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Dynamical IMC-growth calculation
MR-11601; No of Pages 6 Microelectronics Reliability xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/mr
Dynamical IMC-growth calculation L. Meinshausen a,b, K. Weide-Zaage a,⁎, H. Frémont b a b
RESRI Group Institute of Microelectronic Systems (IMS), Leibniz Universität Hannover, Appelstraße 4, 30167 Hannover, Germany Laboratoire IMS, Université Bordeaux I, Talence, 33405, France
a r t i c l e
i n f o
Article history: Received 25 May 2015 Received in revised form 22 June 2015 Accepted 23 June 2015 Available online xxxx Keywords: Simulation IMC growth Migration Reliability Packaging and assembly Package on package
a b s t r a c t Material movement between solder joints and their contact pads leads to the formation of intermetallic compounds at the contact surfaces. Concentration gradients are responsible for this material movement. The intermetallic compound growth during temperature storage and AC/DC electromigration tests on 12 × 12 mm Amkor® PoP with SnAg3.0Cu0.5 ball grid arrays including direct SnAgCu to Cu contacts at their bottom bumps was investigated. Based on the resulting increase in the IMC thickness the average mass flux of Cu and Sn were calculated. The activation energies (EA) diffusion constants (D0), effective charges (Z*) and heats of transport (Q*) are determined by measurement. With these parameters the mass fluxes due to concentration gradients, electromigration and thermomigration are calculated and the results were implemented in a routine for the dynamical calculation of the IMC-growth. Finally these calculations were validated by measurements. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction The miniaturization of integrated circuits is limited by physical and economic reasons. Nevertheless three dimensional packaging solutions enabled a further increase in the number of functions. Unfortunately the stacking of components goes apart with an increasing number of solder contacts on the same foot print and leads to a shrinking size of the solder contacts. The formation of intermetallic compounds (IMCs) starts during the reflow process. The IMC layer thickness after reflow is found to be independent from the bump size [1,2]. The thickness of the IMCs after reflow mainly depend on the reflow temperature profile, the solder itself and the bond pad finish [1]. Later material movements due to electromigration (EM), thermomigration (TM) or concentration gradients lead to an additive IMC growth. This leads to the result that with a shrinking bump size the IMC layers become more and more important. Especially micro bumps with a diameter of less than 40 μm IMCs can be transformed to full IMC contacts [3–5]. Based on the knowledge of the IMC-growth the development of aging models for BGAs and concepts for the fabrication of IMC joints for IC stacks with μBGAs will be possible. Finally the growth kinetics of solder based IMCs is an important process parameter for the establishment of solder based IMC contacts. The existence of IMCs in conventional ball grid arrays has an influence on the reliability of packages. The IMCs are sensitive to mechanical shocks for instance during drop tests [6]. Compared to SnAg3.0Cu0.5 (SAC305) the mobility of Cu and Sn in
⁎ Corresponding author.
the CuSn IMCs (Cu6Sn5 and Cu3Sn) is clearly reduced [7]. This leads to EM induced void formation between IMCs and the solder (Fig. 1) [8,9]. 2. Measurement and Simulation of IMC-growth 2.1. Short description of the parameter determination necessary to calculate IMC formation Before implementing an user routine into a Finite Element Model (FEM) the IMC formation was rationalized by extracting the related material parameters: activation energy (EA), diffusion constants (D0), heat of transport (Q*) and effective charge values (Z*) for the relevant elements (Cu, Sn,) in the relevant IMCs (Cu3Sn, Cu6Sn5), from experimental results [10,11]. The intermetallic compound growth in SAC305 ball grid array for 12 × 12 mm Amkor® SAC305 PoP packages was investigated. The IMC formation was measured and simulated for the direct SAC–Cu contacts of the bottom part of the PoP structure (Fig. 2). At the beginning of the experimental procedure the amount of IMC being formed during the temperature storage (TS) tests was determined by SEM and the related mass fluxes of Cu and Sn in Cu3Sn, Cu6Sn5 were calculated. Following EA and D0 of Cu and Sn could be extracted. Further the SEM measurements (Fig. 3 a/b) were used to design the FEM model. Afterwards the TS tests were combined with an alternated current (AC) (50 Hz) to induce temperature gradients due to local Joule heating. While the temperature gradients lead to TM, an effective mass flux due to EM was suppressed by the rapid directional changes of the current flow. Based on the TM induced mass flux values, Q* of Cu, Sn in both Cu–Sn IMCs could be determined. Lastly the TS tests were combined with a direct current (DC). Like during the AC tests an
http://dx.doi.org/10.1016/j.microrel.2015.06.052 0026-2714/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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Fig. 1. EM induced void formation at the contact interfaces of solder joints.
