THERMOMIGRATION VERSUS ELECTROMIGRATION IN ... · Thermomigration versus Electromigration in...

Thermomigration versus Electromigration in Lead-Free Solder Alloys

10/3/2007 Abdulhamid 1

THERMOMIGRATION VERSUS ELECTROMIGRATION IN MICROELECTRONICS SOLDER JOINTS

Mohd F. Abdulhamid, Cemal Basaran1,

Electronic Packaging Lab, University at Buffalo, SUNY

Buffalo, NY 14260

Yi-Shao Lai Advanced Semiconductor Engineering, Kaohsiung, Taiwan 811, ROC

ABSTRACT

Competing mechanisms of electromigration and thermomigration in flip chip SnAgCu (SAC) solder

joints was studied experimentally. A chain of solder joints were stressed at 2.0 × 104 Amps/cm2, 2.4 × 104

Amps/cm2, and 2.8 × 104 Amps/cm2 current density at room temperature. In the test vehicle, some solder

joints were exposed to a combination of electromigration and thermomigration, while some others were

exposed to thermomigration alone. The changes in the intermetallic compound (IMC) microstructure were

observed with scanning electron microscope (SEM) under thermomigration alone and when both migration

processes are present. In all cases, Cu6Sn5 IMC at the hot side disintegrated while at the cold side

thickened. The dissolution of the IMC at the hot side and the thickening at the cold side is a result of

temperature and diffusion driving force. It is shown that thermomigration driving force, when present is

much larger than electromigration.

Keywords: diffusion, thermomigration, electromigration, lead-free solder

1 Corresponding author: [email protected]



INTRODUCTION

When a metal conductor is subjected to an electrical potential difference, the current enters from anode

side and travels to cathode side, on the other hand, the electrons travel from cathode to anode side.

Electromigration is a mass diffusion-controlled phenomenon. When a metal conductor is subject to a

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 current. As a result the degradation

of the conductor occurs mainly in two forms, in the anode side the atoms will accumulate and finally form

hillocks and the vacancy condensation in the cathode side will form voids. Both hillocks and voids will

cause the degradation of the material and eventual failure. The physical mechanism of electromigration has

been extensively investigated for pure metal confined thin films (films attached to a thick non-conducting

substrate, primarily VLSI lines). Black [1] established the relationship between the mean time to failure

and current density for confined thin films. The experiments by Blech [2] 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 stress gradient.

From engineering perspective, the electromigration studies conducted so far have been mostly

empirical studies aimed at developing a relationship between the current density and the mean time to

failure (rupture of a thin film) Black [1], Shatzkes and Lloyd [3], Korhonen et al [4]. Several researchers

reported their observations of electromigration in solder joints K. Zeng and K. N. Tu [5], Lee et al [6],

Tang and Shi [7], Brandenburg and Yeh [8], Liu et al. [9, 10], Hu and Harper [11], Basaran et al. [12, 13],

Ye at al [14-17]. These studies are basically experimental observations in Pb/Sn solder alloys.

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 [17] hence it is

outside the scope of this paper. Electromigration is a mass transport in a diffusion-controlled process

under certain driving forces. The driving force here is more complicated than what is involved in a pure

diffusion process, in which the concentration gradient of the moving species is the only component. The

electrical driving forces for electromigration consist of the electron wind force and the direct field force.



The electron wind force refers to the effect of momentum exchange between the moving electrons and the

ionic atoms which happens due to scattering of valence electrons when an electrical charge – a direct field

force – is applied to a conductor. When current density, which is proportional to the electron flux density, is

high enough, this momentum exchange effect becomes significant, resulting in a noticeable mass transport

referred to as electromigration. Low melting point alloys when used at elevated temperature (> 0.5 Tmelt in

Kelvin) are prone to have considerable diffusivity. Solder joints in electronics packaging are prime

examples of this category. For example, melting point of eutectic Pb37/Sn63 solder alloy is 183°C which

corresponds to 0.65 Tmelt at room temperature. The nature of electromigration in solder alloys (especially

lead free solder alloys) is currently investigated and is expected to be different from that in metal

interconnect lines, i.e Cu and Al, Ye et al [18]. This is primarily due to the fact that Cu and Al have much

higher melting temperature and the microstructures of a typical solder alloy and pure metal VLSI

interconnect lines are totally different. The fact that there are more than one diffusive species in solder alloy

makes the problem more complex.

