Critical length of electromigration for eutectic SnPb solder stripe
C. C. Wei and Chih Chen
Citation: Applied Physics Letters 88, 182105 (2006); doi: 10.1063/1.2200158
View online: http://dx.doi.org/10.1063/1.2200158
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/88/18?ver=pdfcov Published by the AIP Publishing
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Critical length of electromigration for eutectic SnPb solder stripe
C. C. Wei and Chih Chena兲
Department of Material Science and Engineering, National Chiao Tung University, Hsin-chu, 30050 Taiwan, Republic of China
共Received 25 January 2006; accepted 15 March 2006; published online 4 May 2006兲
The critical length of eutectic SnPb solder was investigated using solder stripes. By employing focus ion beam, solder stripes of various lengths, including 5, 10, 15, 20, 30, 100, and 200 m, can be fabricated. Length-dependent electromigration behavior was observed, which implies that there may be back stress under stressing. The critical length was determined to be between 10 and 15m under stressing by 2⫻104A / cm2at 100 ° C, and the corresponding critical product was between 20 and 30 A / cm. Both values show good agreement with their theoretical values. © 2006 American
Institute of Physics. 关DOI:10.1063/1.2200158兴
With the portable devices becoming smaller and more compact in size, flip-chip technology has been adopted for fine-pitch packaging in microelectronics industry.1Area ar-ray of tiny solder joints can be fabricated on Si chips to achieve high-density packaging. In addition, as the required performance continues to increase, the input/output共I/O兲 pin count of flip-chip products has dramatically increased and the current that each bump needs to carry continues to in-crease, resulting in higher current density flowing in each solder bump. Therefore, electromigration共EM兲 has become an important reliability issue in solder joints.2–4
A lot of research has been done on electromigration of solder joints. However, only a few studies have been focused on the measurement of fundamental electromigration param-eters of solder. Liu et al. found that the dominant diffusion species was Sn atoms in a thin SnPb stripe when stressed at room temperature.5 Huynh et al. conducted another elec-tromigration study at 150 ° C using V-groove samples, and found that Pb atoms were the dominant diffusion species.6 Yeh et al. used Blech structure to measure the threshold cur-rent density.7However, one of the fundamental parameters of electromigration, the critical length, has not been measured experimentally. The critical length represents the stripe length below which there was no electromigration damage due to balanced back stress.8 The critical length for the Al and Cu lines has been investigated, from which an very im-portant parameter, critical product, can be obtained.8,9 The critical length of solder has not been measured because it is very difficult to prepare short solder stripes. In this letter, we report a technique that is capable of fabricating solder stripes with various lengths down to a few microns. Therefore, the critical length for solder can be obtained experimentally.
In general, the mass transport by electromigration in Blech specimens is governed by the following equation:8,10
J =CD kTZ *eE −CD kT d⍀ dx , 共1兲
where J is the net electromigration flux, C is the atomic concentration per unit volume, D is the diffusivity, Z* is the effective charge number, E is the electric field, k is Boltz-mann’s constant, T is the absolute temperature, is the
hydrostatic stress in the metal, and⍀ is the atomic volume. The first term on the right-hand side of the equation repre-sents the flux due to electromigration, whereas the second term stands for the opposite flux due to back stress.10 Under the same current density, the shorter the stripe is, the higher the back stress will be. Back stress increases with decreasing stripe length due to higher stress gradient. At the critical length, the stress balances with the wind force, and thus there is no net electromigration flux. If we assume that −d/ dx is equal toc/ Lc, the critical length can thus be expressed as
Lc=
c⍀ Z*eE=
c⍀
Z*ej, 共2兲
wherecis the stress at the critical length, Lcis the critical
length, j is the applied current density, andis the resistivity of the stripe.
