Void Coarsening Research Articles

Study of migration and coalescence of voids driven by electric current stressing in solder interconnects using phase field simulation

Voids in solder interconnects play a crucial role in influencing performance and reliability of solder interconnects, and even lead to the open failure of electronics, especially when high density electric current flowing through the solder interconnects. In this paper, the morphological evolution and migration behaviour of the voids in the solder domain of solder interconnects under electric current stressing is investigated using a developed phase field model. Results show that the surface energy drives the coalescence of voids, and large size voids grow up at the expense of small size ones. The voids migrate along the electric current direction, and the current density distribution and void distribution interactively affect the evolution and migration of the voids. The high magnitude of electric field can potentially induce the open-circuit failure, and the void size is affected by the electric field. Moreover, the voltage across the solder domain increases as the voids migrate to the cathode side. Furthermore, the electric field can promote the void coarsening, and the void migration velocity increases almost linearly with the magnitude of the electric field.

An analysis of two classes of phase field models for void growth and coarsening in irradiated crystalline solids

A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also found that a type B model reduces to a generalized one-sided classical Stefan problem in the case of a high driving thermodynamic force associated with the void growth stage, while it reduces to a generalized one-sided Mullins-Sekerka problem when the driving force is low in the case of void coarsening. The latter case corresponds to the famous rate theory description of void growth. Type C models, which include point defect concentrations and a non-conserved order parameter to distinguish between the void and solid phases and employ coupled Cahn-Hilliard and Allen-Cahn equations, are shown to represent mixed diffusion and interfacial kinetics. In particular, the Allen-Cahn equation of model C reduces to an interfacial constitutive law representing the attachment and emission kinetics of point defects at the void surface. In the limit of a high driving force associated with the void growth stage, a type C model reduces to a generalized one-sided Stefan problem with kinetic drag. In the limit of low driving forces characterizing the void coarsening stage, however, the model reduces to a generalized one-sided Mullins-Sekerka problem with kinetic drag. The analysis presented here paves the way for constructing quantitative phase field models for the irradiation-driven nucleation and growth of voids in crystalline solids by matching these models to a recently developed sharp interface theory.

Aging Mechanisms in Electrodeposited Cobalt-Hardened Gold Coatings

Electrodeposited cobalt-hardened gold (Au(Co)) coatings are used on electrical connectors and contacts requiring resistance to mechanical wear as well as low electrical contact resistance. However, conventionally electrodeposited Au(Co) films grown using direct current (DC) electroplating method possess complex, porous microstructures. An open question is how this porosity affects the susceptibility of these coatings to potential electrical and mechanical failure. To test the hypothesis that microstructural voids degrade the coating stability, we conducted an elevated temperature aging study to compare Au(Co) grown with a void microstructure, using conventional deposition processes, with Au(Co) grown without a void microstructure, using a new pulsed-plating process developed at Sandia national laboratories. Using characterization techniques including scanning electron microscopy, transmission electron microscopy, transmission Kikuchi diffraction, atomic force microscopy, sheet resistance measurements, nanoindentation, and atom-probe tomography, we will demonstrate how porous coatings degrade by coarsening of voids, reactions of coatings with substrates, and diffusion of the hardening agent Co from the film to the substrate/coating interface with increased annealing temperature which in turn negatively affect the coatings’ structural integrity and the stability of electrical and mechanical properties. In contrast, we will show that non-porous Au(Co) coatings display stable low resistance, surface morphology, interface with substrates, and no development of voids or diffusion of Co in the microstructure with increased annealing temperature. Figure 1

Void formation in ODS EUROFER produced by hot isostatic pressing

Positron annihilation experiments were performed on oxide dispersion strengthened (ODS) and non-ODS EUROFER prepared by mechanical alloying and hot isostatic pressing. The results revealed the presence of small voids in these materials in the as-HIPed conditions. Their evolution under isochronal annealing experiments was investigated. The coincidence Doppler broadening spectra of ODS EUROFER exhibited a characteristic signature attributed to positron annihilation in Ar-decorated voids at the oxide particle/matrix interfaces. The variation of the positron annihilation parameters with the annealing temperature showed three stages: up to 623 K, between 823 and 1323 K, and above 1323 K. In the temperature range 823–1323 K void coarsening had effect. Above 1323 K some voids annealed out, but others, associated to oxide particles and small precipitates, survived to annealing at 1523 K. Transmission electron microscopy observations were also performed to verify the characteristics of the surviving defects after annealing at 1523 K.

