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This paper reports the changes in morphology and topographic roughness on the surface of a pristine TlGaS e 2 layered crystal caused by an external electric field applied perpendicular to the layer plane at room temperature. These electric-field-induced surface reconstructions and modifications in the TlGaS e 2 sample were monitored through x-ray reflectivity, x-ray diffraction, and atomic force microscopy techniques. Two distinct electric-field-induced surface responses have been observed: the shifting of the XRD peaks to the higher Bragg angles and the variations in the XRR curves depending on the strength and polarity of the applied external electric fields. AFM results show that the applied electric field leads to a reproducible transformation of the surface roughness of the TlGaS e 2 single crystal from smooth to disheveled, with well-defined depth protrusions. The relaxation time of these surface topological configurations induced under an applied dc electric field was found to be much longer than a few days. The electrostatic capacitive behavior of this two-dimensional semiconducting material is believed to be caused by lattice distortions and the formation of inner stresses (strains) during electric field poling, as well as a drop in the unit-cell characteristics of TlGaSe2. The current–voltage (I–V) measurements show a pronounced nonlinear relationship for a previously poled sample. This nonlinearity is attributed to the field-effect-induced capacitance in TlGaS e 2. Electromigration of intrinsic defects such as Se-anion vacancies, which are already present in the crystal lattice structure of virgin TlGaS e 2 , may diffuse into the sample surface from a bulk (or vice versa) during electric field applications. Finally, employing DFT simulations, we present that the Se-anion vacancy model may be beneficial because changes in the charge state of metal ions positioned around selenium vacancies could be expected. The slightly asymmetric capacitance with respect to the polarity of the bias potential applied to the top surface of TlGaS e 2 is justified by our theoretical calculations. [ABSTRACT FROM AUTHOR]

In this work, the electromigration dispersion (EMD) due to the charged electrolytes in microchannels is considered without using the thin electrical double layer assumption. The electrokinetic flow and transport of ions are actuated within a rectangular micro-/nanochannel having a negative surface charge density under the influence of an external electric field. Due to the local variation of the conductivity and the nonvalidity of the electroneutrality condition, the local electric field varies as a function of the solute concentration, wall surface charge density, valency, and Debye layer length. The resulting electrokinetic flow due to the external electric field drives the fluid along with the charged species, where the Taylor–Aris dispersion separates the solutes into their different constituents. The local concentration dependence of the electric field leads to the formation of concentration profiles that are slightly asymmetric with respect to the standard Gaussian distribution. Including a finite Debye layer thickness has an effect on the advection of the species as well as the diffusion of the species. It is found that in cases where Debye layers are thicker, the species advects faster within the microchannel. This might give valuable insights into the nature of the EMD. Our model aims to predict the evolution of ionic concentration at all positions within the channel. A study of the higher-order statistics in skewness and kurtosis has also been conducted to obtain a better understanding of the idealized model consisting of a buffer solution. [ABSTRACT FROM AUTHOR]

Scanning x-ray microbeam topography and fluorescence experiments were conducted in situ to study the electromigration behavior of a 0.5 μm thick, 10 μm wide, and 200 μm long Al(0.25 at. % Cu) conductor line with 1.5 μm-thick SiO2 passivation on a single crystal Si substrate. The strain sensitivity of x-ray topography measurement allowed detailed examination of the electromigration-induced stress distribution and evolution in the conductor line in response to the depletion of Cu solute early in the electromigration process. Upon electromigration at 0.4 MA/cm2 and 303 °C, a short-range stress gradient was quickly induced by Al migration in the Cu-depleted cathode region to counteract further Al flow. The stress gradient was fully developed during the 5.3 h incubation time, extending over the critical Blech length of about 66 μm from the cathode end. Plastic deformation then occurred at the downstream end of the Cu-depleted region. The preferential electromigration of Cu did not cause detectable stress change outside the Cu-depleted region, except for the significant stress development from the Al2Cu precipitation at the anode end which appeared to initiate the fracture in the passivation. Preliminary finite difference modeling was undertaken to simulate the experimental observations, from which important parameters dictating electromigration in Al(Cu) line were extracted: an apparent effective valence of −5.6 and −1.9 for Cu and Al in Al(Cu), respectively, and a critical Cu concentration of 0.16 at. % above which Al grain boundary diffusion is effectively blocked. [ABSTRACT FROM AUTHOR]

A comprehensive physics-based modeling framework for electromigration (EM) in copper nano-interconnects is presented. It combines the three stages of stress evolution, void nucleation, and void dynamics in a single fully coupled and consolidated platform. Mechanical stress evolution, pre- and post-void nucleation, and its impact on void dynamics are deciphered, which enables accurate predictions of EM aging processes as validated by dedicated EM experiments. Subsequently, the experimentally validated model is utilized to shed light on the impact of a number of manufacturing variables, namely, line extension, via taper angle, and the effectiveness of the via bottom flux divergence point. A linear correlation between the ion leakage through the via bottom barrier and the peak tensile stress at the cathode was observed in long lines. In short lines, a blocked cathode end with atomic leakage through the anode end weakens the back-stress effect and threatens the Blech effect induced interconnect immortality. Increasing the line extension length was shown to increase the EM lifetime by about 40%. This impact was saturated beyond 1 critical dimension of line extension. On the other hand, the via taper angle increased the upstream EM lifetime by about twofold when the taper angle was increased from 0° to 30°, which indicates that the change of via taper angle has a stronger impact on EM lifetime compared to the line extension. [ABSTRACT FROM AUTHOR]

In order to measure the migration parameters of nuclides in bentonite more conveniently, an improved through-discharge electromigration method was developed. In this method, the nuclides first were driven by the electric field to migrate through the bentonite column fast, then discharged with the carrier fluid, and finally collected automatically for measurement. Meanwhile, based on the analysis of the important process in the method, the solution equation for deriving the migration parameters of nuclides was established. Furthermore, two kinds of through-discharge electromigration devices were designed in term of the different nuclide sorption behaviors onto the bentonite, and the electromigration breakthrough curves of 88Sr and 239Pu in bentonite were obtained for the first time. The result indicated that the improved electromigration technology was quite efficient for acquiring the migration parameters of 88Sr with weak adsorption capacity. However, it was found that more experimental data were needed to support the analysis of 239Pu migration behavior because of its complex electrochemistry reaction with bentonite. [ABSTRACT FROM AUTHOR]