The heat generated under high electrical current density Joule heating is highly localized. Joule heating

is directly proportional to current density. Current crowding effect makes Joule heating localized. Hence,

there is a thermal gradient in the medium, which leads to thermomigration. Thermomigration cannot be

ignored especially when the thermal gradient is large, in which case the thermomigration can be the

dominant migration process. Ye et al. [17].

Thermomigration, which is mass migration that takes place due to high temperature gradient, has been

known as a cause of failure in solder joints [14, 19, 20]. This phenomenon is very similar to Soret effect in

fluids. High thermal resistivity across substrate/solder joint interfaces and differential conductivity of

components in a electronic package lead to significant temperature gradient that causes thermomigration

[14]. The cross section area of the aluminum trace in the Si die in a typical flip-chip module is much

smaller than that of the solder ball, thus making the aluminum interconnect one of the major contributors to

the electrical resistance in the module. During high current stressing, the largest Joule heating is generated

in the Al or Cu interconnect trace. 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 to cold side [21]. In a recent study of Sn-Pb solder, it



is reported that Sn migrates to the hot side while Pb drifts to the cold side [20]. In this study, the solder ball

was subjected to 1.6 × 104 Amps/cm2 current density at 150°C ambient temperature with an approximated

1000°C/cm gradient. The co-existence of thermomigration in conjunction with electromigration may assist

electromigration if the higher temperature side coincides with the cathode side, and counter it if the hot side

is the anode side [14, 19]. If during current stressing, thermomigration dominates electromigration, void

nucleation would happen near the anode side if the anode side is also the hotter side. In this paper, a chain

of flip chip package, solder joints were subjected to high current stressing of 2.0 × 104 Amps/cm2, 2.4 × 104

Amps/cm2, and 2.8 × 104 Amps/cm2 in order to study the competition between electromigration and

thermomigration forces in the same test vehicle. Due to the configuration of the metal trace, some of the

solder joints are exposed to a combination of electromigration and thermomigration, while some solder

joints are exposed only to thermomigration. The intermetallic compound (IMC) microstructure on both the

die side and PCB substrate sides are observed using scanning electron microscope (SEM). The objective of

this paper is to study influence of thermomigration alone (TM), thermomigration as well as

electromigration but in the opposite direction (TM-EM), and thermomigration in the same direction of

electromigration (TM+EM).

EXPERIMENTAL SETUP

The test vehicle is shown in Fig. 1, which is a 27 × 27 × 1.14 mm3 flip-chip package, It involves a 7.62

× 7.62 × 0.74 mm3 silicon die interconnected to a 0.3 mm thick two-layer substrate with 720 solder mask

defined 95.5Sn-4Ag-0.5Cu (SAC 405 in wt %) solder joints bonded with 96.5Sn-3Ag-0.5Cu (SAC 305)

presolder. The pitch between adjacent solder joints is 270 µm. The diameter of the solder joint is 140 µm

while the standoff after flip-chip bond is 100 µm. Surface finish of the Cu pad on the substrate side is either

bare or coated with electroless plated Ni/Au, for which the thickness of Ni is 5 µm while that of Au is 0.05

µm. On the Si die side, the diameter of the tri-layer Ti/Ni(V)/Cu under bump metallurgy (UBM) is 110 µm

whereas the thickness is 3 µm. The Nitride passivation is 1.5 µm thick and its opening is 90 µm. The Al

trace in the die is 65 µm wide and 1 µm thick while the Cu trace on the substrate is 65 µm wide and 15 µm

thick. The diameter of the Al pad is 140 µm. The soldermask opening is 110 µm and the diameter of the Cu

pad 140 µm.



