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Void formation in solder joints under power cycling conditions and its effect on reliability
Microelectronics Reliability xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Void formation in solder joints under power cycling conditions and its effect on reliability J. Meia,d, , R. Hauga, S. Hinderbergerb, T. Grözingerc, A. Zimmermannc,d ⁎
a
Robert Bosch GmbH, Robert-Bosch-Strasse 2, 71701 Schwieberdingen, Germany Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen c Hahn-Schickard, Allmandring 9B, 70569 Stuttgart, Germany d Institute for Micro Integration (IFM), University of Stuttgart, Allmandring 9B, 70569 Stuttgart, Germany b
ABSTRACT
When electronic assemblies are experiencing high current loading conditions, thermo-mechanical mismatch induced from the local Joule heating of the component and electromigration (EM)-induced void formation can lead to the failure of the solder interconnect. Scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) are adopted to investigate the microstructural evolution of solder joints of shunt components subjected to current stressing. Voids and micro-cracks initiate at the corner of solder meniscus, where the maximal divergence of material flux density is located on the basis of finite element method (FEM) simulation. The EM-induced voids introduce higher accumulated plastic strain in the solder joints, which will result in reduction in the lifetime of the electronic assemblies.
1. Introduction Automotive electronics are often experiencing environments of vibration, mechanical shock and thermal fluctuation induced from internal or external sources. Among all the electronic components, shunts exhibit relatively high reliability under passive temperature cycling test due to the small coefficient of thermal expansion (CTE) mismatch between the shunts (≈16.5 ppm/K) and printed circuit boards (PCBs) (≈15 ppm/K). However, shunts are often subjected to switching cycling in the use conditions and failure has been reported under accelerated power cycling test conditions [1]. It is of great significance to understand the failure mechanism of solder joints of shunt components under power cycling conditions and enable the evaluation of service lifetime of shunt components in the field load. The main failure mechanisms of solder joints exposed to power cycling loading conditions are i) recrystallization-assisted crack nucleation and propagation, ii) electromigration (EM)–induced void formation and consumption of the under bump metallisation (UBM). In most studies, the failure modes in solder joints induced by thermomechanical stress [2,3] and EM [4,5] are addressed separately. The EMinduced degradation is highly affected by the Sn grain orientation. The damage mode is dominated by Sn self-diffusion when the c-axis of β-Sn grains is perpendicular to the electron flow direction. When the c-axis of β-Sn grains is parallel to the electron flow direction, an excessive dissolution of UBM will take place since the diffusivity of Cu or Ni along the c-axis is a few magnitudes higher than along the a-axis or b-axis of
⁎
β-Sn and higher than the Sn self-diffusion [6,7]. Ma [8] has investigated the coupling conditions of electromigration and thermal cycling and found out the lifetime under coupling conditions is significantly shortened owing to the EM-induced voids and micro-cracks in solder materials [9,10]. The thermo-mechanical stress in the solder joints of shunt components, which is generated by current stressing, has been investigated in an earlier study [1]. The aim of this work is focusing on the evaluation of the degradation of solder joints resulting from EM. SEM and EBSD analysis are carried out on the shunt units after different cycles of current stressing. The power cycling test is simulated in Ansys workbench and the simulation of void formation agrees well with the experimental observation. The distribution of accumulated plastic strain in the solder joint is evaluated by taking the void formation into account. 2. Materials and methods 2.1. Power cycling test Shunt components as shown in Fig. 1 are mounted on PCBs. The assemblies are connected to power supplies which provide the loading condition as displayed in Fig. 2 and are placed in a temperature chamber which maintains at constant temperature of 90 °C. The test condition is chosen to investigate the application conditions of the components, where shunts are often experiencing short current pulses
Corresponding author. E-mail address: [email protected] (J. Mei).
https://doi.org/10.1016/j.microrel.2019.06.042 Received 13 May 2019; Received in revised form 19 June 2019; Accepted 20 June 2019 0026-2714/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: J. Mei, et al., Microelectronics Reliability, https://doi.org/10.1016/j.microrel.2019.06.042
Microelectronics Reliability xxx (xxxx) xxxx
J. Mei, et al.
Fig. 1. Configuration of the shunts.
