Issue link: https://iconnect007.uberflip.com/i/455818
38 SMT Magazine • February 2015 cant energy barrier. The statistics of these block- ing regions (barriers) determines the whisker length statistics. It is derived to be close to log- normal in the proximity of the most likely sizes, while decaying much faster for sizes well above the average. It should be emphasized however that such blocking energy barriers have finite heights WB. Therefore, they can be overcome after significant waiting times t W =t 0 exp(W B / kT) allowing for sufficient number of attempt- to-escape events, each taking time t 0 where kT is the thermal energy. This explains the obser- vation of whiskers resuming growth after a con- siderable time (approaching a year) of lethargy. Based on this reasoning and using the standard techniques of the physics of random systems, it is possible to derive the probabilistic distribu- tion of whisker length. Its explicit mathemati- cal form turns out to be cumbersome; however, the qualitative features are quite simple and are illustrated in Figure 9. 7. The concept of field induced nucleation and growth of metal filaments is neither unique nor very new; in a quantitative form it was put forward in the recently developed field induced nucleation theory. Here we would like to men- tion some applications of that concept concern- ing objects that may be related to metal whis- kers in their underlying physics. Our first example is represented by the shunting entities observed in various elec- tronic elements (mostly in semiconductor and insulator films) that are conductive filaments developed in the host of relatively insulating materials subject to electric bias. There is a con- siderable R&D activity, often in industrial set- tings, including different technologies, such as microelectronics, thin film photovoltaics, light emitting diodes, etc., in the course of which the problem is considered from different points of view, often ignoring a possibility of common mechanism based on the field induced electro- static energy gain. Side by side with the detrimental effects of shunting, there is a strong research effort to understand possible beneficial effects of for- mation of conductive filaments under electric bias. They include, first of all, the technologies of phase change and resistive memories, where the structure states with and without the con- ductive filament are used as the two logic states of the memory element. Some illustrations are given in Figure 10. Shown in Figure 11 are needle-like structures that appear on the surface of a liquid metal in a strong perpendicular electric field. The nature Figure 8: in the flat portion of the electrostatic free energy F e , the whisker surface energy F a forms a barrier W b in the total whisker energy F=F a +F e . in this diagram, W is the whisker nucleation barrier. Figure 9: an example of the predicted probabi- listic distribution of whisker lengths vs. its best fit approximation by the log-normal distribution. note that the best fit (least square) approxima- tion provides good fit in the middle part of the distribution, while it is less successful in the re- gions of both very long and very short whiskers. eLeCTrOSTaTIC MeCHaNISM OF NuCLeaTION aNd GrOWTH OF MeTaL WHISKerS continues Feature