Fig. 2. Scheme of the investigated PoP, red indicated Ni_X finish. Top of the bottom bump without Ni finish.
accelerated IMC formation speed was observable compared to TS test without an applied current. The applied DC current of 1A led to void formation in the solder joints and the IMC formation speed was influenced by the direction of the current flow [8–12]. Both effects clearly indicate the presence of EM. A difference between the mean IMC thickness and
shape at the upper and the lower contact surfaces also indicated the presence of a TM induced mass flux. By comparing the IMC dimensions for upstream and the downstream case the EM induced mass flux could be extracted. After extrapolation of the diffusion related mass flux values also the TM induced mass fluxes were available. Based on these results Z* values at three different temperatures and Q* values for four different temperatures were extracted. The Q* values of Cu and Sn in Cu3Sn are two orders of magnitude higher than those of the same elements in Cu6Sn5 shown in Table 1. 2.2. Simulation flow and diffusion induced mass flux In Fig. 4 the principle motion of Cu during the IMC growth is shown. Cu flows from the pads (right side) into the solder (left side) during the IMC formation. After the aging test a part of the Cu atoms (blue dots) can be found in Cu3Sn resulting a thickness change. Others already moved into the Cu6Sn5 layer (red dots). The motion of Cu leads to the formation of Cu3Sn at the interface to Cu (hR) as well as at the formation of Cu6Sn5 at the interface of Cu3Sn (hL). In both cases the present Cu atoms (black dots) were integrated into the Cu3Sn layer without being part of the mass flux. To avoid an overestimation of the Cu mass fluxes during aging, these atoms have to be subtracted from the amount of Cu in the added IMC material [12]. The investigations of the IMC growth in solder joints were carried out using the finite element program ANSYS®. The calculation of the IMC layers is based on the local current density, the local temperature gradient and local concentration gradients. After the 3D modeling of the solder joint, based on all available geometrical data from SEM and optical microscope measurements, the thermal electrical finite element simulation is performed. Based on the results of the thermal electrical simulations, the migration related material parameters as well as the results from the thermal electrical simulation the mass flux (MF) due to electromigration (EM) and thermomigration (TM) were calculated with an user routine [13,14]. In the next step the mass flux due to concentration gradients given in Eqs. (1) and (2), was implemented ! with another user routine and the total mass flux ( J ) in the IMCs was calculated. ! EA J ¼ −D0 gradðNÞ exp − kB T
ð1Þ
Table 1 Z* and Q* for Cu and Sn in Cu3Sn and Cu6Sn5.
Fig. 3. SEM pictures a) above bumps b) below traces of the packages used for the reliability measurements.
IMC
Element
TCR [K−1]
Z*
Q* [eV]
Cu3Sn
Cu Sn Cu Sn
1.84 × 10−3 2.7 × 10−3 6.0 × 10−3 6.3 × 10−3
8.9 −8.8 12 −11
−4.4 2.5 −0.03 0.4
Cu6Sn5
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
L. Meinshausen et al. / Microelectronics Reliability xxx (2015) xxx–xxx
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Fig. 4. Simplified Cu mass flux during diffusion driven IMC growth. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 5. Flowchart of the dynamic IMC growth calculation. TE thermal-electrical, MF — mass flux, MFG — sum mass flux TM+ EM.
jgradðNÞj≈
ΔN : ðh þ h0 Þ=2
ð2Þ
D0 is the diffusion coefficient, N the particle concentration, EA the activation energy, kB Boltzmann constant, and h is the IMC layer thickness. The dynamic simulation is split into a variable number of time steps (nmax) and for every time step the thermal and electrical conditions and the actual mass flux can be calculated. With the total ! Cu mass flux the growth speed ( v ) of Cu6Sn5 and Cu3Sn can be calculated with Eqs. (3)–(4). ! ! v Cu3 Sn ¼ J Cu;Cu3 Sn
NCu;Cu − NCu;Cu6 Sn5 NCu;Cu −NCu;Cu3 Sn NCu;Cu3 Sn −NCu;Cu6 Sn5
ð3Þ
Table 2 Temperature coefficients of Z**, the effective charge Z*, the EA for TM and the Q* of Cu [10,11].