The effect of annealing treatment on the electromigration (EM) resistance of low-temperature Cu/Sn-57Bi-1Ag (600 μm)/Cu solder interconnects has been investigated. The annealing treatment of as-soldered Cu/Sn-57Bi-1Ag/Cu solder interconnects caused the obvious coarsening of Bi phases in the bulk solders and a slight reduction in the electric resistance of the solder interconnects. The coarsening of the Bi phases induced a decrease in the Bi/β-Sn phase boundaries and thus a decrease in the EM-induced atomic diffusion flux of Bi atoms during the subsequent current stressing, resulting in the segregation of a thinner Bi phase layer at the anode and a lower increase rate of electric resistance of the solder interconnects. The longer the annealing time, the higher the EM resistance of the solder interconnects. The reductions in both the effective diffusion coefficient of the Bi atoms and the electric resistivity of the bulk Sn-57Bi-1Ag solders induced by the annealing treatment were responsible for the higher EM resistance of low-temperature Sn-57Bi-1Ag solder interconnects. [ABSTRACT FROM AUTHOR]

Cationic lithium polysulfides (LiPSs) within ether‐based electrolytes are essential intermediates pivotal in instigating the shuttle effect. Suppressing the generation of cationic LiPSs is crucial for enhancing the performance of high‐energy‐density Li‐S batteries in practical applications. Herein, for the first time, it is demonstrated that cobalt phthalocyanine (CoPc) can significantly enhance the dissociation of LiPSs, leading to a decrease in cationic LiPSs species within the electrolyte. Employing NMR and in‐situ Raman spectroscopy, it is observed that CoPc interacts with sulfur anions within LiPSs, modifying the dissociation equilibrium of LiPSs in 1,2‐dimethoxyethane (DME)/1,3‐dioxolane (DOL) electrolyte. This CoPc‐mediated shift toward dissociation equilibrium reduces the concentration of cationic LiPSs, effectively suppressing the electromigration of LiPSs intermediates toward the Li anode during the charging process of Li‐S battery. As a result, the Li‐S battery enabled a high reversible areal capacity of 4.2 mAh cm−2 at a high sulfur loading of 5.0 mg cm−2 and a low electrolyte/sulfur (E/S) ratio of 3 µL mgs−1. This work affords a promising strategy for tackling the fundamental challenges regarding Li‐S batteries. [ABSTRACT FROM AUTHOR]

In this study, a Sn37Pb solder joint was subjected to mechanical loading (constant 5 N force applied in the vertical direction) for a duration of 400 h in order to investigate the evolution of micro-voids. Under electromechanical loading, micro-voids exhibited growth and subsequent shrinkage. Solder joint resistance initially increased and then decreased. The decrease in void volume and the reduction in solder joint resistance are both attributed to the creep deformation occurring in the vertical direction of the solder joint. Notably, no significant element migration was observed within the solder joints after 400 h of loading. The significant stress gradients within the solder joints result in increased back stress, thus balancing the electromigration stress and completely suppressing element migration. [ABSTRACT FROM AUTHOR]

We studied the transport properties of graphene–insulator–metal tunneling diodes. Two sets of tunneling diodes with Ti–Cu and Cr–Au top contacts are fabricated. Transport measurements showed state-of-the-art non-linearity and a critical influence of the top metals on the dielectric strength of the tunneling barrier. X-ray photoelectron spectroscopy indicated two methods for enhancing the dielectric strength of the tunneling barrier. These are the optimized seed layers for the growth of high-quality conformal insulators and the selection of appropriate top metal layers with a small diffusion coefficient and electromigration into the Al2O3 barrier. The Cr–Au top contact provides superior characteristics to the Ti–Cu metallization. X-ray photoelectron spectroscopy showed significant diffusion of titanium during the Al2O3 growth and the formation of titanium inclusions after annealing. Chromium diffusion is slower than that of titanium, making chromium contact more suitable for the reliable operation of tunneling diodes. As a result, we demonstrate a 40% improvement in the dielectric strength of the tunneling barrier compared to state-of-the-art metal–insulator–metal diodes. [ABSTRACT FROM AUTHOR]

As the current density increases in electronic devices, electromigration has become a significant factor affecting the reliability of solder joints. In this study, the electromigration characteristics of Sn3.0Ag0.5Cu (SAC305) solder joints were investigated with in-situ experiments and finite element simulation methods. As the duration of current flow rose from 0 to 100 h, the thickness of the intermetallic compound (IMC) at the anode of solder joint S1 increased from 6.86 µm to 26.55 µm, and the thickness of the IMC at the cathode decreased from 5.22 µm to 0.75 µm. The thickness of the IMC at the anode of solder joint S3 increased from 4.91 µm to 23 µm, and the thickness of the IMC at the cathode decreased from 6.83 µm to 0.58 µm. The upper side of the solder point S2 is connected to the Cu wire through which current flows, and electromigration occurs in the horizontal direction, resulting in the formation of a void in the upper right corner of the solder point. The simulation results show that current concentration occur at the corners of solder joints S1 and S3, resulting in an increase of the current density in this area. When electrons move horizontally from the upper surface of the solder joint S2, the solder joint atoms migrate from one side to the other and form voids. The voids further increase the local current density around them and intensifies electromigration in this region. This research is of significance for the design of high-reliability packaging structure. [ABSTRACT FROM AUTHOR]

Hexagonal boron nitride (hBN) holds promise as a solid state, van der Waals host of single photon emitters for on‐chip quantum photonics. The B‐center defect emitting at 436 nm is particularly compelling as it can be generated by electron beam irradiation. However, the emitter generation mechanism is unknown, the robustness of the method is variable, and it has only been applied successfully to thick flakes of hBN (≫ 10 nm). Here, it is used in situ time‐resolved cathodoluminescence (CL) spectroscopy to investigate the kinetics of B‐center generation. It is shown that the generation of B‐centers is accompanied by quenching of a carbon‐related emission at ≈305 nm and that both processes are rate‐limited by electromigration of defects in the hBN lattice. It identifies problems that limit the efficacy and reproducibility of the emitter generation method and solve them using a combination of optimized electron beam parameters and hBN pre‐and postprocessing treatments. It is achieved B‐center quantum emitters in hBN flakes as thin as 8 nm, elucidate the mechanisms responsible for electron beam restructuring of quantum emitters in hBN, and gain insights toward the identification of the atomic structure of the B‐center quantum emitter. [ABSTRACT FROM AUTHOR]

