Numerical prediction of mechanical properties of Pb-Sn solder alloys ...

1392 of ELECTRONIC MATERIALS, Vol. 29, No. 12, 2000 Journal

Gadag Regular and Issue Patra Paper

Numerical Prediction of Mechanical Properties of Pb-Sn Solder Alloys Containing Antimony, Bismuth and or Silver Ternary Trace Elements SHIVA P. GADAG1 and SUSANT PATRA1,2 1.—University of California at San Diego, Electrical and Computer Engineering Dept., 9500 Gilman Drive, La Jolla CA 92093-0407. 2.—Optical Micro-Machines Inc., San Diego, CA 92129

Solder joint interconnects are mechanical means of structural support for bridging the various electronic components and providing electrical contacts and a thermal path for heat dissipation. The functionality of the electronic device often relies on the structural integrity of the solder. The dimensional stability of solder joints is numerically predicted based on their mechanical properties. Algorithms to model the kinetics of dissolution and subsequent growth of intermetallic from the complete knowledge of a single history of time-temperature-reflow profile, by considering equivalent isothermal time intervals, have been developed. The information for dissolution is derived during the heating cycle of reflow and for the growth process from cooling curve of reflow profile. A simple and quick analysis tool to derive tensile stress-strain maps as a function of the reflow temperature of solder and strain rate has been developed by numerical program. The tensile properties are used in modeling thermal strain, thermal fatigue and to predict the overall fatigue life of solder joints. The numerical analysis of the tensile properties as affected by their composition and rate of testing, has been compiled in this paper. A numerical model using constitutive equation has been developed to evaluate the interfacial fatigue crack growth rate. The model can assess the effect of cooling rate, which depends on the level of strain energy release rate. Increasing cooling rate from normalizing to water-quenching, enhanced the fatigue resistance to interfacial crack growth by up to 50% at low strain energy release rate. The increased cooling rates enhanced the fatigue crack growth resistance by surface roughening at the interface of solder joint. This paper highlights salient features of process modeling. Interfacial intermetallic microstructure is affected by cooling rate and thereby affects the mechanical properties. Key words: Solder joint, reflow, solder properties, thermal fatigue, strain rate, creep

INTRODUCTION Soldering is an elegant art and a versatile technique of joining metals and or ceramics or a combination of the two. Although the technique of art of soldering is well known in history, which dates back to the era of Roman times, study of science of soldering and its mechanical properties is relatively recent. Solders and solder joints are considered building blocks of the electronic assembly and packaging technology. The solder joint is not only a mechanical means of attaching components to PCB, but also an electrical (Received July 28, 2000; accepted September 11, 2000) 1392

connection and more often the only means of heat dissipation. Solders and solder joint interconnects play a pivotal role in future developments in electronics with the consequence of continuing trend of its miniaturization, ever-increasing performance demands and reliability. Hence, structural rigidity of the solder joint interconnects along with solder flow, wettability and its chemistry, are critical to longterm, reliable functioning of the device. The structural integrity of the solder joints is determined by mechanical properties of solders such as stress distribution, creep properties, and fatigue life. Solder properties are based on the metallurgical as well as mechanical properties of the bulk solder and

Numerical Prediction of Mechanical Properties of Pb-Sn Solder Alloys Containing Antimony, Bismuth and or Silver Ternary Trace Elements

