Electromigration in lead-free solder joints under high-frequency pulse current: An experimental study

Abstract

The insatiable demand for miniaturization of consumer electronics has brought continuing challenges in the electronic packaging field. As a consequence, immense information processing duties, high current density and large joule heating are exerted on the package, which makes electromigration and thermomigration a serious reliability issue. In this study, high frequency pulse current electromigration degradation experiments were carried out on Sn96.5%Ag3.0%Cu0.5 (SAC305 - by weight) solder joints. During the test, frequency, current density and duty factors are used as controlling parameters. The nominal current density varied from $1.0 \times 10^{5} \frac{A}{{cm}^{2}}$ to $2.1 \times 10^{5} \frac{A}{{cm}^{2}}$ , pulsed direct current frequency ranged from 2 MHz to 10 MHz and duty factor varied between 30% and 80% with a controlled ambient temperature at 70℃. It was observed that mean time to failure was inversely proportional to the current density and duty factor. Higher frequency leads to a shorter lifetime within the frequency range we studied. Scanning electron microscope image shows that damage develops at both current crowding corners and the skin layer of solder joints. A mean time-to-failure relationship of lead-free solder joints under pulsed current loading is proposed based on the experimental data.

Keywords

Pulsed direct current electromigration scanning electron microscope SAC solder joint mean time to failure solder joint resistance

Introduction

There always has been and will continue to be motivation to pack more electronic functionalities and better performance into a smaller volume of space. Due to this insatiable trend in microelectronic devices, Ultra-large-scale-integration (ULSI) interconnect and solder joint sizes reduces continuously to enable a higher degree of integration. As a result of transferring more data through reduced devices size, average current density carried by solder joints has increased from 10³A/cm² to 10⁵A/cm². Owing to the geometry of solder joint connections, significant current crowding exists at Al/Cu trace interconnecting solder bump areas. It induces more serious electromigration (EM) damage, and another byproduct, highly localized joule heating. Hot spots are thus induced and cause intense signal delay in high-speed switching device, especially the complementary metal-oxide-silicon (CMOS) ICs. Both high current density and joule heating make EM and thermomigration a reliability issue for solder joints (Abdulhamid et al., 2009; Basaran et al., 2012; Basaran and Nie, 2004; Campbell and Huntington, 1969; Frankovic et al., 1996; Li et al.; Yao and Cemal, 2012). Mass diffusion mechanism of conductors under electric current loading has four driving forces: electric wind force, chemical potential, thermal gradient and stress gradient (Basaran et al., 2007; Tang and Basaran, 2001). When subjected to direct current (DC) loading, electric wind force drives ions to diffuse from the cathode side of conductors to the anode side; joule heating induced thermal gradient transports atoms from hot spots to their surrounding areas; chemical potential and stress gradient drive mass to diffuse in the opposite direction of the electron wind force. Net effect acting in this mass transport process moves ions from the cathode side toward the anode side of conductors (Blech, 1976; Blech and Herring, 1976). As a result, mass accumulation induces local compression on the anode side, which eventually squeezes mass out of the material surface to form protrusions or hillocks (Basaran et al., 2005; Blech and Kinsbron, 1975; Wei and Basaran, 2012). It causes a short-circuit failure. While on the cathode side, voids growth causes increased local resistivity and current crowding, eventually open-circuit failure. Anode side short-circuit failure is effectively reduced due to polymer filling between conductors and minimum pitch specified in the electronic packaging process. The cathode side open-circuit becomes a major failure phenomenon that this study and the field of electronic packaging are concerned with (Yao and Basaran, 2012).

