Metal Whiskers by V
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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.
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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.
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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
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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. These patches form a sort of random chess p=αE in the electric field E, where α is the po- board as shown in the right display of Figure 2. larizability. The latter is anomalously strong for the needle geometry. The nucleated whiskers 3. The phenomenon of whisker nucleation continue growing to further decrease their en- and growth is attributed to the electrostatic en- ergies in the electric field. ergy gain due to strong polarization of the new- ly created needle-shaped metal particles. The 1. More specifically, the theory is based on conception of whiskers is described based on the concept of strong electric fields, ≤E 0.01-1 the (earlier developed) theory of field induced MV/cm, in the sub-micron proximity of metal nucleation that predicts needle-shaped embry- surfaces. Such fields can be generated by surface os h≤100 nm in length and d~1–10 nm in di- imperfections including “wrong” grain orien- ameter. The mechanism is quite similar to that tations, deformations, oxides, dislocations, or explaining the fact that amber or plastic comb contamination. The importance of this con- attract small pieces of paper: The electric field cept is that it offers a unique pattern consistent polarized small particles making them electric
Figure 2: A sketch of the electric field E near a metal surface, cross-sectional (left) and 3D (right) views.
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Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues dipoles with energy –pE in the driving them in It is worth mentioning that the existence of the region of stronger field E. It is important that strongly anisotropic stretched (needle-shaped) the energy gain due to formation of a polarized metallic particles is due to their strong polariza- metal needle does not depend on the field sign tion gain in the external electric field. In turn, as illustrated in Figure 3. The dipole vector p is that gain is a consequence of their large dipole parallel to the field vector E, so the product –pE moments due to considerable dipole length. As is negative. Another wording would be to say a result, long enough particles become ener- that like charges repel producing an outward getically favorable in the external field in spite stress. It is relieved by expelling some of these of the fact that their surfaces are much great- charges outward via creating a metal whisker er than that of an equivalent volume sphere. with the expelled charge sitting at its far end. The needle-shaped metallic particles dominate These nucleation events take place most easily when the field is greater than a certain critical where the metal surface is locally weak. value as illustrated in Figure 4. This consider- ation provides a physical mechanism of the very existence of extremely high aspect ratio metal whiskers not collapsing into spherical shapes of equivalent volumes. Their energetically favor- able shapes are dictated by the existing electric fields. According to this understanding, whis- kers would inevitably collapse into spherical- like shapes in the absence of external electric fields.
4. Following the nucleation is the growth stage where whiskers increase their length by accretion of material at their bases. The growth kinetics are different for whisker lengths below Figure 3: Sketch of two whiskers of length h and and above the characteristic charge patch di- diameter d on a metal surface with local electric mension L. In particular, growth rates turn out fields E (of opposite directions) inducing the to be extremely low for short (h< Figure 4: Competition between the surface tension and the electrostatic polarization. 34 SMT Magazine • February 2015 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues sion L, after which the growth rate remains on distances h Figure 5: Top left: free energy vs. whisker length h where the downhill slope corresponds to the growth stage of whiskers; W is the nucleation barrier, h0 is the critical nucleation dimension of the needle-shaped embryo. The shape of that slope is determined by the charged patch model shown to the right of the free energy plot where r is the distance from a metal surface and L is the characteristic patch dimension. Bottom: the free energy vs. whisker length with the marked regions of qualitatively different dependencies. February 2015 • SMT Magazine 35 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues Figure 7: A sketch of whisker growth through a space of a fluctuating electric field: Figure 6: Sketch of the whisker growth rates vs. • Rapid growth while either + or – fields time. Solid lines represent the two limiting cases dominate along the length. within the domains of their applicability (h< in some local regions, the further energy gain in red). The corresponding pathways for whis- can be achieved via the diameter increase (i.e., ker growth can be kinked in order to collect as whiskers get thicker intermittently with the pe- many as possible color matched regions. This riods of faster length increase). A snapshot of explains how whiskers can be kinked. It should many such whisker lengths and diameters will be noted