Cu3Sn Cu6Sn5
α [1/K]
TCR [1/K]
Z*
EA,TM [eV]
Q* [eV]
0.06 0.13
2.91 × 10−3 2.62 × 10−3
8.2 16.4
0.57 0.49
−0.86 3.8
Fig. 6. EM and TM induced mass flux of Cu in Cu6Sn5 at 138 °C/1A [1/μm2s].
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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Table 3 Material parameters of Cu3Sn and Cu6Sn5 used in the simulations [10,11].
Cu3Sn Cu6Sn5
EA [eV]
N [1/m3]
grad (N) [1/m4]
D0 [m2/s]
0.808 0.58
3.9 × 1028 2.6 × 1028
1.7 × 1033 2.1 × 1032
1.3 × 10−8 2.9 × 10−9
Table 4 Temperature coefficients of Z**, the effective charge Z*, the EA for TM and the Q* of Cu used in the calculation [10,11].
Cu3Sn Cu6Sn5
α [1/K]
TCR [1/K]
Z*
EA,TM [eV]
Q* [eV]
0.06 0.13
2.91 × 10−3 2.62 × 10−3
8.2 16.4
0.57 0.49
−0.86 3.8
! ! v Cu6 Sn5 ¼ J Cu;Cu6 Sn5
N Cu;Cu3 Sn − NCu;SnAgCu NCu;Cu3 Sn − NCu;Cu6 Sn5 NCu;Cu6 Sn5 − NCu;SnAgCu
Fig. 8. Mass flux Cu5Sn6 bottom bump, black dots from measurement red dots median values from simulation.
ð4Þ While the values out of the measurements represent averaged values only, the simulations restore the information about geometrical influences, like local current crowding and temperature gradients, on the IMC formation speed. The simulation enables the use of local information about the IMC growth which was lost by the use of averaged values for the mathematical interpretation of the experimental results. The dynamic IMC growth simulation flowchart is shown in Fig. 5. For the calculation of the electromigration (EM) and thermomigration (TM) mass flux Eqs. (5) and (6) are used. The heat of solution HS was also required for the calculation of the thermomigration in Eq. (6), with Q* as the heat of transport. ! ! NeZ j ρel EA exp − J EM ¼ D0 kB T kB T
ð5Þ
! N ðQ þ HS Þ EA þ HS ð Þ J TM ¼ −D0 grad T exp − kB T kB T2
ð6Þ
Fig. 7. Mass flux Cu3Sn bottom bump, black dots from measurement red dots median values from simulation.
Z* and the Q* of Cu in Cu3Sn and Cu6Sn5 have to be known. Z* is temperature dependent due to electron scattering at crystal defects in the IMC layers. Hence Z* has to be calculated (Eq. (7)). The used temperature coefficients, Z* and Q* values are given in Table 2. 2 2 Z ðTÞ ¼ Z ½1 þ α ðT−300 KÞ−Z ½1 þ TCR ðT−300 KÞ
ð7Þ
The electromigration induced mass flux as well as the thermomigration induced mass flux is shown in Fig. 6. The electromigration is clearly affected by current crowding shown in figure [8,9]. For the extraction of material parameters from the experimental results, averaged values were used. Hence information about the influence of current crowding on the IMC formation was lost. A three dimensional FEA allows the reconstruction of the current crowding effect by combining
Fig. 9. The (J-EM), (J-TM), and diffusion induced (J-Dif) mass fluxes of Cu in Cu6Sn5, total mass flux (J-Sum) of Cu [1/μm2s], bottom bump at the top surface upstream is shown.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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from the simulation as well as the trend line is shown. The simulation results fit well to the experimental results. The deviation from the trend line for 140 °C, 150 °C and 185 °C can be explained by the fact that the EA was taken from the interpolation of the measurement values for 100 °C up to 150 °C. The mass flux values at 185 °C were extrapolated from the test results at 140 °C. The experimental and the Cu5Sn6 median values from the simulation as well as the trend line is shown in Fig. 8. The estimated mass flux at 138 °C was too high. Like for Cu3Sn, a difference between the simulation and the test results appeared for 140 °C and 150°.
