Electromigration Flux Research Articles

Interfacial Reaction and Electromigration Failure of Cu Pillar/Ni/Sn-Ag/Cu Microbumps under Bidirectional Current Stressing.

The electromigration behavior of microbumps is inevitably altered under bidirectional currents. Herein, based on a designed test system, the effect of current direction and time proportion of forward current is investigated on Cu Pillar/Ni/Sn-1.8 Ag/Cu microbumps. Under thermo-electric stressing, microbumps are found to be susceptible to complete alloying to Cu6Sn5 and Cu3Sn. As a Ni layer prevents the contact of the Cu pillar with the solder, Sn atoms mainly react with the Cu pad, and the growth of Cu3Sn is concentrated on the Cu pad sides. With direct current densities of 3.5 × 104 A/cm2 at 125 °C, the dissolution of a Ni layer on the cathode leads to a direct contact reaction between the Cu pillar and the solder, and the consumption of the Cu pillar and the Cu pad shows an obvious polarity difference. However, with a bidirectional current, there is a canceling effect of an atomic electromigration flux. With current densities of 2.5 × 104 A/cm2 at 125 °C, as the time proportion of the forward current approaches 50%, a polarity structural evolution will be hard to detect, and the influence of the chemical flux on Cu-Sn compounds will be more obvious. The mechanical properties of Cu/Sn3.0Ag0.5Cu/Cu are analyzed at 125 °C with direct and bidirectional currents of 1.0 × 104 A/cm2. Compared with high-temperature stressing, the coupled direct currents significantly reduced the mechanical strength of the interconnects, and the Cu-Sn compound layers on the cathode became the vulnerable spot. While under bidirectional currents, as the canceling effect of the electromigration flux intensifies, the interconnect shear strength gradually increases, and the fracture location is no longer concentrated on the cathode sides.

A simplified model of oscillating electrolytes.

Unstable electrophoretic transport leading to oscillations in concentration profiles occur in certain electrolyte systems known as oscillating electrolytes whose eigenmobilities are complex valued. The study of the nonlinear behavior of such systems is of great interest but is constrained due to a high degree of complexity in the governing equations. Here we present a simplified model of unstable electrophoretic transport in a binary system that reduces the governing equations to two partial differential equations only and does away with other equations that characterize acid-base dissociation reactions and electroneutrality. We present analytical expressions for electromigration fluxes and validate the model with full nonlinear simulations. The model exhibits similar nonlinear behavior as the actual unstable electrophoretic system under various initial disturbances. For comparison, we also show that similar modeling for a stable system predicts concentration profiles that quantitatively agree with its nonoscillating dynamics. Moreover, the unique feature of electromigration flux in oscillating electrolytes that unfolds from the modeling led us to find an elegant explanation of the instability mechanism. Our theory gives a qualitative understanding of the existence and growth of large oscillation patterns in oscillating electrolytes.

Modeling and Experimental Study of the Effect of Pore Water Velocity on the Spectral Induced Polarization Signature in Porous Media

AbstractInduced polarization (IP) is increasingly applied for hydrological, environmental and agricultural purposes. Interpretation of IP data is based on understanding the relationship between the IP signature and the porous media property of interest. Mechanistic models on the IP phenomenon rely on the Poisson‐Nernst‐Plank equations, where diffusion and electromigration fluxes are the driving forces of charge transport and are directly related to IP. However, to our knowledge, the impact of advection flux on IP was not investigated experimentally and was not considered in any IP model. In this work, we measured the spectral IP (SIP) signature of porous media under varying flow conditions, in addition to developing and solving a model for SIP signature of porous media, which takes flow into consideration. The experimental and the model results demonstrate that as bulk velocity increases, polarization and relaxation time decrease. Using a numerical model, we established that fluid flow near the particle deforms the electrical double layer (EDL) structure, accounting for the observed reduction in polarization. We found a qualitative agreement between the model and the measurements. Still, the model overestimates the impact of flow rate on SIP signature, which we explain in terms of the flow boundary conditions. Overall, our results demonstrate the sensitivity of the SIP signature to fluid flow, highlighting the need to consider fluid velocity in the interpretation of the SIP signature of porous media, and opening an exciting new direction for noninvasive measurements of fluid flow at the EDL scale.

