This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Mechanics of Materials 41 (2009) Contents lists available at ScienceDirect Mechanics of Materials journal homepage: Low temperature electromigration and thermomigration in lead-free solder joints Cemal Basaran *, Mohd F. Abdulhamid Electronic Packaging Laboratory, University at Buffalo, 212 Ketter Hall, Buffalo, SUNY, NY 14260, USA article info abstract Article history: Received 18 February 2008 Received in revised form 29 July 2009 High current density and high temperature gradient are major reliability concern for next generation nanoelectronic packaging and power electronics. High current density experiments on lead free solder joints coated with NiAu and non-coated Cu pads were conducted at 20, 30, 40 and 50 C ambient temperatures. The time to failure (TTF) shows that solder joints with NiAu coated Cu pads last longer. Results also indicates TTF plot shows that TTF rate increases exponentially when the solder joint temperature is higher than 64% of its melting temperature, and decreases exponentially reaching the maximum lifetime when the temperature is below this threshold temperature. The mass transport activation energy, E a was determined using the test data and it was found to be 2.67 ± 0.05 and 3.65 ± 0.13 ev for coated and non-coated solder joints, respectively. These values are indicative of the dominant diffusion mechanism during the experiment. It was discovered that the thermomigration driving force was as high as electromigration driving force. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction When a metal conductor is subjected to an electrical potential, the current enters from anode side and travels to cathode side, on the other hand, the free valance electrons travel from cathode to anode side. Electromigration is a mass transport in a diffusion-controlled process under certain driving forces. When a metal is subject to a very high current density, the so-called electron-wind transfers part of the momentum to the atoms (or ions) of metal (or alloy) to make the atoms (or ions) move in the direction of the electrons. The collision of electrons and atoms happen due to scattering of free valance electrons. The classical definition of electromigration refers to the structural damage caused by ion transport in metal as a result of high current density. Electromigration is usually insignificant at low current density levels. Qualification of what is high current density is studied extensively by Ye et al. (2003) hence it is outside the scope of this paper. As a result, the degradation of the conductor occurs * Corresponding author. Tel.: ; fax: address: cjb@buffalo.edu (C. Basaran). mainly in two forms, in the anode side the atoms will accumulate and finally form hillocks (or extrusions) and the vacancy concentration in the cathode side will form voids. Both hillocks and voids cause the degradation of the material and eventual failure. Normally cathode side voids will lead to high resistance levels however extrusions on the anode side lead to short circuits. The physical mechanism of electromigration has been extensively investigated for pure metal confined thin films (films attached to a thick Si/SiO 2 substrate, primarily VLSI lines). Black (1969) established the relationship between the mean time to failure and current density for confined thin films. The experiments by Blech (1976) revealed that the stress gradient within the thin film could act as a counter force to electromigration under high current density. In addition, for thin films, he proposed a length scale called Blech s critical length below which mass diffusion due to electrical driving force will be totally counter balanced by a stress gradient, which is compression in anode side and tension in the cathode side. From engineering perspective, the electromigration studies conducted so far have been mostly empirical studies aimed at developing a relationship between the current /$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi: /j.mechmat