Electromigration (EM) is a critical reliability issue in integrated circuits and is becoming increasingly significant as fabrication technology nodes continue to advance. The analysis of the hydrostatic stress, which is paramount in electromigration studies, typically involves solving complex physical equations (partial differential equations, or PDEs in this case), which is time consuming, inefficient and not practical for full-chip EM analysis. In this paper, a novel approach is proposed, conceptualizing circuit interconnect trees as a graph within a graph neural network framework. Using finite element solution software, ground truth hydrostatic stress values were obtained to construct a dataset of interconnected trees with hydrostatic stress values for each node. An improved Graph Convolutional Network (GCN) augmented with edge feature aggregation and attention mechanism was then trained employing the dataset, yielding a model capable of predicting hydrostatic stress values for nodes in an interconnect tree. The results show that our model demonstrated a 15% improvement in the Root Mean Square Error (RMSE) compared to the original GCN model and improved the solution speed greatly compared to traditional finite element software. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid modelling approach that combines physics-based electromigration modelling (PEM) and statistical methods to evaluate the electromigration (EM) limits of nano-interconnects in mesh networks. The approach, which is also compatible with standard Place and Route (P&R) tools and practises, takes into account the positive impact of network redundancy on EM current limits. The numerical simulations conducted in this study show that conventional methods underestimate the EM current limits of a power delivery network (PDN) unit-cell by 80% due to their lack of consideration for redundancy. Additionally, the time-to-failure (TTF) distributions of a PDN unit-cell obtained by the developed modelling framework adhered to a lognormal distribution, where the lognormal sigma, σlogn, exhibits a 55% reduction compared to that of the single constituent interconnects. The study also found the negative voltage (i.e., ground or Vss) grid to be more susceptible to EM than the positive voltage, i.e., Vdd grid. In the examined grid unit-cell design, both the number of interconnect sites prone to voiding and also the magnitude of the peak tensile stress within the nano-interconnects were found to be two times as high in the Vss case compared to Vdd. The lognormal sigma of TFF for the grid unit-cells, σ l o g n − t i l e , show a marked reduction compared to the lognormal sigma of the constituent single interconnects, σ l o g n , with a 50% and 66% decrease compared to single interconnects, for downstream (Vss) and upstream (Vdd), respectively. In addition, σ l o g n − t i l e was three times higher for downstream (Vss) compared to upstream (Vdd), whilst, in contrast, this difference was only 2-fold at the single interconnect level. TTF50% was predicted to be 4.13-fold higher at the grid unit-cell level for the upstream compared to downstream operation, which was also more pronounced than in the single interconnect level where the difference was only 2-fold. This research provides valuable insights into the EM ageing of nano-interconnects in mesh networks and could pragmatically enhance the accuracy of EM compliance evaluation methods. [ABSTRACT FROM AUTHOR]

The nanogap resistive switch holds potential as a candidate for nonvolatile memory, although its durability needs enhancement. This study delves into the operational mechanisms through detailed morphological examination during continuous operation of nanogap resistive switches. By developing a finite element model of nanogaps, we reveal the mechanisms behind the formation of electrode surface hillocks and filaments during continuous switching. Our findings suggest that "set" operations include processes such as field evaporation, electric field-induced diffusion, and field-assisted migration within the gap. Conversely, "reset" operations, driven by Joule heating and electromigration, lead to filament breakage and the creation of a fine gap. This research elucidates device degradation issues, such as periodic fluctuations in set threshold voltage (Vset) and the presence of non-steep set curves, providing both theoretical and experimental insights to improve future device performance. [ABSTRACT FROM AUTHOR]

The paper reveals the influence of Li, B and the composition of metal contacts on the processes of resistive switching in memristive structures M/NC/D/M. After field exposure in structures Cu/(Co50Fe50)x(LiNbO3)100–x/s-LiNbO3/Cu/sitall, Cu/(Co50Fe50)x(LiNbO3)100–x/d-LiNbO3/Cu/sitall and Cu/(Co40Fe40B20)x(SiO2)100–x/d LiNbO3/Cu/sitall at x < 13 was detected a residual voltage (up to 16 mV) due to the electromigration of Li ions, that leading to a "reversible" type of VAC hysteresis and instability of the time dependencies of induced resistive states. In the structures of Cu/(Co40Fe40B20)x(LiNbO3)100–x/s-LiNbO3/Cu/sitall, Cr/Cu/Cr/(Co40Fe40B20)x(LiNbO3)100–x/s-LiNbO3/Cr/Cu/Cr/sitall containing B, the residual voltage is reduced by formation of chemical compounds B with percolated Li atoms. When limiting the electromigration of Li ions, the main mechanism of resistive switching is the processes of electromigration of oxygen vacancies in the dielectric oxide layer. Suppression of residual voltage in the Cr/Cu/Cr/(Co50Fe50)x(LiNbO3)100–x/s-LiNbO3/Cr/Cu/Cr/sitall structure due to the introduction of a Cr buffer layer that does not dissolve Li leads to the absence of bipolar resistive switching in these structures. [ABSTRACT FROM AUTHOR]

Capillary electrophoresis (CE) is a powerful separation technique offering quick and efficient analyses in various fields of bioanalytical chemistry. It is characterized by many well‐known advantages, but one, which is perhaps the most important for this application field, is somewhat overlooked. It is the possibility to perform chemical and biochemical reactions at the nL scale inside the separation capillary. There are two basic formats applicable for this purpose, heterogeneous and homogeneous. In the former, one reactant is immobilized onto a particle or monolithic support or directly on the capillary wall, and the other is injected. In the latter, the reactant mixing inside a capillary is based on electromigration or diffusion. One of the diffusion‐based methodologies, termed Transverse Diffusion of Laminar Flow Profiles, is the subject of this review. Since most studies utilizing in‐capillary reactions in CE focus on enzymes, which are being continuously and exhaustively reviewed, this review covers the atypical applications of this methodology, but still in the bioanalytical field. As can be seen from the demonstrated applications, they are not limited to reactions, but can also be utilized for other biochemical systems. [ABSTRACT FROM AUTHOR]

Several recent theoretical studies have indicated that a relatively simple secretion control mechanism in the epithelial cells lining the stomach may be responsible for maintaining a neutral (healthy) pH adjacent to the stomach wall, even in the face of enormous electrodiffusive acid transport from the interior of the stomach. Subsequent work used Sobol’ Indices (SIs) to quantify the degree to which this secretion mechanism is “self-regulating” i.e. the degree to which the wall pH is held neutral as mathematical parameters vary. However, questions remain regarding the nature of the control that specific parameters exert over the maintenance of a healthy stomach wall pH. Studying the sensitivity of higher moments of the statistical distribution of a model output can provide useful information, for example, how one parameter may skew the distribution towards or away from a physiologically advantageous regime. In this work, we prove a relationship between SIs and the higher moments and show how it can potentially reduce the cost of computing sensitivity of said moments. We define γ -indices to quantify sensitivity of variance, skewness, and kurtosis to the choice of value of a parameter, and we propose an efficient strategy that uses both SIs and γ -indices for a more comprehensive sensitivity analysis. Our analysis uncovers a control parameter which governs the “tightness of control” that the secretion mechanism exerts on wall pH. Finally, we discuss how uncertainty in this parameter can be reduced using expert information about higher moments, and speculate about the physiological advantage conferred by this control mechanism. [ABSTRACT FROM AUTHOR]

The Nernst-Planck-Stokes (NPS) system models electroconvection of ions in a fluid. We consider the system, for two oppositely charged ionic species, on three dimensional bounded domains with Dirichlet boundary conditions for the ionic concentrations (modelling ion selectivity), Dirichlet boundary conditions for the electrical potential (modelling an applied potential), and no-slip boundary conditions for the fluid velocity. In this paper, we obtain quantitative bounds on solutions of the NPS system in the long time limit, which we use to prove (1) the existence of a compact global attractor with finite fractal (box-counting) dimension and (2) space-time averaged electroneutrality \rho \approx 0 in the singular limit of Debye length going to zero, \epsilon \to 0. [ABSTRACT FROM AUTHOR]

