A theoretical analysis of the electromigration-induced void morphological evolution under high current density

In this work, analysis of electromigration-induced void morphological evolution in solder interconnects is performed based on mass diffusion theory. The analysis is conducted for three typical experimentally observed void shapes: circular, ellipse, and cardioid. Void morphological evolution is governed by the competition between the electric field and surface capillary force. In the developed model, both the electric field and capillary force on the void's surface are solved analytically. Based on the mass conversation principle, the normal velocity on the void surface during diffusion is obtained. The void morphological evolution behavior is investigated, and a physical model is developed to predict void collapse to a crack or to split into sub-voids under electric current. It is noted that when the electric current is being applied from the horizontal direction, a circular void may either move stably along the electric current direction or collapse to a finger shape, depending on the relative magnitude of the electric current and surface capillary force. However,the elliptical-shaped void will elongate along the electric current direction and finally collapse to the finger shape. On the other hand, the cardioid-shaped void could bifurcate into two sub-voids when the electric current reaches a critical value.The theoretical predictions agree well with the experimental observations.

Effect of Interconnect Linewidth on Evolution of Intragranular Microcracks Due to Electromigration Analyzed by Finite Element Method

The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there exists critical values of the linewidth hc,the electric fieldχc and the aspect ratioβc.When h>hc,χ<χc orβ<βc,the microcrack will evolve into a stable shape as it migrates along the interconnect line.When h≤hc,χ≥χc orβ≥βc,the microcrack will split into two smaller microcracks.The critical electric field,the critical aspect ratio and the splitting time have a stronger dependence on the linewidth when h≤6.In addition,the decrease of the linewidth,the increase of the electric field or the aspect ratio is beneficial to accelerate microcrack splitting,which may delay the open failure of the interconnect line.

Effect of electromigration and isothermal aging on interfacial microstructure and tensile fracture behavior of SAC305/Cu solder joint

The Cu/Sn-3.OAg-0.5Cu/Cu butting solder joints were fabricated to investigate the evolution of the interfacial intermetallic compound(IMC) and the degradation of the tensile strength of solder joints under the effect of electromigration(EM) and aging processes.Scanning electron microscopy(SEM) results indicated that the Cu_6Sn_5 interfacial IMC presented obvious asymmetrical growth with the increase of EM time under current density of 1.78×10~4 A/cm^2 at 100℃,and the growth of anodic IMC presented a parabolic relationship with time while the cathodic IMC got thinner gradually.However,as for aging samples at 100℃ without current stressing,the Cu_6Sn_5 IMC presented a symmetrical growth with a slower rate than the anodic IMC of EM samples.The tensile results indicated that the tensile strength of the solder joints under current stress declined more drastic with time than the aging samples,and the fracture mode transformed from ductile fracture to brittle fracture quickly while the fracture mode of aging samples transformed from cup-cone shaped fracture to microporous gathering fracture in a slow way.

An energy approach to predict electromigration induced grain rotation under high current density

An energy approach is proposed to describe the electromigration induced grain rotation under high current density. The driving force is assumed to arise from the grain-boundary energy reduction and increase of the inner energy from the joule heating. Energy dissipates by the grain boundary diffusion under electromigration and viscous boundary sliding is considered. Based on the conservation of energy production and dissipation, an equilibrium equation is developed to predict the grain rotation rate analytically. It is recognized that the grain rotates with the reducing of electrical resistivity and inversely proportional to the grain length. The theoretical prediction is compared with the experimental data, which shows good accuracy on the rotation trend and the specific rotation rate.