Scaling relations in shear electroconvective vortices

This paper is devoted to the quantitative understanding of the electroosmotic slip velocity, which is the most essential physical quantity of shear electroconvective (SEC) microfluidics. It is well known that SEC instability caused by the electroosmotic slip velocity is triggered near the permselective membranes. Here, we present for the first time the unifying scaling relations of the electroosmotic slip velocity and overlimiting transport in SEC flow under the moderate voltage. The interplaying effects of the salt flux gradient and voltage result in a slip velocity that loses the pressure flow effect. Determined by both the applied potential and the electrolyte physical properties, the slip velocity is shown to scale as V4/3κ2/3, which deviates significantly from the relation of V2 reported in classical theory [I. Rubinstein and B. Zaltzman, “Equilibrium electroconvective instability,” Phys. Rev. Lett. 114(11), 114502 (2015)]. Since the convection flux and the electromigration flux reached an asymptotic equilibrium, a universal scaling κVPe1/3 was obtained for the overlimiting transport. Detailed direct numerical simulations in conjunction with existing experimental data [R. Kwak et al., “Shear flow of an electrically charged fluid by ion concentration polarization: Scaling laws for electroconvective vortices,” Phys. Rev. Lett. 110, 114501 (2013)] corroborate this novel scaling. Our theory provides a unified view and a perfect interpretation of the existing SEC microfluidics.

Dynamic mobility of surfactant-stabilized nano-drops: unifying equilibrium thermodynamics, electrokinetics and Marangoni effects

A theoretical analysis of the dynamic electrophoretic mobility of surfactant-stabilized nano-drops is undertaken. Whereas the theory for rigid spherical nanoparticles is well developed, its application to nano-drops is questionable due to fluid mobility of the interface and of the surfactant molecules adsorbed there. At zero frequency, small drops with surface impurities are well known to behave as rigid spheres due to concentration-gradient-induced Marangoni stresses. However, at the megahertz frequencies of electroacoustic (and other spectral-based) diagnostics, the interfacial concentration gradients are dynamic, coupling electromigration, advection and diffusion fluxes. This study addresses a parameter space that is relevant to anionic-surfactant-stabilized oil–water emulsions, using sodium-dodecylsulfate-stabilized hexadecane as a specific example. The drop size is several hundred nanometres, much larger than the diffuse-layer thickness, thus motivating thin-double-layer approximations. The theory demonstrates that fluid mobility and fluctuating Marangoni stresses can have a profound influence on the magnitude and phase of the dynamic mobility. We show that the drop interface transits from a rigid/immobile one at low frequency to a fluid one at high frequency. The model unifies electrokinetics and equilibrium interfacial thermodynamics. Therefore, with knowledge of how the interfacial tension varies with electrolyte composition (oil, surfactant and added salt concentrations), the particle radius might be adopted as the primary fitting parameter (rather than the customary -potential) from an experimental measure of the dynamic mobility. This theory is general enough that it might be applied to aerosols and bubbly dispersions (at sufficiently high frequencies).

The open-pin failure of power device under the combined effect of thermo-migration and electro-migration