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the interfacial intermetallics as shown in the flow chart (Fig. 1). REVIEW OF LITERATURE Ainsworth1 in 1971 and more recently, Plumbridge2 reviewed the mechanical properties of solders. Leadtin solders are extensively used for soldering applications of electronic packaging because of their low melting point below 300°C and low freezing range on the order of 10°C. The presence of lead decreases the melting point of the solder. However when Pb-Sn solder alloy melts, both the constituents contribute to wetting by lowering the surface energy of the molten metal and thereby react to the surface of metallization. The wetting helps to spread the solder and penetration of liquid solder into the capillary spaces of the joint assembly.1,3 Since the solder serves to bond the substrates together, its mechanical strength and related properties such as tensile, compression, shear, creep, and fatigue are of vital importance. The resistance of solder to fatigue deformation, monotonic tensile and creep strength to resist overload stresses, creep strength under sustained loads are necessary for both structural and electronic packaging applications.4 Kawashima et al.5 performed uni-axial tension tests on Sn-Pb eutectic at constant temperatures under nominal strain rates of 7E-03 to 7.E-05 to establish Arrhenius type of functional relationships for stressstrain. The microstructural instability arising due to differential strain rate test of the super plastic region were experimentally evaluated from stress-strain rate data of differential strain rate tests of Pb-Sn eutectic alloy over 25–170°C (298 K to 443 K) by Kashyap and Murty.6 Many others have reported work on fatigue strength, creep resistance and thermal cycling tests on solders.1–5,7–11 Fatigue damage is usually the result of stress concentrations caused by dislocation pileups due to inelastic to-and-fro slip motion of lattice defects and due to sliding between the grains at the boundary.7 The experimental work of Grossman8 on shear stress-strain deformation of recrystallized Sn62Pb36Ag2 wt.% solder, has distinctly shown two different deformation mechanisms involving grain boundary sliding and dislocation climb. The effect of cooling rate on the interfacial fatigue crack growth in Sn-Pb solder has been experimentally investigated by Yao and Shang.9 However, solder fatigue life is difficult to predict under thermal cycling because of the time-temperature transient complexity of creep process. Creep strain is probably the most important time-dependent damage accrual factor affecting solder joint reliability. Under continuous loading conditions, creep is a complex function of solder metallurgical structure, temperature, loading time per cycle, applied stress and the spring constant of combined part/lead/board system.10 The effect of cooling rate and shear stress on the steady state shear strain rate of Sn-40Pb solder due to grain boundary diffusion at constant temperature, 65°C has been experimentally investigated by Mei et al.11 In the present work, most of the above extensive experimental data have been

Fig. 1. Flow chart for the mechanical properties of the solder.

utilized to numerically modeling stress-strain rate of tension, fatigue and creep as influenced by temperature and or cooling rates based on either Arrhenius type of constitutive equations. The numerical models on tensile, fatigue and creep have been used to evaluate the effect of alloying the trace elements like antimony or bismuth or silver on mechanical properties of Sn-Pb solder. NUMERICAL RESULTS AND ANALYSIS Metallurgical Properties The metallurgical properties such as dissolution, diffusion of metallization and growth of intermetallic compound (IMC) and wetting metallization and their properties affect the mechanical strength and bulk properties of solders in general. An attempt to model the isothermal process kinetics has been made to understand the dissolution and growth process under a single roof of reflow profile. Dissolution and Growth of Intermetallics by Isothermal Process Kinetics Metallurgical properties involve the process kinetics such as dissolution of solutes during metallization, growth of intermetallic compounds and their reaction rates and diffusion mechanism shown in flow chart (Fig. 1). The dissolution kinetics often involves metallization layers of Ag, Au, Cu, Cr, Ni, etc. which most commonly follow a parabolic relation between amount or thickness of dissolution and duration of time. After completion of dissolution process, solidification starts with growth of intermetallics—Cu3Sn, Cu6Sn5, Ni3Sn4, etc. The dissolution and growth mechanism, by and large obey parabolic growth kinetics which are represented by an exponential Arrhenius equation: x = k(τ)n

(1)

where x = thickness, n = exponent, k = growth parameter, and τ = time. Consider a typical reflow profile, which consists of uniform heating rate during an infrared (IR) preheating cycle and a cooling rate during reflow cycle. At this stage, a simplistic approach to study an isothermal