2.5. Electro- and thermomigration induced IMC-growth
Fig. 10. The (J-EM), (J-TM), and diffusion induced (J-Dif) mass fluxes of Cu in Cu6Sn5, total mass flux (J-Sum) of Cu [1/μm2s], bottom bump at the top surface downstream is shown.
the general migration parameters (Z*, Q*) with the influence of the solder joint geometry on the driving forces of the EM and TM.
The electro- and thermomigration induced IMC-growth was determined. In Figs. 9 and 10 the electromigration induced mass flux J-EM, the thermomigration induced mass flux J-TM, the diffusion induced mass flux J-Dif as well as the total mass flux J-Sum of Cu in Cu6Sn5 upstream and downstream is shown. The values are taken from the Cu bottom bump at the top surface. (See Figs. 11 and 12.) With the help of the local mass flux values the calculation of the dynamical IMC formation is possible. The IMC dimensions at the starting point and at the end of the accelerated test are shown in Fig. 11. As for the experimental results a relatively thick and homogenous IMC layer was formed during the downstream tests, and a relatively thin IMC layer with a clear current crowding profile was formed during the upstream tests.
2.3. Parameter for the IMC-growth calculation
3. Conclusions
The mass flux of Cu and Sn can be induced during the reflow, temperature storage, or the current application during the reliability stress test. For the calculation of the mass flux different material data are necessary and taken from [10,11]. The values are given in Table 3. The used temperature coefficients, Z* and Q* values are given in Table 4. The simulation does not take into account any saturation effects.
The intermetallic compound growth in 12 × 12 mm Amkor® SAC305 ball grid array PoP packages including direct SAC-Cu contacts at their bottom bumps was investigated. Based on the resulting IMC thickness from measurements the average mass flux of Cu and Sn was calculated. The simulated as well as the calculated values for the IMC growth were validated with the measurements. It was shown that the user-routines under the knowledge of the material parameters give the possibility to simulate the IMC-growth in solder bumps. The user routine enables the possibility for the calculation of other material layer growth like IMC formation in AuSn solders in the future.
2.4. Diffusion induced IMC-growth The diffusion induced IMC-growth was determined. In Fig. 7 the Cu mass flux values from the measurement and the Cu3Sn median values
Fig. 11. Cu6Sn5 profile before (left) and after (right) a DC stress test 138 °C (2369 h) and 1A. The effect of current crowding on the IMC formation in the bottom bumps for the up- (right) and the downstream cases (left) is shown in Fig. 12 the white arrows show the principle direction of the mass flux in the IMCs. A good agreement between simulation, calculation and measurement was found caused by the fact that the calculated shape as well as the thickness corresponds to the measured values.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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Fig. 12. The effect of current crowding on the IMC formation in the bottom bumps TStress 161 °C/1A (192 h).
References [1] X.Y. Li, B.S. Wu, X.H. Yang, The formation and evolution of IMC and its effect on the solder joint properties, IEEE, Proceedings of the 6th International Conference on Electronic Packaging Technology (ICEPT), Shenzhen, China, 31 August–2 September 2005 2005, pp. 1–6. [2] B. Salam, N.N. Ekere, D. Rajkumar, Study of the interface microstructure of Sn–Ag–Cu lead-free solders and the effect of solder volume on intermetallic layer formation, IEEE, proceedings of the 51th Electronic Components and Technology Conference (ECTC), Orlando, USA, 29 May–1 June 2001 2001, pp. 471–477. [3] K.N. Tu, Reliability challenges in 3D IC packaging technology, Microelectron. Reliab. 51 (2011) 517–523. [4] Y. Ohara, A. Noriki, K. Sakuma, 10 μm fine pitch Cu/Sn micro-bumps for 3-D super-chip stack, IEEE, Proceedings of the 2nd International 3D System Integration (3DIC), San Francisco, USA, 28–30 September 2009 2009, pp. 1–6. [5] R. Labie, P. Limaye, K.W. Lee, C.J. Berry, E. Beyne, I. De Wolf, Reliability testing of Cu–Sn intermetallic micro-bump interconnections for 3D-device stacking, IEEE, proceedings of the Electronics-System-Integration-Conference (ESTC), Berlin, Germany, 13–16 September 2010 2010, pp. 1–5. [6] T. Matilla, Reliability of High-Density Lead-Free Solder Interconnections Under Thermal Cycling and Mechanical Shock LoadingDissertation Helsinki University of Technology, 2005. 32.