The layout of circuits and solder joints on the flip-chip test vehicle is shown in Fig. 1. Only a single

daisy chain at the edge of the die on the encompassed region is electrified with a constant electric current of

either 1.28 Amp, 1.5 Amp or 1.75 Amp which corresponds to 2.0 × 104 A/cm2, 2.4 × 104 A/cm2, and 2.8 ×

104 A/cm2 current density, respectively, based on the 90-µm passivation opening. The configuration of the

daisy chain, the direction of the current and electron flow, and solder joint number are shown in Fig. 2.

The tests with the exception of 2.1 × 104 A/cm2 current density were carried out until failure at 27°C

room temperature. In each test, for temperature measurements, two thermocouples were used. One

thermocouple is placed at the top of the silicon die, while the other on the epoxy fiber glass at the bottom of

the substrate. The failed test vehicle was sectioned to the center of solder joints by polishing using diamond

suspension. Scanning electron microscope (SEM) equipped with electron dispersive x-ray (EDX) was used

to observe the intermetallic compound (IMC) microstructure changes. A non-tested test vehicle solder joint

was used a reference sample.

NUMERICAL SIMULATION

Since measuring the temperature of the solder ball is not possible, a 3D full model finite element

method (FEM) is employed to estimate the temperature of the top and bottom of the solder ball. This is

necessary because the chip is not symmetric and the daisy chain is located near the edge of the Si die. The

measured temperature at top of the die and bottom of the substrate is used as reference temperatures.

The FEM package 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 load was applied using constant current uniformly over the surface area of the input,

V1+, of the daisy chain and zero electrical potential on the surface of the outlet, P-. The boundary condition

includes heat transfer to the ambient by conduction, radiation and forced convection. The first two

mechanisms of heat transfer were handled automatically by the software by defining unit-compatible Stefan

Boltzmann constant, absolute zero, and sink temperatures. For forced convection, heat transfer coefficient

has to be calculated and input to the model as a film condition. Newton’s law of cooling for flat plate under

forced laminar air flow is used since the chip is flat and acts like a plate. Newton’s law of cooling is defined

as



( )plate s aQ h A T T= −& (1)

where Q& is the heat transfer rate, A is the surface area exposed to the ambient, Ts is the surface area

temperature, and Ta is the ambient temperature. Heat transfer coefficient of the plate, hplate is related to

Nusselt’s number of the plate by,

plate Lkh NuL

= (2)

where k is the thermal conductivity of the fluid, and L is the length of the plate. The Nusselt’s number, NuL

is related to Reynold’s number by,

( )1/ 30.664L LNu Pr Re= (3)

For this equation to be valid, the Reynold’s number must be lower than 3 × 105 which defines laminar flow

region. Reynold’s number can be calculated using

LvLRe ρμ

= (4)

where ρ is fluid density, µ is dynamic fluid viscosity, v is the fluid velocity, and L is the plate length. In this

simulation, v is 0.5 m/s to take into account the air flow. The Reynold’s numbers at 20°C are 252 and 893

for die and substrate, respectively.

Material properties and other parameters are taken from Lai and Kao [22]. The underfill where the

daisy chain is modeled, has a thermal conductivity value of 0.55 W/m°C, and the remaining has a value of

4.5 W/m°C based on the average of area ratios of bumps and underfill [22]. The substrate is modeled as

laminates of BT and 15 µm thick Cu layers which occupy 10% of the layer due to scarcity of the trace

layout.