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growth process and its equivalent time (ti), based on work of Schaefer et al.,12 has been extended for the kinetics of dissolution as well as growth of intermetallic.13 This involves subdivision of the reflow profile into equal time intervals. The dissolution and growth processes are then treated as isothermal reactions during each time interval. An average temperature (Tavg) is then calculated for ith interval as a mean of Ti and Ti–1. Reaction kinetics is then given by an Arrhenius equation:  Q  Ci = Co ⋅ exp −   R ⋅ T

(2)

where kinetic coefficient, Ci = k for dissolution kinetics, and Cj = D, diffusivity for a growth kinetics. In order to predict thickness of dissolution or growth of a layer in the isothermal process, a given time interval is then discretized into an equivalent time interval which is given by: tei = (xI–1/Ci)1/N + ∆∆t /2

(3)

where N- new combined exponent = n for dissolution or m for growth. Now, using the concept of equivalent time interval, one can also determine average rate of a reaction for either dissolution or growth kinetics, by Eq. 4: Vavg = dx/dt = N Ci [(x

/Ci )1/N + ∆t /2 ] N–1

i–1

(4)

where N = n or m and Ci = k or D for dissolution or growth kinetics, respectively. One can then calculate the decrease in thickness due to dissolution of metallization and or increase in thickness during growth process by using the following equation: ∆x i–1 = N Ci [(x i–1/Ci )1/N + ∆t /2]N–1 · ∆t

(5)

This can then be either subtracted or added based on the process kinetics involving dissolution or growth respectively. Hence, final thickness at the end of reaction kinetics is represented by ∆x = Xi–1 ± ∆xi–1 (where ∆x is negative for dissolution and positive for growth). The parameters Ci (k or D), exponent N (n or m) are kinetic growth constants which are determined from a series of isothermal experiments. Mechanical Strength of Solder The tensile properties as a function of strain rate and reflow temperature have been numerically determined without alloying as well as alloying with antimony (Sb), bismuth (Bi), and or silver (Ag) for Pb-Sn solder (Figs. 2–5). The effect of solder composition of Pb-Sn binary alloy and the impact of its alloying with Sb, Bi, or Ag on tensile, fatigue, and creep properties is discussed in subsequent sections. Tensile Pb-Sn Solder Many electric and electronic units are mounted in automobiles. Solders are an indispensable means of connecting electronic devices with PCBs. Compared to the indoor electric or electronic appliances, solders joints mounted on automobile are subjected to more

Fig. 2. Numerical prediction of the stress of solder as affected by strain rate sensitivity and temperature for Pb-Sn alloys.

severe temperatures ranging from –30 ~ 140°C. To ensure functionality of the electronic devices inside automobiles, long term reliability of solder joints is required. In order to analyze the stress-strain distribution in the solder joints subjected to mechanical or thermal loading, stress-strain data at various loading conditions and elevated temperatures must be clearly mapped. The experimental tensile test data of Pb-Sn solder by Kawashima et al.5 are numerically simulated. The elevated temperature tensile properties of solder are numerically evaluated. Since solder is expected to exhibit a highly visco-plastic behavior, its stress-strain curve depends on strain rate and temperature. The experimental results of uni-axial tension tests of SnPb eutectic alloy at constant temperatures 25°C, 100°C, 140°C, and 170°C, under nominal strain rate sensitivity, 7E-5, 1.8E-3, and 7.0E-3/s have been numerically simulated. A gradual degradation of strength occurs nearly by 50% from ambient to elevated temperature application at a given strain rate (Fig. 2). For a given range of strain rate, the tensile strength is numerically expressed by Eq. 6: σ = Aε–1/N

(6)

Where coefficients A and N depend on temperature and are given by the expressions:5 N = 0.512 exp(900/T)

(7)

A = 242 exp(356/T)

(8)

