Creep, stress relaxation, and plastic deformation in Sn-Ag and Sn-Zn eutectic solders

Because of the high homologous operation temperature of solders used in electronic devices, time and temperature dependent relaxation and creep processes affect their mechanical behavior. In this paper, two eutectic lead-free solders (96.5Sn-3.5Ag and 91Sn-9Zn) are investigated for their creep and stress relaxation behavior. The creep tests were done in load-control with initial stresses in the range of 10-22 MPa at two temperatures, 25 and 80°C. The stress relaxation tests were performed under constant-strain conditions with strains in the range of 0.3-2.4% and at 25 and 80°C. Since creep/relaxation processes are active even during monotonie tensile tests at ambient temperatures, stress-strain curves at different temperatures and strain rates provide insight into these processes. Activation energies obtained from the monotonic tensile, stress relaxation, and creep tests are compared and discussed in light of the governing mechanisms. These data along with creep exponents, strain rate sensitivities and damage mechanisms are useful for aiding the modeling of solder interconnects for reliability and lifetime prediction. Constitutive modeling for creep and stress relaxation behavior was done using a formulation based on unified creep plasticity theory which has been previously employed in the modeling of high temperature superalloys with satisfactory results.     

Temperature Dependence of Creep and Hardness of Sn-Ag-Cu Lead-Free Solder

The creep behavior and hardness of Sn-3.5Ag-0.7Cu solder were studied using Berkovich depth-sensing indentation at temperatures of 25°C to 125°C. Assuming a power-law relationship between the creep strain rate and stress, an activation energy of 40 kJ/mol and stress exponents of 7.4, 5.5, and 3.7 at 25°C, 75°C, and 125°C, respectively, were obtained. The results revealed that, with increasing temperature, the creep penetration and steady-state creep strain rate increased whereas the stress exponent decreased. The stress exponent and activation energy results also suggested that the creep mechanism is dislocation climb, assisted by diffusion through dislocation cores in Sn. Furthermore, the hardness results exhibited a decreasing trend with increasing temperature, which is attributed to softening at high temperature.     

Evaluation of the mechanical properties of a ternary Sn-20In-2.8Ag solder

The Sn-20In-2.8Ag solder alloy is a potential lead-free solder for replacing the traditional Sn-Pb solders. In this study, the mechanical properties of the bulk material are reported by tensile test at various strain rates and temperatures. The Sn-20In-2.8Ag solder possessed a solidus and liquidus between 170.8°C and 195.5°C. The ultimate tensile strength (UTS) and elongation were 59.3 MPa and 50.2% at a strain rate of 10⁻³ s⁻¹ at room temperature. Moreover, the UTS of this alloy decreased, but its elongation increased, with increasing testing temperature. Stress exponents of Sn-20In-2.8Ag alloy varied from 6.5 at room temperature to 4 at 100°C, and the activation energy for creep was 51.0 kJ/mol at the higher temperature range from 50°C to 100°C. The typical intergranular creep fracture mode was observed in Sn-20In-2.8Ag solder during tensile creep deformation.     

Effect of Homogenization on the Indentation Creep of Cast Lead-Free Sn-5%Sb Solder Alloy

Creep behavior of cast lead-free Sn-5%Sb solder in unhomogenized and homogenized conditions was investigated by long time Vickers indentation testing under a constant load of 15 N and at temperatures in the range 321–405 K. Based on the steady-state power law creep relationship, the stress exponents were found for both conditions of the material. The creep behavior in the unhomogenized condition can be divided into two stress regimes, with a change from the low-stress regime to the high-stress regime occurring around 11.7 × 10⁻⁴ < (H _V /E) < 18 × 10⁻⁴. The low stress regime activation energy of 54.2 kJ mol⁻¹, which is close to 61.2 kJ mol⁻¹ for dislocation pipe diffusion in the Sn, and stress exponents in the range 5.0–3.5 suggest that the operative creep mechanism is dislocation viscous glide. This behavior is in contrast to the high stress regime in which the average values of n = 11.5 and Q = 112.1 kJ mol⁻¹ imply that dislocation creep is the dominant deformation mechanism. Homogenization of the cast material resulted in a rather coarse recrystallized microstructure with stress exponents in the range 12.5–5.7 and activation energy of 64.0 kJ mol⁻¹ over the whole ranges of temperature and stress studied, which are indicative of a dislocation creep mechanism.     