Non-linear dynamics of microstructure evolution and hyper void-lattice formation

Irradiation damage accumulation in metals is studied via a dynamical description of the evolution of a system of interacting crystal defects, focusing on the complex behavior caused by system instability and symmetry-breaking. The case of a supercritical void ensemble in a temperature range where void growth is significantly affected by vacancy emission is specifically considered. Conditions of instability are found in the growth dynamics of the void system, the resulting bifurcation of which causes the shrinkage of some voids and the growth of others, resulting in coarsening of the ensemble. The presence of a small amount of one-dimensionally migrating self-interstitials with mean-free path comparable to the average distance between voids can bias the void coarsening process, such that the non-aligned voids have a much larger probability to shrink than the aligned ones. The post-bifurcation evolution leaves voids aligned along the crystallographic directions to form an imperfect lattice with empty lattice sites eventually filled by preferred nucleation. For this process to occur the irradiation temperatures must be higher than 0.4 of the melting temperature. The typically low number densities of voids at these temperatures necessarily entail a void lattice parameter much larger than when vacancy emission is negligible. The implication of the formation of the hyper void-lattice, an appellation adopted from earlier studies, on properties of one-dimensionally migrating self-interstitials is also discussed.

Dynamics of the self-assembly of nanovoids and nanobubbles in solids

Experiments show that vacancies in solids may coalesce into voids and self-organize into a superlattice. The voids have diameters around 10 nm and spacing of tens of nanometers. This paper develops a phase-field model to study this behavior, which incorporates the free energy of mixing, interfacial energy and elastic energy. Vacancy diffusion is described by a Cahn–Hilliard type nonlinear diffusion equation, which couples the vacancy distribution field and the stress field. The reduction of the mixing energy drives spinodal decomposition. The reduction of the interfacial energy drives void coarsening. The long-range elastic interaction and elastic anisotropy significantly affect superlattice formation and may essentially limit void coarsening.

Photomechanical spallation of molecular and metal targets: molecular dynamics study

Microscopic mechanisms of photomechanical spallation are investigated in a series of large-scale molecular dynamics simulations performed for molecular and metal targets. A mesoscopic breathing sphere model is used in simulations of laser interaction with molecular targets. A coupled atomistic-continuum model that combines a molecular dynamics method with a continuum description of the laser excitation and subsequent relaxation of the conduction band electrons is used for metal targets. Similar mechanisms of the laser-induced photomechanical spallation are observed for molecular and metal targets. For both target materials, the relaxation of compressive stresses generated under conditions of stress confinement is found to be the main driving force for the nucleation, growth and coalescence of voids in a subsurface region of an irradiated target at laser fluences close to the threshold for fragmentation. The mechanical stability of the region subjected to the void nucleation is strongly affected by the laser heating and the depth of the spallation region in bulk targets is much closer to the surface as compared with the depth where the maximum tensile stresses are generated. Two stages can be identified in the evolution of voids in laser spallation, the initial void nucleation and growth, with the number of voids of all sizes increasing, followed by void coarsening and coalescence, when the number of large voids increases at the expense of the quickly decreasing population of small voids. The void volume distributions are found to be relatively well described by the power law N(V)∼V-τ, with exponent gradually increasing with time. Comparison of the simulation results obtained for Ni films of two different thicknesses and bulk Ni targets suggests that the size/shape of the target plays an important role in laser spallation. The reflection of the laser-induced pressure wave from the back surface of a film results in higher maximum tensile stresses and lower threshold fluence for spallation. As the size of the film increases, the locations of the spallation region and the region of the maximum tensile stresses are splitting apart and the threshold fluence for spallation increases.

