Electromigration is the transport of atoms in metal conductors at high electronic current-densities which creates voids in the conductors and increases the conductors＇ electrical resistance. It was delineated in 1961...Electromigration is the transport of atoms in metal conductors at high electronic current-densities which creates voids in the conductors and increases the conductors＇ electrical resistance. It was delineated in 1961 by Huntington; then modeled by the empirical electrical resistance formula derived by Black in 1969 to fit the dependences of the experimental electrical resistance and failure data on the electrical current density and temperature. Tan in 2007 reviewed 40-years＇ ap- plications of the empirical Black formula to conductor lines interconnecting transistors and other devices in silicon integrated circuits. Since the first Landauer theory in 1957,theorists have attempted for 50 years to justify the drift force or electron momentum transfer assumed by Black as some electron-wind force to impart on the metal atoms and ions to move them. Landauer concluded in 1989 that the electron wind force is untenable even considering the most fundamental and complete many-body quantum transport theory. A driftless or electron-windless atomic void model for metal conductor lines is reviewed in this article. It was developed in the mid-1980 and described in 1996 by Sah in a homework solution. This model accounts for all the current and temperature dependences of experimental resistance data fitted to the empiri- cal Black formula. Exact analytical solutions were obtained for the metal conductor line resistance or current, R （t）/R （0） = J（t）/J（0） = [1-2（t/τα）^1/α]^-1/2 ,in the bond-breaking limit with α = 1 to 2 and diffusion limit with α = 2 to 4,from low to high current densities, where τα is the characteristic time constant of the mechanism, containing bond breaking and diffusion rates and activation energies of the metal.展开更多
体心立方(body⁃centered cubic,BCC)金属W作为微型化器件中重要的互连材料,其电迁移行为对小尺寸集成电路的稳定性至关重要。本文利用原位透射电子显微(transmission electron microscopy,TEM)技术,在原子尺度下研究了电迁移诱导BCC金属...体心立方(body⁃centered cubic,BCC)金属W作为微型化器件中重要的互连材料,其电迁移行为对小尺寸集成电路的稳定性至关重要。本文利用原位透射电子显微(transmission electron microscopy,TEM)技术,在原子尺度下研究了电迁移诱导BCC金属W表面结构动态演变过程。结果表明,自由表面是主要电迁移路径;而{110}面和<111>方向分别是优选的迁移面迁移方向;电迁移过程中W表面形成特定的原子台阶或锯齿状结构。对于非低能晶面{002},在电流作用下仍能发生定向迁移,形成新的台阶结构。研究结果揭示了电迁移过程中表面结构的演化规律,为优化BCC金属材料的微观结构设计、提高其在高电流密度环境下的结构性能稳定性提供借鉴。展开更多
The electromigration induced microstructure evolution and damage in asymmetric Cu/Sn-58Bi/Cu solder interconnects were investigated by in-situ SEM observation, focused ion beam （FIB） microanalysis and finite element...The electromigration induced microstructure evolution and damage in asymmetric Cu/Sn-58Bi/Cu solder interconnects were investigated by in-situ SEM observation, focused ion beam （FIB） microanalysis and finite element （FE） simulation. The SEM results show that the electromigration-induced local degradation of microstructures, i.e., segregation of Bi-rich phase and formation of microcracks, in the asymmetric solder interconnects is much severer than that in the symmetrical ones. FIB-SEM microanalysis reveals that the microregional heterogeneity in electrical resistance along different electron flowing paths is the key factor leading to non-uniform current distribution and the resultant electromigration damage. Theoretical analysis and FE simulation results manifest that the current crowding easily occurs at the local part with smaller resistance in an asymmetric solder interconnect. All results indicate that the asymmetric shape of the solder interconnect brings about the difference of the electrical resistance between the different microregions and further results in the severe electromigration damage.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
The Cu/Sn-3. OAg-0.5Cu/Cu butting solder joints were fabricated to investigate the evolution of the interfacial intertnetaUic compound （ IMC ） and the degradation of the tensile strength of solder joints under the e...The Cu/Sn-3. OAg-0.5Cu/Cu butting solder joints were fabricated to investigate the evolution of the interfacial intertnetaUic 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 Cu6Sn5 interfacial IMC presented obvious asymmetrical growth with the increase of EM time under current density of l. 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 Cu6Sn5 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.展开更多