however that each kink entails certain therefore show broad statistical distributions deformation energy loss, so the whisker geom- that are mutually uncorrelated. etry will optimize between the gain in electro- Figure 7 illustrates the process of whisker static energy and loss in deformation energy growth in a 2D fashion where the color coding due to kinking. (These subtle features remain is such that upward and downward local elec- unaccounted quantitatively in the current elec- tric field directions are shown in respectively trostatic whisker theory.) Furthermore, some red and blue. The sign fluctuations of the field configurations of color-matched regions pres- at large distances shown in Figure 5 do not ent pathways parallel or partially parallel to the eliminate the polarization energy gain. Indeed, surface; this explains the observed longitudinal consider a long metal whisker as a succession of or circumferential striations shown in dash in many small metal rods, each occupying a small Figure 7. range of more or less constant field. They have local dipole moments p=aE, and partial electro- 6. In the course of growing at h>>L, whis- static energies pE=aE2 that are quadratic in field kers encounter rare local regions of abnormally and do not cancel each other. Taking into ac- low electric fields where its further growth is count the explanation in Figures 3 and 5, it is blocked. The blockage is due to the fact that intuitively clear that the maximum polarization further growth in these low field regions can- and electrostatic energy gain are achieved for not overweigh the energy loss due to increase in the “color-matched” whiskers (all in blue or all surface area: the latter increase presents a signifi- 36 SMT Magazine • February 2015 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues Figure 8: In the flat portion of the electrostatic free energy FE, the whisker surface energy FA forms a barrier WB in the total whisker energy F=F +F . In this diagram, W is the whisker A E Figure 9: An example of the predicted probabi- nucleation barrier. listic distribution of whisker lengths vs. its best fit approximation by the log-normal distribution. Note that the best fit (least square) approxima- cant energy barrier. The statistics of these block- tion provides good fit in the middle part of the ing regions (barriers) determines the whisker distribution, while it is less successful in the re- length statistics. It is derived to be close to log- gions of both very long and very short whiskers. normal in the proximity of the most likely sizes, while decaying much faster for sizes well above the average. It should be emphasized however shunting entities observed in various elec- that such blocking energy barriers have finite tronic elements (mostly in semiconductor and heights WB. Therefore, they can be overcome insulator films) that are conductive filaments after significant waiting times t =t exp(W / W 0 B developed in the host of relatively insulating kT) allowing for sufficient number of attempt- materials subject to electric bias. There is a con- to-escape events, each taking time t where kT 0 siderable R&D activity, often in industrial set- is the thermal energy. This explains the obser- tings, including different technologies, such as vation of whiskers resuming growth after a con- microelectronics, thin film photovoltaics, light siderable time (approaching a year) of lethargy. emitting diodes, etc., in the course of which the Based on this reasoning and using the standard problem is considered from different points of techniques of the physics of random systems, it view, often ignoring a possibility of common is possible to derive the probabilistic distribu- mechanism based on the field induced electro- tion of whisker length. Its explicit mathemati- static energy gain. cal form turns out to be cumbersome; however, Side by side with the detrimental effects of the qualitative features are quite simple and are shunting, there is a strong research effort to illustrated in Figure 9. understand possible beneficial effects of for- mation of conductive filaments under electric 7. The concept of field induced nucleation bias. They include, first of all, the technologies and growth of metal filaments is neither unique of phase change and resistive memories, where nor very new; in a quantitative form it was put the structure states with and without the con- forward in the recently developed field induced ductive filament are used as the two logic states nucleation theory. Here we would like to men- of the memory element. Some illustrations are tion some applications of that concept concern- given in Figure 10. ing objects that may be related to metal whis- Shown in Figure 11 are needle-like structures kers in their underlying physics. that appear on the surface of a liquid metal in Our first example is represented by the a strong perpendicular electric field. The nature 38 SMT Magazine • February 2015 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues Figure 10: Illustrations of the electric field induced conductive filaments in resistive memory devices. of such needles remains obscure, although the shape of their pedestals is explained as the so- called Taylor cones representing an equilibrium (between the electrostatic polarization and the surface tension) geometry of a metal surface. From the perspectives of this paper’s philoso- phy, these needles, metal whiskers, and those responsible for shunting and solid state mem- ory features are all mutually related due to the electrostatic