(a) 10000 power cycles (PCs) Fig. 2. Current profile of the power cycling test.
with the pulse duration of few ms to 1 s and with the current range similar to the test condition illustrated in Fig. 2. The pulse duration is decided to be 2 s in this work to accelerate the testing time and to prevent the overheating of the components and PCBs. As described in an earlier work [1], the self-heating of the investigated shunts is asymmetric. Fig. 3 presents the infrared (IR) thermography measurement of the shunts under a representative loading condition. The terminal of the shunt which is connected to the anode of the power supply is experiencing around 20 °C higher temperature than the terminal on the cathode side. The asymmetric heat generation is reversed when the current direction is switched. This phenomenon can be explained by the Peltier effect which takes place at the junction between the terminal (Cu) and resistive element (CuNi alloy).
(b) 15000 PCs Fig. 4. Cross-sectional analysis of the shunts.
2.2. Failure mode analysis Some shunt units are removed from the chamber at a different number of power cycles and analysed with cross-sectioning to monitor the degradation of solder joints at early stages before the electrical
Fig. 3. Top view of shunt in optical and IR domains during current stressing in two directions (current: 34 A, pulse length: 3 s, room temperature). 2
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failure. As shown in Fig. 4(a), some void-like damage initiates at the corner of the solder meniscus after current stressing. The crack propagates later through the bulk solder and the interface between the terminal and solder, leaving an open circuit in the left solder joint as displayed in Fig. 4(b). No obvious damage is observed in the right solder joint. This polarity effect in the failure mode is resulting from the asymmetric heat generation of the shunts under active current load. Scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) are further performed on the shunt components to investigate the failure mechanism, especially the void-like damage
initiating at the corner of the solder meniscus. The step size for EBSD analysis has been defined to be 1.4 μm to capture the microstructural evolution. The large angle grain boundaries (LAGB) of Sn which yield a misorientation larger than 10° are marked as black lines. As displayed in Fig. 5(a), only 2 large Sn grains are observed in the left solder joint after soldering process. Two twin boundaries might have grown inside of the right solder joint. However, no significant difference in microstructure has been observed between both sides of the solder joint before power cycling test. After 5000 PCs as shown in Fig.5(b), voids and micro-cracks are initiating at the corner of the meniscus of left solder
(a) as reflow (0 PC)
(b) 5000 PCs Fig. 5. SEM and EBSD analysis of solder joints at different testing cycles. 3
Microelectronics Reliability xxx (xxxx) xxxx
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(c) 10000 PCs
(d) Region of Interest (ROI) A
(e) ROI B Fig. 5. (continued)
joint. New grains are formed due to recrystallization, predominantly at the solder standoff. More LAGBs are detected in the solder standoff as well. The right solder joint is comprised of a quasi-single grain of Sn and no obvious microstructural change is observed after 5000 PCs. Larger voids at the corner of meniscus and more LAGBs at the standoff are detected in the left solder joint after 10,000 PCs as depicted in Fig. 5(c), whereas the right solder joint exhibits a quasi-single grain of Sn similar to what is observed after 5000 PCs. The polarity of microstructural evolution in both sides of the solder joints is owing to the higher temperature distribution in the left solder joint. Thermo-mechanical fatigue cracks tend to initiate and propagate at the recrystallized region with LAGBs [11]. However, the voids and micro-cracks are formed at the corner of the solder meniscus instead of the solder standoff where more LAGBs are detected. Therefore, the degradation mechanism for the observed voids and micro-cracks is
likely to be EM rather than recrystallization-assisted crack nucleation. The voids and micro-cracks formed in ROI A are presented in Fig.5(d) with larger magnification. They are formed in the interface between the intermetallic compounds (IMCs) layer and solder, whereas the voids displayed in ROI B are located in the solder and close to the interface. This observation could be explained by the orientation of Sn grain at the corner of meniscus. At ROI A, the c-axis of β-Sn is almost parallel to the electron direction. Therefore, the diffusion of Cu is dominant in EM. At ROI A, the c-axis of β-Sn is almost parallel to A thinner IMC layer is observed and voids are formed at the interface due to the depletion of Cu. At ROI B, the c-axis of β-Sn is approximately perpendicular to the electron direction and the Sn self-diffusion becomes the dominant diffusion, which leads to the depletion of Sn and voids in the solder.
4
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Table 1 Main parameters for EM. N kB T e Z*
j ρ0 ρ α D0 EA
: : : : : :
atomic density Boltzmann constant local temperature electron charge effective charge number current density
: : : : :
resistivity at reference temperature T0 resistivity at T temperature coefficient of resistivity coefficient of diffusion activation energy
Fig. 6. Simulation model of the assembly of shunts.