The paper reveals the influence of Li, B and the composition of metal contacts on the processes of resistive switching in memristive structures M/NC/D/M. After field exposure in structures Cu/(Co50Fe50)x(LiNbO3)100–x/s-LiNbO3/Cu/sitall, Cu/(Co50Fe50)x(LiNbO3)100–x/d-LiNbO3/Cu/sitall and Cu/(Co40Fe40B20)x(SiO2)100–x/d LiNbO3/Cu/sitall at x < 13 was detected a residual voltage (up to 16 mV) due to the electromigration of Li ions, that leading to a "reversible" type of VAC hysteresis and instability of the time dependencies of induced resistive states. In the structures of Cu/(Co40Fe40B20)x(LiNbO3)100–x/s-LiNbO3/Cu/sitall, Cr/Cu/Cr/(Co40Fe40B20)x(LiNbO3)100–x/s-LiNbO3/Cr/Cu/Cr/sitall containing B, the residual voltage is reduced by formation of chemical compounds B with percolated Li atoms. When limiting the electromigration of Li ions, the main mechanism of resistive switching is the processes of electromigration of oxygen vacancies in the dielectric oxide layer. Suppression of residual voltage in the Cr/Cu/Cr/(Co50Fe50)x(LiNbO3)100–x/s-LiNbO3/Cr/Cu/Cr/sitall structure due to the introduction of a Cr buffer layer that does not dissolve Li leads to the absence of bipolar resistive switching in these structures. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) semiconductors, such as monolayer MoS2, has emerged as a profound material platform in the post‐Moore era due to their versatile applications for high‐performance transistors, memories, photodetectors, neuristors, and so on. Nevertheless, the inherent defects in these atomically thin materials have given rise to significant hysteresis in their field‐effect transistors (FETs), resulting in shifted threshold voltages and elevated power consumptions not only on single‐device levels but also at circuitry scales. We herein report that, by vertically integrating an in‐plane ferroelectric, NbOCl2, with monolayer MoS2 FETs, the hysteresis in both the output and transfer curves of the latter can be greatly suppressed, which we attribute to compensated electromigration currents by the polarization currents of the 2D ferroelectric. This work opens a new avenue to hysteresis‐free 2D transistors without necessitating defect‐free channels, thus allowing for their use in high driving‐voltage scenarios such as power electronics. [ABSTRACT FROM AUTHOR]

Due to the continuous miniaturization and high current-carrying demands in the field of integrated circuits, as well as the desire to save space and improve computational capabilities, there is a constant drive to reduce the size of integrated circuits. However, highly integrated circuits also bring about challenges such as high current density and excessive Joule heating, leading to a series of reliability issues caused by electromigration. Therefore, the service reliability of integrated circuits has always been a concern. Sn-based solders are widely recognized in the industry due to their availability, minimal technical issues during operation, and good compatibility with traditional solders. However, solders that are mostly Sn-based, such as SAC305 and SnZn, have a high melting point for sophisticated electronic circuits. When Bi is added, the melting point of the solder decreases but may also lead to problems related to electromigration reliability. This article reviews the general principles of electromigration in SnBi solder joints on Cu substrates with current flow, as well as the phenomena of whisker formation, voids/cracks, phase separation, and resistance increase caused by atomic migration due to electromigration. Furthermore, it explores methods to enhance the reliability of solder joint by additives including Fe, Ni, Ag, Zn, Co, RA (rare earth element), GNSs (graphene nanosheets), FNS (Fullerene) and Al2O3. Additionally, modifying the crystal orientation within the solder joint or introducing stress to the joint can also improve its reliability to some extent without changing the composition conditions. The corresponding mechanisms of reliability enhancement are also compared and discussed among the literature. [ABSTRACT FROM AUTHOR]

In situ transmission electron microscopy was used to observe the electromigration-driven sliding behavior of twinned face-centered cubic-Co fillers sliding inside multi-walled carbon nanotubes with an inner-diameter step. Each filler contained a twin boundary located at the nanotube inner-diameter step. Under application of an electric current, the twinned Co fillers moved across the steps and changed their diameter, and the position of the twin boundary was maintained at the nanotube inner-diameter step. [ABSTRACT FROM AUTHOR]

The review provides an overview of recent developments and applications of capillary electromigration (CE) methods for the determination of important physicochemical parameters of various (bio)molecules and (bio)particles. These parameters include actual and limiting (absolute) ionic mobilities, effective electrophoretic mobilities, effective charges, isoelectric points, electrokinetic potentials, hydrodynamic radii, diffusion coefficients, relative molecular masses, acidity (ionization) constants, binding constants and stoichiometry of (bio)molecular complexes, changes of Gibbs free energy, enthalpy and entropy and rate constants of chemical reactions and interactions, retention factors and partition and distribution coefficients. For the determination of these parameters, the following CE methods are employed: zone electrophoresis in a free solution or in sieving media, isotachophoresis, isoelectric focusing, affinity electrophoresis, electrokinetic chromatography, and electrochromatography. In the individual sections, the procedures for the determination of the above parameters by the particular CE methods are described. [ABSTRACT FROM AUTHOR]

This study improves and expands the scope of application of the theoretical model previously proposed by the authors, which describes the relationship between the strength and electromigration (diffusion) properties of interfaces formed by connected materials. In the developed model, a linear relationship is established between the values of the work of reversible interface separation and electromigration activation energy in the interface. Estimates are made and the coefficients of the resulting relation are compared with experiments studying electromigration in a copper conductor coated with a protective dielectric. Using also the model previously developed by the authors, which describes the dependence of the quantity on the concentrations of nonequilibrium lattice defects presenting in the volumes of connected materials, a number of effects due to the influence of such defects on processes caused by electromigration are predicted and studied. This study shows that by introducing nonequilibrium lattice defects in the form of atomic interstitial or substitutional impurities into the volumes of the joined materials, we can effectively influence on the characteristics of the electromigration instability of the shape of the interlayer boundary. For interstitial impurities, quantitative analytical estimates of the impurity concentration required to significantly change (both increase and decrease) the characteristic growth time of the instability of the shape of an initially flat interface are performed. [ABSTRACT FROM AUTHOR]