3 1224 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) density and the mean time to failure (rupture of a thin film) (Black, 1969; Shatzkes and Lloyd, 1986; Korhonen et al., 1993). Several researchers reported their observations of electromigration in solder joints (Zeng and Tu, 2002; Lee et al., 2001; Tang and Shi, 2001; Brandenburg and Yeh, 1998; Liu et al., 1999, 2000; Hu and Harper, 1998; Basaran et al., 2005a, 2005b; Ye et al., 2003, 2003a, 2003b, 2003c). These studies are basically experimental observations at room temperature and above in Pb/Sn solder alloys, where influence of thermomigration is mostly ignored. Thermomigration can be a by-product of electromigration due to Joule heating. Ye et al. (2003a) was the first to show that the effect of thermomigration on solder joints is as serious as that of electromigration and cannot be ignored especially when the thermal gradient is large, in which case the thermomigration can be the dominant mass-transport process. The co-existence of thermomigration in conjunction with electromigration can assist electromigration if the higher temperature side coincides with the cathode side, and counter electromigration if the hot side is the anode side (Ye et al., 2003a). Thermomigration, which is mass transport that takes place due to a high temperature gradient, has been shown to cause failure in solder joints (Ye et al., 2003a; Huang et al., 2006). This phenomenon is very similar to the Soret effect (Platten, 2006; Soret, 1979) in fluids. Under high temperature gradient free valance electrons scatter and transfer part of their kinetic energy to atoms which start to diffuse. High thermal resistivity across die side pad/solder joint interface and differential conductivity of components in an electronic package lead to significant temperature gradients that can cause thermomigration (Ye et al., 2003a). The cross sectional area of the aluminum (or copper) trace in a Si die in a typical flip-chip module, is much smaller than that of the solder ball, thus making the aluminum (or Cu) interconnect one of the major contributors to joule heating in the module. During high current density stressing, the highest Joule heating is generated in the Al (or Cu) interconnect. Since copper traces in the substrate printed wire board (PWB) is normally one order of magnitude thicker than Al traces on the die side, copper trace on PWB side carry lower current density, thus less Joule heating is generated compared to that of generated by Al trace in Si die. As a result a large thermal gradient is maintained across the solder joint. A temperature gradient of 1200 C/cm was reported to cause thermomigration in In Pb solder, where both In and Pb move in the direction of the gradient, from hot side to cold side (Roush and Jaspal, 1982). In a recent study of Sn Pb solder Huang et al. (2006) reported that Sn migrates to the hot side while Pb drifts to the cold side where the solder balls were subjected to A/cm 2 current density at 150 C ambient temperature with an approximate 1000 C/cm gradient. In this study, a chain of flip-chip package solder joints were subjected to a high current stressing of A/cm 2 at 20, 30, 40 and 50 C ambient temperatures in order to study the effect of low temperature on electromigration and thermomigration interaction. This is the first such study in the published literature, to the best of our knowledge. 2. Experimental setup The test vehicle used in this experiment is shown in Figs. 1 and 2. The solder joints in the test vehicle are 95.5Sn 4Ag 0.5Cu (SAC 405 in wt%) bonded with 96.5Sn 3Ag 0.5Cu (SAC 305) presolder. The Al/Ni(V)/Cu under bump metallurgy (UBM) on top of the solder joint has a thickness of 3 lm. The Al trace in the Si die is 65 lm wide and 1 lm thick. The Cu trace on the PWB substrate has a dimension of 65 lm width and 15 lm thick. There are two types of Cu pad used in the test vehicles. One is a bare Cu pad and the other is coated with electroless NiAu of which Ni and Au thicknesses are 5 and 0.05 lm, respectively. The NiAu coating acts as a diffusion barrier. Solder joint standoff height (from top of soldermask to top of solder ball) is 100 lm, and passivation opening diameter is 90 lm. The passivation opening is used as a basis to calculate the nominal current density. Maximum current density at the current crowding point is calculated with finite element analysis. Only a single daisy chain is electrified with a constant electric current of 2.5 A which corresponds to A/cm 2 nominal current density in the solder joint based on the 90-lm passivation opening. The applied current produces a A/cm 2 current density in the Al trace in the Si die, and A/cm 2 in the Cu trace on the substrate based on the width and thickness of the respective traces. The configuration of the daisy chain, the direction of the current and electron flow, and solder joint numbers are shown in Fig. 2. During testing, the daisy chain shown in Fig. 2, was connected to a constant DC power supply with the positive terminal connected to V1+, while the negative terminal to P, as shown in Fig. 1. To measure the temperature created by Joule heating due to the current, two thermocouples were used. One was placed on top of Si die above the daisy chain, and the other was on the bottom of the substrate below the daisy chain. In the test vehicle shown in Fig. 1, there are multiple rows of daisy chain solder balls that can be powered on row at a time. Thermal chamber used in this experiment is a Thermotron SA-36-CHV which has a 1 m 3 test compartment equipped with two 30-horsepower (22.4 kw) compressors. Cooling performance, given by the manufacturer, to cool kg (250 lbs) of aluminum from +85 to 54 C is 30 C/min on average. Compared to the weight of our test Fig. 1. Circuit and solder joints on flip-chip test vehicle.