3.2. Simulation of void formation and strain distribution The EM-induced void formation and its effect on the interconnect reliability is simulated by the procedure illustrated in Fig. 8. The temperature distribution evaluated from thermal-electric analysis serves as input for structural analysis. The evolution of atomic density with respect to testing time t is described by:
3. Simulation 3.1. Electro-thermal simulation The assembly of shunts is modeled in Ansys workbench and the temperature change induced by current pulses is evaluated via FEM simulation (Fig. 6). Current is applied to the Cu pad of PCB, which flows through the shunt component to the other side of the Cu pad where voltage is defined to be 0 V. The temperature increase of the assembly due to Joule heating is cooled down by heat transfer to the environment via convection with coefficient of 25 W/(m2·K). The asymmetric selfheating is reproduced by taking the Peltier effect into account and the temperature distribution in the solder is shown in Fig. 7. The higher temperature in the left solder joint leads to the earlier recrystallization and degradation observed in SEM and EBSD analysis. Based on the results of the electro-thermal simulation, the divergence of material flux due to EM can be evaluated. The material flux density and the divergence of material flux density are modeled by Eqs. (1)(2). The meaning of the parameters is described in Table 1.
Jem =
N e Z* j kB T
divj (Jem ) =
EA kB T 2
EA kB T
D0 exp
1 + T
0
div jtotal ) +
(3)
where div jtotal ) is the total divergence of material flux. In this work, electromigration is the dominant term comparing to thermomigration and stressmigration. Therefore, only divergence of material flux due to EM is considered in the simulation. Zhang [12] defined the criterion for void formation such that void initiation is given when the local atomic concentration is less than 85% of the initial concentration. The elements exceeding the threshold value will be selected into a cluster. The stiffness of the elements in the cluster will be reduced in the structural analysis so that the elements act as voids. The evolved solder geometry and the corresponding distribution of accumulated plastic strain at various numbers of power cycles are illustrated in Fig. 9. Table 2 lists the number of elements which are defined as voids at a different number of power cycles and the corresponding volume weighted averaged (VWA) accumulated plastic strain. At 5000 PCs, no large voids are formed in the solder joint which is in agreement with the SEM analysis. At 10000 PCs, 22 elements (1.12% volume fracture of solder joints) exceeding the criterion are defined as voids. The critical location for void formation corresponds well with the voids and micro-cracks observed in the SEM analysis and the voids lead to a slight increment in accumulated plastic strain in the evolved solder geometry. At 15000 PCs, significant material depletion (20.02% volume fracture of solder joints) occurs mainly at the solder meniscus and
(1)
Jem grad T
N =0 t
(2)
Fig. 7 presents the distribution of divergence of material flux density in the solder joint. The maximal divergence of material flux density is located at the corner of the meniscus, which corresponds well with the location of the initiation of voids and micro-cracks.
Fig. 7. Simulation results of solder joint at the end of the current pulse.
5
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Fig. 8. Procedure for simulation of void formation.
(a) no void simulation
(b) 5000 PCs
(c) 10000 PCs
(d) 15000 PCs
Fig. 9. Accumulated plastic strain in solder joints with voids simulation.
the accumulated plastic strain in the solder joint is tremendously increased. The coalescence of voids leads to greater lifetime reduction compared to multiple voids distribution [13]. The effect of Sn grain orientation on the diffusion properties is not considered in the simulation.
Table 2 Simulation results. Power cycles
Nr. of voids elements (volume fracture)
0 5000 10,000 15,000
0 (0%) 1 (0%) 22 (1.12%) 336 (20.02%)
Max. accumulated plastic strain [−] 2.44e-3 2.44e-3 4.03e-3 4.92e-3
VWA accumulated plastic strain [−] 1.229e-3 1.229e-3 1.589e-3 2.379e-3
4. Conclusions The void formation in solder joints of shunt components under power cycling conditions is investigated experimentally and 6
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numerically. Voids and micro-cracks initiate at the corner of the solder meniscus, where the maximal divergence of material flux density is located. The Sn grain orientation has great influence on the failure mode due to the highly anisotropic properties of β-Sn. The void formation is simulated by defining a criterion for void initiation and the stiffness of the elements which are defined as voids will be reduced. The simulated voids at a different number of testing cycles show good agreement with the SEM analysis. The accumulated plastic strain in the solder joint will be significantly increased when coalescence of voids takes place. This could explain the remarkable reduction of lifetime of electronic assembly subjected to coupling thermo-mechanical fatigue and electromigration.