Although most electronic applications, especially power switching and digital circuitry in chips, involve pulse rather than continuous signals, previous studies focused mainly on EM in direct current (DC) bias (Basaran et al., 2003, 2004, 2008; Basaran and Lin, 2007, 2008; Basaran and Nie, 2007; Li et al, 2008a, 2008b; Li and Basaran, 2009; Lin and Basaran, 2005; Ye et al., 2003a, 2003b, 2003c, 2003d, 2003e, 2004, 2006, 2008). EM under pulse current loading is different in the sense that there exists a pulse-off time every loading period. Lifetime of solder joints is longer than those subjected to DC loading under otherwise the same conditions (Brooke, 1987; English et al., 1972; Hatanaka et al., 1989; Hu et al., 1993; Liew et al., 1989; Tao et al., 1998). Mass transportation mechanism during pulse-on time is exactly the same as in DC loading. During pulse-off time, however, electron wind force vanishes. Under pulsed direct current (PDC) stressing, the electron wind force causes a concentration gradient between the anode and the cathode side of conductors; and then, between current pulses, some of the atoms/vacancies stream back, obeying Fick's conventional law of diffusion. In other words, this self-healing effect during load-off period could relieve partially the damage caused during previous pulse-on period (Jiang et al., 1994; Root and Nagalingam, 1985; Shingubara et al., 2004). This mechanism is known as retroactive effect. Current crowding at Cu/Al line and the solder bump intersection causes highly localized joule heating in that region. Although direction of thermal driving force does not change during the pulse history, the amount of joule heating is reduced because of heat dissipation during load-off time. Thanks to retroactive effect and reduced joule heating, lifetime of conductors powered on the PDC is usually longer. For deposited thin film connections, it is observed to be between 1/r (English et al., 1972; Schoen, 1980) and 1/r² (Brooke, 1987; Maiz, 1989; Towner and van de Ven, 1983) of DC lifetime at equal peak current densities, with r being the pulse duty cycle. Based on the principle of projecting load-on current to DC current loading at the same peak current density, Schoen (Schoen, 1980) proposed a modified Black's time to failure (TTF) model for thin films to account for the lifetime enhancement of conductors under pulsed current loading. Damage relaxation is found to be a temperature-dependent time constant. However, with the broad adoption of Ball Grid Array (BGA) and Column Grid Array (CGA) in the electronic packaging industry, there are no reported similar studies for solder joints in literature. Due to the obvious different degradation mechanism between metallic thin films and solder alloys, it is clear that accurate data about EM failure of lead-free solder joints under pulse current stressing are required to better predict reliability of electronics and accurate timing of signal transport.

Experimental setup

Test vehicles

Electromigration mean time to failure (MTTF) of lead-free solder joints subjected to pulse current loading is investigated experimentally. The specially designed flip-chip package with a schematic cross-sectional view of the solder joint is shown in Figure 1. Lead-free Sn96.5%Ag3.0%Cu0.5 (SAC305 - by weight) solder joints connect the chip to printed circuit (PC) board. The pitch between adjacent solder bumps is 270 µm. Diameter of solder bump is 112 µm with a 105 µm standoff height. Cu pad of the substrate is surface finished with electroless plated Ni/Au, for which the thickness of Ni is 5 µm while that of Au is 0.05 µm. Diameter of tri-layer Ti/Cu/Ni under bump metallurgy (UBM) is 112 µm with the thickness of 3 µm. The Nitride passivation layer is 1.5 µm thick with a 90 µm opening. Deposited Al thin film connection of 65 µm widths and 1 µm thickness forms circuitry on the silicon die side. Copper trace of 65 µm width and 15 µm thickness of the PC board side contacts the bottom of solder joints. The substrate solder mask opening is 110 µm. Detailed dimension and material finish information of the test vehicle is listed in Table 1.

Table 1.

Dimension of the flip chip test vehicle package (Peng Su, 2009).

Features	Dimension
Package size	27.3 × 27.3 × 1.14 mm
Die size	7.62 × 7.62 × 0.74 mm
UBM	Ti 0.1 µm/Cu 0.5 µm/Ni 2 µm
UBM diameter	112 µm
Passivation opening	90 µm
Al trace on silicon	65 µm × 1 µm
Bump size	112 µm in diameter 105 µm in standoff
Bump pitch	270 µm
Substrate pad finish	Electroless Ni/Au on Cu Ni 5 µm/Au 0.05 µm/Cu 5 µm
Substrate presolder	Sn 3% Ag 0.5% Cu
Substrate Cu trace	65 µm × 15 µm
Substrate solder mask opening	110 µm

UBM: under bump metallurgy.

