Chapter Thirteen

Fatigue damage in microelectronic packages

H. Lu & R. Das Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada

Abstract

This chapter aims to present some background on electronic-package configuration (structure and material) and packaging mechanics, followed by a brief introduction to a computer vision technique measuring the solder-joint deformation. With a summary of recent research on the solder-joint creep and fatigue, the emphasis of the chapter is placed on presenting ongoing research for a new, experimental physics-based methodology for solder-creep fatigue analysis. The common view is that a reliability study for a package should focus on critical areas in the solder interconnects where fatigue failures are deemed to initiate from. Such a study usually has two important aspects. The first is obtaining high-resolution strain measurements in the identified failure-prone local areas at different stages of a thermal cycle. And the second is analyzing the measured deformation for life prediction based on certain well-established criteria of solder failure. In addition to the practical usage of the new methodology, applications of it are expected to contribute to clarifying issues of controversies in the current, conventional-procedure-based reliability assessment.

1 Introduction

Interconnect fatigue due to thermal stress is a common cause of failure for microelectronics and thus a key concern of the packaging reliability. For decades, the design, manufacturing, research and development of the microelectronic packages have been driven by the product renovation and miniaturization. Such a trend is dictated by the continued growth in interconnect density, per package pin-count and footprint, and the enhanced package power consumption as well as the hostile operating conditions. The conventional “build and test” type approaches for design evaluation and reliability assessment can barely meet the challenges, thus necessitating the research for physics-based, innovative, cost- and time-effective methodologies.

WIT Transactions on State of the Art in Science and Engineering, Vol 1, © 2005 WIT Press www.witpress.com, ISSN 1755-8336 (on-line) doi:10.2495/1-85312-836-8/13 436 Advances in Fatigue, Fracture and Damage Assessment

Solder interconnects in a microelectronic package serve as both the electrical connection and the mechanical bond between the components and the carriers. The surface-mount manufacturing technology requires the bumped solder balls on a package substrate be subjected to the solder-reflow process to form solder joints. During the package’s operation, the power on-and-off cycles and the fluctuation in external environment further subject the package to variations of temperature and other environmental parameters. The thermal fatigue of the solder joints due to cyclic deformation is considered as one of the main root causes of the physical disconnect of the joints. The situation gets worse where the CTE (thermal expansion coefficient) of materials on both sides of the solder joints highly mismatch [1]. A typical ceramic power package, as an example, is composed of a ceramic chip with a CTE around 6 ppm/°C and an epoxy-glass chip carrier (i.e., a printed circuit board) of 16 ppm/°C. For such a package, a temperature rise of 100 oC can induce a solder-joint shear deformation with a magnitude of a few per cent.

The ultimate purpose of the reliability study for an electronic package is to predict the “life” span, or the time period for the package to deliver reliable service. In practical terms, the end result of an evaluation is simply a number that represents the thermal cycles to failure for the weakest joint of that package. To realize that, the industry commonly adopts the thermal cycle testing to reach a kind of estimate. The testing is “accelerated” for time efficiency, which means that both the amplitude and frequency of the thermal cycling are enhanced to cause the solder joint to fatigue damage and fracture in a short time period. To correlate the test results with the real package life, however, is a much more complex issue that has been under intensive study in the past. It is noted that while creep fatigue of ordinary metals and alloys usually occurs under elevated temperature [2], solders exhibit time-dependent behaviour even at below the room temperature thanks to their low melting points. The time dependency of solder properties poses challenges to accurately characterize the material parameters as well as to design the accelerated cycle testing and to determine the factor of acceleration for interpreting the test data. Besides, the “acceleration” can create failure modes far different from what actually occurs under service conditions. This situation has been the driving force behind the research for new reliability- assessment methodologies. Ideally, they should be based on testing real packages under real service or processing conditions.

Part A: Basics in electronic packaging

2 Soldering in electronic packaging

The electronic packaging is “the technology of packaging electronic equipment” [3]. The soldering is a process by which two metals or alloys are joined together with a third metal, usually a solder alloy with lower melting point [4]. The soldering process involves both chemical and physical reactions and results in a metallurgical rather than a mechanical contact with the joining materials.

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Soldering ensures the electrical contact at a joint only if the joint possesses sufficient mechanical strength. The reliability of the solder joints depends upon the manufacturing process and the operating conditions the package is subjected to. The former affects mainly the joint formation such as the shape, microstructure, voids and other defects, and the latter induces the joint stress and deformation.