Mechanisms of void coarsening in helium implanted silicon

There has been recent discussion of the mechanisms that give rise to the observed coarsening of void populations introduced into silicon by implanting helium and then annealing to remove the helium. Over the temperature range from approximately 700 to 1000 °C and beyond, further annealing leads to an increase of the average void size and decrease in void density. This paper sets out to calculate the coarsening expected from the two primary potential mechanisms, migration and coalescence (M&C) and Ostwald ripening (OR). The methodology of the calculations is carefully set out together with the surface diffusion and vacancy diffusion parameters on which the mechanisms depend. For moderate anneal temperatures, up to 1000 °C, it would seem unlikely that OR can play any part in void coarsening. On the other hand, M&C calculations show that this mechanism gives results consistent with the size range found in experimental results.

Anomalous coarsening process of voids, steps, and denuded zones on aSi(111)7×7surface

Annealing a silicon surface covered with a submonolayer of $a\ensuremath{-}\mathrm{Si}$ at 600 \ifmmode^\circ\else\textdegree\fi{}C gives a surface with voids that undergo a ripening process. If the uncovered surface has steps, the deposition of the growing and diffusing voids at this high temperature on the step creates a coarsening of the step. The coalescence of the voids with the step creates a denuded zone (in which the density of voids is below the average) both at the upper and the lower terraces. It is shown here that both the exact morphology and the scaling of the step width on one hand, and the density of voids near the step on the other hand, can be analyzed quantitatively. The scaling relations of the step width, the dynamic scaling of the voids, the denuded zones, and the scaling of the diffusion constant with size are shown to be interconnected. Using all these relations, it is possible to get a complete picture of all the characteristics of this anomalous diffusive coarsening phenomenon. So we prove that the void coarsening process is dominated by void diffusion and coalescence and that void diffusion is dominated by boundary vacancy diffusion. Thus the diffusive models of coarsening (described in the mean field by Lifshitz-Slyozov [I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961); C. Wagner, Z. Elektrochem. 65, 581 (1961)]) are nonrelevant in this case.

Diffusional attractions between voids on a Si(111)7×7 surface

Ostwald ripening or coarsening is a term which describes the growth of large domains at the expanse of small ones in the final stages of any phase separation process. Several theories were developed in order to explain this process. All of them are based on the Lifshitz, Slyozov, and Wagner (LSW) model which predicts an increase in the average radius of domains r̄(t)∝t1/3 and a reduction of the number density of domains as a function of time N(t)∝t−1. The LSW model assumes static and circular domains, which are distributed at random. These assumptions were found to be incorrect by many experiments. And more advanced theories were necessary to explain these observations. In our work, we study the coarsening of voids formed in a Si(111)7×7 surface covered by 0.8 bilayers (BL). Besides the expected increase in the diameter of voids and the decrease in the number density, very strong attractions and rapid motion of voids towards each other were clearly observed. The result of the attraction between the voids is coagulation of voids and an increase in the spatial correlations between voids, as the coarsening process progresses, as we indeed observed. This is contradictory to the “ideal gas” picture which is the basis of the LSW model. Basically, this can be explained by a concentration gradient which develops between two voids of different size and the growth of voids in the direction of the larger concentration. However, this model cannot explain the large diffusional motions observed in our experiments. It is proposed that an amplification mechanism exists, whereby the arrival of a diffusing vacancy to the boundary of the void causes the release of several adatoms from the boundary. This process causes a much larger motion than expected by a single vacancy absorption. This picture, which is consistent with the structure of the steps, demonstrates how the microscopic details might have a significant affect on the global coarsening process.