Power efficiency and performance requirements are driving the trend towards smaller interconnects in 3D packaging. Also, significant ongoing effort is aimed at finding alternatives to SnAgCu (SAC) solder alloys, either for low-temperature reflow or high reliability. Therefore, there is a need to characterize such alloys at dimensions relevant to their applications. Typically, such characterization involves testing the devices, followed by cross-sectioning and polishing to observe failure mechanisms. The drawback of this method is that the material removal due to polishing may reduce the amount of data that can be obtained. Also, cross-sectioning the devices renders them unusable for further testing, thus creating a discontinuity in the experiments. In this study, a procedure is outlined for fabricating devices termed in-line microjoints, featuring multiple Cu–solder–Cu junctions in either a straight line or a serpentine arrangement, enabling non-destructive characterization of the solder. Using this procedure, devices can be made with any commercially available solder paste, which enables testing of various alloys. The electromigration of Bi in SnBi low-temperature solder is characterized non-destructively and the diffusivity of Bi is reported at 75°C, 90°C, and 105°C. The reported diffusivity values align with the existing literature on Bi diffusivity. We also report a transient phenomenon in SnBi solder joints, where the initial rate of resistance change is non-linear, followed by a transition to a linear rate. Lastly, tests on the serpentine structures show lower Bi accumulation in regions where current crowding is expected, which is counter-intuitive. [ABSTRACT FROM AUTHOR]

We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two species or the diffusivities and the absolute values of ionic valences are the same if the species are arbitrarily many. In particular, the boundary conditions for the ions are allowed to be inhomogeneous. The proof is based on the energy estimates, integration along the characteristic line and the regularity theory of elliptic and parabolic equations. [ABSTRACT FROM AUTHOR]

High abundance 6Li and 7Li are essential materials for the nuclear industry. In this article, the lithium isotope separation effect and lithium-ion transport of a "lithium salt aqueous solution (anolyte)‖crown ethers–ionic liquid organic solution‖ammonium chloride aqueous solution (catholyte)" electromigration system with B12C4, B15C5 and B18C6 as phase transfer catalysts were investigated systematically. The results show that separation factors can reach 1.028 (B12C4), 1.024 (B15C5) and 1.011 (B18C6), respectively, when LiCl solution is used as the anolyte. The separation effect mainly originated from interfaces between anolytes and organic solutions, and was less affected by an electric field. The separation effect between organic solution and catholytes was greatly affected by the electric field for B12C4 and B15C5 systems, which converted from 7Li-enrichment to 6Li-enrichment with increased voltage. For the B18C6 system it was less affected. Furthermore, lithium ion transport in B12C4, B15C5 and B18C6 systems was greatly promoted by the electric field, with the Li+ concentration in catholytes of B12C4, B15C5 and B18C6 systems increased from 0.088 mg L−1, 0.286 mg L−1 and 0.778 mg L−1 to 8.321 mg L−1, 7.422 mg L−1 and 4.631 mg L−1 respectively as the voltage increased from 2 V to 16 V. The B12C4 system has been confirmed as the optimal solution considering both the Li+ transport and isotope separation effect. [ABSTRACT FROM AUTHOR]

Studies have reported that the electromigration-induced void growth velocity in metal thin films is inversely related to the adhesion strength of the metal thin film with the base and passivation layers. It was also observed that the contribution of interface adhesion strength to electromigration resistance decreases with an increase in temperature. In this study, an expression is derived for the diffusive void growth velocity induced by electromigration from a generalized thermodynamically consistent continuum-based theory for reaction-diffusion driven solid-state interface evolution. This relation captures the effect of adhesion with the base and passivation layers on electromigration resistance of thin metal films. Electromigration experiments were carried out at elevated temperatures and high current density to induce voiding in thin Cu metal film deposited on a base layer of TiN and passivated with TiN or SiNx. The degradation of interface adhesion strength with temperature is modeled using an Andrade-type of relationship. The void growth rates characterized in these experiments are combined with the expression for void growth rate to estimate the interface adhesion strength for the Cu-TiN and Cu-SiNx interfaces. The methodology for estimating the adhesion strength of the metal-passivation layer interface is validated through comparison with interface adhesion strengths from mechanical de-adhesion tests reported in the literature. [ABSTRACT FROM AUTHOR]

Iontophoresis enables the non-invasive transdermal delivery of moderately-sized proteins and the needle-free cutaneous delivery of antibodies. However, simple descriptors of protein characteristics cannot accurately predict the feasibility of iontophoretic transport. This study investigated the cathodal and anodal iontophoretic transport of the negatively charged M7D12H nanobody and a series of negatively charged variants with single amino acid substitutions. Surprisingly, M7D12H and its variants were only delivered transdermally by anodal iontophoresis. In contrast, transdermal permeation after cathodal iontophoresis and passive diffusion was

The paper describes the research and study of the process of electrically induced diffusion of Mn atoms in silicon directly from a Si surface layer that was preliminarily enriched with Mn. To ensure the so-called electrically induced diffusion process, a constant electric field was applied to the investigated samples. It has been revealed that as a result of the diffusion of Mn impurity atoms into samples placed at the negative pole of the electrical diffusion unit, the proportion of Mn atoms was 75.4% (relative to silicon atoms), while in samples placed at the positive pole this indicator tended to be 2.7% (relative to silicon atoms). Besides that, for the first time, an experimental increase in the electro-active concentration of Mn impurity atoms in silicon (at T = 900°C) was detected under the influence of an external constant-value electric field. In this case, the maximum solubility of impurity atoms of Mn at a temperature of T = 900°C was NMn~2.27·1014 cm-3, while the average concentration of electro-active Mn atoms diffused into silicon under the influence of an external constant electric field reached NMn*~2.62·1014 cm-3. [ABSTRACT FROM AUTHOR]

Understanding the underlying factors responsible for higher-than-anticipated local field enhancements required to trigger vacuum breakdown on pristine metal surfaces is crucial for the development of devices capable of withstanding intense operational fields. In this study, we investigate the behavior of nominally flat copper electrode surfaces exposed to electric fields of hundreds of MV/m. Our novel approach considers curvature-driven diffusion processes to elucidate the formation of sharp breakdown precursors. To do so, we develop a mesoscale finite element model that accounts for driving forces arising from both electrostatic and surface-tension-induced contributions to the free energy. Our findings reveal a dual influence: surface tension tends to mitigate local curvature, while the electric field drives mass transport toward regions of high local field density. This phenomenon can trigger the growth of sharper protrusions, ultimately leading to a rapid enhancement of local fields and, consequently, to a runaway growth instability. We delineate supercritical and subcritical regimes across a range of initial surface roughness. Our numerical results are in qualitative agreement with experimentally reported data, indicating the potential practical relevance of field-driven diffusion in the formation of breakdown precursors. [ABSTRACT FROM AUTHOR]