Experimental procedure

The most common method used to evaluate EM failure of a solder joint has been to stress it under constant current loading and measure the time required for open-circuit failure to occur. This method is highly impractical in evaluation of damage of solder joints under pulse current loading and even worse when subjected to AC stressing. Awaited to material healing effect, extremely high current density and long loading time are required for open-circuit failure to happen under PDC or AC conditions. The use of resistometric techniques is thus developed for more practical testing (Hummel and Hoang, 1989; Jiang et al., 1994; Maiz, 1989). In this technique, increase of conductor resistance is used to monitor in an attempt to detect the formation of mass diffusion damage. This theory is based on the fact that EM induces vacancy formation, which reduces the effective conducting area and results in a higher resistance. In this work, TTF is defined as 10% resistance change between minimum and maximum resistance happening during current loading history. The 10% resistance change is adopted because this amount resistance change creates an electrical signal distortion large enough to fail the designed function of most ICs (Basaran et al., 2009). Scheme of the experimental design is shown in Figure 2. Pulse generator/power supply outputs signals at designed voltage, frequency and duty cycle. Two multimeters programmed by a computer server collect resistance reading every 5 sec by four-wire method shown in Figure 3. Principle of four-wire scheme is (1) a voltmeter parallel connected to the circuitry measures voltage reading on the conductor; (2) an amp-meter series connected to the circuitry measures current reading; (3) the multimeter then automatically divides voltage by the current reading, and gives the in-situ resistance. Flip-chip package used in this study is specially designed to exclude Cu/Al trace's EM noise from our test. As seen from Figure 4, pulse current signal flows through two solder joints and one aluminum trace in R₁, but only one solder joint and one aluminum trace in R₂. To exclude Al/Cu trace's EM damage effect, R₁ and R₂ are measured at the same time, and the exact resistance of one solder bump is given by R₁-R₂. One thermometer is programmed to measure temperature on the silicon chip side and PC board side every 30 sec. The test vehicle was put in a thermal chamber with an ambient temperature of 70℃, which is normal operating temperature of most consumer electronic IC devices.

Time varying electric signals lead to a thermal transient in test vehicles. This transient can be substantial for high current densities that it actually affects the mass transport. Thermal relaxation time used to characterize this joule heating induced mass diffusion is in the μs range for SAC alloys. To exclude the thermal transient effect, PDC current stressing with frequencies of 2 MHz to 10 MHz was employed in the test vehicle. Duty factor defined as the time ratio of pulse-on period over one loading period varies from 0.3 to 1.0. Nominal current density, calculated at center cross section of the solder joint, varies from $1.0 \times 10^{5} \frac{A}{{cm}^{2}}$ to $2.1 \times 10^{5} \frac{A}{{cm}^{2}}$ . However, the maximum current density is typically one order of magnitude larger.

Results and discussion

Scanning electron microscope (SEM) experiments were conducted to investigate the vacancy accumulation and intermetallic compound (IMC) growth of our test vehicle. Figure 5(a) is an initial profile of the solder joint, while Figure 5(b) and (c) correspond to solder joint profiles after 50 h and 140 h of PDC current loading at 2 MHz, respectively. It can be seen that PDC current loadings introduce vacancy growth in solder joints instead of metal films. Essential voids accumulation is observed at the current crowding corner, which fails the designed function of circuitry. The EM process in aluminum traces initiate at a current density about two orders higher than that of solder joints, which is one of the major reasons why Al instead of copper is used as deposited thin film interconnect in substrate manufacture. We are confident that the resistance comes from the lead-free solder bump instead of the deposited aluminum thin film. The SEM image also shows vacancy development at both current crowding corners and skin layer of the solder joint. This phenomenon is not observed in DC cases (Basaran et al., 2005, 2009; Brandenburg and Yeh, 1998; Zhang et al., 2002). When conductors subjected to time varying electromagnetic field, secondary current flow is induced, which alleviates part of current flow at the center of conductors while strengthens it in the skin layer. The net current distributes with the highest value at the skin layer and decreases exponentially toward the center cross section. This phenomenon is referred to as “skin effect” and causes more damage to skin layer of solder joints than other parts. IMC thickening is observed to grow toward the center of solder joints.

Effective resistance test

Instead of being constant, measured resistance is found to be function of current density, duty factor and pulse frequency as shown in Figure 6. Resistance is observed to grow linearly with larger current density. This agrees with literature observation. Figure 6(b) is the frequency dependence of effective impedance. It can be seen that effective impedance is stable from 1 MHz to 10 MHz for tests shown in the figure. It goes down exponentially when we further increase the pulse frequency. Matthiessen's rule states that the total resistance of a sample is the sum of all the individual contributions. Nonlinear regression gives the following relationship between the effective resistance, current density and frequency with a confidence value of 92%,

R = α \cdot j - β \cdot f^{γ} + R_{0}

(1)

where,

α = 2.8 \times 10^{- 4}

is current density parameter, j is current density in A/cm²,

β = 0.004

and

γ = 1.8

are frequency parameters and f is frequency in MHz.

As for the duty factor, the exact linear relationship is observed. Larger duty factor results in a higher resistance as shown in Figure 6(c). The relationship is given as

R = ɛ \cdot d + θ

(2)

where, ɛ is duty factor parameter and d is the duty factor.