With the miniaturization of electronic products, power devices sustain more and more operations under high power, high frequency, and high integration. Power electronic devices are subjected to high operating temperature and current density, which poses a serious challenge on the packaging materials. An open-pin failure was found on a metal-oxide-semiconductor field-effect transistor (MOSFE) device after operated for 3−4 a under high current density condition. The lead frame material is C194 alloy, belonging to Cu-Fe-P alloy, which is a copper base alloy strengthened by dispersion. The operating temperature of the MOSFET device is in the range of 88 − 120°C at the full working current of about 15 A from the drain to the source, while the gate current is relatively small in a milliampere level. Failure analysis is conducted on the open-pin MOSFET device. According to the investigations by scanning electron microscopy (SEM) and energy dispersive spectrometer (EDS), two intermetallic compounds (IMCs), Cu3Sn and Cu6Sn5, were formed at both the C194 alloy/Sn-Pb and the Cu/Sn-Pb solder interfaces. However, the crack is always initiated at the C194 alloy/Sn-Pb solder interface, no matter for the source or the drain. Usually, the crack would initiate at the cathode side due to the sole effect of electro-migration. In this work, the crack initiated at the cathode side for the drain, but at the anode side for the source. According to the working condition of the MOSFET device, this failure crack can be attributed to the combined effects of electro-migration and thermo-migration on multi-element interfacial diffusion and vacancy migration. In detail, for the source of MOSFET device, the direction of Cu thermo-migration flux is opposite to the electro-migration flux, while the thermo-migration flux is large so that it can compensate the effect of electro-migration flux, thus leading to the crack at the anode. For the drain of device, the direction of Cu thermo-migration flux is the same as that of electro-migration, which leads to a severe cracking at the cathode. Moreover, in order to reveal the cracking process, SEM analysis was conducted on the fracture surface where plenty of fine Fe-rich granules and some Cu-Sn IMCs were observed. Furthermore, the electron probe micro analysis (EPMA) demonstrated that these fine Fe-rich granules form a continuous layer adjacent to the crack. Transmission electron microscopy (TEM) and selected area electron diffraction (SAED) were also conducted in order to characterize the interfacial microstructure with Fe-rich granules/layer. At the C194/IMC interface, the Fe granules with body-centered cubic (bcc) structure accumulated as a continuous layer with an obvious grain growth compared to the uniformly dispersing Fe granules within the C194 alloy matrix. The existence of segregated Fe layer and Kirkendall voids would weaken the original bonding between C194 and IMC, so the crack always initiated along the Fe layer or Kirkendall voids when the thermal stress or mechanical stress applied. Above all, this coupled open-pin failure mode and its mechanism would provide a theoretical guidance for the optimization of product process and the improvement of service life.

Comparison and mechanism of electromigration reliability between Cu wire and Au wire bonding in molding state

Electromigration (EM) reliability and failure analysis of Cu wire and Au wire bonding processes on Al substrates after molding were investigated and compared systematically. According to the resistance as a function of EM time trend, there were four stages during the EM test for wire bonding that can tentatively be referred to as the fluctuating resistance stage, stable resistance stage, rapidly increasing resistance stage and quick failure stage of the sample. When the applied current was 1.8 A on a wire with a diameter of 20 μm (at a current density of 5.7 × 105 A/cm2), the lifetimes of the Cu wire and Au wire bonding processes were 1032 h and 119 h, respectively, according to Weibull analyses. Two kinds of failure modes were observed: wire fracture and first bond fracture. Almost 90% of the failed samples belonged to wire fracture category. After the EM test, the thickness of intermetallic compounds (IMCs) at the anode interface was similar to that at the cathode interface for both the Cu wire and Au wire bonding cases, which means that the normal polarity effect during electromigration did not occur here. However, the thickness of the IMCs at the Au/Al bonding interface was thicker than that at the Cu/Al interface for both the aged and EM samples. Voids and cracks were observed within the Au wire-bonding interface. It is suspected that the Cu wire bonding process had a slower thermal diffusion and smaller EM flux than those of the Au wire bonding process. Due to a decrease in vacancy flux within the Cu wire bonding region, the cracks were also suppressed, which greatly extended the lifetime of the Cu wire bonds.