[7] L. Meinshausen, K. Weide-Zaage, H. Frémont, Migration induced material transport in Cu–Sn IMC and SnAgCu micro bumps, Microelectron. Reliab. 51 (2011) 1860–1864. [8] K. Weide-Zaage, H. Frémont, L. Wang, Simulation of migration effects in PoP, IEEE EuroSimE, 2008. [9] W. Feng, K. Weide-Zaage, et al., Electrically driven matter transport effects in PoP interconnections, IEEE–EuroSimE, 2009. [10] L. Meinshausen, H. Frémont, K. Weide-Zaage, Plano: Micro. Rel. (2014) http://dx.doi. org/10.1016/j.microrel.2014.09.030. [11] L. Meinshausen, “Modeling the SAC Microstructure Evolution under Thermal, Thermomechanical and Electrical Constraints”, PhD Theses No. 2014BORD0149 (2014). [12] L. Meinshausen, H. Frémont, K. Weide-Zaage, et al., Electro- and thermomigrationinduced IMC formation in SnAg3.0Cu0.5 solder joints on nickel gold pads, IEEE Microelectron. Reliab. 53 (9–11) (2013) 1575–1580. [13] K. Weide-Zaage, Untersuchungen von Stromdichte-, Temperatur- und Massenflussverteilungen in Viastrukturen integrierter SchaltungenDissertation VDI Verlag, Düsseldorf, 1994. 9–11 (in German). [14] K. Weide-Zaage, IEEE, Mechanical & Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2010.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/mr
Dynamical IMC-growth calculation L. Meinshausen a,b, K. Weide-Zaage a,⁎, H. Frémont b a b
RESRI Group Institute of Microelectronic Systems (IMS), Leibniz Universität Hannover, Appelstraße 4, 30167 Hannover, Germany Laboratoire IMS, Université Bordeaux I, Talence, 33405, France
a r t i c l e
i n f o
Article history: Received 25 May 2015 Received in revised form 22 June 2015 Accepted 23 June 2015 Available online xxxx Keywords: Simulation IMC growth Migration Reliability Packaging and assembly Package on package
a b s t r a c t Material movement between solder joints and their contact pads leads to the formation of intermetallic compounds at the contact surfaces. Concentration gradients are responsible for this material movement. The intermetallic compound growth during temperature storage and AC/DC electromigration tests on 12 × 12 mm Amkor® PoP with SnAg3.0Cu0.5 ball grid arrays including direct SnAgCu to Cu contacts at their bottom bumps was investigated. Based on the resulting increase in the IMC thickness the average mass flux of Cu and Sn were calculated. The activation energies (EA) diffusion constants (D0), effective charges (Z*) and heats of transport (Q*) are determined by measurement. With these parameters the mass fluxes due to concentration gradients, electromigration and thermomigration are calculated and the results were implemented in a routine for the dynamical calculation of the IMC-growth. Finally these calculations were validated by measurements. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction The miniaturization of integrated circuits is limited by physical and economic reasons. Nevertheless three dimensional packaging solutions enabled a further increase in the number of functions. Unfortunately the stacking of components goes apart with an increasing number of solder contacts on the same foot print and leads to a shrinking size of the solder contacts. The formation of intermetallic compounds (IMCs) starts during the reflow process. The IMC layer thickness after reflow is found to be independent from the bump size [1,2]. The thickness of the IMCs after reflow mainly depend on the reflow temperature profile, the solder itself and the bond pad finish [1]. Later material movements due to electromigration (EM), thermomigration (TM) or concentration gradients lead to an additive IMC growth. This leads to the result that with a shrinking bump size the IMC layers become more and more important. Especially micro bumps with a diameter of less than 40 μm IMCs can be transformed to full IMC contacts [3–5]. Based on the knowledge of the IMC-growth the development of aging models for BGAs and concepts for the fabrication of IMC joints for IC stacks with μBGAs will be possible. Finally the growth kinetics of solder based IMCs is an important process parameter for the establishment of solder based IMC contacts. The existence of IMCs in conventional ball grid arrays has an influence on the reliability of packages. The IMCs are sensitive to mechanical shocks for instance during drop tests [6]. Compared to SnAg3.0Cu0.5 (SAC305) the mobility of Cu and Sn in
⁎ Corresponding author.