4 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 2. Schematic of the electrified daisy chain, direction of current and electron flow, and solder ball number. vehicle (0.5 g), capacity of the test chamber is very large in such a way that the ambient temperature in the chamber would not be affected by the heat generated by the chip. It should be pointed out that the use of such a large capacity thermal chamber is intentional. Instrumentation includes a programmable DC power supply and a 2-channel thermocouple reader. In situ real time data were recorded by a digital data acquisition system. The temperatures at the top of die and the bottom of substrate were recorded at every 5 s, while the system electrical resistance was monitored at every second. Failure is defined as when the system electrical resistance exceeds 1 X, in all cases, as to avoid melting of solder joint and consequently destroying the microstructure. Following the electrical stressing, samples were sliced and near mirror polished to the center of the solder joint using automated polishing machine with programmable polishing head. The final surface finish was polished using 0.05-lm silica suspension to obtain a very smooth surface, thus ensuring accurate microstructural morphology analysis. Microstructural morphology and intermetallic compound (IMC) elemental analyses were performed on the prepared samples using backscatter scanning electron microscope (SEM) equipped with energy dispersive X-ray (EDX). 3. Finite element analysis A 3D full model finite element method (FEM) is employed to estimate the temperature at the top and bottom of the solder ball. FEM estimation of temperature field was necessary due to very small size of solder joint height (100 lm). 3D unabridged analysis was necessary because the module is not symmetric and the daisy chain is located near the edge of the Si die. The measured temperatures at top of the die and bottom of the substrate are used as reference temperatures. The FEM package (ABAQUS) used in this investigation was able to solve coupled thermal electrical analysis by using the built in coupled thermal electrical brick element for the electrified daisy chain. For non-electrically conductive material, heat transfer brick element was used. The electrical current was applied using constant current uniformly over the surface area of the pad V1+, of the daisy chain and zero electrical potential on the surface of the outlet, P. The surface boundary conditions include heat transfer to the ambient by conduction, radiation and forced convection. Heat radiation to the ambient was handled automatically by the software by defining unit-compatible Stefan Boltzmann constant, absolute zero, and sink temperatures. For natural and forced convection, heat transfer coefficients had to be calculated and input to the model as a film constant. Newton s law of cooling for flat plate under forced air flow is used since the chip is flat and acts similar to a plate. Newton s law of cooling is defined as (Ellison, 1984) Q c ¼ h c A s ðt s T a Þ ð1þ where Q c is the heat transfer rate, A s is the surface area exposed to the ambient, T s is the surface area temperature, and T a is the ambient temperature. Forced convection heat transfer coefficient of the plate, h c is related to Nusselt s number of the plate by h c ¼ k L Nu L where k is the thermal conductivity of the fluid and L is the length of the plate. The average Nusselt s number over the plate surface, Nu L is related to Reynold s number by pffiffiffiffiffiffiffi Nu L ¼ 0:664ðPrÞ 1=3 Re L ð3þ ð2þ where Pr is the Prandtl number and Re L is the Reynold s number. The respective formulae for these numbers are Pr ¼ lc p k Re L ¼ qvl l ð4þ ð5þ where q is fluid density, l is dynamic fluid viscosity, v is the fluid velocity, C p is the specific heat, k is the thermal conductivity and L is the plate length. Natural convection heat transfer coefficient is defined as (Ellison, 1984) h c ¼ k P Nu P ð6þ

5 1226 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) The difference between forced and natural convection is that instead of using the actual length in calculating heat transfer coefficient, natural convection uses characteristic length, P. For horizontal surface, P is defined as P ¼ W L 2ðW þ LÞ ð7þ where W and L are width and length, respectively. For vertical surface P = H, the height of the surface. Eq. (6) was simplified Zahn and Stout (1997) to take into account the directionality of the surface, h p ¼ yðdt n P 3n 1 Þ where y ¼ C k g n q2 b Pr ð9þ l 2 C and n are constants depending on the surface heating and cooling fluid properties; g and b are gravity acceleration and volumetric thermal expansion coefficient, respectively. For air cooled horizontal surface facing upward, C = 0.15 and n=0.33, while C = 0.27 and n = 0.25 for downward facing surface (Ellison, 1984). These pairs are used when T s > T a (Ellison, 1984). Combining Eqs. (8) and (9), and substituting with these pairs, yields h p;up ¼ 0:15y up ðt s T a Þ 0:33 P 0:01 h p;down ¼ 0:27y down ðt s T a Þ 0:25 P 0:25 ð8þ ð10þ ð11þ Values of y up and y down for different ambient temperatures are tabulated in Table 1. The total heat transfer coefficient is (Guenin et al., 1995; Shaukatullah et al., 1994) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h total ¼ 3 h 3 nc þ h3 fc þ h rad ð12þ where h rad is automatically calculated by ABAQUS. The air velocity in the chamber was 140 m/s. At this value, the Reynold number for the substrate is , and for the die top, respectively. Both numbers are still in the laminar flow region. For flat plate, the air flow is considered laminar when the Reynold number is less than (Ellison, 1984). The FEM analyses at all ambient temperatures employed v = 140 m/s, except for 20 C ambient temperature which uses v = 60 m/s. To make sure that the assumption of laminar flow is valid; the Reynold numbers are calculated. Reynold s numbers and the corresponding forced convection heat transfer coefficients, h fc, are listed in Table 2. Table 1 Values of y up and y down used in FEM analysis. Ambient temperature ( C) y up y down Material thermal conductivities used the simulation is listed in Table 3. Since only the electrified daisy chain is modeled, an effective thermal conductivity value of 4.5 W/m C is used for the remaining underfill based on the average of area ratios of bumps and underfill (Lai and Kao, 2006). The substrate is modeled as a laminate of BT epoxy fiberglass and 15 lm thick Cu layers which occupy 10% of the layer (Lai and Kao, 2006). 4. Discussion of observations The time to failure of both sets of test vehicles at different ambient temperature are presented in Table 4. With the exception for 20 C ambient temperature, solder joint with NiAu coated Cu pad lasted longer than the one without NiAu coating. The top of die and bottom of substrate temperatures, obtained from the experiment, and from FEM analysis are listed in Table 5. The values in Table 5 are plotted in Fig. 3. The discrepancy between measurements and FEA calculation at 20 and 30 C at bottom substrate is probably due to lack of accurate material properties at these temperatures Metallurgical analysis Unstressed solder interfaces for both NiAu coated and uncoated Cu pad are shown in Fig. 4. At hot (top) and cold (bottom) interface, a layer of IMC can be observed for both types of Cu pads. In the case of uncoated Cu pad, the IMC is identified as Cu 6 Sn 5, while NiAu coated Cu pad IMC is identified as (Cu,Ni) 6 Sn 5. For the bare Cu pad, the IMC can clearly be observed and has a finger-like shape on both hot and cold side. The solder ball with NiAu coated Cu pad shows a thinner IMC because the NiAu coating is a diffusion barrier which blocks the supply of Cu from the Cu pad from diffusing into the solder bulk. In other words, the Cu supply comes from Cu layer on the UBM at the top of the solder joint and from the solder bulk. In the case of bare Cu pad, additional supply of Cu comes from the uncoated Cu pad. In the test vehicles, the layout of the aluminum trace and solder joints, expose some solder joints to a combination of electromigration and thermomigration, while some others were exposed to thermomigration alone. In this experiment, the hotter side is the die side. The direction of thermomigration is from hot to cold side (or downward), while the direction of electromigration is dependent on the direction of the electron flow. In (Fig. 2), solder joint 4 subjected to thermomigration, and electromigration in the opposite directions (TM EM), solder joint 7 experienced thermomigration and electromigration in the same direction (TM + EM), and both solder joints 5 and 6 experienced thermomigration only (TM). Cross sectional areas of tested solder joints are shown in Figs. 5 8 for ambient temperatures ranging from 20 to 50 C. The figures show the direction of thermomigration (TM) and electromigration (EM), with arrows. At all ambient temperatures, no damage to Al trace is observed.