Indentation Creep of Lead-Free Sn-5Sb Solder Alloy with 1.5 wt% Ag and Bi Additions

Creep behavior of the ternary Sn-5Sb-1.5Ag and Sn-5Sb-1.5Bi alloys was studied by indentation testing at 298 and 370 K, and compared to that of the binary Sn-5Sb base alloy. Among all tested materials, as indicated by their minimum creep rates, Sn-5Sb-1.5Bi showed the highest creep resistance followed by Sn-5Sb-1.5Ag and Sn-5Sb. The superiority of the Bi-containing alloy is mainly due to the microstructural refinement and solid solution hardening effects of Bi in the Sn matrix, while the improvement in the creep resistance of the Ag-containing alloy is caused by the formation of spherical and rod-shaped Ag₃Sn particles. The stress exponent values in the range 11.0–12.2 are close to those determined by tensile and impression creep testing of the same alloys reported in the literature. These high stress exponents together with the activation energies of 58–70 kJ/mol may suggest that the dominant creep mechanism is dislocation creep.     

A Method to Identify Steady Creep Strain from Indentation Creep Using a New Reference Area of Indentation

For the design of high-density electronic packages, finite element method (FEM) analyses to evaluate strength reliabilities of solder joints should be conducted by employing the material parameters which can precisely reflect the creep properties of solder joints in actual electronic equipment. To obtain accurate results of the structural analyses of the solder joints, a method to evaluate the steady-state creep deformation in situ must be developed. The indentation creep test is an effective method to evaluate the creep properties of the solder joints in situ; however, the creep properties obtained by this method do not give the same results as those obtained by tensile creep tests using bulk specimens. In this paper, the indentation creep test at 1 N loading for 9,000 s duration was experimentally conducted to confirm that the steady-state creep deformation obtained by the indentation creep test did not coincide with that by the tensile creep tests using bulk specimens. To identify the reason, the indentation creep simulation was conducted by FEM analysis. As a result, it was found that the reference area used to obtain the creep strain from the indentation creep test should be modified. A method to obtain the new reference area is proposed from comparisons of experiments with simulations. Finally, this paper shows that the creep properties obtained by the indentation creep test using the new reference area coincided with those obtained by tensile creep tests using bulk specimens.     

The constitutive creep equation for a eutectic Sn-Ag alloy using the modified theta-projection concept

Creep data for a eutectic tin-silver alloy at temperatures between 298 K and 398 K have been analyzed using the modified theta-projection concept, instead of the steady-state creep constitutive equation in the following formula: ɛ_cr=A {1−exp(−αt)}+B {exp(αt)−1}, where A, B, and α are constants to be experimentally determined. The equation describes well the creep curves of the eutectic tin-silver alloy up to the tertiary stage. All constants exhibited power law relationships with the applied stress. The rate constant, α, has a high stress exponent, which is attributed to dispersion strengthening. The rate constant a and the strain factor B only showed temperature dependence, while the strain factor A was independent of temperature. The activation energy for α was 65 kJ/mol at high stresses and 90 kJ/mol at low stresses. The energies suggest that the dislocation pipe diffusion and the lattice diffusion are predominant at high stresses and low stresses, respectively.     