A mesocosm study of electrokinetic-assisted phytoremediation of atrazine-polluted soils

Phytoremediation, an ecological remediation technology based on the use of plants, can be combined with electrokinetic treatment for the removal of both inorganic and organic pollutants from soils. Electrokinetic-assisted phytoremediation (EKPR) of atrazine was tested in a mesocosm scale experiment using ryegrass (Lolium perenne L.). Two mock-ups with dimensions of 2.25 (L) × 0.49 (W) × 0.50 (H) m were initially filled with an unpolluted low plasticity clay soil and used to carry out an EKPR test and another electrokinetic remediation (EKR) one after spiking the soil with atrazine at a dose of 2 mg kg−1. Experiments were conducted for 19 days using a DC electrical field of 0.6 V cm−1 applied continuously without changing polarity. Samples of soil, plants and soil pore water corresponding to ten different soil sections of each mock-up were taken and analysed throughout the experiment. Soil pH followed an increasing profile from the anode to the cathode, although it kept moderate values in the range of 7.53–9.62. Electro-osmosis, gravity and plant roots (in the EKPR series) influenced the final distribution of water and atrazine in the soil. Additionally, the electromigration flux had a relevant role in the atrazine residues transport during the EKPR process. Concentration values of atrazine residues remaining in the different soil sections were in good agreement with those of the soil pore water, with most of the atrazine being accumulated in the cathode section. Atrazine was mainly removed from soils by biochemical degradation, which was greatly improved by ryegrass plants; the overall atrazine removal yield was increased from 40.20% (unplanted mock-up) to 61.01% (planted mock-up).

Electrokinetic-assisted phytoremediation of atrazine: Differences between electrode and interelectrode soil sections

Electrokinetic-assisted phytoremediation (EKPR) has been recently proposed by us to remediate soils contaminated by atrazine, a common pesticide in agrarian areas. The goal of this work was to study the differences of electrochemical and biological processes occurred in the different soil sections (anode, cathode and interelectrode section) of the pots used in an EKPR test carried out with maize and a low permeability soil spiked with atrazine. An initial atrazine soil concentration of 5 mg kg−1 was used; the electric current (with voltage gradients of 2 and 4 V cm−1) was applied during 14 days, 4 h a day and changing the polarity of the electrodes each 2 h. This operation mode avoided the extreme soil pH values, although it tended to increase throughout the EKPR test causing soil alkalinisation, especially in the cathode. As a result, maize growth was poorer in the electrode soil sections. Atrazine and its metabolites, deethylatrazine and deisopropylatrazine, were taken up and accumulated in the maize tissues in a different extent depending on the soil section considered, showing the mobilization of atrazine by the electric current. The best results were found for the 2 V cm−1 treatment, for which the presence of maize increased 20–30% the overall atrazine removal in the cathode and middle sections of the planted pots as compared to the unplanted pots, showing the ability of EKPR to improve the efficiency of the electrokinetic remediation. Electromigration and electroosmotic flux contributed to transport atrazine and its metabolites throughout the soil.

Electromigration Effect on Kinetics of Cu–Sn Intermetallic Compound Growth in Lead-Free Solder Joint

Intermetallic compounds (IMCs) growth is often accompanied by void and crack formation. It can reduce the mechanical properties and reliability of solder joints. In this paper, based on the Cu mass transport mechanisms, a theory model is established to analyze the IMC growth behaviors on Cu/Sn/Cu interconnection structures. The influence of IMC dissolution process is considered to investigate the polarity effect of electromigration (EM) on kinetics of IMC growth. Verified by reported experimental data, the model can accurately calculate the thickness of IMC growth under specific temperature and current stressing. The model reveals that during thermal aging, the thickness growth of IMC on Cu–Sn interfaces has a parabolic curve relationship with time. While under current stressing, EM Cu flux in Sn solder accelerates the anode’s IMC growth and motivates the transition of its thickness growth from parabola-like curves to a linear-like relationship. The cathode’s IMC will reach constant thickness with stressing time, which can be primarily determined by the dynamic equilibrium between Cu dissolution flux and chemical Cu flux. When the initial thickness of IMC is larger than this constant, the IMC on the cathode side follows a parabola-like curve to dissolve. Otherwise, it follows a parabola-like curve to increase.

