Electromigration Conditions Research Articles

Measuring residual stresses in individual on-chip interconnects using synchrotron nanodiffraction

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.

Desulfurization of molten steel with molten slag using the electrochemical method

The desulfurization in metallurgical process is electrochemical reaction in nature. Desulfurization using the electrochemical method was proposed with the CaO-MgO-Al2O3 molten slag covering molten steel. Effect of an applied external DC voltage, which varied from 0 to 8V, was discussed. The results indicated that sulfur in molten steel could be removed effectively with applied external voltage. According to the mechanism analyses of the desulfurization under the applied external voltage, kinetics formulae were developed, and the model calculated results that were in agreement with the experimental values. The transfer coefficient of sulfur in molten slag under electromigration conditions was approximately 2.09?10-5 m?s-1?V-1. The desulfurization of molten steel with molten slag can be promoted by increasing the applied voltage, reducing the partial pressure of atmospheric oxygen, strengthening the stirring intensity of the reaction system, and optimizing the composition and properties of the slag.

Drift of two-dimensional vacancy islands on the Si(100) surface under electromigration conditions

The paper presents an experimental study of morphological changes of the Si(100) surface under electromigration conditions that was carried out using the in situ method involving ultrahigh vacuum reflection electron microscopy. The study aims to determine the temperature dependence of the effective electric charge of an adsorbed atom on the Si(100) surface. A system of concentric two-dimensional vacancy islands was formed on the surface of Si(100) samples by low-energy argon ion sputtering and subsequent high-temperature annealing. Quasi-equilibrium conditions were created on the sample surface by compensating the sublimating flow from the surface from an external silicon source. The video images of the drift of vacancy islands were recorded under the conditions of electromigration with the compensation of sublimation. Based on the processing and analysis of video images, the authors described the dependence of the velocity of motion of vacancy islands on the Si(100) surface for various temperatures and the direction of the electric current along and across the dimer rows with the (2 × 1) superstructure inside the island. It is shown that the drift rate of vacancy islands does not depend on their size under quasi-equilibrium conditions. A simplified one-dimensional theoretical model has been constructed. It includes one atomic step moving by a detachment of atoms from the step and their drift under the force of electromigration in the absence of desorption and deposition of atoms on the surface. Based on the proposed model, the effective electric charge is estimated, and the temperature dependence of the effective charge in the temperature range of 1010 to 1120 °C is obtained. The absolute value of the effective charge decreases linearly with increasing temperature. The sign of the effective charge is negative, and its average value is Z = –0.5 ± 0.3 elementary charges. The obtained results can be used for creating structures with a countable number of atomic steps and act as secondary measures of height with reference to the silicon crystal lattice.

Kinetics of transformation of the atomic step bunches shape under electromigration conditions on the Si(001) surface

The quality of the epitaxial structures is significantly influenced by both the initial surface morphology and its transformation during growth. One of the phenomena of surface roughness of silicon occurring during annealing, growth, exposure to electric current, and adsorption of foreign material is the formation of step bunches. The paper presents experimental studies of the transformation kinetics of an atomic step bunches shape on the Si(001) surface that were carried out under electromigration conditions when heated by a constant electric current down the steps in the temperature range of 1000–1150 °С. The samples were annealed in an ultra-high vacuum chamber of a reflection electron microscope, followed by quenching to room temperature. The dependence of the average distance between steps on the number of the bunch steps was observed using an atomic force microscope under atmospheric conditions. It was found that the experimentally obtained dependence obeys a power law (l ∝ Nα), where α varies from –0.68 to –0.36. The study confirmed the change in the elastic interaction potential of steps in bunches with the increase in temperature. The results of the work advance understanding of a bunching process of Si(001) at elevated temperatures.