6 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Table 2 Reynold s number for die and substrate used in the simulation. Ambient ( C) R e die top R e substrate h fc die top (W/ m 2 K) h fc substrate (W/m 2 K) 50 29, , ,334 96, ,303 89, ,073 35, Table 3 Thermal conductivity used in the simulation. Data from Lai and Kao (2006). Component Die 150(T/300) 4/3 Underfill 0.55 Soldermask 0.26 Passivation 0.26 BT 0.33 Cu 389 Al 237 Thermal conductivity (W/m C) Table 4 Test vehicle time to failure data for both NiAu-coated and uncoated Cu pad at different ambient temperatures. Ambient temperature ( C) Time to failure (h) Without coating NiAu coated (Table 9) provides the temperature gradient and current density in each solder joint. Cross section of the solder joints tested at 20 C (Fig. 5), and 30 C (Fig. 6) ambient temperature, show partial melting in solder joints 6 (TM), and 7 (EM + TM). At both ambient temperatures, at the cold side (bottom interface) of solder joints 6 and 7, thicker-than-original Cu 6 Sn 5 layer IMC is observed, especially for bare Cu pad joint. At the hot side (top interface), Cu 6 Sn 5 IMC is not observed at failure. At 20 C ambient temperature (Fig. 5), solder joints 4 (TM EM) and 5 (TM) show delamination between UBM and solder bulk (Fig. 9), which is a sign of poor adhesion between the two due to lack of bonding agent, which in this case is the Cu 6 Sn 5 IMC layer. At the end of testing, no IMC layer is observed at the hot (top) side, while a thicker Cu 6 Sn 5 layer is observed at the cold (bottom) side. The delamination and the absence of Cu 6 Sn 5 IMC layer are due to the disintegration of the Cu 6 Sn 5 IMC into Cu and Sn atoms. At 30 C ambient temperature (Fig. 6), solder joint 4 shows some Cu 6 Sn 5 IMC at the hot (top) side, but not as thick as initial one. Solder joint 5, 6 and 7 show no Cu 6 Sn 5 IMC at the hot (top) side, and some crack but not resulting in total separation between UBM and solder bulk. At 40 C ambient temperatures (Fig. 7), no crack and delamination are observed at the solder joint and Cu pad in interface. For NiAu coated Cu pad, solder joint 6 shows no Cu 6 Sn 5 IMC at hot interface, while solder joint 7 shows the least Cu 6 Sn 5 IMC at the hot interface than solder joints 4 and 5. For uncoated Cu pad, solder joint 6 and 7 show some Cu 6 Sn 5 IMC at the UBM interface. The absence of Cu 6 Sn 5 IMC at the solder joint 6 UBM interface for NiAu coated Cu pad is due to thinner Cu 6 Sn 5 IMC layer before the stressing compared to the uncoated one, as shown in Fig. 4, and disintegration of the IMC during stressing. The NiAu diffusion barrier blocks additional Cu atoms from diffusing into the solder bulk. At 50 C ambient temperature (Fig. 8), for solder joint with NiAu coated Cu pad, solder joint 6 shows the least IMC at the hot interface. Solder joint 4 shows Cu 6 Sn 5 IMC which is comparable to that of the unstressed solder. For bare Cu pad, only solder joint 4 shows Cu 6 Sn 5 IMC comparable to that of unstressed solder. We emphasized that this joint has thermomigration and electromigration in opposite direction. The others solders joints have no observable Cu 6 Sn 5 IMC. Partial cracks can be seen at UBM interface for all uncoated solder joints Finite element analysis Finite element heat transfer analysis was done to approximate the temperature field at the top and base of the solder ball because of difficulty of measuring temperature at these points. The difference between the measured and calculated temperature at top of die and bottom of substrate is shown in Fig. 3. It shows when a constant air velocity was assumed to calculate forced convection heat Table 5 Measured and FEA calculated temperatures for tests at different ambient temperatures. 95% lower confidence (LCL) and upper confidence level (UCL) are also listed. Ambient Location Experimental data curve fit Measured temperatures FEA calculation Mean Std. dev. 95% LCL 95% UCL 20 C Die top Subs bot C Die top Subs bot C Die top Subs bot C Die top Subs bot