Current sustainability and electromigration of Pd,Sc and Y thin-films as potential interconnects

The progress on novel interconnects for carbon nanotube(CNT)-based electronic circuit is by far behind the remarkable development of CNT-field effect transistors.The Cu interconnect material used in current integrated circuits seems not applicable for the novel interconnects,as it requires electrochemical deposition followed by chemical-mechanical polishing.We report our experimental results on the failure current density,resistivity,electromigration effect and failure mechanism of patterned stripes of Pd,Sc and Y thin-films,regarding them as the potential novel interconnects.The Pd stripes have a failure current density of(8~10)×106 A/cm^2(MA/cm^2),and they are stable when the working current density is as much as 90% of the failure current density.However,they show a resistivity around 210 μΩ·cm,which is 20 times of the bulk value and leaving room for improvement.Compared to Pd,the Sc stripes have a similar resistivity but smaller failure current density of 4~5 MA/cm^2.Y stripes seem not suitable for interconnects by showing even lower failure current density than that of Sc and evidence of oxidation.For comparison,Au stripes of the same dimensions show a failure current density of 30 MA/cm^2 and a resistivity around 4 μΩ·cm,making them also a good material as novel interconnects.

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

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

Damage of Interconnects by Electromigration Induced Surface Evolution

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Inhibition of Electromigration in Eutectic SnBi Solder Interconnect by Plastic Prestraining

Plastic prestraining was applied to a solder interconnect to introduce internal defects such as dislocations in order to investigate the interaction of dislocations with electromigration damage. Above a critical prestrain, Bi interfacial segregation to the anode, a clear indication of electromigration damage in SnBi solder interconnect, was effectively prevented. Such an inhibiting effect is apparently contrary to the common notion that dislocations often act as fast diffusion paths. It is suggested that the dislocations introduced by plastic prestraining acted as sinks for vacancies in the early stage of the electromigration process, but as the vacancies accumulated at the dislocations, climb of those dislocations prompted recovery of the deformed samples under current stressing, greatly decreasing the density of dislocation and vacancy in the solder, leading to slower diffusion of Bi atoms.

Energy variation in diffusive void nucleation induced by electromigration

An energy approach is proposed to describe electromigration induced void nucleation based on phase transformation theory.The chemical potential for an individual migrated atom is predicted by diffusion induced back stress equivalent principle.After determining the chemical potential for the dilfusing atoms,the Gibbs free energy controlling the void nucleation can be determined and the mass diffusion process is considered.The critical void radius and nucleation time are determined analytically when the Gibbs free energy approaches the extreme value.The theoretical predictions are compared with the experimental results from literatures and show good accuracy.The proposed model can also be applied to other diffusion induced damage processes such as thermomigration and stress migration.

Temperature-Aware Electromigration Analysis with Current-Tracking in Power Grid Networks

Electromigration(EM)is a severe reliability issue in power grid networks.The via array possesses special EM characteristics and suffers from Joule heating and current crowding,closely related to EM violations.In this study,a power grid EM analysis method was developed to solve temperature variation effects for the via array EM.The new method is based on the temperature-aware EM model,which considers the effects of self-heating and thermal coupling of interconnected lines in a power grid.According to the model,the proposed methodology introduces a locality-driven strategy and current tracking to perform full-chip EM assessment for multilayered power grids.The results show that temperature due to Joule heating indeed has significant impacts on the via EM failure.The results further demonstrate that the proposed method might reasonably improve efficiency while ensuring the accuracy of the analysis.

Numerical Simulation on Intergranular Microcracks in Interconnect Lines Due to Surface Diffusion Induced by Stress-,Electro-and Thermo-migration

Based on the weak formulation for combined surface diffusion and evaporation-condensation,a governing equation of the finite element is derived for simulating the evolution of intergranular microcracks in copper interconnects induced simultaneously by stressmigration,electromigration and thermomigration.Unlike previously published works,the effect of thermomigration is considered.The results show that thermomigration can contribute to the microcrack splitting and accelerate the drifting process along the direction of the electric field.The evolution of the intergranular microcracks depends on the mechanical stress field,the temperature gradient field,the electric field,the initial aspect ratio and the linewidth.And there exists a critical electric fieldχ_c,a critical stress field■,a critical aspect ratioβ_c and a critical linewidth■.When■or■,the intergranular microcrack will split into two or three small intergranular microcracks.Otherwise,the microcrack will evolve into a stable shape as it migrates along the interconnect line.The critical stress field,the critical electric field and the critical aspect ratio decrease with a decrease in the linewidth,and the critical linewidth increases with an increase in the electric field and the aspect ratio.The increase of the stress field,the electric field or the aspect ratio and the decrease of the linewidth are not only beneficial for the intergranular microcrack to split but also accelerate the microcrack splitting process.

