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44 SMT Magazine • February 2015 10. Conclusions The above theory describes metal whickers as a result of metal nucleation and growth in ran- dom electric fields induced by charged patches on metal surfaces. The underlying approaches are typical of the physics of phase transitions and disordered systems. This work presents the first whisker theory yielding simple analytical results more or less consistent with the observa- tions. The successes, the remaining questions, and possible experimental verifications of this theory are summarized next. 10.1 What is understood 1) Why whiskers are metallic: High (metal- lic) electric polarizability is required for suffi- cient energy gain due to whisker formation in external (surface) electric fields. 2) Why whiskers grow more or less perpen- dicular to the surface and yet can have con- figurations parallel to the surface: Such are the dominating directions of the surface electric field that include significant fluctuation along the surface. 3) Why whisker parameters are broadly sta- tistically distributed: This reflects fluctuations in metal surface fields induced by mutually un- correlated charged patches. 4) Correlation between whiskers and ver- satile morphology factors, such as (i) grains whose orientation is different from the major orientation of the tin film, (ii) dislocations and dislocation loops, and (iii) mechanical stresses capable of surface buckling, surface contami- nations; all related to local surface charges and their induced electric fields. Some metals are more prone to develop whiskers because they can easier form charged patches by absorbing ions, and creating dislocations, grain boundar- ies, or stresses. 5) Why external electric bias can significant- ly affect whisker growth. (It is rather difficult, yet possible, beyond this paper framework, to understand how the electric bias can be not a significant factor in whisker kinetics.) 6) Why the characteristic whisker evolution exhibits a certain pattern: long incubation pe- riod followed by almost constant growth rate that eventually saturates. The predicted incu- bation (dormant) time and subsequent growth rate agree with the observations. 7) Why whisker parameters are broadly dis- tributed statistically. The predicted distribution of whisker lengths is close to the observed log- normal statistics around its central part. 10.2 What is not understood 1) The microscopic nature of whiskers, their correlation with specific surface defects, chemi- cal aspects of whisker development. 2) The role of whisker crystalline structure in their evolution process. 3) Whisker growth in 3D random electric field. This includes whisker winding and kink- ing. 4) Possible role of surface (or grain bound- ary) diffusion limiting whisker growth. 5) Possible hydrodynamic drag moving sur- face material uniformly along with ions. 6) Inter-whisker interactions limiting their concentration and affecting growth. This in- cludes the stage of whisker ripening. 7) Role of Pb in suppressing whiskering. 10.3 Possible experimental verification The predicted dependencies of nucleation and growth kinetics vs. electric field, tempera- ture, and controlled contamination could be verified experimentally. 1) Whisker nucleation and growth in exter- nal electric fields. This can be attempted, e.g., in flat plate capacitor configuration for a whis- ker inside SEM where the electric field is readily controlled, or under e-beam in an accelerator. In all cases, care should be taken to avoid signif- icant Joule heating and/or electron drag effects (i.e., using voltage rather than current power source). An ongoing project in our group has generated preliminary results showing that the electric field in combination with high relative humidity can lead to anomalously rapid whis- ker growth (one week under 3000 V/cm in a capacitive configuration; 10–20 hours of medi- cal accelerator e-beam charging a glass substrate under Sn film). 2) Whisker nucleation and growth under controlled contamination of metal surface with solutions of charged nano particles. 3) Whisker nucleation and growth under the conditions of strong surface electric fields eLeCTrOSTaTIC MeCHaNISM OF NuCLeaTION aNd GrOWTH OF MeTaL WHISKerS continues Feature

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