684–690. [2] S.Y. Yang, I. Kim, S.B. Lee, A study on the thermal fatigue behavior of solder joints under power cycling conditions, IEEE Trans. Compon. Packag. Technol. 31 (1) (Mar. 2008) 3–12. [3] J. Li, J. Karppinen, T. Laurila, et al., Reliability of lead-free solder interconnections in thermal and power cycling test, IEEE Trans. Compon. Packag. Technol. 32 (2) (Jun. 2009) 302–308. [4] Y.X. Wang, Y. Yao, L.M. Keer, A statistical mechanics model to predict electromigration induced damage and void growth in solder interconnects, Phys. A Stat. Mech. Appl. 468 (Feb. 2017) 195–204. [5] Y.L. Lin, C.W. Chang, C.M. Tsai, et al., Electromigration-induced UBM consumption and the resulting failure mechanisms in flip-chip solder joints, J. Electron. Mater. 35 (5) (May 2006) 1010–1016. [6] M. Lu, D. Shih, P. Lauro, et al., Effect of Sn grain orientation on electromigration degradation mechanism in high Sn-based Pb-free solders, Appl. Phys. Lett. 92 (21) (May 2008) 211909, , https://doi.org/10.1063/1.2936996. [7] H. Sun, M. Huang, Dominant effect of Sn grain orientation on electromigrationinduced failure mechanism of Sn-3.0Ag-0.5 Cu flip chip solder interconnects, 18th ICEPT, Sep. 2017, pp. 1296–1299, , https://doi.org/10.1109/ICEPT.2017.8046676. [8] H.C. Ma, J.D. Guo, J.Q. Chen, et al., Prediction model of lifetime for copper pillar bumps under coupling effects of current and thermal cycling, J. Mater. Sci. Mater. Electron. 27 (2) (Feb. 2016) 1184–1190. [9] H.C. Ma, J.D. Guo, J.Q. Chen, et al., The reliability of copper pillar under the coupling of thermal cycling and electric current stressing, J. Mater. Sci. Mater. Electron. 27 (9) (Sep. 2016) 9748–9754. [10] Q.S. Zhu, F. Gao, H.C. Ma, et al., Failure behavior of flip chip solder joint under coupling condition of thermal cycling and electrical current, J. Mater. Sci. Mater. Electron. 29 (6) (Mar. 2018) 5025–5033. [11] L. Yin, L. Wentlent, L. Yang, et al., Recrystallization and precipitate coarsening in Pb-free solder joints during thermomechanical fatigue, J. Electron. Mater. 41 (2) (Feb. 2012) 241–252. [12] Y. Zhang, Electromigration failure prediction and reliability evaluation of solder bumps for FCBGA package, Eng. Trans. 63 (2) (Jan. 2015) 215–232. [13] P. Wild, D. Lorenz, T. Grözinger, et al., Effect of voids on thermo-mechanical reliability of chip resistor solder joints: experiment, modelling and simulation, Microelectron. Reliab. 85 (Jun. 2018) 163–175.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors thank Robert Bosch GmbH, University of Stuttgart and Hahn-Schickard for the scientific support. References [1] J. Mei, R. Haug, O. Lanier, et al., Effect of Joule heating on the reliability of solder joints under power cycling conditions, Microelectron. Reliab. 88–90 (Sep. 2018)
7
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Void formation in solder joints under power cycling conditions and its effect on reliability J. Meia,d, , R. Hauga, S. Hinderbergerb, T. Grözingerc, A. Zimmermannc,d ⁎
a
Robert Bosch GmbH, Robert-Bosch-Strasse 2, 71701 Schwieberdingen, Germany Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen c Hahn-Schickard, Allmandring 9B, 70569 Stuttgart, Germany d Institute for Micro Integration (IFM), University of Stuttgart, Allmandring 9B, 70569 Stuttgart, Germany b
ABSTRACT
When electronic assemblies are experiencing high current loading conditions, thermo-mechanical mismatch induced from the local Joule heating of the component and electromigration (EM)-induced void formation can lead to the failure of the solder interconnect. Scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) are adopted to investigate the microstructural evolution of solder joints of shunt components subjected to current stressing. Voids and micro-cracks initiate at the corner of solder meniscus, where the maximal divergence of material flux density is located on the basis of finite element method (FEM) simulation. The EM-induced voids introduce higher accumulated plastic strain in the solder joints, which will result in reduction in the lifetime of the electronic assemblies.