The electromigration (EM) behavior of graphene‐doped twinned copper composite (GC–Cu) and nanotwinned copper (NT–Cu) redistributed layers (RDLs) are investigated. Firstly, the GC–Cu has longer lifetimes under various test conditions. For example, the GC–Cu RDL took 291 h to reach a 20% resistance increase, while the NT–Cu RDL took 117 h under the same condition of 120 °C and 106 A cm−2. Secondly, thinner oxidation layer and slighter voiding phenomena are detected on GC–Cu RDLs. When the line width and spacing (L/S) of RDL decreased from 20/20 μm to 10/10 μm, new failure modes, i.e., fracture of oxide layer, separation between the oxide layer and copper matrix are also detected, demonstrating the increasing thermal mismatch. Combined with the finite element analysis (FEA), there is simultaneous current aggregation and stress concentration around the voids, which should further cause the degradation of RDL. Above all, this study gives insights into the material design in the fine‐pitch RDL structure. [ABSTRACT FROM AUTHOR]

Cu-cored solder interconnects have been demonstrated to increase the performance of interconnect structures, while the quantitative understanding of the effect of the Cu-cored structure on microstructure evolution and atomic migration in solder interconnects is still limited. In this work, the effect of the Cu-cored structure on phase migration and segregation behavior of Sn-58Bi solder interconnects under electric current stressing is quantitatively studied using a developed phase field model. Severe phase segregation and redistribution of Bi-rich phase are observed in the Cu-cored Sn-58Bi interconnects due to the more pronounced current crowding effect near the Cu core periphery. The average current density and temperature gradient in Sn-rich phase and Bi-rich phase decrease with an increase in the diameter of the Cu core. The temperature gradient caused by Joule heating is significantly reduced owing to the presence of the Cu core. Embedding of the Cu core in the solder matrix could weaken the directional diffusion flux of Bi atoms, so that the enrichment and segregation of the Bi phase towards the anode side are significantly reduced. Furthermore, the voltage across the solder interconnects is correspondingly changed due to the phase migration and redistribution. [ABSTRACT FROM AUTHOR]

Recent development in heterogeneous integration for high-performance chips (HPC) demands higher power, which induces a higher level of current density per through-silicon via (TSV) and redistribution layer (RDL) interconnects. Change in electrical and thermomechanical properties during long-term current stressing can result in negative impact on signal integrity and reliability of the device. In this study, test samples of Si interposers containing TSVs with a multilayered RDL structure at the top were tested under current densities ranging from 1 × 105 A/cm2 to 2.5 × 105 A/cm2 at 200°C in vacuum. Microstructural changes were observed in the current-carrying TSVs, and the circuit resistance increased sharply during the test. This increase was associated with several damage modes, including migration of Sn and Ag from solder, and Ni from under-bump metallization, driven by electromigration, leading to alloying and formation of reaction products. A volume increase associated with phase transformations and electromigration-induced void formation defects are identified under highly accelerated testing conditions, which potentially affect the long-term reliability of TSV-containing structures and need to be considered in design and manufacturing protocols for devices and packages. [ABSTRACT FROM AUTHOR]

A systematic study based on self-consistent dynamical simulations is presented for the morphological evolutionary behavior of an isolated thin Ge/Si nanoisland (quantum dot) on a rigid substrate exposed to electromigration forces. This morphological evolution is basically induced by the anisotropic surface drift diffusion, driven by the capillary forces, the lattice mismatch stresses, and the wetting potential. In this study, we have mainly focused on the size and shape development kinetics of quantum dots, known as the "Stranski–Krastanov" (SK) morphology, influenced by applied electromigration stresses. Emphasis is given to the effects of rotational symmetry associated with the anisotropic diffusivity in 2D space (i.e., quantum wires in 3D). The pointed bullet-shaped "Stranski–Krastanov" islands with high aspect ratios, ξ = 0.77, are formed at the cathode edge, while the whole nanoisland slightly creeps out of the initial computational domain. The favorable configuration of the Ge20/Si80 alloy test module, which resulted in ζ = 0.37 enhancement in the contour surface area, has a dome shape attached to the [010] top surface of the Si substrate with a zone axis of {010}/ ⟨ 001 ⟩. The anisotropic surface diffusion dyadic has a fourfold rotational symmetry axis [001] lying on the (001) plane of the Si substrate, and its major axis is tilted at about ϕ = 45° from the applied electrostatic field extended along the longitudinal axis [100] of the substrate. This particular experiment resulted in a SK singlet peak with a small satellite with a very small aspect ratio of ≅0.2 that may be appropriate for the conception of quantum optoelectronic devices or inter-band structures to generate photoelectrons having large energy spectra, thereby increasing the efficiency of photovoltaics exposed to solar radiations. [ABSTRACT FROM AUTHOR]

As the dimensions of interconnects in integrated circuits continue to shrink, an urgent need arises to understand the physical mechanism associated with electromigration. Using x-ray nanodiffraction, we analyzed the stresses in Blech-structured pure Cu lines subjected to different electromigration conditions. The results suggest that the measured residual stresses in the early stages of electromigration are related to relaxation of stresses caused by thermal expansion mismatch, while a developing current-induced stress leads to reductions in the residual stress after longer test times. These findings not only validate the feasibility of measuring stress in copper lines using nanodiffraction but also highlight the need for a further understanding, particularly through in situ electromigration experiments with x-ray nanodiffraction analysis. [ABSTRACT FROM AUTHOR]

The current densities in nowadays electronic circuitry are close to the electromigration threshold that may result in the fracture of circuits due to electromigration, hampering further miniaturization of integrated chips. Flexible electronic devices, which use a flexible material instead of rigid silicon as a substrate, might be prone to fracture problems also due to obligatory mechanical deformation. However, finding the location of fractured nanogaps and in situ repairing such atomic‐scale fractured circuits are currently unavailable. To this end, a method is developed to in situ heal nanogaps as large as 20 nm between metallic electrodes on the polyimide (PI)‐covered substrate via voltage sweeping, which is typically employed to generate nanogaps rather than heal nanogaps. The reconnection of nanoelectrodes is realized only when the underneath PI is treated with oxygen plasma etching. Assisted by X‐ray photoelectron spectroscopy, it is revealed that inductively coupled O2 plasma etching not only changes the surface topography but also changes the chemical binding structure of PI, which in return can be used to immobilize metal atoms migrating along the PI surface to gradually close the nanogap, providing an in situ self‐healing paradigm for repairing the atomic scale fractured circuits. [ABSTRACT FROM AUTHOR]

Solid solutions CsAg4Br3 –хI2 +х (x = 0.38; 0.50; 0.68) are prepared by solid-state synthesis; the single phase of the products is confirmed using the methods of X-ray diffraction and differential scanning calorimetry. The studies of electrotransport characteristics of CsAg4Br3 –хI2 +х involve measuring the ionic conductivity by the four-probe method in the temperature interval from –50 to +120°C and estimating its electronic component by the Hebb–Wagner method. It is shown that in the studied interval of compositions, the ionic conductivity of CsAg4Br3 –хI2 +х solid solutions is practically independent of x, approaching the conductivity of the well-known superionic conductor RbAg4I5. The activation energy of conduction is found to be about 10 kJ mol–1 for all compounds studied. The oxidation potential determined by the method of stepwise polarization for CsAg4Br3 –хI2 +х solid solutions is considerably higher as compared with RbAg4I5, being in the range of 0.75–0.78 V (vs. Ag0/Ag+). The high electrochemical characteristics of CsAg4Br3 –хI2 +х (0.38 ≤ x ≤ 0.63) and the absence of polymorphic transitions in the considered interval from –160°С to the melting point (175–178°С) make these materials promising for the use in electrochemical devices, especially in low-temperature applications. [ABSTRACT FROM AUTHOR]