NUMERICAL RESULTS AND OBSERVATION

An untested solder joint SEM image is shown in Fig. 3. The image shows regular Cu6Sn5 IMC

microstructure at both the UBM and Cu pad interfaces. The magnified view of silicon die and substrate side

interface in virgin solder ball is shown in Fig. 4. At both UBM/solder and Cu pad/solder interfaces, the

IMC is identified as Cu6Sn5. The IMC at both interfaces is formed during reflowing process where molten

Sn-rich solder reacts with metallic substrate, such as Cu in this case. While the formation of IMC is



important during reflowing to ensure metallurgical bonding, excessive growth of IMC is not desirable since

it weakens the interface joints [23]. The untested solder balls did not have excessive IMC.

During testing, the daisy chain shown in Fig. 2, was connected to a constant DC power supply with the

positive terminal connected to top of solder joint 11, labeled as V1+, while the negative terminal to P-, as

shown in Fig. 1. Joule heating is generated on the Si die side due to the Al trace when the daisy chain is

electrified. The excellent thermal conductivity of Si helps to spread the heat to all the solder joints, thus

maintaining a thermal gradient in the solder joints. This is in good agreement with the FEM analysis results

as shown in Table 2, where in all stressing cases, the solder top temperatures for solder 4, 5 and 7 are nearly

the same. These temperatures are slightly higher than the Si die top temperature in all cases.

The temperatures obtained from FEM heat transfer analysis were compared to the measured values.

From Table 1, the FEM analysis results give a very good estimate of the actual temperatures. Since the

analysis results are in good agreement with the measured temperatures, the analysis can be used to estimate

the temperatures, and current densities of the solder balls and aluminum trace.

It is well established that thermomigration occurs form hot side to cold side. Solder joints 5 and 6

experience thermomigration only (TM) where the temperature gradient is from top (hot Si die side) to

bottom (cold substrate side). Solder joints 4 and 10 experience thermomigration as well as electromigration

but in the opposite directions (TM-EM), while solder joint 7 and 11 experience thermomigration and

electromigration in the same direction as electromigration (TM+EM).

The temperature maps for solder 4, 5 and 7 are shown in Fig. 5, while Table 2 shows the temperatures

at the top and bottom of the solder balls at different current stressing conditions. From the results, the

temperature gradient can be calculated. In each case, solder 7 has the highest temperature gradient while

solder 5 has the lowest. The highest temperature gradient is 1200°C/cm at 2.8×104 A/cm2 current stressing.

The current density maps for solder 4 and 7 are shown in Fig. 6, while Table 3 shows the maximum,

minimum, and nominal current densities for these solders at different current stressing levels. From Table 3,

it can be seen that solder 7 maximum current density is 1.5 times higher than the nominal value due to

current crowding. The current crowding is due to very thin (1 µm) Al trace on the die side. Current

crowding in solder 4 is not as severe as in solder 7 due the thickness of the Cu trace, which is 15 times

thicker than the Al trace.



FEM temperature and current density results for Al trace is shown in Fig. 7 and Fig. 8, respectively.

The nominal current density based on the cross section of the Al trace is 1.97 × 106 A/cm2, 2.31 × 106

A/cm2, and 2.69 × 106 A/cm2, corresponding to 1.28 A, 1.5 A and 1.75 A current stressing. Although the

current density is 2 orders of magnitude higher than that on the solder balls, the maximum temperature in

the Al trace is only 176.3°C, which is about 27% of its melting temperature. The maximum temperature

location is where current crowding occurs, which is near the sharp inner corners of the Al trace. At

locations that connect the trace to top of solder ball, the current density is the lowest.

Fig. 9 shows solder joints at Si die/UBM and Cu pad/solder interface and for solder joints that

experience TM (solder 5), TM-EM (solder 4) and TM+EM (solder 7) for 2.0 × 104 A/cm2 current stressing.

The stressing was stopped after 887 hours and no failure was observed. The average top of die and bottom

of substrate temperatures are 78°C and 66°C, respectively. Solder joint 7 which experience the most severe

diffusion driving force (because of concurrent TM and EM driving forces) shows no void nucleation or

crack. In the joints shown in Fig. 9, Cu6Sn5 IMC at the top side is not observed compared to untested

solder joint. Islands of Cu6Sn5 IMC can be seen near the Cu pad/solder interface in all solder balls. The

thickness of Cu6Sn5 IMC is about the same thickness as the untested sample.