A Novel and Optimized Method for Electro-focusing and Moving Neutralization Reaction Boundary Formed by HCl and NaOH

A novel method is developed for electro-focusing and moving neutralization reaction boundary (MNRB) created with HCl and NaOH. The optimized conditions are screened out. By using this method, the experiments are performed on MNRB formed with HCl and NaOH in agarose gel. The experiments are quantitatively in coincidence with the predictions with the theory of moving chemical reaction boundary (MCRB).

Effect of pad geometry on current density and temperature distributions in solder bump joints

Three-dimensional thermo-electrical finite element analyses were conducted to simulate the current density and temperature distributions in solder bump joints with different pad geometries.The effects of pad thickness,diameter and shape on current density and temperate distributions were investigated respectively.It was found that pads with larger thickness or/and diameter could reduce current density and temperature in solder bump significantly.Pad shapes affected the current density and temperature distributions in solder bumps.The relatively low current density and temperature didn't occur in the bump joint with traditional rounded pad but occurred in bump joints with octagonal and nonagonal pads respectively.Therefore,optimized pad geometry may be designed to alleviate the current crowding effect and reduce the bump temperature,and therefore delay electromigration failure and increase the mean-time-to-failure.

An analytical model to predict diffusion induced intermetallic compounds growth in Cu-Sn-Cu sandwich structures

A mass diffusion model is developed to describe the growth kinetics of Cu6Sn5 intermetallic compounds(IMC)in the Cu-Sn-Cu sandwich structure.The proposed model is based on the local interfacial mass conversation law where interfacial Cu/Sn reactions and atomic diffusion are considered.Theoretical analysis shows that the IMC thickness growth is proportional to the square root of the product of the diffusion coefficient and time.The proposed model can explain the polarity effect of electromigration on kinetics of IMC growth where all the parameters have clear physical meaning.The theoretical predictions are compared with experimental results and show reasonable accuracy.

Enhancement of Effective Accumulation of Atoms during Fabrication of Al Microsphere

Microspheres of Al have been successfully fabricated utilizing electromigration using sudden change in geometrical shape of a specimen. The experimental sample was a passivated Al line with a hole at the transitional area of the sample. The hole was used to control the accumulation and discharge process. The formation of the microsphere is enhanced by controlling temperature and current density. The atomic flux was increased with the increasing current density that was happened along the electron flow direction in the small region at the geometrical shape of the sample.

Analysis of mobilization of inorganic ions in soil by electrokinetic remediation

Saline soil has imposed a serious threat on many expressway engineering and agricultural areas.This paper describes the performance of saline soil treatment using electrokinetic remediation technology.Comparison study involving sample soil and in situ soil is carried out.Two different electric fields,i.e.,uniform and non-uniform are utilized to promote the migration of inorganic ions contained in the soil toward the electrode area.The effects of different electric field types and potential gradient ion migration rate in soil are investigated.The test result reveals that a uniform electric field of a constant potential gradient of 1 V/cm drives the Cl-through the sample soil at a rate of 1.36 cm/h.Moreover,larger potential gradients could make ions migrate faster,but more electrical energy is consumed in such a way.Compared with uniform electric field,the non-uniform process maintains the soil pH values more effectively and consumes less electrical energy.A desirable result of removing Na+in soil is expected using electrokinetic remediation technology under four-times scaling up of soil volume.

Progress on Soldering Failure Analysis During the Period of Enlistment in Micro-Nanoelectronic Packaging

With development of miniaturization,high integration,multifunction and high efficiency of electronic packaging technology,a higher requirement for soldering material and its enlistment property is needed.It is easily subjected to reliability failure for electronic products or components packaged with micro/nanoelectronic packaging technology.In this paper,research process and some typical failure mechanisms on interconnect solder point reliability are discussed,including electro-migration (EM),thermal migration (TM),K-cavity,corrosion,electrochemical migration (ECM) and whisker growth,etc.It provides the basic data for the new generation of micro/nano-packaging technique to improve the fine-pitch jointing reliability.