The diffusion behavior of Cu and Ni atoms undergoing liquidesolid electromigration（L-S EM） was investigated using Cu/Sn/Ni interconnects under a current density of 5.0 103A/cm2 at 250℃. The flowing direction of ele...The diffusion behavior of Cu and Ni atoms undergoing liquidesolid electromigration（L-S EM） was investigated using Cu/Sn/Ni interconnects under a current density of 5.0 103A/cm2 at 250℃. The flowing direction of electrons significantly influences the cross-solder interaction of Cu and Ni atoms, i.e., under downwind diffusion, both Cu and Ni atoms can diffuse to the opposite interfaces; while under upwind diffusion,Cu atoms but not Ni atoms can diffuse to the opposite interface. When electrons flow from the Cu to the Ni, only Cu atoms diffuse to the opposite anode Ni interface, resulting in the transformation of interfacial intermetallic compound（IMC） from Ni3Sn4into（Cu,Ni）6Sn5and further into [（Cu,Ni）6Sn5t Cu6Sn5], while no Ni atoms diffuse to the opposite cathode Cu interface and thus the interfacial Cu6Sn5 remained.When electrons flow from the Ni to the Cu, both Cu and Ni atoms diffuse to the opposite interfaces,resulting in the interfacial IMC transformation from initial Cu6Sn5into（Cu,Ni）6Sn5and further into[（Cu,Ni）6Sn5t（Ni,Cu）3Sn4] at the anode Cu interface while that from initial Ni3Sn4into（Cu,Ni）6Sn5and further into（Ni,Cu）3Sn4at the cathode Ni interface. It is more damaging with electrons flowing from the Cu to the Ni than the other way.展开更多
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 st...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.展开更多
The effects of temperature on Cu pad consumption and intermetallic compound（IMC） growth were investigated under current stressing. The Cu/Sn-3.0Ag-0.5Cu（SAC305）/Cu solder joints were used, with a certain current d...The effects of temperature on Cu pad consumption and intermetallic compound（IMC） growth were investigated under current stressing. The Cu/Sn-3.0Ag-0.5Cu（SAC305）/Cu solder joints were used, with a certain current density of 0.76×104A/cm^2 at 100, 140, 160 and 180 °C. The constitutive equations of cathode Cu pad consumption and anode interface IMC growth are established, respectively, based on the loading time and sample temperature. The cathode Cu pad consumption（δ） increases linearly with the loading time and the consumption rate shows parabolic curve relationships with sample temperature. The anode interface IMC thickness（δ1） increased is linearly with the square root of loading time and the interface IMC growth coefficient shows parabolic curve relationship with sample temperature. The δ and δ1 have different variation laws under current stressing, due to the current facilitating larger amount of IMC formation in the bulk solder.展开更多
The site preferences, fast and huge anisotropic diffusion mechanisms of Cu （Ag） in β-Sn as well as their reduction on the self-diffusivity of Sn, have been investigated using the first-principles and ab initio mole...The site preferences, fast and huge anisotropic diffusion mechanisms of Cu （Ag） in β-Sn as well as their reduction on the self-diffusivity of Sn, have been investigated using the first-principles and ab initio molecular dynamics methods. We have found that Cu prefers the interstitial site, whereas Ag is preferable in the substitutional site, which is mostly dominated by their different size factors. Electronic structure further evidences that the d-s hybridization between the solute and the host atom also contributes to the site preferences. It is also deduced that the fast diffusion of Cu （Ag） is mostly due to the interstitial diffusion mechanism and their diffusivity can be correlated with the amount of their respective interstitial solution. Their faster diffusion along the c-axis can be attributed to the extremely low migration energy barrier caused by the straight tunnel of considerable size with the screw axis symmetry of 2π/4 along the c-axis. Furthermore, it is found that during the process of diffusion the interstitially dissolved Cu （Ag） atoms would combine with the nearby Sn-vacancy and further annihilate the vacancy, thereby reducin~ the self-diffusion of Sn.展开更多
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 ...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.展开更多
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 ex...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.展开更多
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 inter...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.展开更多
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 ...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.SAg0.7Cu（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-73Ni UBM （2121 h）, Fe-45Ni 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.展开更多
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 w...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.展开更多
基金financial support of the projects from the National Natural Science Foundation of China (Nos. 51475072 and 51171036)
文摘The diffusion behavior of Cu and Ni atoms undergoing liquidesolid electromigration（L-S EM） was investigated using Cu/Sn/Ni interconnects under a current density of 5.0 103A/cm2 at 250℃. The flowing direction of electrons significantly influences the cross-solder interaction of Cu and Ni atoms, i.e., under downwind diffusion, both Cu and Ni atoms can diffuse to the opposite interfaces; while under upwind diffusion,Cu atoms but not Ni atoms can diffuse to the opposite interface. When electrons flow from the Cu to the Ni, only Cu atoms diffuse to the opposite anode Ni interface, resulting in the transformation of interfacial intermetallic compound（IMC） from Ni3Sn4into（Cu,Ni）6Sn5and further into [（Cu,Ni）6Sn5t Cu6Sn5], while no Ni atoms diffuse to the opposite cathode Cu interface and thus the interfacial Cu6Sn5 remained.When electrons flow from the Ni to the Cu, both Cu and Ni atoms diffuse to the opposite interfaces,resulting in the interfacial IMC transformation from initial Cu6Sn5into（Cu,Ni）6Sn5and further into[（Cu,Ni）6Sn5t（Ni,Cu）3Sn4] at the anode Cu interface while that from initial Ni3Sn4into（Cu,Ni）6Sn5and further into（Ni,Cu）3Sn4at the cathode Ni interface. It is more damaging with electrons flowing from the Cu to the Ni than the other way.