Study of electromigration in Sn-Ag-Cu micro solder joint with Ni interfacial layer

This paper reports the extreme sensitivity of the microstructure evolution in Sn-Ag-Cu (SAC) micro-solder joint, consisting of 15–20 µm thick solder alloy and electrolytic Ni plated Cu electrodes, to electromigration (EM) conditions resulting from a kinetic competition between the growth of Ni3Sn4 intermetallic compound (IMC) and EM of Sn in solder matrix. Microstructural analysis of samples tested at various conditions reveals that the voiding in the solder joint develops to the full extent only when the EM rate of Sn in the solder alloy is sufficiently greater than the growth rate of Ni3Sn4 IMC because the IMC phase is EM-inactive. The decisive evidence for such behavior is found from the samples tested at 160 and 170 °C under 35 kA/cm2. The samples tested at 170 °C show the classic solder joint microstructure that typically develops under the influence of EM, that is the exaggerated growth of Ni3Sn4 at the anode as a result of Ni-EM and voids at the cathode interface of the joint as a result of Sn-EM. Contrarily, such characteristic features are not found in samples tested at 160 °C, instead, the joint is fully converted to Ni3Sn4 without sign of its biased growth and voiding activities. The near absence of biased EM microstructure at 160 °C is believed to result from the stress-gradient developed by Sn EM counteracting the EM force on Ni. No such effect is at work at higher temperatures due to the significantly higher initial Sn EM rate which leads to voids and reduces the stress gradient.

On the interfacial phase growth and vacancy evolution during accelerated electromigration in Cu/Sn/Cu microjoints

In this work, we integrate different computational tools based on multi-phase-field simulations to account for the evolution of morphologies and crystallographic defects of Cu/Sn/Cu sandwich interconnect structures that are widely used in three dimensional integrated circuits (3DICs). Specifically, this work accounts for diffusion-driven formation and disappearance of multiple intermetallic phases during accelerated electromigration and takes into account the non-equilibrium formation of vacancies due to electromigration. The work compares nucleation, growth, and coalescence of intermetallic layers during transient liquid phase bonding and virtual joint structure evolution subjected to accelerated electromigration conditions at different temperatures. The changes in the rate of dissolution of Cu from intermetallics and the differences in the evolution of intermetallic layers depending on whether they act as cathodes or anodes are accounted for and are compared favorably with experiments. The model considers non-equilibrium evolution of vacancies that form due to differences in couplings between diffusing atoms and electron flows. The significance of this work lies in understanding the vacancy transport due to the difference in intrinsic diffusion of elements in different features of the microstructure, and the severe unidirectional convective flux of atoms due to the enforced electron wind that ultimately paves the road to study nucleation of microvoids.

Surface nanopattern formation due to current-induced homoepitaxial nanowire edge instability

Physical nanopatterning based on a precise control of macroscopic forcing is an essential tool of nanoscale science and technology. Using an externally applied electric field as the macroscopic force, we report here a computational study on the formation of surface nanopatterns consisting of single-layer homoepitaxial islands as a result of a morphological instability that can occur under edge electromigration conditions on the straight edge of a single-layer nanowire grown epitaxially on a crystalline substrate. Direct dynamical simulations based on a model that has been validated experimentally for the Ag/Ag system show that the current-induced nanowire edge instability causes the breakup of the nanowire and leads to the formation of uniformly distributed islands, arranged in linear or V-shaped arrays, which are uniformly sized with nanoscale dimensions. The simulation results are supported by linear stability theory and demonstrate that the geometrical features of the island patterns and the island sizes can be controlled precisely by controlling the electric field direction with respect to the nanowire axis and the electric field strength. Our findings have important implications for developing physical nanopatterning approaches toward enabling future nanofabrication technologies.

Controlling the wetting transitions of nanoparticles on nanopatterned substrates using an electric current.

We study the behavior of a nanoparticle under electromigration on a nanopatterned surface. We show that electromigration allows one to control the wetting transitions of the nanoparticle. Suitable surface electromigration conditions to observe these transitions can be achieved with electric currents larger than 1μA. Using kinetic Monte Carlo simulations and analytical modeling, we determine the phase diagram of the wetting states, showing how wetting multistability is affected by electromigration. In addition, we show that the dynamics of the transitions is controlled by surface diffusion in our simulations, and we provide a quantitative expression for the transition time.