Void evolution simulation in neutron-irradiated vanadium

Void evolution in high dose neutron irradiated vanadium is studied with the use of newly created numerical code. To calculate void densities measured in vanadium at high temperatures, the vacancy selfdiffusion energy must be as high as 3.5 eV and the concentration of oxygen must be sufficient to provide surface energy of voids as low as 1.2 J/m 2. Due to the size dependence of void preference, high dose modeling revealed a possibility for void coarsening in vanadium at low temperatures, low void surface energies (caused by oxygen chemisorption) and low dislocation densities. With increasing dislocation density, maximum void concentrations increase significantly at low temperatures while at high temperatures the situation is reversed. The dose required to reach maximum void number density has a minimum at intermediate temperatures. The highest swelling is predicted for low dislocation densities and high oxygen concentrations in the initial stage of irradiation and vice versa at high doses.

Solid‐Phase Epitaxy of Thin Silicon Film on Si(111) Surface Studied by Scanning Tunneling Microscopy

AbstractSolid‐phase epitaxy (SPE) of thin silicon film with a thickness of 0.2–2 bilayers (BL) on Si(111)‐(7 × 7) surface was studied by scanning tunneling microscopy. At small coverage, the SPE growth proceeds via coarsening of islands. As the coverage exceeds the percolation threshold, a ‘mirror’ process consisting of coarsening of voids in the continuous layer takes place. The SPE growth of a thicker continuous layer results in a partly disordered flat surface, displaying a mixture of different reconstructions. Quantitative characterization of this surface by the formalism of pair distribution functions reveals an anisotropy in the orientational order that may indicate that SPE occurs preferably in the step direction. A possibility to use an SPE‐grown layer as a two‐dimensional model for bulk processes in solids is discussed.

A mechanism of formation and properties of the void lattice in metals under irradiation

We propose a new mechanism of interaction between voids, which is based on the elastically induced absorption of self-interstitial dislocation loops (SIA-loops) from the matrix. The main peculiarity of this dislocation interaction is its rigid relation to the crystal structure, namely, it arises only in the crystals, where SIA-loops can glide, and exists only between voids lying along the same loop-gliding directions. Void ordering is shown to originate from competition between the dislocation interaction and radiation-induced diffusion coarsening of voids, which leads to shrinkage of unfavourably positioned voids, if the void density exceeds the critical value. Voids in the superlattice thus formed have immediate neighbours along the loop-gliding directions, copying the host lattice due to the coincidence of the loop-gliding directions with close-packed directions of the matrix. The proposed model explains why the superlattice forms more readily in bcc than fee metals and gives analytical expressions for the void lattice parameter and stationary size, being in good agreement with experimental data over the whole temperature range of superlattice formation.

Void coarsening during the annealing of neutron irradiated molybdenum

The annealing effect on the void swelling of neutron irradiated molybdenum is investigated in the present work. The behavior of voids during post-irradiation annealing is analyzed using a reaction rate equation. The best agreement of experimental results with the reaction rate equation is found when the reaction order is 2. This fact indicates that there is an interaction between voids during the post-irradiation annealing of molybdenum. Activation energy for void annealing is about 2.0 eV. From these results void migration or void coarsening by pipe diffusion of vacancies is discussed as the mechanism of void annealing.

Void Coarsening During Irradiation of Stainless Steel

It is of interest in fast breeder reactor design to know whether saturation of void-related swelling in stainless steel occurs at high neutron fluences. One factor which may preclude saturation is a coarsening of the void structure, which would essentially reduce the rate of decrease of intervoid spacing. The HEDL JEM-1000 electron microscope was used to produce very high equivalent neutron fluences by irradiating an annealed Type 316 stainless steel specimen with 1 MeV electrons at 600°C; stereomicrographs made at regular fluence increments were used to determine the nature and extent of void coarsening reactions. The specimen did not contain helium, so the void distribution is inherently more coarse (larger mean void size, lower void concentration) than would be the case for neutron irradiation.