Combing equations (1) and (2), resistance vs. current density, pulse frequency and duty factor is defined as,

R = α \cdot j + ɛ \cdot d - β \cdot f^{γ} + R_{0}

(3)

It can be seen that effective resistance linearly depends on current density and duty factor but has an exponential relationship with pulse frequency. Parameters α, β, γ and ɛ are positive and depend on solder alloy material and construction.

Due to the varied measured resistance, test data are normalized as R/R₀ with respect to the stressing time for comparison purposes. R equals to R₁-R₂ as shown in Figure 4, which is the resistance of one solder joint. R₀ is the initial value of resistance at 70℃.

Current density dependence of electromigration MTTF

EM is an electric current driving mass transport process. As a consequence, electron wind force is the main material degradation mechanism. Larger current density induces more EM damage and also leads to an increased resistance (Basaran et al., 2009). Figure 7(a) is the initial temperature profile of solder bump under PDC. It can be seen that joule heating reaches a stable state after about 10 min of current loading. Temperature on the silicon chip temperature cycles from 73.5 to 72.8 in a period of 150 sec for the rest of the loading history. The actual thermal transient is observed to lag far behind the current loadings, so we are confident that the material degradation results from EM rather than thermomigration. Figure 7(b)–(e) shows resistance evolution in solder joints subjected to current density from $1.3 \times 10^{5} \frac{A}{{cm}^{2}}$ up to $2.1 \times 10^{5} \frac{A}{{cm}^{2}}$ , at a constant duty factor of 0.5 and frequency of 4 MHz. Resistance is observed to change up and down continuously with the average value growing during the entire loading history. The reduction in resistance reflects damage healing effect during load-off period. It can be seen that larger current density shortens significantly the lifetime. At a current density of $1.3 \times 10^{5} \frac{A}{{cm}^{2}}$ , the solder joint lasts 49 h before threshold resistance is reached; it lasts 23 h when the current density is increased to $1.8 \times 10^{5} \frac{A}{{cm}^{2}}$ . At a current density of $2.1 \times 10^{5} \frac{A}{{cm}^{2}}$ , however, it only takes 0.8 h for failure to happen. The reduced resistance after failure is due to temperature drop from 70℃ to ambient temperature. It is also seen that, at high current density, resistance grows at an almost constant rate due to EM with no observable healing, which is typically found in the DC EM damage process. All test results are summarized in Table 2. The MTTF data is averaged from several tests with identical controlling parameters.

Table 2.

Experimental results of MTTF of lead-free solder joints subjected to PDC current stressing at a constant temperature of 70℃.

Dependence	Current density (A/cm²)	Duty factor (%)	Frequency (MHz)	MTTF_PDC (h)
Current density	1.0 × 10⁵	50	4	49.2
	1.3 × 10⁵	50	4	44.7
	1.6 × 10⁵	50	4	32
	1.8 × 10⁵	50	4	23.5
	2.1 × 10⁵	50	4	0.83
Duty factor	1.3 × 10⁵	30	4	78.1
	1.3 × 10⁵	50	4	44.7
	1.3 × 10⁵	60	4	37.5
	1.3 × 10⁵	80	4	19.5
Frequency	1.3 × 10⁵	50	2	169.5
	1.3 × 10⁵	50	4	44.7
	1.3 × 10⁵	50	6	42
	1.3 × 10⁵	50	8	3.3
	1.3 × 10⁵	50	10	1.7

MTTF: mean time to failure; PDC: pulsed direct current.

MTTF vs. current density data are plotted in Figure 8. To obtain a current density dependent MTTF, non-linear regression is performed at a constant duty factor and pulse frequency. With a confidence value of 83.5%, the following relationship is obtained,

MTTF = 5.5 \times 10^{9} \times c^{- 1.6}

(4)

where MTTF is mean time to failure in hours and c is the nominal current density in A/cm². Lifetime shortens seriously with increased current density at elevated frequency.