Phase-field simulations of intermetallic compound evolution in Cu/Sn solder joints under electromigration

In this work, we present a preliminary model based on the multiphase-field formalism that is used to investigate the evolution of intermetallic compound (IMC) layers in the Cu/Sn solder system under electromigration conditions. The simulation considers the concurrent evolution of the Cu3Sn and Cu6Sn5 IMC layers under electrochemical driving forces. We use CALPHAD descriptions for the thermodynamics of the bulk phases (Cu, Sn and both IMCs) and incorporate electrochemical contributions to the total free energy of the microstructure in order to simulate the evolution of the interfacial microstructure due to mass–current couplings. The simulation considers grain-boundary diffusion as the dominant mechanism for chemical-potential-driven mass flux. The simulation considers the effect of current density and polarity on the growth of IMCs. The simulations are in turn compared to experimental measurements of growth rates, morphology of IMC grains and evolution of interface roughness. The analysis of experiments and simulations suggest that back-stress resulting from the non-equilibrium vacancy generation due to diffusive flux imbalance among the individual diffusants (Cu and Sn) plays a fundamental role in the evolution of the IMC layers. Overall, the simulations and experiments show good qualitative agreement.

Drift of adatoms on the (111) silicon surface under electromigration conditions

The existence of the drift of adatoms on the surface that is induced by an electric current heating a sample under the conditions of sublimation, homoepitaxial growth, and quasiequilibrium on the (111) silicon surface at temperatures above 1050°C has been shown by in situ ultrahigh-vacuum reflection electron microscopy and ex situ atomic-force microscopy. It has been found that the direction of the drift of adatoms is independent of the supersaturation value on the surface. Under these conditions, the drift of adatoms occurs towards underlying terraces, i.e., at 1050–1240°C at the resistive heating of the sample by step-up direct electric current and at 1250–1350°C by step-down current. The presence of the drift of adatoms indicates that adatoms have an effective charge whose value at 1280°C is estimated as 0.07 ± 0.01 of the elementary charge.

Micro Structure Observation and Reliability Behavior of Peripheral Flip Chip Interconnections with Solder-Capped Cu Pillar Bumps

PoP (Package on Package) structures have been used widely in digital consumer electronics products such as digital still cameras and mobile phones. However, the final stack height from the top to the bottom package for these structures is higher than that of the current stacked die packages. To reduce the height of the package, a flip chip technology is used. Since the logic chips of mobile applications use a pad pitch of less than 80 μm or less, an ultra-fine-pitch flip chip interconnection technique is required. The C4 (Controlled Collapse Chip Connection) flip chip technology is widely used in area array flip chip packages. The C4 was named after the four initial characters which are C of Controlled Collapse Chip Connection. The collapse of the molten solder is controlled by the individual opening of solder resist on each pad on the substrate so that the chip can be connected onto the substrate. However, C4 is not suitable in the ultra-fine-pitch flip chips because the such a individual opening which is suitable for the ultra-fine-pitch cannot be made on the substraete. Instead of the C4 flip chip technology, the new interconnection technique was developed using the solder capped Cu pillar bumps. It is very easy to control the space between the die and the substrate by adjusting the Cu pillar height even when a large slit window opening exists on a group of pads on the substrate. Since the collapse control of the solder bumps is not necessary, we call the process C2 (Chip Connection). The C2 was named after the two initial characters which are C of Chip Connection. The solder capped Cu pillar bumps are connected to Cu substrate pads, which are a surface treated with OSP (Organic Solder Preservative), by reflow with no-clean processes. This technology creates the SMT (Surface Mount Technology)/flip chip hybrid assembly for SoP (System on Package) use. We have produced 50 μm pitch interconnections and observed the micro structure and tested their reliability. Some voids in the solder joint were observed after the reflow process. The results of warpage measurements and FEM (Finite Element Method) analyses suggest that these voids are the shrinkage voids caused by the wide temperature range of the solder liquid phase and the substrate warpage. Since they are not the stress induced voids, they didn't affect the reliability test. The increase in interconnection resistance during the reliability test was compared between the C2 interconnection and Au stud-solder interconnection. Since the resistance increase of the C2 interconnection is much smaller than that for the Au stud-solder interconnection, it is clear that the C2 flip chip technology provides robust solder connections at low cost. Also the C2 structure with a low-k device was evaluated and no failures were observed at 1,500 cycles in the TC (Thermal Cycle) test. In addition to the fine-pitch interconnections, a die thickness of 70 μm is required to reduce the final stack height. The reliability performance of the C2 flip chip with the die thicknesses 20 μm, 70 μm and 150 μm was also discussed using a PEG (Post-Encapsulation Grinding) method in which the die is ground to less than 70 μm after joining and underfilling. Finally the electromigration tests were performed on the 80 μm pitch C2 interconnection. The tests showed that the solder capped Cu pillar structure has high endurance against electromigration and no failure data was recorded up to 1,000 hrs with several electromigration conditions regardless the direction of electron flow.