the CuSn IMCs (Cu6Sn5 and Cu3Sn) is clearly reduced [7]. This leads to EM induced void formation between IMCs and the solder (Fig. 1) [8,9]. 2. Measurement and Simulation of IMC-growth 2.1. Short description of the parameter determination necessary to calculate IMC formation Before implementing an user routine into a Finite Element Model (FEM) the IMC formation was rationalized by extracting the related material parameters: activation energy (EA), diffusion constants (D0), heat of transport (Q*) and effective charge values (Z*) for the relevant elements (Cu, Sn,) in the relevant IMCs (Cu3Sn, Cu6Sn5), from experimental results [10,11]. The intermetallic compound growth in SAC305 ball grid array for 12 × 12 mm Amkor® SAC305 PoP packages was investigated. The IMC formation was measured and simulated for the direct SAC–Cu contacts of the bottom part of the PoP structure (Fig. 2). At the beginning of the experimental procedure the amount of IMC being formed during the temperature storage (TS) tests was determined by SEM and the related mass fluxes of Cu and Sn in Cu3Sn, Cu6Sn5 were calculated. Following EA and D0 of Cu and Sn could be extracted. Further the SEM measurements (Fig. 3 a/b) were used to design the FEM model. Afterwards the TS tests were combined with an alternated current (AC) (50 Hz) to induce temperature gradients due to local Joule heating. While the temperature gradients lead to TM, an effective mass flux due to EM was suppressed by the rapid directional changes of the current flow. Based on the TM induced mass flux values, Q* of Cu, Sn in both Cu–Sn IMCs could be determined. Lastly the TS tests were combined with a direct current (DC). Like during the AC tests an
http://dx.doi.org/10.1016/j.microrel.2015.06.052 0026-2714/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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Fig. 1. EM induced void formation at the contact interfaces of solder joints.
Fig. 2. Scheme of the investigated PoP, red indicated Ni_X finish. Top of the bottom bump without Ni finish.
accelerated IMC formation speed was observable compared to TS test without an applied current. The applied DC current of 1A led to void formation in the solder joints and the IMC formation speed was influenced by the direction of the current flow [8–12]. Both effects clearly indicate the presence of EM. A difference between the mean IMC thickness and
shape at the upper and the lower contact surfaces also indicated the presence of a TM induced mass flux. By comparing the IMC dimensions for upstream and the downstream case the EM induced mass flux could be extracted. After extrapolation of the diffusion related mass flux values also the TM induced mass fluxes were available. Based on these results Z* values at three different temperatures and Q* values for four different temperatures were extracted. The Q* values of Cu and Sn in Cu3Sn are two orders of magnitude higher than those of the same elements in Cu6Sn5 shown in Table 1. 2.2. Simulation flow and diffusion induced mass flux In Fig. 4 the principle motion of Cu during the IMC growth is shown. Cu flows from the pads (right side) into the solder (left side) during the IMC formation. After the aging test a part of the Cu atoms (blue dots) can be found in Cu3Sn resulting a thickness change. Others already moved into the Cu6Sn5 layer (red dots). The motion of Cu leads to the formation of Cu3Sn at the interface to Cu (hR) as well as at the formation of Cu6Sn5 at the interface of Cu3Sn (hL). In both cases the present Cu atoms (black dots) were integrated into the Cu3Sn layer without being part of the mass flux. To avoid an overestimation of the Cu mass fluxes during aging, these atoms have to be subtracted from the amount of Cu in the added IMC material [12]. The investigations of the IMC growth in solder joints were carried out using the finite element program ANSYS®. The calculation of the IMC layers is based on the local current density, the local temperature gradient and local concentration gradients. After the 3D modeling of the solder joint, based on all available geometrical data from SEM and optical microscope measurements, the thermal electrical finite element simulation is performed. Based on the results of the thermal electrical simulations, the migration related material parameters as well as the results from the thermal electrical simulation the mass flux (MF) due to electromigration (EM) and thermomigration (TM) were calculated with an user routine [13,14]. In the next step the mass flux due to concentration gradients given in Eqs. (1) and (2), was implemented ! with another user routine and the total mass flux ( J ) in the IMCs was calculated. ! EA J ¼ −D0 gradðNÞ exp − kB T
ð1Þ
Table 1 Z* and Q* for Cu and Sn in Cu3Sn and Cu6Sn5.
Fig. 3. SEM pictures a) above bumps b) below traces of the packages used for the reliability measurements.