energy gain. 8. Because of its counterintuitive nature, Figure 11: Structures pulled up by a strong electric the discussion about strong electric fields in the field on the surface of a molten metal[3]. near surface regions of real metals may require further comment. These fields can arise from spatial variations of the work function depend- ing on multiple imperfections in structure and tributions. The electrons will always move to composition. At the first glance, the existence minimize the system free energy; this leads to of such fields may appear contradictory. Indeed, non-uniform charge distributions in non-ho- free electrons in metals have a tendency to mogeneous systems. In other words, not only screen electric charge fluctuations, thereby sup- the existence of surface electric fields and their pressing electric fields. However, as explained corresponding electric charge variations are ful- in the next section, the role of free electrons is ly consistent with the concept of free electrons, exact opposite. Their ability to move underlies but it is due to free electrons that different local the electric charge variations. regions of a metal can exchange electric charges To avoid any misunderstanding, it is not the minimizing the system free energy. It is widely condition of local electroneutrality, but rather known in the physics of semiconductors (but that of minimum free energy that determines has not been applied to metals often) that it is the electric charge (and other parameters) dis- not the electric potential j, but rather the elec- February 2015 • SMT Magazine 39 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues Figure 12: A sketch of a spatial distribution of the electric potential including two regions with the relative- ly low (left) and relatively high (right) chemical potential m. To utilize that difference in chemical poten- tials, the electrons partially moved from right to left creating non-uniform electric charge distribution and its corresponding non-uniform electric potential j and electric field E. The quantity that remains constant throughout the region is the electro-chemical potential F = m + ej where e is the electron charge. trochemical potential F = m + ej that needs to be presence of grain boundaries can be essential. constant in space in order to minimize the sys- Before pointing at more specific factors behind tem free energy. Here, m is the chemical poten- electric field variations, the following general tial (change in the system energy in response to examples (i–iii) are aimed at illustrating the un- the change of number of particles in it by one; derlying physics. the difference in chemical potentials between two substances equals minus that of the corre- i. Consider local stresses (due to grain bound- sponding work functions). The chemical poten- aries, dislocations, or external loads) modulat- tial is sensitive to all kind of chemical features, ing interatomic distances in a metal, thus mak- deformations, defects, etc. Figure 12 shows how ing some local regions denser than the others. the concentrations of particles n are significantly Because of these local variations, some re- different in the two regions with different chem- gions will present deeper potential wells for the ical potentials. As a result, the particles move to electrons (a phenomenon known as the defor- the region of lower chemical potential. Because mation potential D = dm / du 1 eV where u is of the accumulated electric charge, there is now the dilation). Should these regions be mutually electric field E in the system. However, its cor- independent, the Fermi level positions would responding drift current nEb (b is the mobility) vary between them. However, because they are is totally balanced by the diffusion current Ddn/ connected, the free electrons will move to level dx, where D is the diffusion coefficient and x is out the Fermi level across the entire system thus the coordinate in the direction of concentration minimizing the system free energy. As a result, gradient. The important conclusion is that it is the above regions become electrically charged. a metal where there is no current while the elec- tric field is not vanishing. ii. Spatial variations in chemical composi- It follows from the latter that some struc- tion of alloys would similarly result in modula- tural or compositional inhomogeneities are tions of work function, which will be leveled needed for the electric charge redistribution out in the course of electron redistribution cre- triggering whisker growth. Grain structure can ating local electric fields similar to the previous be one (but not the only) example of such inho- example. mogeneities. This is consistent with the general observation that whiskers are unlikely on metal iii. The extreme case of the latter is present- surfaces built of very large grains, and that the ed by a contact of different metals with unequal 40 SMT Magazine • February 2015 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues work functions. The free electrons will move is qualitatively similar to the above mentioned between these metals to equalize their Fer- example (ii) of the chemical composition varia- mi levels. This makes the metals electrically tions. Certain features of surface morphology, charged. The same phenomenon underlies the particularly, its roughness, may result in the existence of Schottky barriers and p-n junctions electron redistribution caused by the corre- in semiconductors. In the case of metal cou- sponding modulations of microscopic struc- ples, it