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32 SMT Magazine • February 2015 problem warrants new theoretical approaches. They need to be made quantitative in order to allow experimental verifications and satisfy the standard scientific criteria. This paper discusses one such approach based on the electrostatics of metal surfaces. It may appear rather contradictory in the light of a common perception (taught in the under- graduate physics) that neutral metal surfaces cannot have electric charges or fields. We will see however that the latter is true only for ideal metal surfaces (containing no imperfections, such as grain boundaries, contamination, dis- locations, etc.), and that real metal surfaces can present rich electrostatics including strong elec- tric fields significantly varying across the sur- face. A theory of metal whiskers presented here is consistent with many published observations and provides some quantitative analytical re- sults. The appearance of whiskers is described as the electric field induced nucleation of needle- shaped particles. It is triggered by the energy gain F E =−p⋅E due to the induced whisker dipole p=αE in the electric field E, where α is the po- larizability. The latter is anomalously strong for the needle geometry. The nucleated whiskers continue growing to further decrease their en- ergies in the electric field. 1. More specifically, the theory is based on the concept of strong electric fields, E≤0.01-1 MV/cm, in the sub-micron proximity of metal surfaces. Such fields can be generated by surface imperfections including "wrong" grain orien- tations, deformations, oxides, dislocations, or contamination. The importance of this con- cept is that it offers a unique pattern consistent with the observed wide variety of factors, in the first glance unrelated to each other, all having strong effects on whisker growth: stresses of me- chanical and electric nature, material morphol- ogy and composition, surface contaminations, including the effects of humidity. According to that concept, all these factors are responsible for significant electric fields in the near surface region of a metal. The surface electric field be- comes a common denominator of whisker driv- ing forces. This new hypothesis remains to be carefully tested against all the available data and focused experiments including purposely created electric fields. 2. Being overall neutral these metal surfaces are composed of oppositely charged patches formed as a result of electron redistribution minimizing the system free energy. The patches are characterized by certain surface charge den- sity and dimensions L~1−10 μm, maybe even shorter, ~0.1 mm, for fine crystalline grain struc- ture. These patches form a sort of random chess board as shown in the right display of Figure 2. 3. The phenomenon of whisker nucleation and growth is attributed to the electrostatic en- ergy gain due to strong polarization of the new- ly created needle-shaped metal particles. The conception of whiskers is described based on the (earlier developed) theory of field induced nucleation that predicts needle-shaped embry- os h≤100 nm in length and d~1–10 nm in di- ameter. The mechanism is quite similar to that explaining the fact that amber or plastic comb attract small pieces of paper: The electric field polarized small particles making them electric eLeCTrOSTaTIC MeCHaNISM OF NuCLeaTION aNd GrOWTH OF MeTaL WHISKerS continues Feature Figure 2: A sketch of the electric field e near a metal surface, cross-sectional (left) and 3D (right) views.