3 Level of electronic packaging

The electronic packaging is usually divided into several levels, such as the component level (Level 1), module level (Level 2) and chassis level (Level 3) [3,5], etc. The component-level packaging requires technologies for attaching and interconnecting silicon microcircuits to the next-level packaging, and also for protecting the microcircuits from possible attacks from the environment. The structure and material configuration of the component-level package is determined depending upon whether the hermetic (ceramic) or the non-hermetic (plastic) packaging technology is used. In a hermetic package the silicon die is bonded to the cavity of a ceramic package, which is sealed by a lid with the thermal-expansion rate closely matching the package. Fine wires are used to interconnect the metal pads on the silicon die to the leads. As illustrated in Fig. 1 for a leadless chip carrier, the interconnection to the PCB (printed circuit board) is realized via soldering the leads to the metalized area outside the package. For a non-hermetic configuration, the silicon die is bonded to a heat spreader that is typically a part of a leadframe. Interconnection is made either

Figure 1: Hermetic and non-hermetic packaging configuration [3].

438 Advances in Fatigue, Fracture and Damage Assessment with thin wires between the die pads and the leads or directly between the leads and pads. Once interconnection is made, the entire assembly is encapsulated in epoxy to provide the protection from the environment.

Module-level packaging interconnects components to the next-level packaging. Specifics of the module-level packaging configuration vary depending on whether the through-hole technology or the SMT (surface-mount technology) is used. A through-hole technology module typically uses dual-inline-package (DIP) packaging for interconnecting the microcircuits. The leads on these components are soldered into the holes in a PCB to interconnect with other components and the chassis. Where thermal performance is addressed, a heat sink may be attached to the PCB directly underneath the component. SMT, on the other hand, solders the components directly to the pads on the surface of a PCB. The SMT components are usually smaller in size than the DIP parts and can be mounted on both sides of the module to result in increased packaging density. Since no leads are necessary for interconnecting with the PCB, the components may be mounted on the back surface of the module to increase the usage of real estate. Bonding a heat sink to the PCB can enhance the heat dispersion to improve thermal performance of a SMT module. In some cases additional plated through holes (PTH) are used for better thermal conduction between the component and heat sink.

Chassis-level packaging usually includes support rails to which the modules are mounted and a motherboard with connectors, which provides the necessary electrical interconnection to other modules and the main-chassis connectors. The modules may be mounted to the chassis by spring-loaded clips and mechanically actuated clamps and bolts, etc.

4 Electronics-packaging configurations

The package architectures developed in the past decades are usually classified into these major configurations [3,5]:

• Ball-grid arrays (BGA) • Multi-chip modules (MCM) • Flip-chips • Chip-on-board (COB) • Chip-scale package (CSP)

A BGA package, as the schematic in Fig. 2 shows, is characterized by the arrays of solder balls bumped onto the bottom of the package. BGA technology allows controlled height of the solder joints to be realized during the soldering process. Underfill material can be applied to fill between the package and the PCB for improving the thermal performance and mechanical durability of the solder joints.

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A MCM package may be simply defined as one containing more than one chip. As shown in Fig. 3 the technology realizes incorporation of multiple chips in a single package, effectively increasing the packaging density.

In a conventional ball grid array, the rear surface of the die is bonded to a substrate and the latter is further interconnected to the PWB via solder joints. A flip-chip configuration is shown in Fig. 4. The component die is mounted with the active surface facing the PWB and it is interconnected to the PWB directly via beam leads or solder bumps, without a substrate. By providing a true chip- scale configuration, the flip-chip technology better meets the requirement of high-speed electrical-signal transfer.

Top view

Bottom view Solder Ball

Figure 2: A photograph and a schematic of a ball grid array component.

Molding compound

Wire Chip Board A Chip B

Solder Ball

Figure 3: A multi-chip module package.

Underfill Encapsulant Silicon Die

PCB Conducive Bump

Figure 4: A flip-chip assembly.

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The chip-on-board (COB) technology mounts the silicon die directly to the PCB either by using die-attaching adhesive or wire bonding, or via the flip-chip technology. In some cases an encapsulant is applied to cover the chip and the interconnection for protecting the die from environmental attack.

