On the growth behavior of multiple whiskers generated on Sn/Cu plating −Predicting the growth behavior of the longest whiskers using whisker length distributions

Although several studies have examined whisker growth on Sn/Cu plating, research on whisker growth laws remain limited, particularly regarding the collective growth characteristics of multiple whiskers on plated surfaces. In this study, tin-plated copper (Sn/Cu) samples were prepared and used to observe the generation and growth characteristics of numerous whiskers, which are known to grow on Sn-plated surfaces over a long time (380 days). Moreover, the statistical distribution of the lengths of multiple whiskers occurring on the sample surfaces over a certain period (hereafter referred to as whisker length distribution) was focused on. The whisker length distribution was approximated using a three-parameter Weibull distribution. The whisker growth rate (dl w /dt) could be quantitatively evaluated by focusing on the change in the whisker length distribution over time. The growth behavior of the longest whiskers, which pose the highest risk, was assessed by examining l w at F(l w ) = 99.9%, while the growth of whiskers with average length was characterized using l w at F(α) = 63.2%. Based on the experimental observations and chemical reaction kinetics, a whisker growth law and a growth rate equation were defined. Good agreement was observed between the whisker growth law and the experimental results. • Whisker length distribution can be well approximated by a three-parameter Weibull distribution. • At time t, whisker growth rate dl w /dt is proportional to (l wSAT −l w ). • Based on the reaction rate process theory, whisker growth law and whisker growth rate expressions are proposed. • Based on the whisker length distribution, we investigated the growth behavior of whiskers by focusing on the whisker lengths at several cumulative probabilities F(l w ). • The growth behavior of the longest whisker can be understood by focusing on the change in l w over time at F(l w ) = 99.9% in the whisker length distribution. • IMCAR/IMCARSAT, nw/nwSAT, and α/αSAT initially increase with time and gradually converge to unity, exhibiting similar trends.