At a given temperature, the higher strain rate gives rise to higher strengths in the stress-strain curves. The tensile strength obtained at a nominal strain gradually decreased due to diffuse necking.5 The stress-strain curves of strain rate, 7.0E-4/s obtained by numerical method for eutectic alloy are in close agreement with the experimental results of Kawashima et al.5 and Satoh.14 The tensile strength expressed by the power law in Eq. 6 gives reasonably good estimation of the depen-


Fig. 3. Effect of antimony addition to Pb-Sn eutectic alloy composition on mechanical properties of the solder.

dence of tensile stress on strain rate sensitivity and temperature effects. A perfectly elasto-plastic model can be applied to simulate the stress-strain curves as a function of strain rate sensitivity and temperature, for a magnitude of allowable strain for practical solder joints. Fatigue Pb-Sn/Cu Solder In isothermal fatigue increasing strain range decreases fatigue life. At low temperature (< 0.3 times the absolute melting point, Tm), low cycle fatigue data of many metals may follow the Coffin-Manson relationship3,15 Nfβ · εp = Constant (β = 0.37–0.5 at 25~150°C at 0.3 Hz in shear test). Von Mises Equivalent strain (εv) can be used to correlate fatigue data obtained from tensile fatigue with that obtained from shear fatigue test by equivalent Von Mises Strain (εv ):

γ = 1.7321*εv

(9)

Since tensile strain is equivalent of Von Mises strain (εv ≡ εt), tensile strain can be estimated from shear strain. Isothermal fatigue tests on Sn–40%Pb solder over a temperature range of –25~125°C have yielded, a relation between number of cycles to failure, Nf and ∆γ−plastic strain range: 3,4,7,15  1.14  Nf =    ∆γ p 

1.96

(10)

and the plastic strain range, ∆γ p =

(α 1 − α 2 )∆T ⋅ L t

(11)

where αi = CTE of two substrates 1 and 2, ∆T = temperature difference, L = joint length, t = thickness. Most commonly occurring failure are due to thermal fatigue of the solder joints, affecting the reliability and durability of microelectronic device. The failures may involve development of fatigue cracks and/ or progressive growth of incipient flaws.8 The signifi-

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cance of interfacial failures has been attributed to the thermal fatigue of Sn-Pb solder joints in IC chips, where joints break at the interface between the solder and substrate. It has become apparent that life span of a solder joint in service is largely controlled by formation and propagation of interfacial cracks. The cooling rates used in the numerical model are 100°C/s for water quenching, 1°C/s for air cooling and 0.01°C/s for furnace cooling. The interface between solder alloy and Cu contained an intermetallic layer made of Cu6Sn5 (η-phase) with single crystal structure. This type of cell-like intermetallic phase created a wavy interface pattern between solder and the intermetallic phase. The roughness of the interface was found to increase with the cooling rate. At times hollow intermetallic hexagonal rod-like whiskers formed by screw dislocation when solder reacted with Cu. The IMC rods had no effect on the bulk tensile properties but decreased ductility and initiated failures at the interface of intermetallic, having an average fracture toughness 5 MPa-√m.16–18 Fatigue Crack Growth Model: Fatigue-crack growth behavior in the Sn-Pb/Cu joints for different cooling rate is numerically evaluated and shown in Fig. 3 as a function of cooling rate and strain energy release rate, ∆G, in terms of growth-rate per cycle, da/dN. Fatigue crack growth rate can be expressed as a power-law function of strain energy release rate: da = C ⋅ (∆G)m dN

(12)