Atomic arrangement of copper atoms in a carbon nanotube channel under electromigration conditions

The atomic arrangement of copper atoms in a carbon nanotube (CNT) channel junction due to electromigration processes is examined using molecular dynamics simulations. A bias voltage is applied along the channel to induce an electromigration force on copper atoms. The results show that the different magnitudes of voltages affect the flow phenomenon of the copper mass, in which the copper mass rotates while flowing through the channel junction. The thermal vibration of copper atoms and interactive forces between the copper mass and the junction play important roles in influencing the atomic configuration of the flow material at the channel junction.

Morphological Stability of Diffusion Couples Under Electric Current

We consider the growth and morphological stability of an intermediate phase growing in a binary diffusion couple under electromigration conditions. The growth rate of the intermediate phase depends primarily on the direction of the electromigration current. Current flow that drives the diffusing species enhances growth of the intermediate phase, while current flow in the opposite direction slows growth. The morphological stability of the interfaces between the intermediate phase and the terminal phases depends on the current direction, the relative conductivities of the phases, and the thickness of the intermediate phase. We find that, when the intermediate phase has a higher conductivity than the terminal phases, the current direction that enhances growth of the intermediate phase can also cause an instability. Alternatively, when the conductivity of the intermediate phase is lower than the surrounding phases, the current direction that slows growth can cause an instability. Instability also requires that the thickness of the intermediate phase be larger than some critical value.

Effects of surface diffusional anisotropy on the current-driven surface morphological response of stressed solids

A comprehensive analysis is presented of the effects of surface diffusional anisotropy on the morphological stability of planar surfaces of stressed crystalline solids under the simultaneous action of an electric field. The analysis is based on self-consistent dynamical simulations of driven surface morphological evolution in conjunction with linear stability theory. Results are reported of a systematic study of the effects on the surface morphological response of varying surface diffusional anisotropy parameters; these include the direction of the applied electric field with respect to fast surface diffusion directions, the surface crystallographic orientation, and the strength of the anisotropy that increases with decreasing temperature. For face-centered cubic crystalline solids under stress, we find that there exists a preferred direction for the applied electric field that optimizes their surface morphological response. In addition, we find that for these solids under given surface electromigration conditions, the morphological response of their ⟨111⟩-oriented surfaces is superior to that of their ⟨100⟩-oriented and ⟨110⟩-oriented surfaces. Furthermore, we demonstrate that increasing the strength of the surface diffusional anisotropy in these materials has beneficial effects on their surface morphological stability under the simultaneous action of an electric field. Our predictions can provide guidance for experimental studies of surface morphological response to the combined action of electric fields and mechanical stresses, as well as for tailoring operating conditions to improve the mechanical reliability of thin films in service.

Atomistic simulation of self-diffusion in Al and Al alloys under electromigration conditions

The effect of alloying elements on the self-diffusion behavior of Al under electromigration conditions was investigated using nonequilibrium molecular dynamics. The corresponding defect structures were also characterized energetically by Mott–Littleton approach. Pd, Cu, Mn, and Sn were found to be the most effective alloying elements that may retard the electromigration failure by increasing the activation energy for self-diffusion of Al. This increase in the activation energy is believed to be either because of the dragging effect that may be experienced in a coupled substitutional-vacancy defect structure or the energy penalty for the separation of this couple.

Temporal evolution of step-edge fluctuations under electromigration conditions

The temporal evolution of step-edge fluctuations under electromigration conditions is analysed using a continuum Langevin model. If the electromigration driving force acts in the step up/down direction, and step-edge diffusion is the dominant mass-transport mechanism, we find that significant deviations from the usual $t^{1/4}$ scaling of the terrace-width correlation function occurs for a critical time $\tau$ which is dependent upon the three energy scales in the problem: $k_{B}T$, the step stiffness, $\gamma$, and the bias associated with adatom hopping under the influence of an electromigration force, $\pm \Delta U$. For ($t < \tau$), the correlation function evolves as a superposition of $t^{1/4}$ and $t^{3/4}$ power laws. For $t \ge \tau$ a closed form expression can be derived. This behavior is confirmed by a Monte-Carlo simulation using a discrete model of the step dynamics. It is proposed that the magnitude of the electromigration force acting upon an atom at a step-edge can by estimated by a careful analysis of the statistical properties of step-edge fluctuations on the appropriate time-scale.

