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Figure Legend: Tin whiskers on (matte) tin-plated copper alloy lead-frames used for integrated circuit (IC) terminations. Courtesy of Peter Bush (University of Buffalo-SUNY)
Phys. Rev. Applied 1, 044001 – Published 15 May 2014.
V. G. Karpov
Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606, USA.
Abstract
The nature of metal whiskers remains a mystery after several decades of research. No single pattern has been established to explain the observed whisker correlations with structural defects, mechanical stresses, and contaminations. Here, it is proposed that the electric charges on metal surfaces and their induced local electric fields can present such a pattern. These charges can be produced by various factors, such as surface imperfections, contaminations, oxide states, grain boundaries and random orientations of grains in the polycrystalline surface, and external or internal mechanical stresses (through the deformation potential). The sign of such surface charges varies between different locations (i. e. the electrons are redistributed nonuniformly) forming a random chess board of negatively and positively charged patches with the characteristic linear dimensions in the range of microns. From the energy point of view, the existence of metal whiskers is attributed to the energy gain due to electrostatic polarization of metal filaments in the near surface electric field. In other words, the filaments arise because similar charges repel one another, producing an outward stress. Some of these like charges are expelled upward by creating metal whiskers. This process can be described as the electrostatically driven filament nucleation; it can be especially efficient where the material is locally weak. Following nucleation is the whisker growth stage. It is shown that whiskers first grow at extremely slow rates which accelerate drastically and then remain time independent as the whisker lengths exceed the characteristic linear dimension of the charge patches. Beyond that length, the whisker growth is affected by random fields of the neighboring patches. In some regions, such fields create energetically unfavorable electric polarization that prevents further growth. The statistics of such unfavorable regions calculated in the proposed theory determines the probabilistic distribution of whisker lengths; it is shown to be approximately log-normal. Overall, the proposed theory provides closed form expressions and quantitative estimates for the whisker nucleation and growth rates and the range of whisker parameters. Many questions remain open. For example, this theory can’t yet describe the materials science aspects, such as whisker growth down to the detail of individual metal grains and why some metals are prone to more whiskers than others; neither has it described inter-whisker interactions and their 3D evolution in random electric fields.