7 1228 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Actual and Calculated Temperatures Die top and substrate bottom temperatures (C) Die top (exp) Subs bottom (exp) Curve fit on exp data Die top (simul) Subs bottom (simul) Ambient temperature (C) Fig. 3. Actual and calculated temperature of top of Si die and bottom of substrate. Fig. 4. Interfaces for unstressed solder. Left column: (a) top and (b) bottom interface for solder with uncoated Cu pad. Right column: (c) top and (d) bottom interface for solder with Ni/Au coated Cu pad. transfer coefficient, the model is fairly accurate for die top temperature at all ambient temperatures. For substrate bottom temperature, the model is fairly accurate for only 40 and 50 C ambient temperature, but under predicts at 20 and 30 C. It also shows the difference between top and bottom temperature is reasonably constant (a mean of 19 C) for all cases, however, from curve fit of the measured data, the temperature difference lessens as ambient temperature gets warmer. Clearly, the model used in this study cannot predict the solder joint temperatures at 20 and 30 C ambient temperatures because it could not take into account the change in difference between top and bottom temperature as ambient temperature gets higher. The solder joint temperature and current density maps from FEM analysis are shown in Figs. 10 and 11, respectively. A cross sectional profiles of the same maps are shown in Fig. 12. These maps give a good idea of how the current density and temperature are distributed in the joint. The current density and temperature map for Al trace are shown in Figs. 13 and 14, respectively. The current density in the Al trace is two orders of magnitude higher than that of in the solder joint. The nominal current density is A/cm 2 based on the cross section of the Al trace. The maximum temperature generated by the current density at 20 C ambient is 143 C, which is only 45% of it melting temperature ( K). However, we observed melting of the solder joints 6 and 7 at 20 and 30 C ambient temperatures. This is probably due to higher interfacial thermal resistance than we are using. However, it should also be pointed out that solder 6 could be experiencing electron charge swirling. Lai et al. (2007) have shown that although the electric current passes by on top of the

8 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 5. Solder at 20 C ambient temperature. solder interconnect, it creates a vertical current density field around the UBM. At the solder top and Al trace interface, the temperature of Al trace is comparable to the top of solder (Table 6). This validates the assumption that most of the heat on top of the solder joint comes from the Al trace. This also explains why non-electrified solder joint 6 has the highest temperature compared to the others in all stressing cases. At 20 and 30 C ambient temperatures, top of solder joint 6 melts because of high temperature as proven by FEA. We should point out that FEA assumes a perfect interface at solder-al trace contact, but this is not realistic. Although the nominal current density for the solder joint is A/cm 2, the current density at the current crowding point is A/cm 2 (151% higher) due to current crowding, as in solder joint 4 shown in Fig. 10. The current crowding occurs at the entry and exit points of current flow.

