FEATURE Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers by V. G. Karpov parameters and predicts statistical distribution DepArTMenT OF pHYSiCS AnD ASTrOnOMY, of their lengths. The details of the underlying univerSiTY OF TOleDO mathematical treatments have been presented in a recent publication[1] . Here, the emphasis is on a more intuitive level, and the references are Abstract omitted. Metal whiskers can grow across leads of Metal whiskers are hair-like protrusions ob- electric equipment causing short circuits, arc- served at surfaces of some metals; tin and zinc ing, and raising significant reliability issues. examples are illustrated in Figure 1. In spite The nature of metal whiskers remains a mystery of being omnipresent and leading to multiple after several decades of research. Here, their failure modes in the electronics industry, the existence is attributed to the energy gain due mechanism behind metal whiskers remains to electrostatic polarization of metal filaments unknown after more than 60 years of research. in the electric field induced by a metal surface. While not formally proclaimed, some consen- The field is induced by surface imperfections: sus, at a rather qualitative level, is that whiskers contaminations, oxide states, grain boundaries, can represent a stress relief phenomenon. How- etc. This theory provides closed form expres- ever, that never led to any quantitative descrip- sions and quantitative estimates for the whisker tion including order-of-magnitude estimates of nucleation and growth rates, explains whisker whisker parameters. 28 SMT Magazine • February 2015 FEATURE ELECTROSTATIC MECHANISM OF NUCLEATION AND GROWTH OF METAL WHISKERS continues Figure 1: SeM pictures of tin (left) and zinc (right) whiskers (courtesy of the nASA electronic parts and Packaging [NEPP] program). As a brief survey of relevant data, it should More appealing is an informal list of ob- be noted that whiskers grow up to ~1–10 mm servations given below with the permission of in length and vary from ~100 nm to ~30 μm its author, Dr. Gordon Davy[2]. It reflects the in thickness. Their parameters are characterized perspectives and the spirit of the live whisker by broad statistical distributions: side by side research, shared by many in the community with fast-growing whiskers there can be oth- of Tin Whisker Group teleconferences. It has ers, on the same surface, whose growth is much proved extremely useful for the author of this slower or completely stalled. The metal surface paper allowing multiple comparisons between conditions play a significant role. In particular, the theory and the experiment. oxide structure and various contaminations are important factors determining whisker con- • There are no “tin whisker experts.” Work- centration, growth rate and dimensions. The ers in the field differ only in their degree of metal grain size appears to be less significant perplexity in the face of so many inconsis- for small grains (nanometers to few microns), tencies. while whiskers are unlikely for very large grains, • Nominally identical specimens may dem- recrystallization can be of importance. Various onstrate drastically different densities and additives can have significant effects on whis- growth rates. ker growth, such as Pb strongly suppressing tin • Density may differ greatly from one region whiskering. Electric bias was reported to expo- of a specimen to another; on a finer scale, nentially increase whisker growth rate, which there is a whisker growing here, but not was attributed to the effects of electric current, there. although other publications reported no bias ef- • Growth is at the base (i.e., the film), not fect on whisker growth and even the negative the tip. effect of bias suppressed whiskering. A common • Growth may be from the tin-substrate in- observation is that whiskers grow from the root terface or from near the tin surface. rather than from the tip, and the material re- • Growth rate is often not constant. A whis- quired for their growth is supplied from large ker may stop growing for a while, then distances through long range surface diffusion start growing again. rather than from a narrow neighboring proxim- • Growth rate is zero at low and high tem- ity; there is no surrounding dent formed in the peratures, and seems to peak at about 25– course of whisker growth. 