At low strain energy release rates, the fatigue crack growth rate decreases rapidly with strain energy release rate to approach a fatigue threshold, ∆Gth crack growth rate. For the numerical study of fatigue crack growth rate affected by cooling rate (Fig. 3), the experimental conditions of Daping Yao and Jian Shang9 were used. The cooling rate used for water quenching was 100°C/s and nearly 1/100th of the quenching rates (~1°C/s) were used for cooling by normalizing. The cooling rates of 1/100th of the normalizing rates (~0.01°C/s) were used for the annealing rates. The fatigue growth parameters determined experimentally from their work9 were used for numerical prediction of fatigue crack growth using Eq. 12. A comparison of the fatigue crack growth rates for the three cooling indicates that the rate of cooling has a profound effect on the strain energy release rate. Fatigue crack growth at rates higher than 10–4 mm/cycle, the curve turns upward and moves into unstable fast fracture as the strain energy release rate approaches the fracture resistance of the interface.9 Increasing the cooling rate from furnace cooling to water quenching enhanced the fatigue resistance to interfacial crack growth by up to 50% at low strain energy release rate. However, at high strain energy release rate fatigue crack resistance was affected by 100%. The increasing cooling rates have enhanced the fatigue crack growth resistance. The increased resistance to fatigue crack growth is attributed to

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grain refinement at the interface of solder joint18 and surface roughness effects.19 Alloying with Antimony or Bismuth and or Silver Algorithms have been developed to study the mechanical strength of solders and to numerically predict the tensile strength as a function of solder composition and the strain rate. Solder composition has a direct bearing on the tensile properties of the solder. Tensile properties are also sensitive to the rate of testing. In this paper, experimental data have been compiled from various sources1,2,4,5 from the available literature are used to assess the mechanical properties of solders from the numerical point of their analysis. The addition of antimony as a ternary trace element in Pb-Sn alloy promotes the room temperature aging and imparts better mechanical properties— tensile and creep strengths as well as ductility and fracture toughness.4 The mechanical properties of antimony addition to Sn-Pb solder alloy are illustrated in Fig. 4. Antimony addition by 2 wt.% to 4 wt.% increases tensile as well as shear strength of lead-tin alloy. However, Izod impact strength is not significantly altered by antimony additions. The percentage elongation, an index of ductility increases up to approximately 2.5%, and then drops with additional antimony. The creep resistance of the Pb-Sn alloy increases linearly with addition of antimony. Tinantimony solders also exhibit excellent monotonic and creep strength for applications involving high structural load and elevated temperature service. This clearly depicts dependence of the bulk mechanical properties on the micro-mechanical properties such as microstructure and micro-hardness. McCormack et al.20 developed lower melting point Sn-Pb alloy solder by adding ternary traces of Bismuth up to 8 wt.%. The composition of Sn-42Pb-8Bi melts 10°C lower than the eutectic Sn-37Pb alloy and has a narrow range of melting less than 10°C with a liquidus of 175°C and solidus of 171°C. However, the alloy with additional 0.5% silver exhibits excellent paste reflow and fillet formation has a pasty range of 6°C. The presence of silver in quaternary alloy helps in the refinement of microstructure. This composition of Sn-41.75Pb-8Bi-0.5 Ag alloy has at least 25% higher tensile strength and ductility than eutectic Sn-Pb alloy. The improved mechanical properties are attributed to micro-mechanical properties involving refinement of microstructure resulting in increased micro-hardness. Numerical predictions of stress-strain data at various reflow temperature and strain rate, by analytical programs are based on the extensive experimental results from the literature for validation.8–18 This is useful to readily estimate the stress-strain distribution of eutectic Pb-Sn solder at a given strain rate for various reflow temperatures. Numerical analysis indicate the highest peak in tensile strength for a composition 62%Sn-36% Pb containing 2% ternary trace element of Ag at high strain (50 mm/s) as well as elevated temperature (100°C) in Fig. 5. The numerical programs have proved to be a versa-

Figure 4. Tensile strength of the solder varying with the composition, strain rate, and temperature for Pb-Sn alloys (containing 2–5% Ag).