1. Introduction Automotive electronics are often experiencing environments of vibration, mechanical shock and thermal fluctuation induced from internal or external sources. Among all the electronic components, shunts exhibit relatively high reliability under passive temperature cycling test due to the small coefficient of thermal expansion (CTE) mismatch between the shunts (≈16.5 ppm/K) and printed circuit boards (PCBs) (≈15 ppm/K). However, shunts are often subjected to switching cycling in the use conditions and failure has been reported under accelerated power cycling test conditions [1]. It is of great significance to understand the failure mechanism of solder joints of shunt components under power cycling conditions and enable the evaluation of service lifetime of shunt components in the field load. The main failure mechanisms of solder joints exposed to power cycling loading conditions are i) recrystallization-assisted crack nucleation and propagation, ii) electromigration (EM)–induced void formation and consumption of the under bump metallisation (UBM). In most studies, the failure modes in solder joints induced by thermomechanical stress [2,3] and EM [4,5] are addressed separately. The EMinduced degradation is highly affected by the Sn grain orientation. The damage mode is dominated by Sn self-diffusion when the c-axis of β-Sn grains is perpendicular to the electron flow direction. When the c-axis of β-Sn grains is parallel to the electron flow direction, an excessive dissolution of UBM will take place since the diffusivity of Cu or Ni along the c-axis is a few magnitudes higher than along the a-axis or b-axis of
⁎
β-Sn and higher than the Sn self-diffusion [6,7]. Ma [8] has investigated the coupling conditions of electromigration and thermal cycling and found out the lifetime under coupling conditions is significantly shortened owing to the EM-induced voids and micro-cracks in solder materials [9,10]. The thermo-mechanical stress in the solder joints of shunt components, which is generated by current stressing, has been investigated in an earlier study [1]. The aim of this work is focusing on the evaluation of the degradation of solder joints resulting from EM. SEM and EBSD analysis are carried out on the shunt units after different cycles of current stressing. The power cycling test is simulated in Ansys workbench and the simulation of void formation agrees well with the experimental observation. The distribution of accumulated plastic strain in the solder joint is evaluated by taking the void formation into account. 2. Materials and methods 2.1. Power cycling test Shunt components as shown in Fig. 1 are mounted on PCBs. The assemblies are connected to power supplies which provide the loading condition as displayed in Fig. 2 and are placed in a temperature chamber which maintains at constant temperature of 90 °C. The test condition is chosen to investigate the application conditions of the components, where shunts are often experiencing short current pulses
Corresponding author. E-mail address: [email protected] (J. Mei).
https://doi.org/10.1016/j.microrel.2019.06.042 Received 13 May 2019; Received in revised form 19 June 2019; Accepted 20 June 2019 0026-2714/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: J. Mei, et al., Microelectronics Reliability, https://doi.org/10.1016/j.microrel.2019.06.042
Microelectronics Reliability xxx (xxxx) xxxx
J. Mei, et al.
Fig. 1. Configuration of the shunts.
(a) 10000 power cycles (PCs) Fig. 2. Current profile of the power cycling test.
with the pulse duration of few ms to 1 s and with the current range similar to the test condition illustrated in Fig. 2. The pulse duration is decided to be 2 s in this work to accelerate the testing time and to prevent the overheating of the components and PCBs. As described in an earlier work [1], the self-heating of the investigated shunts is asymmetric. Fig. 3 presents the infrared (IR) thermography measurement of the shunts under a representative loading condition. The terminal of the shunt which is connected to the anode of the power supply is experiencing around 20 °C higher temperature than the terminal on the cathode side. The asymmetric heat generation is reversed when the current direction is switched. This phenomenon can be explained by the Peltier effect which takes place at the junction between the terminal (Cu) and resistive element (CuNi alloy).
(b) 15000 PCs Fig. 4. Cross-sectional analysis of the shunts.