Duty factor dependence of electromigration MTTF

Figure 9 shows resistance evolution of solder joints under PDC loading with the duty factor varying from 30% to 80% at a constant current density of $1.3 \times 10^{5} \frac{A}{{cm}^{2}}$ and frequency of 4 MHz. Resistance is observed to fluctuate up and down during the whole loading history. Joule heating is responsible for the initial resistance change as discussed in the above section. After the thermal steady state is reached, EM induced mass transport contributes to the following resistance change. Effective resistance does not grow continuously during the current loading. As discussed above, chemical potential gradient and stress gradient always retard electron wind force driven mass diffusion and restore partially the mass transportation during load-on time. With a duty factor of 30%, the solder joint fails after 78 h current loading; it lasts 43 h when the duty factor is increased to 50% and only 37 h at duty factor of 60%. When we increase duty factor to 80%, however, solder joints failed in just 21 h. It implies an obvious duty factor dependence of MTTF of solder joints. This is important since pulse signals in ICs are rarely symmetrical and within the generality of a design rule the possibility of arbitrary pulse current needs to be considered (Maiz, 1989). Owing to the uneven pulse signals, conductors may fail before their designed lifetime.

Curve fitting results of MTTF vs. duty factor are shown in Figure 10. Higher duty factor results in a decreased MTTF. Non-linear regression gives the following duty factor dependence of electromigration MTTF of solder joints subjected to PDC with a 97.9% confidence value:

MTTF = 18.6 \times r^{- 1.2}

(5)

Frequency dependence of electromigration MTTF

Frequency dependence of resistance of lead-free solder joints is shown in Figure 11, with a constant current density of $1.3 \times 10^{5} \frac{A}{{cm}^{2}}$ and duty factor of 50%. The minimum frequency is set at 2 MHz to avoid thermal transient induced material damage. It is observed that higher frequency shortens the lifetime of solder joints. At 2 MHz the threshold resistance change happens after 192 h of current loading. At 4 MHz, the same amount resistance change happens in 45 h. It fails, however, in 3.3 h at a frequency of 8 MHz and 1.7 h at 10 MHz. This phenomenon can be credited to the skin effect discussed above. High frequency generates a stronger eddy current that intensifies the current flow at the skin layer of conductors but alleviates it at the center cross section. It makes actual current density subjected by solder joints much larger than the nominal value.

Non-linear regression curve fitting of MTTF vs. frequency is shown in Figure 12. It is obvious that a quadratic relationship exists between MTTF and pulse frequency. With a 95.8% confidence value, the following relationship is obtained,

MTTF = 626.3 \times f^{- 1.8}

(6)

Electromigration MTTF equation of lead-free solder joints under PDC loadings

From above discussion, we conclude that larger current density, higher duty factor and higher frequency lead to a shorter lifetime of solder joints. Combining equations (4)–(6), we obtain the following MTTF equation of lead-free solder joints under PDC, which takes into account of frequency, duty factor and current density dependence.

MTTF = α \times c^{- 1.6} \times r^{- 1.2} \times f^{- 1.8}

(7)

After incorporating the Arrhenius temperature dependence term, we propose the MTTF equation of lead-free solder joints subjected to pulse current loadings as follow,

MTTF = \frac{α}{c^{1.6} \cdot r^{1.2} \cdot f^{1.8}} e^{\nabla E / kT}

(8)

where MTTF is in h, c is current density in A/cm², r is duty factor, f is frequency in MHz, E is vacancy activation energy in

Kg \cdot \frac{μ m^{2}}{(s^{2} \cdot mol)}

, k is Boltzmann's constant and T is temperature in Kelvin. It can be seen that, with an exponent of 1.8, the frequency term is the most serious contributing factor to EM damage of solder joints; current density comes as the second most serious damage factor. The duty factor term, which has an exponent of 1.2, is the least serious factor. We conclude that at a constant power output, higher duty factor and lower current density should be used to minimize the EM damage.

Conclusions

Electromigration damage of lead-free solder joints subjected to PDC current loading was investigated experimentally. Due to the material healing effect at load-off time, lifetime of solder joints subjected to PDC loading is considerably longer than those subjected to DC loading under otherwise the same conditions. SEM image shows that damage develops at both current crowding corners and the skin layer of solder joints instead of the whole cross section under DC loadings. It is found that higher current density, higher duty factor or higher frequency shortens lifetime of solder joints. With an exponent of 1.8, frequency of PDC loadings proves to be the most serious factor in EM damage, while current density and duty factor contribute less to the damage with exponent values of 1.6 and 1.2, respectively. An MTTF equation is proposed for lead-free solder joints subjected to pulse current loadings. At the same power output, EM damage could be alleviated by using a larger duty factor and smaller current density pulse signals.

Footnotes

Acknowledgments

This research project has been sponsored by the US Navy, Office of Naval Research, Advanced Electrical Power Program under the direction of Terry Ericsen. We would like to express our sincere appreciation to Dr. Yi-Shao Lai, director at ASE, for providing his support of the test vehicles for this program.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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