The CSP technology is becoming increasingly popular and the new designs of CSP packages are used in devices from mobile phones, PC cards, telecommunication systems, flash memories, microprocessors to various military applications. The main advantage of a CSP (see Fig. 5) over a BGA package is its smaller package real estate, which is usually below 1.2 times the size of the silicon die.

Figure 5: A cross-sectional view of a chip-scale package.

5 Materials for soldering

The solder is used in the form of paste containing small particles of solder powder mixed with a flux. The solder paste in appropriate volume, shape and position is printed to the pads on the chip carrier through a dispenser. The primary functions of the paste are to hold the components in place prior to solder reflow and to provide the flux for cleaning the pad during the reflow. The solder powder is made of small spherical or irregular-shaped solder clumps. The flux contains inert solids, activators, viscosity modifiers and other substances. The inert solids serve to provide a solution to dissolve the activators and to act as an oxygen barrier to minimize the oxidation of the solder joint during the reflow process. The activators serve as cleaning agents to remove pad oxidation. The viscosity modifiers are used to adjust the paste-viscosity characteristics.

5.1 Component placement and reflow for assembly

Following the solder-paste printing, the component placement and reflow process take place. The components pre-bumped with solder balls are placed in such a way that the positions of the solder balls match precisely the pads on the PWB. During the reflow-soldering process, the solder balls and the paste undergo a temperature cycle. The solder balls melt, re-solidify and cool down to finally form the joints between the component and the chip carrier. A reflow thermal cycle typically constitutes of four stages as illustrated in Fig. 6. The first

Advances in Fatigue, Fracture and Damage Assessment 441 is the preheat section during which the temperature ramps up; the second is the stabilization section during which the temperature is held constant; the reflow section that follows ramps the temperature up to that exceeding the solder melting point; and the final section is the cool-down section that brings the assembled unit back to room temperature.

Temp

Reflow temperature ramp 220oC

Stabilization o 150 C Cool down

Pre heating o o 2 C/min – 2.5 C/min

Time (in minutes, depends on the process)

Figure 6: A typical temperature versus time curve for reflow soldering.

During the first stage, the PWB is heated up to the flux-activation temperature (130˚C to 150˚C) following a pre-determined ramp rate. The actual ramp rate ranges widely. An overly fast ramp risks ceramic-component cracking, whereas too slow a ramp prolongs the production. The stabilization temperature ranges between 140 and 160˚C. This stage prepares the PCB for solder reflow and allows necessary time for the activated flux to clean the pads and for the trapped volatiles to evaporate. The third stage of reflow ramp-up quickly raises the temperature of the assembly to above the solder melting temperature. The maximum reflow temperatures for the assembly ranges between 200 and 220˚C depending on the component materials. Using a reflow temperature over 250˚C could risk component damage and the degradation of the PCB . During the final cool-down stage, the temperature of the assembly is quickly lowered to below the solder melting point to minimize the oxidation of the joints and to result in a fine solder crystalline structure. An assembly emerging from the reflow oven with under-solidified solder may jeopardize the joint integrity. There are five major reflow-heating techniques including inert atmosphere soldering, vapor- phase reflow, infrared reflow and natural-convection reflow, of which the most common one is the forced-air convection reflow. The forced-air convection yields an increased rate of heat transfer to the board and disperses the heat more evenly across the assembly.

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5.2 Inter-metallic layer in a solder joint

A solder joint must form on the inter-metallic layers between the pure solder and the base metal, as shown in Fig. 7. A solder joint simply solidified over the base metal usually ends up with no metallurgical contact with the metal, weakening the bonding strength [6]. However, an inter-metallic layer contains a number of brittle compounds of the solder and base metal, adversely affecting the integrity of the joint and posing additional challenges to the joint strength. Failure analysis on cracked joints due to mechanical or thermal loads indicates that the cracks usually initiate from the inter-metallic layers.

Figure 7: Inter-metallic layer between solder and base metal.