Solder joints that were subjected to 2.4 × 104 A/cm2 current stressing are shown in Fig. 10. The test

vehicle failed after 693 hours. The average hot and cold temperatures are 103°C and 93°C, respectively. As

observed in the earlier test, Cu6Sn5 IMC at the hot side is not observed. In this case, crack can be seen in all

the solder joints, with solder joint 7 experiencing the worst because of TM and EM forces acting in the

same direction. At the cold side for all solder balls, the Cu6Sn5 IMC appears thicker than the untested

sample. In this case, no Cu6Sn5 island observed compared to the previous test.

Solder joint 7 under the 2.8 × 104 A/cm2 current density melted as shown in Fig. 11. In this case, the

average hot and cold temperatures are 135°C and 126°C, respectively. The test vehicle failed after 562

minutes (9.37 hours). At the hot side, as in other tests, there no Cu6Sn5 IMC layer formation. At the cold

side, the IMC layer is thicker than the untested solder ball and some IMC islands are observed.

In all 3 stressing cases, the absence of Cu6Sn5 IMC at the hot interface is evident. A thickening of IMC

layer at bottom side can be observed, and there was no damage due to electromigration or melting to the Al

trace.



DISCUSSION

Although the nominal current density based on the cross section of the Al trace is 1.97 × 106 A/cm2,

2.31 × 106 A/cm2, and 2.69 × 106 A/cm2, corresponding to 1.28 A, 1.5 A and 1.75 A current stressing,

damage to Al trace was not observed in all cases. From FEM analysis, the maximum Al temperature is

176.3°C, which is 27% of its melting temperature (660.32°C). The Al maximum temperature is not

favorable for diffusion, consequently electromigration since it is less than 50% than melting temperature,

and too low to melt the trace.

The crack in all cases is partly a result of IMC being decomposed to Cu and Sn under high thermal

gradient according to

6 5Cu Sn 6Cu + 5Sn⇒ (5)

According to Cu-Sn phase diagram, Cu6Sn5 is stable up to 415°C, which seems to contradict the

observations. A 2D phase diagram plots element concentration as a function of temperature, and does not

take into account diffusion driving forces such as electromigration and thermomigration. It can be

concluded that the disintegration is not due to temperature alone, but it is due to combination of

temperature and diffusion driving forces. In this paper, both or either one of the driving forces is driving Cu

atoms, which is the dominant diffusion species [24], to the cold side. In case of thermomigration the driving

force drives Cu from hot to cold side, while electromigration from cathode to anode.

The temperature at the top side of solder balls for 2.4 × 104 A/cm2 and 2.8 × 104 A/cm2 stressing cases,

the temperatures at the top of the solder balls are about 104°C and 143°C, which correspond to 47% and

66%, respectively, of its melting temperature (217°C). These temperatures are favorable to induce

diffusion. Cracks can be seen at top of solder ball 4, 5, and 7 due to diffusion of Cu from the UBM and

Cu6Sn5 to the cold side. This is consistent with observation where thickening of Cu6Sn5 is observed at the

cold side of solder balls for these two cases. The migration of Cu to the cold side follows Fick’s law of

diffusion [25],

*

*cucu cu

D CC Q dT dUJ D Z eEx kT T dx dx

⎛ ⎞∂= − + − −⎜ ⎟∂ ⎝ ⎠

(6)

where Jcu is Cu flux, and Dcu is copper diffusivity rate. The first term is diffusion due to concentration

gradient, second is electromigration, third is thermomigration, and the last is stress gradient. Based on the



thicknesses of Cu6Sn5 IMC at solder 4 (which experienced TM-EM), solder 5 (which experienced TM

only), and solder 7 (which experienced TM+EM) cold sides, it can be said that thermomigration dominates

in the diffusion process, or in other words, thermomigration driving force is stronger than electromigration

in this experiment. The crack is a result of Cu migration to the cold side. When Cu atoms from the UBM

and Cu6Sn5 IMC migrate and left their locations, voids are created. When these voids coalesce, cracks are

formed.