50°C. 30 SMT Magazine • February 2015 FEATURE ELECTROSTATIC MECHANISM OF NUCLEATION AND GROWTH OF METAL WHISKERS continues • Growth can be promoted by thermal cy- • Whiskers eventually penetrate polymer cling. (including Parylene) coatings, with the ap- • Growth rate is zero below a threshold film parent exception of “whisker-tough.” thickness and approaches zero for high • Whiskers appear to not penetrate thin caps film thickness. It appears to be zero for of certain metals, and readily penetrate bulk tin. thicker caps of other metals. • For sputtered films, the growth rate ap- • Whiskers appear to not penetrate thin films pears to be a minimum for near-zero resid- of tailored ceramics produced by chemical ual stress, and greater for tensile as well as vapor deposition if the substrate has been compressive stress. properly prepped. • Growth rate is somewhat higher at high humidity. To emphasize the most challenging ques- • Growth rate seems to be higher from fine- tions, here is the author’s short list: grained microstructure. • Growth rate can be increased by some • A mystery of high aspect ratios, height/ kinds of residues on the surface. diameter up to ~10,000 not seen in other • Most metals dissolved in tin appear to in- physics. Why wouldn’t metal whiskers col- crease growth rate. The one exception is lapse into spheres, as other droplets do to Pb. The mechanism may have to do with minimize surface energy? altering the grain structure to equiaxed • Is their relation to metals of essence? In (from columnar). other words, why are metal whiskers met- • I do not recall hearing of the effect of small al? amounts of Pb (~1%) in Sn for vapor-de- • What is behind the metal whiskers ran- posited films, or even for very thin electro- domness? Why do they grow here but plated films. not there, why are their parameters so dis- • Distribution of thickness and length are persed, and what makes it so difficult to log-normal. controllably grow or predict their appear- • There appears to be no correlation between ance? thickness and length. • What does Pb do in suppressing whiskers? • Median thickness is about 3 μm. • Longest whisker reported: ~25 mm. Multiple attempts to understand the mecha- • Thinnest and thickest whiskers reported: nisms of whiskers growth revolved around the ~100 nm, ~20 μm. role of surface stresses relived by whisker pro- • Various growth morphologies: needle-like, duction, dislocation effects, oxygen reactions, odd-shaped eruptions, occasional branch- and recrystallization. It was shown stress gradi- es, and there may longitudinal or circum- ents along with certain assumptions about sys- ferential striations. Acicular (needle-like) tem parameters can explain tin whisker growth whiskers may be bent or kinked, and may rates but not their existence, shapes and sta- not have the same thickness along the en- tistics. Overall, these attempts have not led to tire length. verifiable quantitative predictions. • Long whiskers are in constant motion in The 60-year old whisker challenge thus re- air—can be compared to Brownian mo- mains outstanding against the background of tion. other historical developments in natural sci- • Whiskers have an oxide coating ~1–3 nm ences. As an example, the fundamentally new thick, even in vacuum. (Growth rate is log- phenomenon of superconductivity was discov- arithmic.) ered in 1911 and explained in 1957, taking a • A whisker that melts exits the skin, leaving shorter time to understand than metal whiskers, it behind. in spite of being the first encounter of the mac- • Whiskers penetrate even a thick oxide film roscopic quantum phenomena physics. This (grown by prolonged exposure to steam). remarkable elusiveness of the metal whisker February 2015 • SMT Magazine 31 FEATURE ELECTROSTATIC MECHANISM OF NUCLEATION AND GROWTH OF METAL WHISKERS continues problem warrants new theoretical approaches. with the observed wide variety of factors, in the They need to be made quantitative in order to first glance unrelated to each other, all having allow experimental verifications and satisfy the strong effects on whisker growth: stresses of me- standard scientific criteria. chanical and electric nature, material morphol- This paper discusses one such approach ogy and composition, surface contaminations, based on the electrostatics of metal surfaces. including the effects of humidity. According to It may appear rather contradictory in the light that concept, all these factors are responsible of a common perception (taught in the under- for significant electric fields in the near surface graduate physics) that neutral metal surfaces region of a metal. The surface electric field be- cannot have electric charges or fields. We will comes a common denominator of whisker driv- see however that the latter is true only for ideal ing forces. This new hypothesis remains to be metal surfaces (containing no imperfections, carefully tested against all the available data such as grain boundaries, contamination, dis- and focused experiments including purposely locations, etc.), and that real metal surfaces can created electric fields. present rich electrostatics including strong elec- tric fields significantly varying across the sur- 2. Being overall neutral these metal surfaces face. A theory of metal whiskers presented here are composed of oppositely charged patches is consistent with many published observations formed as a result of electron redistribution and provides some quantitative analytical re- minimizing the system free energy. The patches sults. The appearance of whiskers is described as are characterized by certain surface charge den- the electric field induced nucleation of needle- sity and dimensions L~1−10 μm, maybe even shaped particles. It is triggered by the energy shorter, ~0.1 mm, for fine crystalline grain struc- gain FE=−p⋅E due to the induced whisker dipole ture.