Theoretical analysis of current-driven interactions between voids in metallic thin films

We analyze the electromigration-induced interactions between voids in metallic thin films using self-consistent numerical simulations of current-driven void morphological evolution. We focus on the interactions between two voids that, if isolated, they would be morphologically stable and migrate at constant speed along the metallic thin film. It is demonstrated that, under certain electromigration conditions, two such different-sized voids migrating in the same direction along a metallic thin film can lead to stable time-periodic states characterized by wave propagation on a void’s surface or cause failure prior to or following their coalescence. Moreover, various complex phenomena are revealed, including void breakup into two morphologically stable voids following the coalescence of the original two voids and voids attempting to pass each other. In numerous cases, it is noteworthy that the void-void interactions examined arise due to a larger void migrating faster than an originally leading smaller one in a finite-width conducting film with anisotropic material properties, contrary to the conventional notion that smaller voids migrate faster than larger ones for electromigration-driven void motion. These results set the stage toward a fundamental understanding of the current-driven dynamics of populations of interacting voids in metallic interconnect lines. Finally, our analysis predicts that void breakup preceded by void coalescence can cause an abrupt increase in the electrical resistance of an interconnect line, in qualitative agreement with observations from accelerated electromigration testing experiments.

A Modified Electromigration Test Structure for Flip Chip Interconnections

Due to decreasing dimensions, electromigration becomes a major concern for flip chip joint reliability. A novel test structure for in-situ monitoring of electromigration in a flip chip connection is proposed. With this structure, small resistance changes at the cathodic and anodic sides can be mounted separately. This allows studying the asymmetric behavior of solder joints under electromigration conditions. The design of the new test structure is described and compared to the traditional measurement method. As a first test case, a Cu-Sn-Cu flip chip joint, stressed with a current of 6000Amp/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at 150degC, is studied. First tests clearly indicate diverging resistance values when comparing the cathodic and anodic side of the flip chip bumps. Microstructural analysis shows extensive Cu-migration from cathode to anode

Effects of electromigration-induced void dynamics on the evolution of electrical resistance in metallic interconnect lines

The effects of void dynamics under electromigration conditions on the electrical resistance evolution in metallic thin-film interconnects are examined based on self-consistent dynamical simulations. Changes in the interconnect line resistance are found to depend strongly on electromigration-induced void morphological changes and are explained on the basis of void extension across the linewidth and void surface area evolution at constant void volume. The void morphological evolution may lead to stable steady or time-periodic line resistance response or to abrupt resistance increase associated with failure. Our computational results imply that electrical resistance increases should not be attributed only to void formation or void growth and that electrical resistance oscillations are not due to alternating defect generation and annihilation. The results are in excellent agreement with analytical scaling theories and qualitatively consistent with a large set of experimental electrical resistance measurements.

Analysis of Electromigration- and Stress-Induced Dynamical Response of Voids Confined in Metallic Thin Films

AbstractA theoretical analysis based on self-consistent dynamical simulations is presented of electromigration- and stress-induced surface morphological response of voids confined in metallic thin films. The analysis predicts the onset of stable time-periodic states for the void surface morphological response, which is associated with current-driven wave propagation on the void surface. This time-periodic response is demonstrated under certain electromigration conditions and detailed response diagrams are presented which map the corresponding parameter space to regions of steady, time-periodic, and unstable surface morphological response. The evolution of the electrical resistance of these thin films also is computed, providing an interpretation for experimentally observed time-periodic response of the electrical resistance of metallic interconnect lines on the basis of current-driven void morphological evolution. In addition, we demonstrate significant effects on the electromigration-induced morphologically stable void migration of mechanical stress application in a metallic thin film. Specifically, we find that under certain electromechanical conditions, elastic stress can cause substantial retardation of void motion, as measured by the constant speed of electromigration-induced translation of morphologically stable voids. More importantly, this effect suggests the possibility for complete inhibition of void motion under stress.