The temperature for 2.0 × 104 A/cm2 stressing case was only 73°C, which is about 34% of melting

temperature. The temperature is low and not conducive for diffusion, consequently, no crack at the hot side

and thickening of Cu6Sn5 IMC at the cold side are observed. Additionally, some Cu6Sn5 IMC at the hot side

can be observed.

The decomposition of Cu6Sn5 IMC was not observed in isothermal aging tests for similar system [26-

28]. Studies on isothermal aging showed that over time Cu6Sn5 IMC formed during reflow of Sn-rich solder

on Cu pad grows to two layers, a thinner Cu3Sn near the Cu pad and Cu6Sn5 near the solder [28-30].

CONCLUSIONS

In summary, the failure of solder joints in these test vehicles can be attributed to thermomigration.

Cracks and the decomposition of Cu6Sn5 can be observed at the hot interface when the samples failed. The

crack and decomposition is a result of Cu diffusion to the cold side under thermal gradient driving force.

The absence of Cu6Sn5 is not observed in similar system under isothermal aging suggests that the IMC

decomposition to Sn and Cu atoms, happens under the thermal gradient force. In all experiments, Cu and

atoms drift to the cold side, which is indicated by thickening of Cu6Sn5 IMC layer.

Observed results indicate that thermomigration driving forces can be as strong electromigration forces

or even stronger. These results are in agreement with earlier findings reported by Ye et al. [14], where

themomigration forces were competing with electromigration forces.

Based on our observations we can state that in next generation nanoelectronics not just temperature

levels but also temperature gradient will be a major reliability concern.



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LIST OF FIGURES

Fig. 1 Layout of circuit and solder joints on flip-chip test vehicle.

Fig. 2 Schematic of the electrified daisy chain, direction of current and electron flow, and solder ball number.

Fig. 3 An untested test vehicle solder joint showing IMC microstructure at both UBM and Cu pad interfaces. The crack at the UBM near the passivation layer might be due to manufacturing process.

Fig. 4 Magnified view of Si die and substrate side interface of untested solder joint showing Cu6Sn5 IMC.

Fig. 5 Temperature profile showing maximum temperature at the top side and minimum at the bottom. Minimum and maximum values are shown in Table 2.

Fig. 6 (a) Current crowding at lower right corner on solder 4. (b) Current crowding at upper right corner on solder 7. Maximum and minimum current crowding values are presented in Table 3.

Fig. 7 Temperature map (in °C) for Al trace at different current stressing. The maximum temperature is about 27% of melting temperature of Aluminum.

Fig. 8 Current density map (in A/µm2) for Al trace on the die side. On top of the solder ball, the density is 8 order of magnitude smaller that at the connecting trace.

Fig. 9 From top to bottom, (a) TM – solder #5, (b) TM-EM – solder #4, and (c) TM+EM – solder #7 for sample under 2.0 × 104 A/cm2 current stressing.

Fig. 10 From top to bottom, (a) TM – solder #5, (b) TM-EM – solder #4, and (c) TM+EM – solder #7 for sample under 2.4 × 104 A/cm2 current stressing.

Fig. 11 From top to bottom, (a) TM – solder #5, (b) TM-EM – solder #4, and (c) melted TM+EM – solder #7 for sample under 2.8 × 104 A/cm2 current stressing.



Fig. 1 Layout of circuit and solder joints on flip-chip test vehicle.



Fig. 2 Schematic of the electrified daisy chain, direction of current and electron flow, and solder

ball number.



Fig. 3 An untested test vehicle solder joint showing IMC microstructure at both UBM and Cu pad

interfaces. The crack at the UBM near the passivation layer might be due to manufacturing process.



Fig. 4 Magnified view of Si die and substrate side interface of untested solder joint showing Cu6Sn5

IMC.