5.3 Tin-lead solder

A special feature of the solder materials is their low melting temperatures (typically below 250 oC). The solders provide inexpensive, mass producible and generally reliable multi-material interconnections for microelectronic assemblies. The commonly used soft solders in SMT are the eutectic and near- eutectic alloys of tin and lead, such as 63Sn/37 Pb and 60Sn/40 Pb [6, 7]. The popularity of tin, lead and their alloys is due to their low melting temperatures and wide availability. Other types of solder alloys are developed for special needs such as those of tin/lead based in combination with other metals and lead- free ones. The eutectic PbSn solder melts at around 183oC. In typical applications, the solder-joint temperature ranges between 65 and 80 per cent of its melting temperature on the absolute temperature scale. Table 1 summarizes the various solder materials and their applications, and Table 2 lists the mechanical properties of the solders. Table 2 shows that the solder of 63% tin 37% lead has good tensile strength, shear strength, impact strength, and resistance to creep. The PbSn solder of this composition is called the eutectic solder, which has a single melting temperature. The eutectic solder virtually solidifies immediately upon removal of heat, going through no pasty stage. The good operational feature allows for predictable soldering and fast cycle times.

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Table 1: Solder materials for different application and their characteristics [6,7].

Solder Applications Characteristics

Low-temperature Deforms easily. Needs Bismuth soldering Aggressive fluxes. High-temperature Toxic. Good tensile Cadmium-silver applications strength Cadmium-zinc Soldering aluminium Toxic Low-temperature Indium Deforms easily soldering, wets glass Good high-temperature High-temperature properties, good fatigue Lead-silver applications strength. Medium or low flow properties Non-toxic. Good high- temperature properties. High-temperature and Better electrical Tin-antimony food-industry conductivity and applications strength than tin-lead solders. Good wetting. Improved mechanical properties over tin-lead solders. Can not be used Tin-antimony-lead General purpose with zinc due to brittle zinc-antimony inter- metallic compounds Good process General purpose, and the Tin-lead characteristics and the most widely used solders best understood solders. Used for soldering medical or high- Non-toxic but expensive. Tin-Silver precision instruments. Good high-temperature High-temperature properties. applications Tin-zinc Soldering aluminium Zinc-aluminium Soldering aluminium

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Table 2: Mechanical properties of tin -lead solder alloys [6, 7].

Tin Tensile Shear Elongation Elastic Izod Stress to (wt.%) strength strength (%) modulus impact produce (MPa) (MPa) (GPa) strength 0.01%/day (J) creep rate (kPa) 0 12 12 55 18.0 8.1 1700 5 28 14 45 18.5 9.5 1400 10 30 17 30 19.0 10.8 20 33 20 20 20.0 15.0 30 34 28 18 21.0 16.3 790 40 37 32 25 23.7 19.0 50 41 36 35 26.9 20.3 860 60 52 39 40 30.0 20.3 63 54 37 37 31.5 20.3 2300 70 54 36 30 35.0 19.0

5.4 Lead-free solder

The latest intensive research for Pb-free solders is driven by the international legislations regulating Pb use for environmental protection [8]. The transition from PbSn to Pb-free solder is deemed to be imminent though the effort to find proper replacements has been complicated by numerous interacting factors that have to be considered. Among these are the solder and solder-paste composition, the flux and the surface finishes of the PCB and the components, etc. No single alloy is seen as a simple replacement for the tin-lead eutectic, though the SnAgCu family and a few other alloys seem to hold the best promise. SnAgCu solders have a relatively high melting point as seen from Table 3. The eutectic SnBi alloy has a melting temperature lower than the eutectic SnPb, but the issue is its cost effectiveness.

Table 3: Some lead-free solder alloys and their melting points.

Melting Alloys temperature oC Sn96.5Ag3.5 221 Sn95Sb5 232–240 Sn95.5Ag3.8Ci0.7 –217 Sn95.8Ag3.5Cu0.7 –217 Sn99.3Cu0.7 227 Sn96.2Ag2.5Cu0.8Sb0.5 213–218 Sn97Cu2.0Sb0.8Ag0.2 226–228 Sn91.8Ag3.4Bi4.8 202–215 Sn42Bi58 138

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Part B: Solder fatigue and creep

6 Basics of metal fatigue and creep

Wöhler in 1830 noticed that a metal or alloy subjected to repeated or fluctuating stress failed at a stress level much lower than what was required in a single application of load [2]. Failure occurred under cyclic loading is called fatigue failure, presumably because the failure is generally observed to occur after a considerable period of service. According to the classical metallurgical sense, fatigue failures caused by cyclic stress and strain are accompanied by permanent damages to the materials. Fatigue usually results in a brittle fracture appearance and shows little gross deformation. Fatigue failure is particularly insidious for it occurs with no obvious pre-warning. Three basic factors are necessary to cause a fatigue failure: a tensile stress of a sufficient magnitude; a variation (or fluctuation) of the applied stress of a sufficient range and a sufficient number of stress cycles applied. There are additional variables that could alter the conditions for failure, including the stress concentration, environment, temperature, overload, metallurgical structure and residual stress, etc. A fracture failure usually evolves in two stages: that of the initiation of the fatigue cracks and that of the propagation of the cracks under load cycling.