Atoms constructing an interconnecting metal line in a semiconductor device are transported by electron flow in high density. This phenomenon is called electromigration, which may cause the line failure. In order to ch...Atoms constructing an interconnecting metal line in a semiconductor device are transported by electron flow in high density. This phenomenon is called electromigration, which may cause the line failure. In order to characterize the electromigration failure, a comparison study is carded out with some typical phenomena treated by fracture mechanics for thin and large structures. An example of thin structures, which have been treated by fracture mechanics, is silica opti- cal fibers for communication systems. The damage growth in a metal line by electromigration is characterized in compar- ison with the crack growth in a silica optical fiber subjected to static fatigue. Also a brief comparison is made between the electromigration failure and some fracture phenomena in large structures.展开更多
Recently, a governing parameter for electromigration damage in passivated polycrystalline lines, AFD*gen, was formulated considering the effect of the atomic density gradient. In this study, a prediction metho...Recently, a governing parameter for electromigration damage in passivated polycrystalline lines, AFD*gen, was formulated considering the effect of the atomic density gradient. In this study, a prediction method for electromigration failure in a passivated polycrystalline line was proposed using AFD*gen. The characteristics of film used for prediction is established in advance using a method based on AFD*gen. The film characteristics of metal lines with different lengths were determined experimentally by AFD*gen_based method. From the film characteristics obtained, both lifetime and location of failure in the passivated polycrystalline lines were predicted through numerical simulation of failure process. Good agreement has been shown between the predicted and the experimental results concerning both lifetime and location of failure.展开更多
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 inn...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.展开更多
The electromigration behavior of eutectic SnAg solder reaction couples was studied at various temperature （25 and 120℃ when the current density was held constant at 104 A/cm^2 or 5×10^3 A/cm^2. Under the curren...The electromigration behavior of eutectic SnAg solder reaction couples was studied at various temperature （25 and 120℃ when the current density was held constant at 104 A/cm^2 or 5×10^3 A/cm^2. Under the current density of 104 A/cm^2, scallop type Cu6Sn5 spalls and migrates towards the direction of electron flow at room ambient temperature （25℃）, but transforms to layer type Cu3Sn and leaves Kirkendall voids in it at high ambient temperature （120℃）. Under the current density of 5×10^3 A/cm^2 plus room ambient temperature, no obvious directional migration of metal atoms/ions is found. Instead, the thermal stress induced by mismatch of dissimilar materials causes the formation of superficial valley at both interfaces. However, when the ambient temperature increases to 120℃, the mobility of metal atoms/ions is enhanced, and then the grains rotate due to the anisotropic property of β-Sn.展开更多
In order to obtain both high electromigration （EM） reliability and free-dimensional control in high-frequency surface acoustic wave （SAW） devices, 4-layered Ti/Al-Mo/Ti/Al-Mo electrode films were investigated on 1...In order to obtain both high electromigration （EM） reliability and free-dimensional control in high-frequency surface acoustic wave （SAW） devices, 4-layered Ti/Al-Mo/Ti/Al-Mo electrode films were investigated on 128° Y-X LiNbO3 substrates by sputtering deposition. The resuits indicated that the 4-layered films had an improved EM reliability compared to conventional Al-0.5wt.%Cu films. Their lifetime is approximately three times longer than that of the Al-0.5wt.%Cu films tested at a current density of 5 x 107 A/cm^2 and a temperature of 200℃. Moreover, the 4-layered films were easily etched in reactive ion etching and fine-dimensional control was realized during the pattern replication for high-frequency SAW devices. For the 4-layered films, an optimum Mo quantity and sputtering parameters were very significant for high EM reliability.展开更多
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...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.展开更多
