Size effect on Distributions of the Times To Failure and Times To Transformation
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Abstract
Failure of finite size 2D solder contact is equivalent to phase transformation in a finite 2D system. First-order phase transformations proceed due to multiple nucleation and consequent growth of new phase grains inside the old phase matrix. The nucleation and growth of the pancake voids due to the electromigration along the tin/copper interface are considered. This problem is essential due to the flip-chip technology and the miniaturization of the solder bump size. Kinetics of this process is usually described by KJMA equations (Kolmogorov-Johnson-Mehl -Avrami). Size dependencies of Times To Failure (TTF) and Times To Transformation (TTT) distributions and their main characteristics are modeled. The danger of early failures due to the broadening of TTF distribution makes the size effect study an important issue in microelectronics. Broadening of TTT distribution is essential for phase transformations in the ensembles of micro- and nanoparticles. With decreasing size the TTF and TTT distributions steadily transform from the normal distribution to Poisson one via lognormal or Weibull (with changing optimized parameters). Histograms of the computer experiments were fitted by various distributions. The best approximations were obtained by our own distribution, by lognormal distribution and by 3-parametric Weibull distribution. Analytical approximations for transient regimes are suggested.
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References
Tu K.-N. (2010). Electronic thin-film reliability. New York: Cambridge University Press.
Tu K.-N. (2007). Solder joint technology. New York: Springer.
Tu K.-N., Gusak A. M. (2014). Kinetics in nanoscale materials. New Jersey: John Wiley & Sons.
Kolmogorov A. N. (1937). On the Statistical Theory of the Crystallization of Metals. Izv. AN SSSR. Ser. matem. (Bulletin of the Academy of Sciences of the USSR, Mathematics Series), 1(3), 355-359.
Avrami M. (1939). Kinetics of phase change. I General theory. The Journal of Chemical Physics, 7(12), 1103-1112.
Johnson W. A., Mehl R. F. (1939). Reaction Kinetics in Processes of Nucleation and Growth. Transactions of the American Institute of Mining and Metallurgical Engineers, 135, 416-442.
Vairagar A. V., Mhaisalkar S. G., Krishnamoorthy A., Tu K. N., Gusak A. M., Meyer M. A., Zschech E. (2004). In situ observation of electromigration-induced void migration in dual-damascene Cu interconnect structures. Applied Physics Letters, 85(13), 2502-2504.
Tian T., Gusak A. M., Liashenko O. Y., Han J. K., Choi D., Tu K. N. (2012). A new physical model for life time prediction of Pb-free solder joints in electromigration tests. Electronic Components and Technology Conference (ECTC), 2012 IEEE 62nd, 741-746.
Delcourt O., Descamps M., Hilhorst H. J. (1991). Size effect in a nucleation and growth transformation. Ferroelectrics, 124(1), 109-114.
Berg B. A., Dubey S. (2008). Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory. Physical Review Letters, 100(16), 165702.
Alekseechkin N. V. (2008). On the kinetics of phase transformation of small particles in Kolmogorov’s model. Condens Matter Physics, 11(4(56)), 597-613.