基金support by the National Natural Science Foundation of China(Grant 11772257)Natural Science Foundation of Shaanxi Providence(Grant 2020JM-103)Fundamental Research Funds for the Central Universities(Grant G2019KY05212).
文摘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.
基金Project(51174069)supported by the National Natural Science Foundation of China
文摘The effects of temperature on Cu pad consumption and intermetallic compound（IMC） growth were investigated under current stressing. The Cu/Sn-3.0Ag-0.5Cu（SAC305）/Cu solder joints were used, with a certain current density of 0.76×104A/cm^2 at 100, 140, 160 and 180 °C. The constitutive equations of cathode Cu pad consumption and anode interface IMC growth are established, respectively, based on the loading time and sample temperature. The cathode Cu pad consumption（δ） increases linearly with the loading time and the consumption rate shows parabolic curve relationships with sample temperature. The anode interface IMC thickness（δ1） increased is linearly with the square root of loading time and the interface IMC growth coefficient shows parabolic curve relationship with sample temperature. The δ and δ1 have different variation laws under current stressing, due to the current facilitating larger amount of IMC formation in the bulk solder.
基金supported by the ‘Hundred Talents Project’ of the Chinese Academy of Sciences and from the Major Research Plan (Grant No. 91226204)the Key Research Program of Chinese Academy of Sciences (Grant No. KGZD-EW-T06)+2 种基金the National Natural Science Foundation of China (Grant Nos. 51474202 and 51174188)the Beijing Supercomputing Center of CAS (including its Shenyang branch)the high-performance computational cluster in the Shenyang National University Science and Technology Park
文摘The site preferences, fast and huge anisotropic diffusion mechanisms of Cu （Ag） in β-Sn as well as their reduction on the self-diffusivity of Sn, have been investigated using the first-principles and ab initio molecular dynamics methods. We have found that Cu prefers the interstitial site, whereas Ag is preferable in the substitutional site, which is mostly dominated by their different size factors. Electronic structure further evidences that the d-s hybridization between the solute and the host atom also contributes to the site preferences. It is also deduced that the fast diffusion of Cu （Ag） is mostly due to the interstitial diffusion mechanism and their diffusivity can be correlated with the amount of their respective interstitial solution. Their faster diffusion along the c-axis can be attributed to the extremely low migration energy barrier caused by the straight tunnel of considerable size with the screw axis symmetry of 2π/4 along the c-axis. Furthermore, it is found that during the process of diffusion the interstitially dissolved Cu （Ag） atoms would combine with the nearby Sn-vacancy and further annihilate the vacancy, thereby reducin~ the self-diffusion of Sn.
基金supported by the National Natural Science Foundation of China (Grant 11572249)the Aerospace Technology Foundation (Grant N2014KC0068)the Aeronautical Science Foundation of China (Grant N2014KC0073)
文摘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.
基金supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20141407)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘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.
基金supported by the Natural Science Foundation of Jiangsu Province of China (No.BK20141407)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘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.
基金financially supported by the National Key Research and Development Program of China(Grant No.2017YFB0305501)the National Natural Science Foundation of China(Grant Nos.51401218 and 51171191)the Osaka University Visiting Scholar Program(Grant No.J135104902)
文摘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.SAg0.7Cu（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-73Ni UBM （2121 h）, Fe-45Ni 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.
基金The authors would like to acknowledge the financial support by the National Natural Science Foundation of China(Grants 11572249 and 11772257)the Fundamental Research Funds for the Central Universities(Grant G2019KY05212).
文摘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.