To investigate the critical length of solder, short Blech stripes down to a few micrometers need to be fabricated. We have reported a technique for fabricating solder Blech stripes of 370m long in a Si trench.7 Nevertheless, it is quite challenging to fabricate short solder stripes because it is very difficult to reflow the solder on underbump metallization 共UBM兲 of less than 20m long. In addition, the thickness of the solder stripe was not uniform at both ends, since the two ends were thinner due to reflow and polishing process. To overcome these problems, focus ion beam 共FIB兲 was em-ployed to fabricate short stripes from the 370-m-long sol-der stripe. Figure 1共a兲 shows the SnPb stripe of 370m long fabricated using our previous approach. The stripe was 80m wide and 2.1m thick. FIB was used to etch away part of the stripe, and desired lengths of solder stripes can thus be fabricated on a Blech specimen. Figure 1共b兲 shows the stripes with abrupt edges fabricated by the above tech-nique. The FIB etched away three solder slices of 80 ⫻10m2at the desired positions. Various lengths, including 10, 30, 100, and 200m, can be fabricated on a Blech speci-men. Figure 1共c兲 shows the tilt-view scanning electron mi-croscopy共SEM兲 image for one of the surfaces after the FIB etching. The solder layer was almost etched away and it became discontinuous. The intermetallic compounds共IMCs兲 below the solder were also etched slightly, but it was still continuous. They might not migrate during the electromigra-tion test, because Cu6Sn5and Cu3Sn IMCs have higher melt-ing point and higher elastic modulus. They were expected to
a兲Author to whom correspondence should be addressed; electronic mail:
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have better electromigration resistance. The etching depth was controlled so that the Ti film remained intact, and thus it was able to carry the stressing current. Since the remaining solder/IMC on the etched surface became isolated, and their length might be shorter than the critical length of solder and IMC, they did not migrate during current stressing, thus af-fecting the electromigration behavior of the neighboring sol-der stripes. The sample was annealed at 150 ° C for 5 h prior to electromigration testing to remove the damage in the sol-der caused by FIB etching.
Figure 2 shows the cross-sectional schematic for the sol-der stripes in Fig. 1共b兲. The IMC was about 0.8m thick, and the SnPb solder was about 1.3m thick. There was a 400 nm Cu metallization layer on a 120 nm Ti film before the reflow process, and it was almost consumed after the reflow process. Thus, there was almost no additional IMC formation during electromigration testing. Because the solder was thinner on both ends of the solder stripe in Fig. 1共a兲, the electromigration behavior for the solder stripe on the far left was not considered. During electromigration test, a constant current was applied through the pads on the two ends. There was around 80% of the applied current drifting in the solder strip, 19% in the IMC layer, and only 1% in the Ti layer.
Critical length of the solder stripe could be determined using these short strips. Figure 3共a兲 shows the same
speci-men in Fig. 1共b兲 after stressing by the current density of 5⫻104A / cm2 at 100 ° C for 104 h. It is found that elec-tromigration occurred in the three solder stripes of 30, 100, and 150m long. In addition, the longer the stripe is, the higher the electromigration rate will be. Length-dependent electromigration behavior was also observed on the solder stripes, which means that there may be back stress in the solder stripe under stressing. The critical length is below 30m from these results. To further explore the critical length, shorter solder stripes of 5, 10, 15, 20, and 30m long were fabricated, as shown in Fig. 4共a兲. Lower current density of 2⫻104A / cm2was used in order to determine the critical length more precisely. After the stressing condition at 100 ° C for 490 h, electromigration occurred in the stripes longer than 15m as indicated by the arrows in Fig. 4共b兲, yet no depletion was observed in those of 5 and 10m long, as shown in the figure. Therefore, the critical length for eu-tectic SnPb solder was determined to range between 10 and 15m. The corresponding critical product was between 20 and 30 A / cm.