IMC
Element
TCR [K−1]
Z*
Q* [eV]
Cu3Sn
Cu Sn Cu Sn
1.84 × 10−3 2.7 × 10−3 6.0 × 10−3 6.3 × 10−3
8.9 −8.8 12 −11
−4.4 2.5 −0.03 0.4
Cu6Sn5
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
L. Meinshausen et al. / Microelectronics Reliability xxx (2015) xxx–xxx
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Fig. 4. Simplified Cu mass flux during diffusion driven IMC growth. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 5. Flowchart of the dynamic IMC growth calculation. TE thermal-electrical, MF — mass flux, MFG — sum mass flux TM+ EM.
jgradðNÞj≈
ΔN : ðh þ h0 Þ=2
ð2Þ
D0 is the diffusion coefficient, N the particle concentration, EA the activation energy, kB Boltzmann constant, and h is the IMC layer thickness. The dynamic simulation is split into a variable number of time steps (nmax) and for every time step the thermal and electrical conditions and the actual mass flux can be calculated. With the total ! Cu mass flux the growth speed ( v ) of Cu6Sn5 and Cu3Sn can be calculated with Eqs. (3)–(4). ! ! v Cu3 Sn ¼ J Cu;Cu3 Sn
NCu;Cu − NCu;Cu6 Sn5 NCu;Cu −NCu;Cu3 Sn NCu;Cu3 Sn −NCu;Cu6 Sn5
ð3Þ
Table 2 Temperature coefficients of Z**, the effective charge Z*, the EA for TM and the Q* of Cu [10,11].
Cu3Sn Cu6Sn5
α [1/K]
TCR [1/K]
Z*
EA,TM [eV]
Q* [eV]
0.06 0.13
2.91 × 10−3 2.62 × 10−3
8.2 16.4
0.57 0.49
−0.86 3.8
Fig. 6. EM and TM induced mass flux of Cu in Cu6Sn5 at 138 °C/1A [1/μm2s].
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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Table 3 Material parameters of Cu3Sn and Cu6Sn5 used in the simulations [10,11].
Cu3Sn Cu6Sn5
EA [eV]
N [1/m3]
grad (N) [1/m4]
D0 [m2/s]
0.808 0.58
3.9 × 1028 2.6 × 1028
1.7 × 1033 2.1 × 1032
1.3 × 10−8 2.9 × 10−9
Table 4 Temperature coefficients of Z**, the effective charge Z*, the EA for TM and the Q* of Cu used in the calculation [10,11].
Cu3Sn Cu6Sn5
α [1/K]
TCR [1/K]
Z*
EA,TM [eV]
Q* [eV]
0.06 0.13
2.91 × 10−3 2.62 × 10−3
8.2 16.4
0.57 0.49
−0.86 3.8
! ! v Cu6 Sn5 ¼ J Cu;Cu6 Sn5
N Cu;Cu3 Sn − NCu;SnAgCu NCu;Cu3 Sn − NCu;Cu6 Sn5 NCu;Cu6 Sn5 − NCu;SnAgCu
Fig. 8. Mass flux Cu5Sn6 bottom bump, black dots from measurement red dots median values from simulation.
ð4Þ While the values out of the measurements represent averaged values only, the simulations restore the information about geometrical influences, like local current crowding and temperature gradients, on the IMC formation speed. The simulation enables the use of local information about the IMC growth which was lost by the use of averaged values for the mathematical interpretation of the experimental results. The dynamic IMC growth simulation flowchart is shown in Fig. 5. For the calculation of the electromigration (EM) and thermomigration (TM) mass flux Eqs. (5) and (6) are used. The heat of solution HS was also required for the calculation of the thermomigration in Eq. (6), with Q* as the heat of transport. ! ! NeZ j ρel EA exp − J EM ¼ D0 kB T kB T
ð5Þ
! N ðQ þ HS Þ EA þ HS ð Þ J TM ¼ −D0 grad T exp − kB T kB T2
ð6Þ
Fig. 7. Mass flux Cu3Sn bottom bump, black dots from measurement red dots median values from simulation.