Mechanisms of Creep Deformation in Pure Sn Solder Joints

The work reported here concerns the creep of pure Sn solder joints with Cu metallization (Cu||Sn||Cu). Steady-state creep tests in shear are combined with electron backscatter diffraction (EBSD) analysis of the evolution of the microstructure during creep to clarify the deformation mechanism and the nature of the microstructural evolution. The creep behavior of the joint changes significantly with temperature. At low temperature (65°C), two distinct creep mechanisms are observed. Low-stress creep is apparently dominated by grain boundary sliding, as evidenced by the low stress exponent (n ≈ 4), low activation energy (Q ≈ 42 kJ/mole), and significant grain rotation during creep. High-stress creep is dominated by bulk deformation processes, evidenced by a high stress exponent (n ≈ 9), an activation energy like that for bulk diffusion (Q ≈ 70 kJ/mole), and a relatively fixed microstructure. At high temperature all aspects of its behavior are consistent with deformation by bulk creep mechanisms; the stress exponent and activation energy are high (n ≈ 5 to 7, Q ≈ 96 kJ/mole), and despite significant grain coarsening, the microstructure retains (and strengthens) a fixed [001] texture. The results suggest that a “segmented” constitutive equation of Dorn type is most suitable for the low-temperature behavior, while a “hyperbolic” constitutive equation may be preferable at high temperature.     

Impression Creep Behavior of Zn-Sn High-Temperature Lead-Free Solders

This study examines the microstructure and impression creep behavior of the high-temperature Zn-20 wt.%Sn, Zn-30 wt.%Sn, and Zn-40 wt.%Sn solders under constant punch stress in the range of 25 MPa to 300 MPa and at temperatures in the range of 298 K to 425 K. Analysis of the data showed that, for all loads and temperatures, the Zn-20Sn alloy had the lowest creep rates, and thus the highest creep resistance, among all materials tested. This is attributed to the lower volume fraction of the soft Sn-rich phase with a continuous morphology which acts as the matrix encompassing the harder Zn phase. The stress exponents and activation energies were in the range of 4.0 to 6.1 and 40.0 kJ mol⁻¹ to 45.3 kJ mol⁻¹, respectively. Based on the obtained stress exponents and activation energy data, it is proposed that dislocation climb is the controlling creep mechanism. However, the observed decreasing trend of creep activation energy with stress suggests that two parallel mechanisms of lattice-diffusion-controlled and pipe-diffusion-controlled dislocation climb are competing. Dislocation climb controlled by dislocation pipe diffusion is the controlling mechanism at high stresses, whereas climb of edge dislocations is the controlling mechanism at low stresses.     

Room-temperature indentation creep of lead-free Sn-5%Sb solder alloy

Creep behavior of the lead-free Sn-5%Sb solder alloy was studied by long-time Vickers indentation testing at room temperature. Four different conditions of the material were examined. These were unhomogenized cast (UC), homogenized cast (HC), unhomogenized wrought (UW), and homogenized wrought (HW) conditions. Based on the steady-state power-law creep relationship, the stress exponents were determined through different methods of analysis, and in all cases, the calculated exponents were in good agreement. The stress exponent values of about 5 and 12, depending on the processing route of the material, are very close to those determined by room-temperature conventional creep testing of the same material reported in the literature. For the HW condition, the n value of about 5 together with a very fine grain size of 4.5 μm and a high volume fraction of second-phase particles of 8.6% may suggest that dislocation climb is the creep mechanism. For all other conditions with different grain sizes and second-phase volume fractions, however, the high n value of 12 implies that the operative creep mechanism is dislocation creep, which is independent of grain size.     

The correlation between stress relaxation and steady-state creep of eutectic Sn-Pb