9 Author's personal copy 1230 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 6. Solder at 30 C ambient temperature. The temperature profile map (Fig. 12) shows the temperature is a function of solder height, temperature is highest at the top and decreases in lower part. The temperature difference between top of solder joint and top of die, and bottom of solder and bottom of substrate are listed in Table 6, for top, and (Table 7), for bottom as obtained from FEA. The temperature difference between solder top and die top is less than the difference between solder bottom and bottom of substrate for the same ambient temperature. This variation is due to the fact that Si die has better thermal conductivity that the substrate layer. Heat is dissipated faster to the ambient through Si die than through the PCB substrate. The temperature difference between solder joint and die, or substrate can be used to estimate the temperature gradient for solder joint tested. Before temperature gradient in the solder joint can be calculated, the solder joint bottom temperature for 20, 30 C ambient must be determined. However the FEM

10 Author's personal copy C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 7. Solder at 40 C ambient temperature. analysis was not able to estimate the temperature in the substrate bottom very accurately, as seen in Table 5 and (Fig. 3). The difference between solder joint bottom and substrate bottom as calculated by FEA is known (Table 7). The substrate bottom temperature is measured in the experiment (Table 5). The solder bottom temperature can be calculated from these measured and calculated values. The values of solder bottom for 20 and 30 C ambient are listed in Table 8. Now, based on the measured data and FEA we can calculate the temperature gradient for each solder joint. The data are provided in Table Discussion Time to failure (TTF) is plotted as a function of ambient temperature both NiAu coated (Fig. 15) and bare Cu pad

11 1232 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 8. Solder at 50 C ambient temperature. solder joints (Fig. 16). Solder joint with NiAu coated Cu pad last longer probably due to the diffusion barrier which limits the Cu diffusion into the solder bulk. This observation is consistent with Lai s et al. (2007) results; solder joint TTF increases as Cu concentration decreases when stressed at 30 C ambient temperature with A/cm 2 current density. The solder alloy used in the experiment was Sn 4Ag 0.5Cu, Sn 3.5Ag 1Cu and Sn 3Ag 1.5Cu. Experimental data curve fits were done to estimate the TTF function. The TTF function has four important characteristics, which are lower and upper asymptotic values, inflection point, and TTF change rate. The TTF function has a generalized form TTF ¼ L þ 1 þ exp Ea k U L h i ð13þ 1 T 1 T i

12 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 9. UBM delamination on top of solder joint 5 when stressed at 20 C ambient temperature. which is a form of Richards growth curve (Richards, 1959). The parameters are: TTF, time to failure; L, lower asymptote value; U, upper asymptote value; E a, activation energy; k, Boltzmann constant; T, temperature; T i, variable inflection point. The TTF function for NiAu non-coated Cu pad solder is TTF ¼ 1 þ exp 2:67 k 93:01 ð14þ 1 1 T 312:5 while, for coated Cu pad solder is 67:84 TTF ¼ 1 þ exp 3:65 k ð1 1 Þ ð15þ T 312:5 In this experiment, L = 0, which means when temperature of the solder is very high (high Joule heating as a consequent of high current), the failure is almost immediate. On the other hand, U = and h, for coated and non-coated Cu pad solder, respectively. U indicates the life of the system if solder temperature is low enough in such a way that failure is not due to electromigration and thermomigration. T i is the same for both solder types because they have same solder material with the same geometry. The value K indicates the temperature at which TTF rate changes. TTF descends exponentially to the lower asymptote as temperature increases above K (to the left of abscissa), while rises exponentially to upper asymptote as temperature decreases below K. This temperature is about 64% of the solder melting temperature. The activation energy, E a, values for non-coated and coated Cu pads from the curve fit are 2.67 ± 0.05 and 3.65 ± 0.13 ev, respectively. As E a increases, the rate of TTF change over temperature also increases as shown in Fig. 17. TTF in this experiment is dependent on diffusivity rate; lower diffusivity rate will result in longer TTF. As a comparison, Cu-in-Sn diffusivity rate is plotted on the same TTF plot. The diffusivity rate is (Mei et al., 1992) 33; 020 cm 2 D Cu-in-Sn ¼ 0:0024 exp RT s ð16þ Activation energy in Eq. (16) is kj/mol. The diffusivity of Cu in Sn in this experiment is about five times faster at 20 C than at 50 C ambient temperature. The most common and still widely used function to predict TTF of metal interconnect subjected to electromigration is Black s equation (Black, 1969a, 1969b, 1967), TTF ¼ A J n exp E a kt ð17þ A is a constant, J and n are current density and its exponent which has a value of 2, respectively. E a is activation energy, k is Boltzmann constant and T is absolute temperature. Brandenburg and Yeh (1998) and Ye (2004) used Black s equation to describe TTF of their tin lead electromigration and thermomigration experiments. Curve fit of data to Black s function can also be used to approximate the activation energy, E a for the onset of diffusion due to electromigration and thermomigration. Ye (2004) used current densities between and A/cm 2, with solder temperature ranges from 373 to 428 K. Brandenburg and Yeh (1998) used current densities between and A/cm 2, with solder temperature ranges from 423 to 448 K. Ye s activation energy value is 0.51 ev, while Brandenburg and Yeh s value is 0.84 ev. The plot in Figs. 15 and 16 include Black s TTF fit for temperature above the inflection temperature (T K). It is obvious that Black s equation does not fit experimental time to failure. Black s equation predicts a very large TTF contrary to the experimental data because Black s equation was developed for thin film on a Si substrate with no temperature gradient. The relationship between diffusivity and temperature is also plotted in Figs. 15 and 16. At 20 and 30 C ambient temperatures, UBM is delaminated from top of solder due to the disintegration of Cu 6 Sn 5 IMC which acts as a bonding agent that provides adhesion between the two parts.