Grain boundary plays a key role in electromigration process of polycrystal interconnection. We take a free volume to represent a ＇vacancy-ion complex＇ as a function of grain boundary specific resistivity, and develo...Grain boundary plays a key role in electromigration process of polycrystal interconnection. We take a free volume to represent a ＇vacancy-ion complex＇ as a function of grain boundary specific resistivity, and develop a new characterisation model for grain boundary noise. This model reveals the internal relation between the boundary scattering section and electromigration noise. Comparing the simulation result with our experimental result, we find the source as well as the form of noise change in the electromigration process. In order to describe the noise enhancement at grain boundary quantitatively, we propose a new parameter--grain boundary noise enhancement factor, which reflects that the grain boundary noise can characterise the electromigration damage sensitively.展开更多
文摘Electromigration is the transport of atoms in metal conductors at high electronic current-densities which creates voids in the conductors and increases the conductors＇ electrical resistance. It was delineated in 1961 by Huntington; then modeled by the empirical electrical resistance formula derived by Black in 1969 to fit the dependences of the experimental electrical resistance and failure data on the electrical current density and temperature. Tan in 2007 reviewed 40-years＇ ap- plications of the empirical Black formula to conductor lines interconnecting transistors and other devices in silicon integrated circuits. Since the first Landauer theory in 1957,theorists have attempted for 50 years to justify the drift force or electron momentum transfer assumed by Black as some electron-wind force to impart on the metal atoms and ions to move them. Landauer concluded in 1989 that the electron wind force is untenable even considering the most fundamental and complete many-body quantum transport theory. A driftless or electron-windless atomic void model for metal conductor lines is reviewed in this article. It was developed in the mid-1980 and described in 1996 by Sah in a homework solution. This model accounts for all the current and temperature dependences of experimental resistance data fitted to the empiri- cal Black formula. Exact analytical solutions were obtained for the metal conductor line resistance or current, R （t）/R （0） = J（t）/J（0） = [1-2（t/τα）^1/α]^-1/2 ,in the bond-breaking limit with α = 1 to 2 and diffusion limit with α = 2 to 4,from low to high current densities, where τα is the characteristic time constant of the mechanism, containing bond breaking and diffusion rates and activation energies of the metal.
文摘体心立方(body⁃centered cubic,BCC)金属W作为微型化器件中重要的互连材料,其电迁移行为对小尺寸集成电路的稳定性至关重要。本文利用原位透射电子显微(transmission electron microscopy,TEM)技术,在原子尺度下研究了电迁移诱导BCC金属W表面结构动态演变过程。结果表明,自由表面是主要电迁移路径;而{110}面和<111>方向分别是优选的迁移面迁移方向;电迁移过程中W表面形成特定的原子台阶或锯齿状结构。对于非低能晶面{002},在电流作用下仍能发生定向迁移,形成新的台阶结构。研究结果揭示了电迁移过程中表面结构的演化规律,为优化BCC金属材料的微观结构设计、提高其在高电流密度环境下的结构性能稳定性提供借鉴。
基金Project(51275178)supported by the National Natural Science Foundation of ChinaProject(20110172110003)supported by ResearchFund for the Program of Higher Education of China
文摘The electromigration induced microstructure evolution and damage in asymmetric Cu/Sn-58Bi/Cu solder interconnects were investigated by in-situ SEM observation, focused ion beam （FIB） microanalysis and finite element （FE） simulation. The SEM results show that the electromigration-induced local degradation of microstructures, i.e., segregation of Bi-rich phase and formation of microcracks, in the asymmetric solder interconnects is much severer than that in the symmetrical ones. FIB-SEM microanalysis reveals that the microregional heterogeneity in electrical resistance along different electron flowing paths is the key factor leading to non-uniform current distribution and the resultant electromigration damage. Theoretical analysis and FE simulation results manifest that the current crowding easily occurs at the local part with smaller resistance in an asymmetric solder interconnect. All results indicate that the asymmetric shape of the solder interconnect brings about the difference of the electrical resistance between the different microregions and further results in the severe electromigration damage.
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 National Natural Science Foundation of China(Grant No.NSFC-U0734006/NSFC-51371083)
文摘The Cu/Sn-3. OAg-0.5Cu/Cu butting solder joints were fabricated to investigate the evolution of the interfacial intertnetaUic 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 Cu6Sn5 interfacial IMC presented obvious asymmetrical growth with the increase of EM time under current density of l. 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 Cu6Sn5 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.