Z* and the Q* of Cu in Cu3Sn and Cu6Sn5 have to be known. Z* is temperature dependent due to electron scattering at crystal defects in the IMC layers. Hence Z* has to be calculated (Eq. (7)). The used temperature coefficients, Z* and Q* values are given in Table 2. 2 2 Z ðTÞ ¼ Z ½1 þ α ðT−300 KÞ−Z ½1 þ TCR ðT−300 KÞ
ð7Þ
The electromigration induced mass flux as well as the thermomigration induced mass flux is shown in Fig. 6. The electromigration is clearly affected by current crowding shown in figure [8,9]. For the extraction of material parameters from the experimental results, averaged values were used. Hence information about the influence of current crowding on the IMC formation was lost. A three dimensional FEA allows the reconstruction of the current crowding effect by combining
Fig. 9. The (J-EM), (J-TM), and diffusion induced (J-Dif) mass fluxes of Cu in Cu6Sn5, total mass flux (J-Sum) of Cu [1/μm2s], bottom bump at the top surface upstream is shown.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
L. Meinshausen et al. / Microelectronics Reliability xxx (2015) xxx–xxx
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from the simulation as well as the trend line is shown. The simulation results fit well to the experimental results. The deviation from the trend line for 140 °C, 150 °C and 185 °C can be explained by the fact that the EA was taken from the interpolation of the measurement values for 100 °C up to 150 °C. The mass flux values at 185 °C were extrapolated from the test results at 140 °C. The experimental and the Cu5Sn6 median values from the simulation as well as the trend line is shown in Fig. 8. The estimated mass flux at 138 °C was too high. Like for Cu3Sn, a difference between the simulation and the test results appeared for 140 °C and 150°.
2.5. Electro- and thermomigration induced IMC-growth
Fig. 10. The (J-EM), (J-TM), and diffusion induced (J-Dif) mass fluxes of Cu in Cu6Sn5, total mass flux (J-Sum) of Cu [1/μm2s], bottom bump at the top surface downstream is shown.
the general migration parameters (Z*, Q*) with the influence of the solder joint geometry on the driving forces of the EM and TM.
The electro- and thermomigration induced IMC-growth was determined. In Figs. 9 and 10 the electromigration induced mass flux J-EM, the thermomigration induced mass flux J-TM, the diffusion induced mass flux J-Dif as well as the total mass flux J-Sum of Cu in Cu6Sn5 upstream and downstream is shown. The values are taken from the Cu bottom bump at the top surface. (See Figs. 11 and 12.) With the help of the local mass flux values the calculation of the dynamical IMC formation is possible. The IMC dimensions at the starting point and at the end of the accelerated test are shown in Fig. 11. As for the experimental results a relatively thick and homogenous IMC layer was formed during the downstream tests, and a relatively thin IMC layer with a clear current crowding profile was formed during the upstream tests.
2.3. Parameter for the IMC-growth calculation
3. Conclusions
The mass flux of Cu and Sn can be induced during the reflow, temperature storage, or the current application during the reliability stress test. For the calculation of the mass flux different material data are necessary and taken from [10,11]. The values are given in Table 3. The used temperature coefficients, Z* and Q* values are given in Table 4. The simulation does not take into account any saturation effects.
The intermetallic compound growth in 12 × 12 mm Amkor® SAC305 ball grid array PoP packages including direct SAC-Cu contacts at their bottom bumps was investigated. Based on the resulting IMC thickness from measurements the average mass flux of Cu and Sn was calculated. The simulated as well as the calculated values for the IMC growth were validated with the measurements. It was shown that the user-routines under the knowledge of the material parameters give the possibility to simulate the IMC-growth in solder bumps. The user routine enables the possibility for the calculation of other material layer growth like IMC formation in AuSn solders in the future.
2.4. Diffusion induced IMC-growth The diffusion induced IMC-growth was determined. In Fig. 7 the Cu mass flux values from the measurement and the Cu3Sn median values
Fig. 11. Cu6Sn5 profile before (left) and after (right) a DC stress test 138 °C (2369 h) and 1A. The effect of current crowding on the IMC formation in the bottom bumps for the up- (right) and the downstream cases (left) is shown in Fig. 12 the white arrows show the principle direction of the mass flux in the IMCs. A good agreement between simulation, calculation and measurement was found caused by the fact that the calculated shape as well as the thickness corresponds to the measured values.
Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052
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Fig. 12. The effect of current crowding on the IMC formation in the bottom bumps TStress 161 °C/1A (192 h).
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Please cite this article as: L. Meinshausen, et al., Dynamical IMC-growth calculation, Microelectronics Reliability (2015), http://dx.doi.org/ 10.1016/j.microrel.2015.06.052