This paper surveys and compares creep and stress relaxation data on finegrained eutectic Sn-Pb. It examines the consistency of the available data on this extensively studied solder material and studies whether stress relaxation offers a reasonable alternative to the more laborious conventional creep tests. The data survey reveals systematic differences between the creep behavior of material that is grain-refined by cold work and recrystallization (“recrystallized”) and that refined by rapid solidification (“quenched”). The recrystallized material has the conventional three regimes of creep behavior: a high-stress region with a stress exponent, n ∼ 4–7 and an activation energy Q ∼ 80 kJ/mole (a bit below that for self-diffusion of Pb and Sn), an intermediate region with n ∼ 2 and Q ∼ 45 kJ/mole (near that for grain boundary diffusion), and a low-stress region with n ∼ 3 and Q ∼ 80 (suggesting a reversion to a bulk mechanism). The quenched material shows only two regions: a high-stress creep with a stress exponent, n ∼ 3–7, and a low-stress region with n ∼ 3. The mechanisms in both regimes have activation energies intermediate between bulk and interface values (50–70 kJ/mole). With minor exceptions, the stress relaxation data and the creep data are in reasonable agreement. Most of the exceptions seem to be related to the difficulty of capturing the full details of grain boundary creep in stress relaxation tests.     

Creep behavior of the ternary 95.5Sn-3.9Ag-0.6Cu solder—Part I: As-cast condition

The compression creep behavior was studied for the ternary solder alloy 95.5Sn-3.9Ag-0.6Cu in the as-cast condition. Samples were tested under stresses of 2–45 MPa and temperatures of −25–160°C. There was a significant variability in the creep curve shape, strain magnitude, and steady-state strain-rate properties. A multivariable linear-regression analysis of the steady-state strain-rate data, using the sinh-law stress representation, indicated two mechanisms distinguished by low- and high-temperature regimes of −25–75°C and 75–160°C, respectively. The sinh-law stress exponent (n) and apparent-activation energy (ΔH) in the −25–75°C regime were 4.4 ± 0.7 kJ/mol and 25 ± 7 kJ/mol (63% confidence intervals), respectively. Those same parameters in the 75–160°C regime were 5.2±0.8 kJ/mol and 95±14 kJ/mol, respectively, for the high-temperature regime. The values of ΔH suggested a short-circuit diffusion mechanism at low temperatures and a lattice or bulk-diffusion mechanism at high temperatures. The stress dependency of the steady-state strain rate did not indicate a strong power-law breakdown behavior or a threshold stress phenomenon. Cracks and grain-boundary sliding were not observed in any of the samples. As the creep temperature increased, a coarsened particle boundary and particle depletion zone formed in the region of fine Ag₃Sn particles that existed between the Sn-rich phase areas. The coarsened particle boundary, as well as accelerated coarsening of Ag₃Sn particles, were direct consequences of the creep deformation process.     

Creep behavior of the ternary 95.5Sn-3.9Ag-0.6Cu solder: Part II—Aged condition

Compression creep tests were performed on the 95.5Sn-3.9Ag-0.6Cu (wt.%) solder. The specimens were aged prior to testing at 125°C, 24 h or 150°C, 24 h. Applied stresses were 2–40 MPa. Test temperatures were −25°C to 160°C. The 125°C, 24-h aging treatment caused the formation of coarsened Ag₃Sn particle boundaries within the larger ternary-eutectic regions. The 150°C, 24-h aging treatment resulted in contiguous Ag₃Sn boundaries in the ternary-eutectic regions as well as a general coarsening of Ag₃Sn particles. The 125°C, 24-h aging treatment had only a small effect on the strain-time curves vis-à-vis the as-cast condition. Negative creep was observed at 75°C for time periods >10⁵ sec and stresses of 3–10 MPa. The creep kinetics exhibited a sinh term (stress) exponent, p, of 5.3±0.6 and an apparent-activation energy, ΔH, of 49±5 kJ/mol when data from all test temperatures were included. A good data correlation was observed over the [−25–125°C] temperature regime. Steady-state creep kinetics exhibited a greater variability in the [125–160°C] regime because of the simultaneous coarsening of Ag₃Sn particles. The aging treatment of 150°C for 24 h resulted in a more consistent stress dependence and better reproducibility of the creep curves. Negative creep was observed in samples aged at 150°C for 24 h when tested at −25°C, 25°C, and 75°C. The values of p and ΔH were 4.9±0.3 kJ/mol and 6±5 kJ/mol, respectively. Only a slight improvement in the data correlation was observed when the analysis examined separated [−25−75°C] and [75–166°C] temperature regimes. Creep testing did not cause observable deformation in any of the sample microstructures.     