Mechanism of improved electromigration reliability using Fe-Ni UBM in wafer level package

Fe-Ni films with compositions of 73wt% of Ni and 45wt% of Ni were used as under bump metallization (UBM) in wafer level chip scale package, and their reliability was evaluated through electromigration (EM) test compared with commercial Cu UBM. For Sn3.8Ag0.7Cu(SAC)/Cu solder joints, voids had initiated at Cu cathode after 300h and typical failures of depletion of Cu cathode and cracks were detected after 1000h EM. While the SAC/Fe-Ni solder joints kept at a perfect condition without any failures after 1000h EM. Moreover, the characteristic lifetime calculated by Weibull analysis for Fe-73Ni UBM (2121h), Fe-45Ni UBM (2340h) were both over three folds to Cu UBM’s (698h). The failure modes for Fe-Ni solder joints varied with the different growth behavior of intermetallic compounds (IMCs), which can all be classified as the crack at the cathodic interface between solder and outer IMC layer. The atomic fluxes concerned cathode dissolution and crack initiation were analyzed. When Fe-Ni UBM was added, cathode dissolution was suppressed due to the low diffusivity of IMCs and opposite transferring direction to electron flow of Fe atoms. The smaller EM flux within solder material led a smaller vacancy flux in Fe-Ni solder joints, which can explain the delay of solder voids and cracks as well as the much longer lifetime under EM.

Statistical analysis of electroconvection near an ion-selective membrane in the highly chaotic regime

We investigate electroconvection and its impact on ion transport in a model system comprised of an ion-selective membrane, an aqueous electrolyte, and an external electric field applied normal to the membrane. We develop a direct numerical simulation code to solve the governing Poisson-Nernst-Planck and Navier-Stokes equations in three dimensions using a specialized parallel numerical algorithm and sufficient resolution to capture the high frequency and high wavenumber physics. We show a comprehensive statistical analysis of the transport phenomena in the highly chaotic regime. Qualitative and quantitative comparisons of two-dimensional (2D) and 3D simulations include prediction of the mean concentration fields as well as the spectra of concentration, charge density, and velocity signals. Our analyses reveal a significant quantitative difference between 2D and 3D electroconvection. Furthermore, we show that high-intensity yet short-lived current density hot spots appear randomly on the membrane surface, contributing significantly to the mean current density. By examining cross correlations between current density on the membrane and other field quantities we explore the physical mechanisms leading to current hot spots. We also present analysis of transport fluxes in the context of ensemble-averaged equations. Our analysis reveals that in the highly chaotic regime the mixing layer (ML), which spans the majority of the domain extent, is governed by advective fluctuations. Furthermore, we show that in the ML the mean electromigration fluxes cancel out for positive and negative ions, indicating that the mean transport of total salt content within the ML can be represented via the electroneutral approximation. Finally, we present an assessment of the importance of different length scales in enhancing transport by computing the cross covariance of concentration and velocity fluctuations in the wavenumber space. Our analysis indicates that in the majority of the domain the large scales contribute most significantly to transport, while the effects of small scales become more appreciable in regions very near the membrane.7 MoreReceived 14 June 2016DOI:https://doi.org/10.1103/PhysRevFluids.1.073601©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectrokinetic flowsNanofluidicsFluid Dynamics

Nuclide separation modeling through reverse osmosis membranes in radioactive liquid waste