2.2. Failure mode analysis Some shunt units are removed from the chamber at a different number of power cycles and analysed with cross-sectioning to monitor the degradation of solder joints at early stages before the electrical
Fig. 3. Top view of shunt in optical and IR domains during current stressing in two directions (current: 34 A, pulse length: 3 s, room temperature). 2
Microelectronics Reliability xxx (xxxx) xxxx
J. Mei, et al.
failure. As shown in Fig. 4(a), some void-like damage initiates at the corner of the solder meniscus after current stressing. The crack propagates later through the bulk solder and the interface between the terminal and solder, leaving an open circuit in the left solder joint as displayed in Fig. 4(b). No obvious damage is observed in the right solder joint. This polarity effect in the failure mode is resulting from the asymmetric heat generation of the shunts under active current load. Scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) are further performed on the shunt components to investigate the failure mechanism, especially the void-like damage
initiating at the corner of the solder meniscus. The step size for EBSD analysis has been defined to be 1.4 μm to capture the microstructural evolution. The large angle grain boundaries (LAGB) of Sn which yield a misorientation larger than 10° are marked as black lines. As displayed in Fig. 5(a), only 2 large Sn grains are observed in the left solder joint after soldering process. Two twin boundaries might have grown inside of the right solder joint. However, no significant difference in microstructure has been observed between both sides of the solder joint before power cycling test. After 5000 PCs as shown in Fig.5(b), voids and micro-cracks are initiating at the corner of the meniscus of left solder
(a) as reflow (0 PC)
(b) 5000 PCs Fig. 5. SEM and EBSD analysis of solder joints at different testing cycles. 3
Microelectronics Reliability xxx (xxxx) xxxx
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(c) 10000 PCs
(d) Region of Interest (ROI) A
(e) ROI B Fig. 5. (continued)
joint. New grains are formed due to recrystallization, predominantly at the solder standoff. More LAGBs are detected in the solder standoff as well. The right solder joint is comprised of a quasi-single grain of Sn and no obvious microstructural change is observed after 5000 PCs. Larger voids at the corner of meniscus and more LAGBs at the standoff are detected in the left solder joint after 10,000 PCs as depicted in Fig. 5(c), whereas the right solder joint exhibits a quasi-single grain of Sn similar to what is observed after 5000 PCs. The polarity of microstructural evolution in both sides of the solder joints is owing to the higher temperature distribution in the left solder joint. Thermo-mechanical fatigue cracks tend to initiate and propagate at the recrystallized region with LAGBs [11]. However, the voids and micro-cracks are formed at the corner of the solder meniscus instead of the solder standoff where more LAGBs are detected. Therefore, the degradation mechanism for the observed voids and micro-cracks is
likely to be EM rather than recrystallization-assisted crack nucleation. The voids and micro-cracks formed in ROI A are presented in Fig.5(d) with larger magnification. They are formed in the interface between the intermetallic compounds (IMCs) layer and solder, whereas the voids displayed in ROI B are located in the solder and close to the interface. This observation could be explained by the orientation of Sn grain at the corner of meniscus. At ROI A, the c-axis of β-Sn is almost parallel to the electron direction. Therefore, the diffusion of Cu is dominant in EM. At ROI A, the c-axis of β-Sn is almost parallel to A thinner IMC layer is observed and voids are formed at the interface due to the depletion of Cu. At ROI B, the c-axis of β-Sn is approximately perpendicular to the electron direction and the Sn self-diffusion becomes the dominant diffusion, which leads to the depletion of Sn and voids in the solder.
4
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Table 1 Main parameters for EM. N kB T e Z*
j ρ0 ρ α D0 EA
: : : : : :
atomic density Boltzmann constant local temperature electron charge effective charge number current density
: : : : :
resistivity at reference temperature T0 resistivity at T temperature coefficient of resistivity coefficient of diffusion activation energy
Fig. 6. Simulation model of the assembly of shunts.