Microstructure and Creep Deformation of Sn-Ag-Cu-Bi/Cu Solder Joints

Sn-Ag-Cu solder is one of the candidate alternatives to Sn-Pb-based solders. In order to improve its performance, different materials have been added to Sn-Ag-Cu-based solders. Several studies on Sn-Ag-Cu-based solders with Bi additions have shown Sn-Ag-Cu-Bi to be a class of solders with good wetting behavior and good performance that show great promise for use in the electronics assembly and packaging industry. To investigate the mechanical reliability of the Sn-Ag-Cu-Bi solders further, single-lap shear creep characteristics have been studied in this work. Dog-bone-type solder joint specimens were formed using five types of solder alloys, Sn-3.0Ag-0.5Cu and Sn-3.0 Ag-0.5Cu-xBi (x = 1 wt.% to 4 wt.%) with Cu substrates, and creep tests were performed at temperatures of 120°C and 150°C under stresses of 5 MPa to 10 MPa. Results indicate that the rupture times for Sn-3.0Ag-0.5Cu-xBi solder joints up to 4 wt.% of Bi are longer than the rupture time for Sn-3.0Ag-0.5Cu. Stress exponents ranged from 3 to 7 for temperatures of 150°C and 120°C with stresses under 10 MPa. Microstructural analyses using scanning electron microscopy (SEM) were performed and related to the creep behavior of the solder joints.     

Partitioned viscoplastic-constitutive properties of the Pb-free Sn3.9Ag0.6Cu solder

The partitioned viscoplastic-constitutive properties of the Sn3.9Ag0.6Cu Pb-free alloy are presented and compared with baseline data from the eutectic Sn63Pb37 solder. Steady-state creep models are obtained from creep and monotonic tests at three different temperatures for both solders. Based on steady-state creep results and creep-test data, a transient creep model is developed for both Pb-free and Sb37Pb solders. A one-dimensional (1-D), incremental analytic model of the test setup is developed to simulate constant-load creep and monotonic and isothermal cyclic-mechanical tests performed over various temperatures and strain rates and stresses using a thermome-chanical-microscale (TMM) test system developed by the authors. By fitting simulation results to monotonic testing data, plastic models are also achieved. The comparison between the two solders shows that Sn3.9Ag0.6Cu has much better creep resistance than Sn37Pb at low and medium stresses. The obtained, partitioned viscoplastic-constitutive properties of the Sn3.9Ag0.6Cu Pb-free alloy can be used in commercial finite-element model software.     

Effects of cooling rate on mechanical properties of near-eutectic tin-lead solder joints

This paper reports the results of a study on the effect of the cooling rate during solidification on the shear creep and low cycle shear fatigue behavior of 60 Sn/40 Pb solder joints, and on bulk solder tensile properties. Solder joints were made with three different initial microstructures by quenching, air-cooling and furnace-cooling. They have similar steady-state strain rates under creep at relatively high shear stresses (i.e. in the matrix creep region) but creep at quite different strain rates at lower shear stresses (i.e. in the grain boundary creep region). These results are ascribed to the refined grain size and less lamellar phase morphology that results on increasing the cooling rate. Tensile tests on bulk solders that were cold-worked, quenched and furnace-cooled show that a faster cooling rate decreases the ultimate strength and increases the ductility at low strain rates. The fatigue life of quenched solder joints is shown to be longer than that of the furnace-cooled joints.     