13 1234 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 10. Current density map (in A/lm 2 ) from FEM analysis. Disintegration of IMC on hot side was studied in depth by Abdulhamid and Basaran (2009). This experiment confirms previous findings. The worst case occurred at top of solder joint 6 and 7, where melting or partial melting are

14 Author's personal copy C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 11. Solder joint temperature map (in C) at different ambient temperatures. 1235

15 Author's personal copy 1236 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 12. Map of current density (left column) and temperature profiles.

16 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Fig. 13. Al trace current density map. Fig. 14. Al trace temperature map at different ambient temperatures. Table 6 Temperature difference between solder joint top and die top from FEM simulations. Ambient 20 C Ambient 30 C Ambient 40 C Ambient 50 C Die top temp: C Die top temp: C Die top temp: C Die top temp: C Solder top Difference Solder top Difference Solder top Difference Solder top Difference Solder # Solder # Solder # Solder #

17 1238 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Table 7 Temperature difference between solder joint bottom and substrate bottom from FEM simulations. Ambient 20 C Ambient 30 C Ambient 40 C Ambient 50 C Subs bot temp: 48.3 C Subs bot temp: 18.6 C Subs bot temp: 6.38 C Subs bot temp: 5.79 C Solder bot Difference Solder bot Difference Solder bot Difference Solder bot Difference Solder # Solder # Solder # Solder # Table 8 Estimated solder bottom temperature for 20 and 30 C ambient. Ambient 20 C Ambient 30 C Subs bot temp: C Subs bot temp: C Difference Solder bot Difference Solder bot Solder # Solder # Solder # Solder # observed. The disintegration is partly a result of IMC being decomposed to Cu and Sn under thermal gradient according to Cu 6 Sn 5 ) 6Cu þ 5Sn ð18þ Cu atoms from the disintegrated IMC migrate to the cold side due to thermal gradient force because diffusivity of Cu is larger than diffusivity of Sn by orders of magnitude. Since a Cu atom is lighter (atomic mass of 63.5 g/mol and Table 9 Temperature gradient at different ambient temperatures. Temperature gradient ( C/cm) Nominal current density (10 4 A/cm 2 ) 20 C ambient 30 C ambient 40 C ambient 50 C ambient Solder # Solder # Solder # Solder # NiAu Coated Solder Time to Failure Top of solder joint 7 temperature (K) Time to failure (hours) TTF (experiment) Curve fit on TTF 95% confidence level Black's TTF fit Cu-in-Sn diffusivity Diffusivity rate (E-08 squared cm/s) /T of top of solder joint 7 (1/K) Fig. 15. TTF plot for NiAu coated Cu pad solder.

18 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) Non Coated Solder Time to Failure Top of solder joint 7 temperature (K) Time to failure (hours) TTF (experiment) Curve fit on TTF 95% confidence level Black's TTF fit Cu-in-Sn diffusivity Diffusivity rate (E-08 squared cm/s) /T of top of solder joint 7 Fig. 16. TTF plot for the bare Cu pad solder. Effect of Increasing E Increasing E Time to failure (hours) Inflection point E1 E2 E3 E1 < E2 < E3 Increasing E 1/T of top of solder joint (1/K) Fig. 17. Effect of increasing E on TTF curve. atomic radius of 1350 Å) than the Sn atom (118.7 g/mol and 1450 Å), and being the dominant diffusion species (Tu, 1973), Cu atoms move faster to the cold side under the thermal gradient driving force. The diffusivity rates, D Cu-in-Sn and D Sn-in-Sn at 20 C are and m 2 /s, respectively, at 190 C, D Cu-in-Sn and D Sn-in-Sn