文摘Atoms constructing an interconnecting metal line in a semiconductor device are transported by electron flow in high density. This phenomenon is called electromigration, which may cause the line failure. In order to characterize the electromigration failure, a comparison study is carded out with some typical phenomena treated by fracture mechanics for thin and large structures. An example of thin structures, which have been treated by fracture mechanics, is silica opti- cal fibers for communication systems. The damage growth in a metal line by electromigration is characterized in compar- ison with the crack growth in a silica optical fiber subjected to static fatigue. Also a brief comparison is made between the electromigration failure and some fracture phenomena in large structures.
文摘Recently, a governing parameter for electromigration damage in passivated polycrystalline lines, AFD*gen, was formulated considering the effect of the atomic density gradient. In this study, a prediction method for electromigration failure in a passivated polycrystalline line was proposed using AFD*gen. The characteristics of film used for prediction is established in advance using a method based on AFD*gen. The film characteristics of metal lines with different lengths were determined experimentally by AFD*gen_based method. From the film characteristics obtained, both lifetime and location of failure in the passivated polycrystalline lines were predicted through numerical simulation of failure process. Good agreement has been shown between the predicted and the experimental results concerning both lifetime and location of failure.
基金supported by the National Natural Science Foundation of China(Grants 11572249 and 11772257)
文摘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.
基金supported by the New Century Talent Support Program, Ministry of Education of China (No.NCET-04-0202)the Beijing Natural Science Foundation Program and Scientific Research Key Program of Beijing Municipal Commission of Education, China (No.KZ200910005004)
文摘The electromigration behavior of eutectic SnAg solder reaction couples was studied at various temperature （25 and 120℃ when the current density was held constant at 104 A/cm^2 or 5×10^3 A/cm^2. Under the current density of 104 A/cm^2, scallop type Cu6Sn5 spalls and migrates towards the direction of electron flow at room ambient temperature （25℃）, but transforms to layer type Cu3Sn and leaves Kirkendall voids in it at high ambient temperature （120℃）. Under the current density of 5×10^3 A/cm^2 plus room ambient temperature, no obvious directional migration of metal atoms/ions is found. Instead, the thermal stress induced by mismatch of dissimilar materials causes the formation of superficial valley at both interfaces. However, when the ambient temperature increases to 120℃, the mobility of metal atoms/ions is enhanced, and then the grains rotate due to the anisotropic property of β-Sn.
基金supported by the National Basic Research Program of China (Nos.2009CB939703 and 2006CB806204)the National High Technology Research and Development Program of China (No.2009AA03Z444)
文摘In order to obtain both high electromigration （EM） reliability and free-dimensional control in high-frequency surface acoustic wave （SAW） devices, 4-layered Ti/Al-Mo/Ti/Al-Mo electrode films were investigated on 128° Y-X LiNbO3 substrates by sputtering deposition. The resuits indicated that the 4-layered films had an improved EM reliability compared to conventional Al-0.5wt.%Cu films. Their lifetime is approximately three times longer than that of the Al-0.5wt.%Cu films tested at a current density of 5 x 107 A/cm^2 and a temperature of 200℃. Moreover, the 4-layered films were easily etched in reactive ion etching and fine-dimensional control was realized during the pattern replication for high-frequency SAW devices. For the 4-layered films, an optimum Mo quantity and sputtering parameters were very significant for high EM reliability.
基金supported by the NSF China (10774002) and the MOST China (No 2006CB932401)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant No.60376023)the Innovative Foundation of Xi’an Applied Materials Inc.China (Grant No.XA-AM-200603)
文摘Grain boundary plays a key role in electromigration process of polycrystal interconnection. We take a free volume to represent a ＇vacancy-ion complex＇ as a function of grain boundary specific resistivity, and develop a new characterisation model for grain boundary noise. This model reveals the internal relation between the boundary scattering section and electromigration noise. Comparing the simulation result with our experimental result, we find the source as well as the form of noise change in the electromigration process. In order to describe the noise enhancement at grain boundary quantitatively, we propose a new parameter--grain boundary noise enhancement factor, which reflects that the grain boundary noise can characterise the electromigration damage sensitively.
