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42 SMT Magazine • February 2015 work functions. The free electrons will move between these metals to equalize their Fer- mi levels. This makes the metals electrically charged. The same phenomenon underlies the existence of Schottky barriers and p-n junctions in semiconductors. In the case of metal cou- ples, it is known as the source of the galvanic action that occurs when two electrochemically dissimilar metals are in contact and a conduc- tive path occurs for electrons and ions to move from one metal to the other. Furthermore, one can imagine a binary mixture of chemically dif- ferent metal grains where the balance of Fermi energy makes the grains of two types charged oppositely. The above cases (i) and (ii) are schematically illustrated in Figure 13. More specifically, the regions of different surface potential (patches) may be due to the polycrystallinity of a metal. The work function will vary between regions of specific grain ori- entations (Figure 14) by typically a few tenths of a volt; these different grain orientations will be qualitatively similar to the above example (iii) of binary metal mixtures. Patch structure may also arise from the presence of adsorbed elements and compounds; that contamination is qualitatively similar to the above mentioned example (ii) of the chemical composition varia- tions. Certain features of surface morphology, particularly, its roughness, may result in the electron redistribution caused by the corre- sponding modulations of microscopic struc- ture parameters similar to the above example (i). They can be caused by dislocations, stress- induced spots of different structure phases, or general electric deformation coupling in combi- nation with stress-induced buckling. Local charges due to stress-induced oxide cracking or ion trapping under the whisker growing layer (say, Sn on Cu substrate) are con- ceivable sources of the above considered surface electric fields as well. Therefore, a surface, that is ideally electrically uniform, may acquire electric surface structure. Here we assume a simple mod- el of uncorrelated charge patches on a metal surface characterized by two parameters: charac- teristic electron surface charge density ne (elec- trons per cm 2 ), and the linear dimension L. In reality, the charge distribution in patches can be nonuniform, possibly concentrating along grain boundaries or other structural imperfections. However, these conceivable complications fall beyond the present scope. The charged patch model is illustrated in Figures 2, 5, and 15. Figure 13: variations in chemical potentials in a locally deformed (left) and locally chemically non-uniform (right) metals. Figure 14: Sketches of wrong grain facets orientation (left) and oxides or other dielectric layers capable of charge accumulation, or ionic contamination spots (right). eLeCTrOSTaTIC MeCHaNISM OF NuCLeaTION aNd GrOWTH OF MeTaL WHISKerS continues Feature