The aim of this work is to investigate the transport mechanism of radioactive nuclides through the reverse osmosis (RO) membrane and to estimate its effectiveness for nuclide separation from radioactive liquid waste. An analytical model is developed to simulate the RO separation, and a series of experiments are set up to confirm its estimated separation behavior. The model is based on the extended NernstePlank equation, which handles the convective flux, diffusive flux, and electromigration flux under electroneutrality and zero electric current conditions. The distribution coefficient which arises due to ion interactions with the membrane material and the electric potential jump at the membrane interface are included as boundary conditions in solving the equation. A high Peclet approximation is adopted to simplify the calculation, but the effect of concentration polarization is included for a more accurate prediction of separation. Cobalt and cesium are specifically selected for the experiments in order to check the separation mechanism from liquid waste composed of various radioactive nuclides and nonradioactive substances, and the results are compared with the estimated cobalt and cesium rejections of the RO membrane using the model. Experimental and calculated results are shown to be in excellent agreement. The proposed model will be very useful for the prediction of separation behavior of various radioactive nuclides by the RO membrane.

Fast electromigration crack in nanoscale aluminum film

The current-induced breakage of 20 nm thin aluminum layers deposited onto capacitor grade polypropylene (PP) films is experimentally studied. Biexponential current pulses of different amplitude (10–15 A) and duration (0.1–1 μs) were applied to the samples. Breakage occurred after fast development of electromigrating ∼200 nm-wide cracks with initial propagation velocity of ∼1 m/s under a high current density of ∼1012 A/m2. The cracks stopped when their lengths reached 250–450 μm. This behavior is explained by the balance of electromigration and stress-induced atomic fluxes.

Temperature-dependent failure mechanism of SnAg solder joints with Cu metallization after current stressing: Experimentation and analysis

Temperature-dependent electromigration failure was investigated in solder joints with Cu metallization at 126 °C, 136 °C, 158 °C, 172 °C, and 185 °C. At 126 °C and 136 °C, voids formed at the interface of Cu6Sn5 intermetallic compounds and the solder layer. However, at temperature 158 °C and above, extensive Cu dissolution and thickening of Cu6Sn5 occurred, and few voids were observed. We proposed a model considering the flux divergency at the interface. At temperatures below 131 °C, the electromigration flux leaving the interface is larger than the in-coming flux. Yet, the in-coming Cu electromigration flux surpasses the out-going flux at temperatures above 131 °C. This model successfully explains the experimental results.

Selective dynamic concentration of peptides at poles of cation-selective nanoporous granules

The authors exposed a non-equilibrium dynamic counterion and coion analyte concentration to an AC electric field to selectively concentrate peptides at the poles of a cation-selective granule. The counterion polarization results from the focusing of the electric field show a discontinuous drop in the intra-granule counterion electromigration flux at the pole. The coion concentration polarization is due to the combined external convective and electromigration fluxes toward the pole that neutralize the accumulating counterions. Because the electromigration mobility of the peptide anion analyte depends on the pH, the authors determined a 20 000-fold high concentration factor for a near-neutral pH of 6.0 to 7.7. Because the peptide is protonated at the acidic pole and its absolute charge ranges from -0.3 to -1.9, the concentration factor scales exponentially with the absolute charge, thus allowing extremely selective concentrations of various peptides, which is demonstrated by fluorescein isothiocyanate tagged angiotensin I (pI ∼ 5.8) and Texas red tagged avidin (pI ∼ 10.5). This dynamic concentration effect can substantially enhance the sensitivity of bio-assays.

Ponderomotive effects during contact formation in microwave sintering

An assessment of the ponderomotive effect contributions to the kinetics of single contact growth during sintering is carried out. A considerable free surface electromigration during microwave sintering in a polarized electromagnetic field is determined at inter-particle interfaces. It is shown that the electromigration flux reaches its maximum near the inter-particle contact edge and it is equivalent to the compressive stress acting on the contact between particles. The compressive stress is proportional to the intensity of the electric field at the inter-particle neck and inversely proportional to the ratio of the grain boundary and surface diffusivities. The electromigration matter transport can substantially accelerate the shrinkage rate during microwave sintering in comparison with conventional sintering.