Creep properties of Sn-8Mass%Zn-3Mass%Bi lead-free alloy

The creep properties of Sn-8mass%Zn-3mass%Bi were investigated and compared with those of other lead-free solders and a Sn-Pb eutectic solder. The creep rupture time decreases with increasing the initial stress and the temperature. For high stresses, the linear relationships between the minimum strain rate and the applied stress were observed. The stress exponents were examined to be 9.3, 7, and 4 at 298 K, 348 K, and 398 K, respectively. For low stresses, the minimum creep rate becomes relatively fast, and the creep resistance diminishes. In this range, secondary creep reduces, and the tertiary creep predominates. The creep properties of Sn-8Zn-3Bi are similar to those of Sn-Ag alloys at high stresses and those of Sn-0.5Cu at low stresses.     

The short and long term properties of a liquid crystalline polymer at elevated temperatures: Characterization and modeling

Tensile and short term (24 h) creep tests were performed on Xydar G930, a liquid crystalline polymer (LCP) with 30 wt.% glass filler, at temperatures and stress levels ranging from room temperature to 175°C and 0.3 fraction ultimate tensile strength (UTS) to 0.8 fraction UTS, respectively. Temperature was found to have an affect on the short term tensile properties. The resulting strain vs time creep curves showed the expected dependence of creep strain on temperature and stress level. Creep compliance curves were derived from the creep curves and showed distinctively nonlinear viscoelastic behavior at all stress levels and temperatures. Creep compliance was found to follow a power law in time. The power law was used to model the stress dependence of creep and the Arrhenius equation was employed to model the temperature dependence up to 120°C. A significant reduction in creep resistance was observed at 175°C. Time-temperature-stress-superposition was used to show that the material followed power law behavior up to 1000 h.     

Impression Creep of a Lead-Free Sn-1.7Sb-1.5Ag Solder Reinforced by Submicron-Size Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Particles

In the present study, the Sn-1.7Sb-1.5Ag solder alloy and the same material reinforced with 5 vol.% of 0.3-μm Al₂O₃ particles were synthesized using the powder metallurgy route of blending, compaction, sintering, and extrusion. The impression creep behavior of both monolithic and composite solders was studied under a constant punching stress in the range of 20 MPa to 110 MPa, at temperatures in the range of 320 K to 430 K. The creep resistance of the composite solder was higher than that of the monolithic alloy at all applied stresses and temperatures, as indicated by their corresponding minimum creep rates. This was attributed to the dispersive distribution of the submicron-sized Al₂O₃ particles in the composite solder. Assuming a power-law relationship between the impression stress and velocity, average stress exponents of 5.3 to 5.6 and 5.8 to 5.9 were obtained for the monolithic and composite materials, respectively. Analysis of the data showed that, for all loads and temperatures, the activation energy for both materials was almost stress independent, with average values of 44.0 kJ mol⁻¹ and 41.6 kJ mol⁻¹ for the monolithic and composite solders, respectively. These activation energies are close to the value of 46 kJ mol⁻¹ for dislocation climb, assisted by vacancy diffusion through dislocation cores in the Sn. This, together with the stress exponents of about 5 to 5.9, suggests that the operative creep mechanism is dislocation viscous glide controlled by dislocation pipe diffusion.     

Impression creep characterization of 90Pb-10Sn microelectronic solder balls at subsolvus and supersolvus temperatures

The creep behavior of Pb-10wt.%Sn, a common high-lead solder used in microelectronic packaging, was studied by impression creep testing of ball-gridarray (BGA) solder balls attached to an organic substrate, both above and below the solvus temperature (408 K). Below the solvus temperature, the solder microstructure consists of roughly equiaxed grains of the Pb-rich solid solution α, which contains <5wt.%Sn in solution, with a coarse dispersion of Sn-rich β precipitates. Here, the creep behavior of the solder is controlled by dislocation climb via dislocation core diffusion, yielding n≈4 and Q≈60 kJ/mole. Above the solvus temperature, where the entire 10wt.%Sn is in solution, the creep mechanism becomes controlled by viscous glide of dislocations, limited by solute drag, with n≈3 and Q≈92 kJ/mole. Based on experimental data, creep equations for the as-reflowed solder in the two temperature regimes are given. Comparison of the present data with those available in the literature showed good agreement with the proposed laws.