is known as the source of the galvanic ture parameters similar to the above example action that occurs when two electrochemically (i). They can be caused by dislocations, stress- dissimilar metals are in contact and a conduc- induced spots of different structure phases, or tive path occurs for electrons and ions to move general electric deformation coupling in combi- from one metal to the other. Furthermore, one nation with stress-induced buckling. can imagine a binary mixture of chemically dif- Local charges due to stress-induced oxide ferent metal grains where the balance of Fermi cracking or ion trapping under the whisker energy makes the grains of two types charged growing layer (say, Sn on Cu substrate) are con- oppositely. ceivable sources of the above considered surface electric fields as well. Therefore, a surface, that is The above cases (i) and (ii) are schematically ideally electrically uniform, may acquire electric illustrated in Figure 13. surface structure. Here we assume a simple mod- More specifically, the regions of different el of uncorrelated charge patches on a metal surface potential (patches) may be due to the surface characterized by two parameters: charac- polycrystallinity of a metal. The work function teristic electron surface charge density ne (elec- will vary between regions of specific grain ori- trons per cm2), and the linear dimension L. In entations (Figure 14) by typically a few tenths reality, the charge distribution in patches can be of a volt; these different grain orientations will nonuniform, possibly concentrating along grain be qualitatively similar to the above example boundaries or other structural imperfections. (iii) of binary metal mixtures. Patch structure However, these conceivable complications fall may also arise from the presence of adsorbed beyond the present scope. The charged patch elements and compounds; that contamination 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). 42 SMT Magazine • February 2015 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues Patch structured electric fields near metal 9. The above estimates lead to the follow- surfaces have been found in multiple works. The ing scenario of whisker evolution. (i) Stage 1: measurements reveal the work function fluctua- Whiskers nucleate in time intervals of one sub- tions of ~0.5 eV induced by L~10 μm patches in second to one day (reflecting fluctuations in some metals. nucleation barriers due to the local field fluc- The charged patch model enables one to tuations); their dimensions upon nucleation estimate the average electric field vs. distance r are h~10–100 nm and d~1–10 nm, with the from the surface. At distances r< where E^ and E|| are respectively the field lengths where feeding by thermal radiation components perpendicular and parallel to the dominates, they evolve further in lateral di- surface, and angular brackets represent averag- rections parallel to the metal surface (not dis- ing. cussed here). Figure 15: Charged patch model. The correlation function g(x) can be approximated as the delta- function (i.e., uncorrelated disorder) at distances x>>L. February 2015 • SMT Magazine 43 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues 10. Conclusions rate agree with the observations. The above theory describes metal whickers as 7) Why whisker parameters are broadly dis- a result of metal nucleation and growth in ran- tributed statistically. The predicted distribution dom electric fields induced by charged patches of whisker lengths is close to the observed log- on metal surfaces. The underlying approaches normal statistics around its central part. are typical of the physics of phase transitions and disordered systems. This work presents the 10.2 What is not understood first whisker theory yielding simple analytical 1) The microscopic nature of whiskers, their results more or less consistent with the observa- correlation with specific surface defects, chemi- tions. The successes, the remaining questions, cal aspects of whisker development. and possible experimental verifications of this 2) The role of whisker crystalline structure theory are summarized next. in their evolution process. 3) Whisker growth in 3D random electric 10.1 What is understood field. This includes whisker winding and kink- 1) Why whiskers are metallic: High (metal- ing. lic) electric polarizability is required for suffi- 4) Possible role of surface (or grain bound- cient energy gain due to whisker formation in ary) diffusion limiting whisker growth. external (surface) electric fields. 5) Possible hydrodynamic drag moving sur- 2) Why whiskers grow more or less perpen- face material uniformly along with ions. dicular to the surface and yet can have con- 6) Inter-whisker interactions limiting their figurations parallel to the surface: Such are the concentration and affecting growth. This in- dominating directions of the surface electric cludes the stage of whisker ripening. field that include significant fluctuation along 7) Role of Pb in suppressing whiskering. the surface. 