STUDY OF UREMIC TOXIN FLUXES ACROSS NANOFABRICATED HEMODIALYSIS MEMBRANES USING IRREVERSIBLE THERMODYNAMICS

IntroductionThe flux of uremic toxin middle molecules through currently used hemodialysis membranes is suboptimal, mainly because of the membranes' pore architecture. AimIdentifying the modifiable sieving parameters that can be improved by nanotechnology to enhance fluxes of uremic toxins across the walls of dialyzers' capillaries. MethodsWe determined the maximal dimensions of endothelin, cystatin C, and interleukin – 6 using the macromolecular modeling software, COOT. We also applied the expanded Nernst-Plank equation to calculate the changes in the overall flux as a function of increased electro-migration and pH of the respective molecules. ResultsIn a high flux hemodialyzer, the effective diffusivities of endothelin, cystatin C, and interleukin – 6 are 15.00 × 10−10 cm2/s, 7.7 × 10−10 cm2/s, and 5.4 × 10−10 cm2/s, respectively, through the capillaries' walls. In a nanofabricated membrane, the effective diffusivities of endothelin, cystatin C, and interleukin – 6 are 13.87 × 10−7 cm2/s, 5.73 × 10−7 cm2/s, and 3.45 × 10−7 cm2/s, respectively, through a nanofabricated membrane. Theoretical modeling showed that a 96% reduction in the membrane's thickness and the application of an electric potential of 10 mV across the membrane could enhance the flux of endothelin, cystatin C, and interleukin – 6 by a factor of 25. A ΔpH of 0.07 altered the fluxes minimally. ConclusionsNanofabricated hemodialysis membranes with a reduced thickness and an applied electric potential can enhance the effective diffusivity and electro-migration flux of the respective uremic toxins by 3 orders of magnitude as compared to those passing through the high flux hemodialyzer.

The Effect of Sn Orientation on Intermetallic Compound Growth in Idealized Sn-Cu-Ag Interconnects

The work reported here explores the influence of crystal orientation on the growth of the interfacial intermetallic layer during electromigration in Cu||Sn||Cu solder joints. The samples were thin, planar Sn-Ag-Cu (SAC) solder layers between Cu bars subject to a uniaxial current. Electron backscatter diffraction (EBSD) was used to characterize the microstructure before and after testing. The most useful representation of the EBSD data identifies the Sn grain orientation by the angle between the Sn c-axis and the current direction. The tested samples included single-crystal joints with c-axis nearly parallel to the current (“green” samples) and with c-axis perpendicular to the current (“red” samples). At current density of 104 A/cm2 (steady-state temperature of ~150°C), an intermetallic layer grew at an observable rate in the “green” samples, but not in the “red” ones. A current density of 1.15 × 104 A/cm2 (temperature ~160°C) led to measurable intermetallic growth in both samples. The growth fronts were nearly planar and the growth rates constant (after an initial incubation period); the growth rates in the “green” samples were about 10× those in the “red” samples. The Cu concentrations were constant within the joints, showing that the intermetallic growth is dominated by the electromigration flux. The measured growth rates and literature values for the diffusion of Cu in Sn were used to extract values for the effective charge, z*, that governs the electromigration of Cu. The calculated value of z* is significantly larger for current perpendicular to the c-axis than along it.

Interpretation of electrokinetic measurements of nanodiamond particles

The electrophoretic mobility of nanodiamond (ND) particles measured using laser Doppler electrophoresis in LiCl, NaCl, KCl and CsCl aqueous solutions is reported. The nanodiamond samples included porous aggregates of detonation nanodiamond (DND) particles, completely disaggregated single-digit DND and monolithic 50nm particles of static high-pressure high-temperature (HPHT) synthesis. Corresponding values of ζ-potential were calculated as functions of electrolyte concentration using different theory of electrophoresis. The use of the Miller formula, which takes into account the electromigration fluxes of ions and electroosmotic flows of solutions in pores of dispersed particles, was found to provide the most accurate ζ-potential values for DND aggregates, while for monolithic ND particles Ohshima's approximation developed for the arbitrary zeta potential value and the Debye length/particle radius ratio is more appropriate.