Size effect on Distributions of the Times To Failure and Times To Transformation

О. А. Bobrov, M. O. Pasichnyy, O. Yu. Liashenko, A. M. Gusak

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.


Keywords


size effect; times to failure; 2D phase transformation; probability distribution; Kolmogorov-Avrami kinetics; flip-chip technology

References


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