19 1240 C. Basaran, M.F. Abdulhamid / Mechanics of Materials 41 (2009) are and m 2 /s (Mei et al., 1992). Cu diffusivity is 4 orders of magnitude higher than Sn diffusivity at 20 C, and 3 orders of magnitude higher at 190 C. This difference in migration speed produces segregation effect in which Cu is seen to migrate to the cold side while Sn accumulating near the hot side, which is consistent with previous studies (Huang et al., 2006; Schroerschwarz and Heitkamp, 1971). The supply of Cu at the chip side is limited to a thin layer on the 3-lm thick UBM. Once the supply is depleted, opening will occur at the location where Cu 6 Sn 5 IMC is located, as shown in Fig. 9. According to Cu Sn phase diagram, Cu 6 Sn 5 IMC is stable up to 415 C, which seems to contradict the observations. However, a 2D phase diagram plots element concentration as a function of temperature, and does not take into account diffusion driving forces, concentration gradient and temperature gradient. It can be concluded that the disintegration is not due to temperature alone, but it is due to combination of high diffusivity (as a result of high temperature) and high diffusion driving force (or thermomigration as a result of high temperature gradient). The temperature influences the diffusivity rate, which is a measure of atom mobility, while thermomigration drives the Cu atoms, from the hot to cold side, away from the existing Cu 6 Sn 5 IMC thus reducing the Cu amount needed to maintain the IMC. The thickening of Cu 6 Sn 5 IMC is observed at cold side (bottom) of the solder joint as expected. At 40 and 50 C ambient temperatures, TTF rate has slowed down considerably (Figs. 15 and 16) during the experiment, no UBM separation from solder joint was observed. In the case of NiAu coated Cu pad, IMC at top of solder joint 6 is absent due to Cu migration to the cold side. Solder joint 6 experienced the highest temperature and temperature gradient in the solder chain (Fig. 11 and Table 9). Although experiencing both electromigration and thermomigration in the same direction, a thin Cu 6 Sn 5 IMC layer is observed on top solder joint 7. This is probably because compared to solder joint 6; solder joint 7 experienced a lower temperature and a lesser thermal gradient. The combination of electromigration and thermomigration in solder joint 7 were slow to drive Cu to the cold side due to a lower temperature that influence Cu diffusivity rate significantly and lesser temperature gradient that in the chain. Solder joint 4 experienced thermomigration and electromigration, but in opposite directions. Although exposed to the second highest temperature and thermal gradient in the solder chain, IMC layer is still present, which indicates electromigration driving force is as strong as that of thermomigration. The absence of Cu 6 Sn 5 IMC at the top of solder joint 6 indicates that thermomigration is as serious as electromigration, and can not be ignored. Ye et al. (2003a) and Yang et al. (2007) have shown that the thermomigration driving force is in the same order of magnitude as that of electromigration. 6. Conclusions High current density and high temperature gradient experiments on solder joint with NiAu coated and noncoated Cu pad were done at 20, 30, 40 and 50 C ambient temperatures. The nominal current density, based on 90-lm passivation opening, was A/cm 2. The time to failure (TTF) data show that NiAu coated Cu pad solder joint last longer that the non-coated ones, since NiAu acts as diffusion barrier. A plot of TTF indicates lower and upper asymptotes, and an inflection point for the given current density. Upper asymptote specifies the maximum lifetime for the load applied. For non-coated joint, maximum lifetime is h, while for NiAu coated joint is h for the given current density. The temperature inflection point denotes a point above which TTF rate increases, and below which TTF rate decreases, exponentially reaching the maximum lifetime. The temperature at which this occurs was determined as K, or 64% of the solder melting temperature. By curve fitting Black s TTF equation for temperatures above K, or at the region where TTF rate is increasing, the activation energy, E a was determined to be 2.67 ± 0.05 and 3.65 ± 0.13 ev for non-coated and coated solder, respectively. These values are close to 2.03 ev (Mei et al., 1992), the self-diffusion activation energy for Cu, which is indicative of lattice diffusion mechanism occurrence during the experiment. The observed disintegration of Cu 6 Sn 5 IMC layer the top of the solder joint is due to the migration of Cu atoms to the cold side under the influence of temperature and temperature gradient. The temperature influences the diffusivity rate while the temperature gradient affects the driving force. The higher the temperature the more mobile the atoms, and the higher the temperature gradient, the larger the driving force is. A combination of high temperature and a lower thermal gradient is present in the 20 and 30 C ambient temperatures, while at 40 and 50 C ambient temperatures the atom mobility is slow but the thermal gradient is high. By observing the disintegration of IMC and the directions of thermomigration and electromigration, it was concluded that thermomigration driving force is as high as that of electromigration, a claim that has been substantiated in other recent findings by measuring the order of magnitude between electromigration and thermomigration (Ye et al., 2003a; Yang et al., 2007). It is also shown that commonly used Black s TTF equation can only be used when temperature gradient in the system is very small. Acknowledgements Authors wish to express their gratitude for the test vehicles provided by Dr. Yi-Sao Lai of Advanced Semiconductor Engineering, Yi-Shao Lai, Kaohsiung, Taiwan. This project has partly been sponsored by US Navy, Office of Naval Research Advanced Electrical Power Systems under the direction of program director Terry Ericsen. References Abdulhamid, M.F., Basaran, C., Influence of thermomigration on lead-free solder joint mechanical properties. Journal of Electronic Packaging Transactions of the ASME 131, Mar. Basaran, C., Hopkins, D.C., Frear, D., Lin, J.K., 2005a. Flip chip solder joint failure modes. Advanced Packaging 14,

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