Solder 4 Solder 5 Solder 7

Fig. 5 Temperature profile showing maximum temperature at the top side and minimum at the bottom. Minimum and maximum values are shown in Table 2.



Solder 4 Solder 7

(a) (b) Fig. 6 (a) Current crowding at lower right corner on solder 4. (b) Current crowding at upper right

corner on solder 7. Maximum and minimum current crowding values are presented in Table 3.



1.28 A (1.97 × 10-2 A/µm2) 1.5 A (2.31 × 10-2 A/µm2) 1.75 A (2.69 × 10-2 A/µm2)

Fig. 7 Temperature map (in °C) for Al trace at different current stressing. The maximum temperature is about 27% of melting temperature of Aluminum.



1.28 A (1.97 × 10-2 A/µm2) 1.5 A (2.31 × 10-2 A/µm2) 1.75 A (2.69 × 10-2 A/µm2)

Fig. 8 Current density map (in A/µm2) for Al trace on the die side. On top of the solder ball, the density is 8 order of magnitude smaller that at the connecting trace.



Solder 5

(a)

Solder 4

(b)

Solder 7

(c) Fig. 9 From top to bottom, (a) TM – solder #5, (b) TM-EM – solder #4, and (c) TM+EM – solder

#7 for sample under 2.0 × 104 A/cm2 current stressing.



Solder 5

(a)

Solder 4

(b)

Solder 7

(c) Fig. 10 From top to bottom, (a) TM – solder #5, (b) TM-EM – solder #4, and (c) TM+EM – solder

#7 for sample under 2.4 × 104 A/cm2 current stressing.



Solder 5

(a)

Solder 4

(b)

Solder 7

(c) Fig. 11 From top to bottom, (a) TM – solder #5, (b) TM-EM – solder #4, and (c) melted TM+EM –

solder #7 for sample under 2.8 × 104 A/cm2 current stressing.



LIST OF TABLES

Table 1 Comparison between measured temperatures and FEM heat transfer results at top of die and bottom of substrate.

Table 2 FEM temperature result for solder 4, 5 and 7 at different current stressing. Table shows minimum and maximum temperature for each solder. A complete temperature profiles are shown in Fig. 5.

Table 3 FEM current density result showing current crowding density is a high as 1.5 of nominal current density. Current density profiles are shown in Fig. 6.



Table 1 Comparison between measured temperatures and FEM heat transfer results at top of die and bottom of substrate.

Temp at 1.28 amps (°C) Temp at 1.5 amps (°C) Temp at 1.75 amps (°C) Location Measured FEM % Error Measured FEM % Error Measured FEM % Error Die top 78 72 7.7 103 103 0 135 140 3.7

Subs bottom 66 66 0 93 93 0 126 126 0



Table 2 FEM temperature result for solder 4, 5 and 7 at different current stressing. Table shows minimum and maximum temperature for each solder. A complete temperature profiles are shown in

Fig. 5. Current (A) 1.28 (2.0×104 A/cm2) 1.5 (2.4×104 A/cm2) 1.75 (2.8×104 A/cm2)

Solder number 4 5 7 4 5 7 4 5 7 Top temp (°C) 72.5 73.0 72.9 103.6 104.3 104.1 142.1 143.3 142.9

Bottom temp (°C) 68.0 69.0 68.1 96.5 98.0 96.6 130.8 133.4 130.9 Gradient (°C/cm) 450 400 480 710 630 750 1130 990 1200



Table 3 FEM current density result showing current crowding density is a high as 1.5 of nominal current density. Current density profiles are shown in Fig. 6.

Density at 1.28 amps (× 104 A/cm2)



Solder 4 Solder 7 Solder 4 Solder 7 Solder 4 Solder 7 Max 2.07 2.95 2.44 3.50 2.85 4.13 Min 0.50 0.54 0.58 0.63 0.67 0.73

Nominal 2.0 2.4 2.8

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