For practical purposes the tensile properties of most engineering metals or alloys are considered to be independent of the time, provided that the rate of loading is limited to a certain range. Under elevated temperatures, however, the strength will become much more dependent on both the strain rate and time of exposure [2]. Phenomenologically, metals and alloys at high temperature behave in many respects like viscoelastic materials. A simple indicator of the creep occurrence of a test sample under a constant load is its length shows a time-dependent increase. Different materials start showing creep behaviour at different temperatures, primarily due to their different melting temperatures.

7 Fatigue in electronic packaging

Electronic components rarely experience conditions of constant stress or strain throughout their lives. Rather, the fluctuations of these terms are typical during manufacturing, testing, shipping, storage and operation. Sources of the cyclic loads may be repeated temperature changes, mechanical vibration or shocks and acoustic noises, etc. To evaluate solder reliability based on the solder material’s static properties represents an over-simplified approach that is far from adequate for package-reliability analysis. Damage examinations on failed packages indicate that under repeated thermal-mechanical stress, micro-cracks grow in solder joints to form gross fatigue cracks near the solder to pad interface. The evidence proved that the fatigue failure dominates the solder interconnects’ failure modes. The solder fatigue in microelectronics is usually categorized as low-cycle fatigue since it usually occurs below 10 000 cycles and the stress level

446 Advances in Fatigue, Fracture and Damage Assessment is usually ranked as high. To characterize and to evaluate the fatigue behaviour requires carefully designed thermal-cycle testing that subjects the package assemblies to alternate temperature extremes.

The cyclic strain-controlled fatigue, as opposed to the stress-controlled fatigue, occurs when the strain amplitude is held constant during load cycling [2]. The strain-controlled cycling can be found in an electronic component under temperature fluctuation or repeated reversed bending. The stress vs. strain hysteresis loop develops during the cycling. The dimensions of the loop can be described by its width ∆ε (the total strain range) and height ∆σ (the total stress range). The total strain range ∆ε consists of the elastic-strain component ∆εe as well as the plastic-strain component ∆εp. The width of the hysteresis loop depends on the range of the cyclic strain. The plastic deformation is not reversible and it causes microstructure coarsening for the solder during temperature cycling. And adversely, the micro-structural change affects the stress–strain response. The appearance of a cyclically stabilized stress–strain curve usually differs from its counterpart obtained under monotonic static loading. The former is usually determined by connecting the tips of stable hysteresis loops obtained from constant-strain-amplitude fatigue tests using specimens cycled at different strain amplitudes [2]. The stress–strain relationship can be described by a power function as follows:

' n' ∆σ = K (∆ε p ) , (1) where n’ is the cyclic strain-hardening exponent and K’ is the cyclic strength coefficient.

7.1 Low-cycle fatigue

When yielding is present in the material the low-cycle fatigue laws, such as the Coffin–Manson relationship [9, 10,49] as follows, commonly apply,

1 1 ∆ ε p c , (2) N f =  22ε f ' where Nf is the mean cycles to failure, ∆εp is the plastic-strain increment, 2'ε f is the fatigue-ductility coefficient and c is the fatigue-ductility exponent.

7.2 High-cycle fatigue

Under dynamic (vibration, shock and acoustic, etc.) loads, the fatigue life is usually governed by the high-cycle fatigue laws, and is typically predicted by the S–N (stress vs. cycles) curve. The cyclic stress applied to the material must be below the material’s yield stress to ensure that no plastic deformation is present. In many cases, the traditional S–N curve is close to a straight line on a log-log plot. The following equation can be used for the calculation of the fatigue life:

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λ K ' . (3) Nf =  σ

In (3), Nf is the mean number of cycles to failure, Κ’ is the fatigue-life multiplier (a materials property), σ is the peak stress and λ is the fatigue exponent.

