K. Hu, R. Rosenberg, K. Y. Lee, Electromigration path in Cu thin-film lines. Applied Physics Letters, 74 (1999) 2945-2947. [6] K. Sasagawa, M. Hasegawa, M. Saka, H. Abé, Governing parameter for electromigration damage in the polycrystalline line with a passivation layer. Journal of Applied Physics, 91 (2002) 1882-1890. [7] M. Hasegawa, K. Sasagawa, M. Saka, H. Abé, Expression of a governing parameter for electromigration damage on metal line ends. Proc. of IPACK’03 (CD-ROM), ASME (2003) IPACK2003-35064. [8] Z. S. Choi, R. Ronig, C. V. Thompson, Activation energy and prefactor for surface electromigration and void drift in Cu interconnects. Journal of Applied Physics, 102 (2007) 083509. [9] C. K. Hu, L. Gignac, R. Rosenberg, Electromigration of Cu/low dielectric constant interconnects. Microelectronics Reliability, 46 (2006) 213-231. [10] C. L. Gan, C. V. Thompson, K. L. Pey, W. K. Choi, Experimental characterization and modeling of the reliability of three-terminal dual-damascene Cu interconnect trees. Journal of Applied Physics, 94 (2003) 1222-1228. [11] R. S. Figliola, D. E. Beasley, Theory and design for mechanical measurements, Second-ed. John Wiley & Sons, Inc., New York, 1995. [12] K. Sasagawa, M. Hasegawa, N. Yoshida, M. Saka, H. Abé, Prediction of electromigration failure in passivated polycrystalline line considering passivation thickness. Proc. of InterPACK’03 (CD-ROM), ASME (2003) IPACK2003-35065.
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