Study on the Length Distribution and the Growth Rate of Sn Whiskers Generated on Sn/Cu Plating System

In this study, the occurrence and growth behavior of many whiskers occurred on the Sn/Cu plating system was observed over a long period of more than 1 year. The growth behavior of whiskers was analyzed statistically and quantitatively using the whisker length distributions and their temporal change. The whisker length distribution was approximated well with the 3 parameter Weibull distribution. Of the three parameters, the location parameter γ was constant at 4.9 μm regardless of the elapsed time. The scale parameter α increased at the beginning of the time and did not change after reaching the constant value. In addition, the scale parameter α almost agreed with the average length of whiskers. The shape parameter m gradually approached from the initial value of 2 to the value of 1 in the later time. In other words, the whisker length distribution was initially in the form of a lognormal distribution, but it changed to an exponential distribution over time. The relationship between whisker length l and an elapsed time t can be approximated well by the exponential function of expression, l = l0{1 − exp(−klt)} and the whisker growth rule is expressed by expression, dl⁄dt = l0klexp(−klt) = kl(l0 − l). Here, l0 is the whisker length at saturation and kl is the experimental constant. Relatively short whiskers with length 20 to 70 μm were slow in growth rate and stopped growing at an early stage. On the other hand, long whiskers grown to over 200 μm grow faster and longer than short whiskers, but finally stopped growing.