3.2. Simulation of void formation and strain distribution The EM-induced void formation and its effect on the interconnect reliability is simulated by the procedure illustrated in Fig. 8. The temperature distribution evaluated from thermal-electric analysis serves as input for structural analysis. The evolution of atomic density with respect to testing time t is described by:
3. Simulation 3.1. Electro-thermal simulation The assembly of shunts is modeled in Ansys workbench and the temperature change induced by current pulses is evaluated via FEM simulation (Fig. 6). Current is applied to the Cu pad of PCB, which flows through the shunt component to the other side of the Cu pad where voltage is defined to be 0 V. The temperature increase of the assembly due to Joule heating is cooled down by heat transfer to the environment via convection with coefficient of 25 W/(m2·K). The asymmetric selfheating is reproduced by taking the Peltier effect into account and the temperature distribution in the solder is shown in Fig. 7. The higher temperature in the left solder joint leads to the earlier recrystallization and degradation observed in SEM and EBSD analysis. Based on the results of the electro-thermal simulation, the divergence of material flux due to EM can be evaluated. The material flux density and the divergence of material flux density are modeled by Eqs. (1)(2). The meaning of the parameters is described in Table 1.
Jem =
N e Z* j kB T
divj (Jem ) =
EA kB T 2
EA kB T
D0 exp
1 + T
0
div jtotal ) +
(3)
where div jtotal ) is the total divergence of material flux. In this work, electromigration is the dominant term comparing to thermomigration and stressmigration. Therefore, only divergence of material flux due to EM is considered in the simulation. Zhang [12] defined the criterion for void formation such that void initiation is given when the local atomic concentration is less than 85% of the initial concentration. The elements exceeding the threshold value will be selected into a cluster. The stiffness of the elements in the cluster will be reduced in the structural analysis so that the elements act as voids. The evolved solder geometry and the corresponding distribution of accumulated plastic strain at various numbers of power cycles are illustrated in Fig. 9. Table 2 lists the number of elements which are defined as voids at a different number of power cycles and the corresponding volume weighted averaged (VWA) accumulated plastic strain. At 5000 PCs, no large voids are formed in the solder joint which is in agreement with the SEM analysis. At 10000 PCs, 22 elements (1.12% volume fracture of solder joints) exceeding the criterion are defined as voids. The critical location for void formation corresponds well with the voids and micro-cracks observed in the SEM analysis and the voids lead to a slight increment in accumulated plastic strain in the evolved solder geometry. At 15000 PCs, significant material depletion (20.02% volume fracture of solder joints) occurs mainly at the solder meniscus and
(1)
Jem grad T
N =0 t
(2)
Fig. 7 presents the distribution of divergence of material flux density in the solder joint. The maximal divergence of material flux density is located at the corner of the meniscus, which corresponds well with the location of the initiation of voids and micro-cracks.
Fig. 7. Simulation results of solder joint at the end of the current pulse.
5
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Fig. 8. Procedure for simulation of void formation.
(a) no void simulation
(b) 5000 PCs
(c) 10000 PCs
(d) 15000 PCs
Fig. 9. Accumulated plastic strain in solder joints with voids simulation.
the accumulated plastic strain in the solder joint is tremendously increased. The coalescence of voids leads to greater lifetime reduction compared to multiple voids distribution [13]. The effect of Sn grain orientation on the diffusion properties is not considered in the simulation.
Table 2 Simulation results. Power cycles
Nr. of voids elements (volume fracture)
0 5000 10,000 15,000
0 (0%) 1 (0%) 22 (1.12%) 336 (20.02%)
Max. accumulated plastic strain [−] 2.44e-3 2.44e-3 4.03e-3 4.92e-3
VWA accumulated plastic strain [−] 1.229e-3 1.229e-3 1.589e-3 2.379e-3
4. Conclusions The void formation in solder joints of shunt components under power cycling conditions is investigated experimentally and 6
Microelectronics Reliability xxx (xxxx) xxxx
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numerically. Voids and micro-cracks initiate at the corner of the solder meniscus, where the maximal divergence of material flux density is located. The Sn grain orientation has great influence on the failure mode due to the highly anisotropic properties of β-Sn. The void formation is simulated by defining a criterion for void initiation and the stiffness of the elements which are defined as voids will be reduced. The simulated voids at a different number of testing cycles show good agreement with the SEM analysis. The accumulated plastic strain in the solder joint will be significantly increased when coalescence of voids takes place. This could explain the remarkable reduction of lifetime of electronic assembly subjected to coupling thermo-mechanical fatigue and electromigration.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors thank Robert Bosch GmbH, University of Stuttgart and Hahn-Schickard for the scientific support. References [1] J. Mei, R. Haug, O. Lanier, et al., Effect of Joule heating on the reliability of solder joints under power cycling conditions, Microelectron. Reliab. 88–90 (Sep. 2018)
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