Fig. 5. Fatigue crack growth rate as a function of cooling and strain energy release rate.

tile tool to assess strength of solder for various compositions from room to elevated temperature applications and low and high strain rates. The 36%Pb62%Sn–2%Ag, has high strength with a rare combination of high ductility, thereby imparting superplastic properties at low strain rate. However, lowest tensile strengths are observed for 10%Sn-90%Pb alloy at both the strain rates and temperatures. CONCLUSIONS Algorithms are developed to model the kinetics of dissolution and growth process for intermetallic compounds (IMC) by isothermal process kinetics. Isothermal process involves discretization of time into equal interval of time over which temperature is averaged between a minimum and maximum reflow temperature over a constant time interval. Algorithms are then used to study the mechanical strength of solders and assess the effect of alloying additions by numerical simulation. Numerical analysis is used to predict a peak tensile strength of a near-eutectic Pb-Sn alloy solder on alloying with 2% Ag, even at a high strain rate of 50 mm/s. Addition of silver (0.5 wt.%) in eutectic Pb-Sn alloy is said to improve reflow of the pasty alloy.


Numerical results indicate addition of antimony up to 2.5 wt.% in near eutectic Pb-Sn solder alloy increases the tensile strength, ductility, shear strength and fracture toughness and decreases thereafter. ACKNOWLEDGEMENTS The first author is grateful for research support by the Defense Advanced Research Project Agency (ARPA) and Dr. Susant Patra for providing an insight to work on the “Design Automation of Solder Joint Mixed Signal Modules” project of which this is an extension on the mechanical properties of the solders joints. The encouragement of Prof. Charles Tu, Chairman, ECE Dept. University of California, San Diego, in the completion of work is gratefully acknowledged. REFERENCES 1. C.J. Thwaites, W.B. Hampshire, Welding Res. Sup. 323 (1976). 2. W.J. Plumbridge, J. Mater. Sci. 31, 2501 (1996). 3. M. Ohring, Reliability and Failure of Electronic Materials and Devices (San Diego, CA: Academic Press, 1998). 4. P.T. Vianco, ASM Handbook (Materials Park, OH: ASM, pp. 964–984. 5. K. Kawashima, T. Ito, and M. Sakuragi, J. Mater Sci. 27,

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6387 (1992). 6. B.P. Kashyap and G.S. Murty, J. Mater. Sci. 18, 2063 (1983). 7. A. Dasgupta, C. Oyan, B. Barker, and M. Pecht, J. Electron. Pkg., ASME Trans. 114, 152 (1992). 8. G. Grossman, IEEE Trans. Comp., Pkg., Mfg., Technol. 22, 71 (1999). 9. D. Yao and J.K. Shang, IEEE Trans. Comp., Pkg., Mfg., Technol. Part-B 19, 154 (1996). 10. R.J. Ross, Jr., L.C. Wen, and G.R. Mon, J. Electron. Pkg., ASME Trans.115, 165 (1993). 11. Z. Mei, J.W. Morris, Jr., M.C. Shine, and T.S.E. Summers, J. Electron Mater. 20, 599 (1991). 12. M. Schaeffer, W. Laub, J.M. Sabee, and R.A. Fournelle, J. Electron. Mater. 25, 992 (1996). 13. S.P. Gadag and S.K. Patra, to be submitted. 14. R. Satoh, M. Ohshima, K. Arakawa, and K. Hirota, J. Jpn. Inst. Metals 49, 26 (1985). 15. S.T. Rao, ASM Handbook, vol. 19 (Materials Park, OH: ASM, pp. 883–891. 16. D. Frear, D. Grivas and J.W. Morris, J. Electron. Mater 16, 181 (1987). 17. D.R. Frear and P.T. Vianco, Metall. Mater. Trans. A 25, 1509 (1994). 18. D.R. Frear, JOM 48, 49 (1996). 19. R.C. McClung and J.C. Newman, Jr., editors, Advances in Fatigue Crack Closure Measurements and Analysis, ASTM STP 1343 (Philadelphia, PA: ASTM, 1999), p. 496. 20. M.T. McCormack, Y. Degani, H.S. Chen, and W.R. Gesick, JOM 48, 54 (1996).