8 Creep in solder alloys

As mentioned above, metals and alloys subjected to a constant load under elevated temperature will creep, i.e., undergo a time-dependent strain increase. Different materials show their respective time dependency of the strength at different “high temperatures.” A temperature considered as “high” for one material may not be so for another. Thus when creep is under consideration, the temperature is often expressed using a relative scale called the “homologous temperature.” A high homologous temperature is typical for all solder materials.

8.1 Homologous temperature for solders

The homologous temperature for a metal is defined as the ratio of the material’s testing temperature to its melting temperature, both on the absolute scale (Kelvin) [2], and is expressed as follows:

To TH = (4) Tm where TH is the homologous temperature, Tm is the absolute melting temperature and To is the absolute test (or reference) temperature. Creep is not an intrinsic materials response but rather a performance-based behaviour that is highly dependent on the testing temperature. A general rule applicable to different metals says that creep is only of engineering significance at a material’s homologous temperature greater than 0.5 [4]. The Pb-Sn solders melt at below 200˚C (473 K). At room temperature, say 20˚C (293 K), the homologous temperature is 0.62, well above the criterion. Experimental evidences have shown that the solder materials do creep at room temperature, which is consistent with that common rule [4]. It is understood that at the high- temperature extreme of a thermal cycle, solder joints should experience significant creep and stress relaxation, while at low temperatures the phenomenon should continue with a slower pace. The classical mechanical properties of solder materials at room temperature, such as the yield and the ultimate strength, may significantly vary depending on testing conditions. This may be a reason for the relatively poor consistency found in published data for the solder static property.

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9 Creep and stress relaxation in solder

Solder creep and fatigue and their interaction have been widely studied in recent decades. Solder joints in electronic packages subjected to field application conditions routinely experience repeated changes of strain and stress. The stress relaxation and creep are usually regarded as mechanistically equivalent though the mathematical formulations of the respective mechanisms differ. A test sample held under constant strain will experience a stress decrease or “relaxation”. Conversely, as the stress is held constant the strain will increase with time due to “creep”. In both cases plastic flow and microstructure changes occur. The distinction between the strain creep and stress relaxation should be noted so that no confusion occurs in interpreting the stress–strain data obtained from either stress- or strain-controlled testing. Fong [11] used Fig. 8 to distinguish one from another. Figure 8(A) describes a stress-controlled fatigue test with a hold time, during which the material creep occurs as the strain–time plot in Fig. 8(C) illustrates. Figure 8(B) describes a strain-controlled test with hold time, for which the stress-strain curve plotted in Fig. 8(D) illustrates the stress relaxation when the material is held at constant strain. Figures 8(A) and (B) qualitatively illustrate the difference between the hysteresis loops for the two different tests.

σ Creep σ b c b Stress-relaxation c ε ε

a d a d

(A) (B)

a ε a ε

b Stress-hold time b Strain-hold time c d c d

t t (C) (D) Figure 8: Strain histories and hysteresis loops for tensile-hold cyclic tests [11]: (A) and (B) stress-hold tests; (C) and (D) strain-hold tests.

In application practices the hold periods in a service cycle for a package resemble either the creep (under stress-controlled conditions) or more commonly

Advances in Fatigue, Fracture and Damage Assessment 449 the stress relaxation (under strain-limited conditions). A majority of the available creep data for solders refers to the minimum strain rates that are unrealistically high compared with what actually happen in real packages in service. A sigmoidal relationship exists between the applied stress and he minimum creep rate, indicating a shift of the dominant deformation mechanism. And the micro-structural alteration or prior strain may have a significant impact on the creep behaviour. For a package under a fast thermal cycle, the solder stress increases at a pace faster than that of the stress relaxation caused by the strain creep, resulting in a net increase of the effective stress. Conversely, the stress relaxation dominates a slow thermal cycle, which results in a low effective stress. In both cases the material damage is done as long as the permanent deformation is caused.

