Numerical prediction of mechanical properties of Pb-Sn solder alloys containing antimony, bismuth and or silver ternary trace elements

Numerical prediction of mechanical properties of Pb-Sn solder alloys containing antimony, bismuth and or silver ternary trace elements

Gadag, Shiva P

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


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 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 j oints 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 the interfacial intermetallics as shown in the flow chart (Fig. 1).


Ainsworth’ 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 deg C and low freezing range on the order of 10 deg 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 ofthe 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 TE-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 deg 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.’ The experimental work of Grossman$ 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 deg C has been experimentally investigated by Mei et al.11 In the present work, most of the above extensive experimental data have been 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.


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

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 severe temperatures ranging from -30 – 140 deg 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 Sn– Pb eutectic alloy at constant temperatures 25 deg C, 100 deg C, 140 deg C, and 170 deg C, under nominal strain rate sensitivity, 7E-5, 1.8E-3, and 7.OE-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).

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.’ The stress-strain curves of strain rate, 7.OE-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 dependence 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

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.” The significance 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 deg C/s for water quenching, 1 deg C/s for air cooling and 0.01 deg C/s for furnace cooling. The interface between solder alloy and Cu contained an intermetallic layer made of Cu,Sn, (I-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-/

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 sources,1,2,4,5 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 deg C lower than the eutectic Sn-37Pb alloy and has a narrow range of melting less than 100C with a liquidus of 1750C and solidus of 1710C. However, the alloy with additional 0.5% silver exhibits excellent paste reflow and fillet formation has a pasty range of 6C. The presence of silver in quaternary alloy helps in the refinement of microstructure. This composition of Sn-41.75Pb-Oi-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.8-111 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 deg C) in Fig. 5.

The numerical programs have proved to be a versatile 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.


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.


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.


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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

(Received July 28, 2000; accepted September 11, 2000)

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