The vast majority of excitatory synaptic connections occur on dendritic spines. Due to their extremely small volume and spatial segregation from the dendrite, even moderate synaptic currents can significantly alter ionic concentrations. This results in chemical potential gradients between the dendrite and the spine head, leading to measurable electrical currents. In modeling electric signals in spines, different formalisms were previously used. While the cable equation is fundamental for understanding the electrical potential along dendrites, it only considers electrical currents as a result of gradients in electrical potential. The Poisson-Nernst-Planck (PNP) equations offer a more accurate description for spines by incorporating both electrical and chemical potential. However, solving PNP equations is computationally complex. In this work, diffusion currents are incorporated into the cable equation, leveraging an analogy between chemical and electrical potential. For simulating electric signals based on this extension of the cable equation, a straightforward numerical solver is introduced. The study demonstrates that this set of equations can be accurately solved using an explicit finite difference scheme. Through numerical simulations, this study unveils a previously unrecognized mechanism involving diffusion currents that amplify electric signals in spines. This discovery holds crucial implications for both numerical simulations and experimental studies focused on spine neck resistance and calcium signaling in dendritic spines. [ABSTRACT FROM AUTHOR]

Solid solutions CsAg4Br3 –хI2 +х (x = 0.38; 0.50; 0.68) are prepared by solid-state synthesis; the single phase of the products is confirmed using the methods of X-ray diffraction and differential scanning calorimetry. The studies of electrotransport characteristics of CsAg4Br3 –хI2 +х involve measuring the ionic conductivity by the four-probe method in the temperature interval from –50 to +120°C and estimating its electronic component by the Hebb–Wagner method. It is shown that in the studied interval of compositions, the ionic conductivity of CsAg4Br3 –хI2 +х solid solutions is practically independent of x, approaching the conductivity of the well-known superionic conductor RbAg4I5. The activation energy of conduction is found to be about 10 kJ mol–1 for all compounds studied. The oxidation potential determined by the method of stepwise polarization for CsAg4Br3 –хI2 +х solid solutions is considerably higher as compared with RbAg4I5, being in the range of 0.75–0.78 V (vs. Ag0/Ag+). The high electrochemical characteristics of CsAg4Br3 –хI2 +х (0.38 ≤ x ≤ 0.63) and the absence of polymorphic transitions in the considered interval from –160°С to the melting point (175–178°С) make these materials promising for the use in electrochemical devices, especially in low-temperature applications. [ABSTRACT FROM AUTHOR]

We consider the Nernst-Planck-Navier-Stokes system describing the electrodiffusion of ions in a viscous Newtonian fluid. We prove the exponential nonlinear stability of constant steady states in the case of periodic boundary conditions in any dimension of space without constraints on the number of species, valences and diffusivities. We consider also the case of two spatial dimensions, and we prove the exponential stability from arbitrary large data. [ABSTRACT FROM AUTHOR]

Introduction: In addition to gap junction conduction, recent reports implicate possible ephaptic coupling contributions to action potential (AP) propagation between successive adjacent cardiomyocytes. Here, AP generation in an active cell, withdraws Na+ from, creating a negative potential within, ephaptic spaces between the participating membranes, activating the initially quiescent neighbouring cardiomyocyte. However, sustainable ephaptic transmission requires subsequent complete recovery of the ephaptic charge difference. We explore physical contributions of passive electrodiffusive ion exchange with the remaining extracellular space to this recovery for the first time. Materials and Methods: Computational, finite element, analysis examined limiting, temporal and spatial, ephaptic [Na+], [Cl-], and the consequent Gaussian charge differences and membrane potential recovery patterns following a ΔV~130 mV AP upstroke at physiological (37°C) temperatures. This incorporated Nernst-Planck formalisms into equations for the time-dependent spatial concentration gradient profiles. Results: Mammalian atrial, ventricular and purkinje cardiomyocyte ephaptic junctions were modelled by closely apposed circularly symmetric membranes, specific capacitance 1 µF cm-2, experimentally reported radii a = 8,000, 12,000 and 40,000 nm respectively and ephaptic axial distance w = 20 nm. This enclosed an ephaptic space containing principal ions initially at normal extracellular [Na+] = 153.1 mM and [Cl-] = 145.8 mM, respective diffusion coefficients DNa = 1.3 x 109 and DCl = 2 x 109 nm²s-1. Stable, concordant computational solutions were confirmed exploring ≤1,600 nm mesh sizes and Δt≤0.08 ms stepsize intervals. The corresponding membrane voltage profile changes across the initially quiescent membrane were obtainable from computed, graphically represented a and w-dependent ionic concentration differences adapting Gauss's flux theorem. Further simulations explored biological variations in ephaptic dimensions, membrane anatomy, and diffusion restrictions within the ephaptic space. Atrial, ventricular and Purkinje cardiomyocytes gave 40, 180 and 2000 ms 99.9% recovery times, with 720 or 360 ms high limits from doubling ventricular radius or halving diffusion coefficient. Varying a, and DNa and DCl markedly affected recovery time-courses with logarithmic and double-logarithmic relationships, Varying w exerted minimal effects. Conclusion: We thereby characterise the properties of, and through comparing atrial, ventricular and purkinje recovery times with interspecies in vivo background cardiac cycle duration data, (blue whale ~2000, human~90, Etruscan shrew, ~40 ms) can determine physical limits to, electrodiffusive contributions to ephaptic recovery. [ABSTRACT FROM AUTHOR]

2,4-Dichlorophenol (2,4-DCP) is difficult to degrade rapidly in the environment due to its stable chemical properties, so it was easy to lead to serious chlorophenol pollution in soil. Consequently, a remediation method which is efficient, safe, and economical is required. In this study, electrokinetic (EK) remediation was used to transfer sodium persulfate (Na2S2O8) into soil to degrade 2,4-DCP, and the effect of several factors (including the addition location of Na2S2O8, applied voltage, and running time) on the remediation efficiency was explored. The concentration of Na2S2O8, residual efficiency of 2,4-DCP and distribution characteristics of pH, and electrical conductivity were analyzed. The results showed that the cathode was the optimal position to add Na2S2O8. Under this condition, Na2S2O8 was uniformly distributed in the whole soil column through electromigration. The optimal removal efficiency of 2,4-DCP in soil by adding Na2S2O8 was approximately 26% when the voltage gradient was 1.0 V/cm and the operating time was 9 days, which was mainly due to the degradation of S2O82−. [ABSTRACT FROM AUTHOR]