To examine whether the measured critical length is rea-sonable, the theoretical value in Eq. 共2兲 was estimated. We take the critical compressive stress in the anode end of the SnPb solder stripe to be the yield strength of solder, which is 27.2 MPa. Wang et al. reported that the stress gradient is linear in an Al stripe of 200m long,11 therefore, it is as-sumed that the gradient in the solder stripe behaves linearly. If we assume that the tensile stress in the cathode end is also 27.2 MPa, the stress difference between the anode side and cathode side will be 54.4 MPa. In addition, Z*,⍀, and are taken to be 30, 2.78⫻ 10−23cm3, and 14.5⫻10−6⍀ cm, re-spectively. By substituting all the parameters in Eq.共2兲, the critical length is estimated to be 11m under the current density of 2⫻104A / cm2, which is quite close to our
experi-FIG. 1.共a兲 Plan-view SEM image for the fabricated solder Blech specimen of 370m long.共b兲 Plan-view SEM image for a solder Blech specimen after FIB etching. Solder stripes of 30, 100, and 200m long were fabri-cated.共c兲 Tilt-view SEM image showing the surface after FIB etching. Sol-der stripe became discontinued after etching.
FIG. 2. Cross-sectional schematic of the solder stripe inside a Si trench. The solder layer and the IMC layer were about 1.3 and 0.8m thick, respectively. FIG. 3. Tilt-view SEM image showing the solder stripes in Fig. 1共b兲 after current stressing of 5⫻104A / cm2at 100 ° C for 104 h. Depletion occurred
for all solder stripes, and it was larger for longer solder stripes.
182105-2 C. C. Wei and C. Chen Appl. Phys. Lett. 88, 182105共2006兲
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mental value. The corresponding value of critical product is 22 A / cm.
It is estimated that the current density required to cause failure in a solder joint is about two orders of magnitude less than that needed for an Al or Cu line to fail.3 Electromigra-tion in a flip-chip solder joint occurs at lower current density because of the high lattice diffusivity in the solder alloys, together with higher resistivity, lower Young’s modulus, and higher effective charge number of the chemical elements in solder alloys than those of Al or Cu. The critical product is 1260 A / cm for a 115m Al stripe at 350 ° C,8whereas it is 3700 A / cm at 340– 400 ° C for dual-damascene Cu/oxide interconnects.9 These values are about 50–150 times larger than those obtained in our experiment. Therefore, the critical product we measured is quite reasonable.
Significant phase redistribution was observed after cur-rent stressing for stripes longer than 15m, as shown in Fig.
4. The Pb-rich phase migrated toward the anode end, and thus Pb atoms were found to be the dominate diffusion spe-cies at 100 ° C. This phase redistribution may have effect on the back stress. In addition, after stressing for a long time, the Pb-rich phase accumulated on the anode end, leaving the Sn-rich phase on the cathode end. This redistribution also affects the yield stresses on the cathode and the anode ends. Further study is needed to address these issues.
In conclusion, eutectic SnPb solder stripes of various lengths have been fabricated using FIB. It is found that no electromigration damage occurred for the 5 and 10m stripes under stressing by the current density of 2 ⫻104A / cm2 at 100 ° C for 490 h, whereas length-dependent electromigration behavior was observed for longer stripes. The critical length was between 10 and 15m, which is quite close to the theoretical value of 11m. The corresponding critical product was between 20 and 30 A / cm, which is approximately two orders of magni-tude smaller than that of the dual-damascene Cu/oxide inter-connects.
The authors would like to thank the National Science Council of the Republic of China for financial support through Grant No. 93-2216-E-009-030.
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1296共1998兲. FIG. 4.共a兲 Back-scattered SEM image showing another solder Blech
speci-men with stripes of 5, 10, 15, 20, and 30m long before current stressing. 共b兲 The same specimen in 共a兲 after current stressing of 2⫻104A / cm2at
100 ° C for 490 h. No depletion was found for the 5 and 10m stripes.
182105-3 C. C. Wei and C. Chen Appl. Phys. Lett. 88, 182105共2006兲
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