3) Why whisker parameters are broadly sta- 10.3 Possible experimental verification tistically distributed: This reflects fluctuations The predicted dependencies of nucleation in metal surface fields induced by mutually un- and growth kinetics vs. electric field, tempera- correlated charged patches. ture, and controlled contamination could be 4) Correlation between whiskers and ver- verified experimentally. satile morphology factors, such as (i) grains 1) Whisker nucleation and growth in exter- whose orientation is different from the major nal electric fields. This can be attempted, e.g., orientation of the tin film, (ii) dislocations and in flat plate capacitor configuration for a whis- dislocation loops, and (iii) mechanical stresses ker inside SEM where the electric field is readily capable of surface buckling, surface contami- controlled, or under e-beam in an accelerator. nations; all related to local surface charges and In all cases, care should be taken to avoid signif- their induced electric fields. Some metals are icant Joule heating and/or electron drag effects more prone to develop whiskers because they (i.e., using voltage rather than current power can easier form charged patches by absorbing source). An ongoing project in our group has ions, and creating dislocations, grain boundar- generated preliminary results showing that the ies, or stresses. electric field in combination with high relative 5) Why external electric bias can significant- humidity can lead to anomalously rapid whis- ly affect whisker growth. (It is rather difficult, ker growth (one week under 3000 V/cm in a yet possible, beyond this paper framework, to capacitive configuration; 10–20 hours of medi- understand how the electric bias can be not a cal accelerator e-beam charging a glass substrate significant factor in whisker kinetics.) under Sn film). 6) Why the characteristic whisker evolution 2) Whisker nucleation and growth under exhibits a certain pattern: long incubation pe- controlled contamination of metal surface with riod followed by almost constant growth rate solutions of charged nano particles. that eventually saturates. The predicted incu- 3) Whisker nucleation and growth under bation (dormant) time and subsequent growth the conditions of strong surface electric fields 44 SMT Magazine • February 2015 feature Electrostatic Mechanism of Nucleation and Growth of Metal Whiskers continues induced by surface plasmon polariton excita- Electronic Parts and Packaging (NEPP) Program tions. This technique could be used for con- is greatly appreciated. SMT trolled growth of metal nanowires of desirable parameters on metal surfaces. References 4) Applications to modern large area thin 1. V. G. Karpov, Electrostatic Theory of Met- film photovoltaic technology where whiskers al Whiskers, Physical Review Applied, 1, 044001 can shunt through the device, thereby causing (2014). significant reliability concerns (which has not 2. Private communication, October 2014, been sufficiently addressed yet). Properly re- slightly abridged here. placing those device metal contacts or surface 3. G. A. Mesyats, Explosive Electron Emis- treatments mitigating whisker growth can im- sion, URO Press, Ekaterinburg, (1998); p.29 prove the device reliability and stability with respect to shunting. Victor Karpov is professor of physics at the University of Acknowledgement Toledo. He has published about The author is grateful to D. Shvydka, A. 200 papers on condensed mat- Vasko, G. Davy, S. Smith, B. Rollins, J. Brusse, ter, physical chemistry, photovol- A. Kostic, and the entire tin whisker teleconfer- taics, and device physics. ence group for useful discussions. The NASA perhaps in industrial quantities through roll-to- Laser-induced Graphene roll processes, Tour said. The research was reported this week in Applied Vital for Flex Electronics Materials and Interfaces. LIG supercapacitors appear able to do everything Rice University scientists advanced their recent capacitors can do, with the added benefits of flex- development of laser-induced graphene (LIG) by ibility and scalability. The flexibility ensures they producing and testing stacked, three-dimensional can easily conform to varied packages—they can be supercapacitors, energy-storage devices that are im- rolled within a cylinder, for instance—without giving portant for portable, flexible electronics. up any of the device’s performance. The Rice lab of chemist James Tour discovered “What we’ve made are comparable to microsu- last year that firing a laser at an inexpensive poly- percapacitors being commercialized now, but our mer burned off other elements and left a film of po- ability to put devices into a 3-D configuration allows rous graphene, the much-studied atom-thick lattice us to pack a lot of them into a very small area,” Tour of carbon. The researchers viewed the porous, con- said. “We simply stack them up. ductive material as a perfect electrode for superca- “The other key is that we’re doing this very sim- pacitors or electronic circuits. ply. Nothing about the process requires a clean Members of the Tour group have since extended room. It’s done on a commercial laser system, as their work to make vertically aligned supercapacitors found in routine machine shops, in the open air.” with laser-induced graphene on both sides of a poly- Ripples, wrinkles and sub-10-nanometer pores mer sheet. The sections are then stacked with solid in the surface and atomic-level imperfections give electrolytes in between for a multi- LIG its ability to store a lot of energy. layer sandwich with multiple microsu- But the graphene retains its ability to percapacitors. move electrons quickly and gives it the The flexible stacks show excellent quick charge-and-release characteris- energy-storage capacity and power tics of a supercapacitor. In testing, the potential and can be scaled up for researchers charged and discharged commercial applications. LIG can be the devices for thousands of cycles made in air at ambient temperature, with almost no loss of capacitance. February 2015 • SMT Magazine 45