Using a recent continuum model of a single-crystal nanowire morphological evolution in the applied axial electric field, an axisymmetric evolution of a microscopically rough nanowire surface is computed. Morphological evolution results in a wire breakup into a cylindrical segments (particles). Breakup time and the number of particles are characterized for various levels of the radial and axial surface roughness. It is shown that electromigration and larger surface roughness lead to a shorter breakup time and the increased number of particles. [ABSTRACT FROM AUTHOR]

To clarify potential issues that may arise in the future when high current densities are applied to joints in electronic power modules, high current density (25 kA/cm2) energization tests were conducted on sintered Ag joints sandwiched between Au and Ag layers. The degradation behavior differed depending on the current direction. The joint that placed the Au layer on the anode side showed a faster increase in voltage and temperature than the one placed on the Au layer at the cathode side, which also fractured at a much shorter energizing time (5 h). Generation and segregation of high-concentration coarse voids, in the same plane and growth of the Ag-Au solid solution layer, were observed in the sintered Ag layer of the joint, which placed the Au layer at the anode side before the fracture. Segregated voids existed near the cathode-side interface between the Ag layer and the surface of the base metal (Ti), and around the anode-side interface between the Ag layer and the Ag-Au solid solution layer. These results imply that the electromigration and diffusion coefficient imbalance between Ag and Au affect the behavior of the void generation and growth of the solid solution layer, which leads to a difference in the lifetime of the joints in the current direction under high current density energization. This indicates that the Au layer placed at the anode of the sintered Ag layer loses the reliability of the sintered Ag joints under the high current density driving electronic power modules. [ABSTRACT FROM AUTHOR]

The combined use of Through Silicon Via (TSV) and metal lines, referred to as TSV-metal lines, is an essential structure in three-dimensional integrated circuits. In-depth research into the electromigration failure mechanism of TSV and the microstructure evolution can serve as theoretical guidance for optimizing three-dimensional stacking. This article conducted electromigration experiments on TSV-metal line structural samples at current densities of 1.0 × 105 A/cm2, 5 × 105 A/cm2, and 1 × 106 A/cm2. Additionally, Electron Back Scattered Diffraction (EBSD) technology was employed to systematically investigate the microstructural evolution of the TSV-metal line structure profiles before and after the application of electrical testing. The results indicate that the current induces a change in the crystal orientation at the TSV-metal interface (TSV/metal interface) and the bottom metal line. This phenomenon notably depends on the initial angle between the grain orientation and the current flow direction. When the angle between the current direction and the grain orientations [001] and [010] is relatively large, the crystals are more likely to deviate in the direction where the angle between the grain orientation and the current is smaller. This is because, at this point, the current direction is precisely perpendicular to the <100> crystal plane family, where the atomic density is lowest, and the energy required for electron transport is minimal. Therefore, the current readily rotates in the direction of this crystal orientation. Before the electromigration tests, areas with a high level of misorientation were primarily concentrated at the TSV/metal interface and the corners of the TSV-metal line. However, these areas were found to be more prone to developing voids after the tests. It is conjectured that the high misorientation level leads to elevated stress gradients, which are the primary cause of cracking failures in the TSV-metal line. As the current density increases from 5 × 105 A/cm2 to 1 × 106 A/cm2, the electromigration failure phenomena in the TSV become even more severe. [ABSTRACT FROM AUTHOR]

With the technological scaling of metal–oxide–semiconductor field-effect transistors (MOSFETs) and the scarcity of circuit design margins, the characteristics of device reliability have garnered widespread attention. Traditional single-mode reliability mechanisms and modeling are less sufficient to meet the demands of resilient circuit designs. Mixed-mode reliability mechanisms and modeling have become a focal point of future designs for reliability. This paper reviews the mechanisms and compact aging models of mixed-mode reliability. The mechanism and modeling method of mixed-mode reliability are discussed, including hot carrier degradation (HCD) with self-heating effect, mixed-mode aging of HCD and Bias Temperature Instability (BTI), off-state degradation (OSD), on-state time-dependent dielectric breakdown (TDDB), and metal electromigration (EM). The impact of alternating HCD-BTI stress conditions is also discussed. The results indicate that single-mode reliability analysis is insufficient for predicting the lifetime of advanced technology and circuits and provides guidance for future mixed-mode reliability analysis and modeling. [ABSTRACT FROM AUTHOR]

Two distinct binary blended concrete mixes were prepared for the study. The first mix involved a cement replacement of 50% slag, denoted as SL. The second mix incorporated a cement replacement of 20% fly ash, referred to as FA. No chlorides were added during the preparation of these concrete specimens. To accelerate chloride transport, electromigration was employed by placing specimens with varying reservoir lengths (ranging from 2.5 cm to 17.5 cm) on their top surfaces. These reservoirs were subsequently filled with a 10% NaCl solution. In this paper, corrosion propagation was monitored over a period of approximately 650 days using electrochemical measurements such as open circuit potential, linear polarization resistance (LPR), and electrochemical impedance spectroscopy (EIS). The evolution of rebar potential, polarization resistance, solution resistance, and corrosion current were analyzed to understand the corrosion behavior. This paper focuses on how the length of the solution reservoirs influences the corrosion-related parameters such as polarization resistance, solution resistance, rebar potential, and corrosion current. During the monitored propagation period, the corrosion current values (last 7 sets of readings) exhibited higher magnitudes for the embedded rebars in specimens made with SL mix in comparison to those made with FA mix. Corrosion current measurements likewise showed an increasing trend as the reservoir lengths increased. None of the specimens had any visible cracks or corroded products that could reach the concrete surface throughout the monitored period. The experimental results provide insights into the corrosion mechanisms and the effectiveness of accelerated corrosion techniques in simulating real-life conditions. [ABSTRACT FROM AUTHOR]

The evolution of primary and interfacial intermetallic compounds in solder joints during electromigration (EM) significantly influences the mechanical properties and reliability of solder joints. In this work, by combining high-resolution x-ray computed tomography and finite element modeling, the 3D evolution of Cu6Sn5 in a solder joint containing a single β-Sn grain with representative orientation was revealed. It is found that the growth of primary Cu6Sn5 rods and the formations of Cu6Sn5 rods/particles within the matrix and on the anode/cathode interfaces are all heavily influenced by local Cu concentrations and Cu diffusion fluxes in β-Sn, which are controlled by the β-Sn orientation and geometry of the solder joint. The unobvious growth of some Cu6Sn5 is also attributed to the high angles between [0001]Cu6Sn5 and [001]β-Sn (>45°). The orientation relationship between β-Sn and Cu6Sn5 also contributes to the growth direction of the newly formed Cu6Sn5 rod. This study provides insight into the mechanisms of EM-induced microstructure evolutions in ball-grid-array solder joints. [ABSTRACT FROM AUTHOR]