Part C: Solder-fatigue models and constitutive relationship

10 Fatigue models for solder-life prediction

Based on the fundamental mechanisms responsible for inducing the solder damage, the models for predicting the fatigue lives of solder joints can be classified into four major categories as follows: (i) the stress-based, (ii) the strain-based, (iii) the energy-based, and (iv) the damage-accumulation-based cases. Fatigue models that fit in none of the above categories are usually empirically based [12]. The stress-based models apply to cases where the sources of force or stress to cause component deformation are due to mechanical vibration or shock. The strain-based fatigue models are applicable to the cases that are dominated by the thermal-fatigue-induced strains in the joints. In these cases, the strains are typically induced by the mismatch of CTE between the materials joined by the solder. The strain-fatigue-induced models can be further divided into groups of plastic-strain-based and creep-strain-based ones. The plastic strain model focuses on the time-independent plastic effect, while the creep strain accounts for the time-dependent deformation. The energy-based fatigue models are the latest in use, which are based on calculating the overall stress–strain hysteresis energy of the system or the solder joints [13]. The damage-based fatigue models are developed based on fracture-mechanics-based approaches in calculating the accumulated damage caused by crack propagation through the solder interconnects [12, 52].

10.1 Plastic-strain-fatigue models

The most well-known Coffin–Manson fatigue model is widely used in fatigue analysis. The total number of cycles to failure, Nf, is depicted as being dependent on the plastic-strain amplitude, ∆εp, the fatigue-ductility coefficient, ∆ε’f, and the fatigue-ductility exponent, c with a relationship as follows [14]:

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∆ε p = ∆ε ' (2N )c . (5) 2 f f The fatigue-ductility coefficient ∆ε’f is approximately equal to true fracture ductility ∆ε f. The fatigue-ductility exponent c varies between –0.5 and –0.7. In applications to solder joints the finite-element analysis (FEA) can be used to determine the plastic strains [12]. The strain results are then used to predict the fatigue life. The version of the Coffin–Manson relation assumes that the fatigue failure is strictly due to the plastic deformation while, elastic strains contribute only a small portion to the fatigue failure. The Coffin–Manson equation that considers plastic deformation is commonly combined with Basquin’s equation to account for the elastic strain [12]. The modified equation is known as the total- strain equation as follows.

∆εσpf' bb =+εε'(2)'(2)f NNfff. (6) 2 E

In (6), ∆ε is the strain range, σ’f is the fatigue-strength coefficient, E is the elastic modules, ε’f is the fatigue ductility, b is the fatigue-strength exponent and c is the fatigue-ductility exponent.

Solomon’s low-cycle fatigue model relates the plastic shear strain to the fatigue cycle as follows:

α ∆γpNp = θ . (7)

In (7), ∆γp is the plastic strain range, Np is the number of cycles to failure, θ is the inverse of the fatigue-ductility coefficient and α is a material constant. The model relates fatigue behaviour to the plastic-shear strain imposed on the solder joint. The application of Solomon’s model requires data for the plastic-strain range that is experimentally collected or determined. The model does not account for creep deformation. The applications to leaded plastic quad flat packages and underfilled flip chip packages have been reported.

Equation (8) gives the form of Engelmaier’s fatigue model [15], 1 1  γ  c N = t . (8) f  '  2 2ε f  The model relates the total number of cycles to failure to the total shear strain, ∆γt, the fatigue ductility coefficient, ε’f and a variable c that is a function of the - –4 –2 frequency and temperature. c = –0.442-6×10 TS +1.74×10 ln(1+f), in which - TS is the mean cyclic temperature (°C) and f is the cycle frequency (cycles

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/day). Engelmaier’s model improves Solomon’s model and Coffin–Manson’s model since it includes the effect of the cycle frequency and temperature.

By applying Miner’s linear-superposition principle, both plastic and creep strain are accounted for in a strain-based fatigue model. This model combines Solomon’s fatigue model with Knecht’s and Fox’s creep model as follows:

111 =+. (9) NNNf pc

In (9) the number of cycles to failure Nf is obtained from knowing Np (the number of cycles to failure due to plastic fatigue obtained from Solomon’s fatigue model) and Nc (the number of cycles to failure due to creep from Knecht and Fox’s creep model) [16].

The fatigue models as described above are based on a consideration that the fatigue failure is mainly driven by the plastic deformation. To calculate the number of cycles to failure Nf requires knowledge of the plastic-strain range. The latter is package specific and is usually obtainable either by application of FEA modeling or by experimental measurement. The solder strain depends on the testing parameters including the ramp rates, dwell temperatures and holding times. These parameters should be deliberated during the design of the test. For the rapid thermal-cycling tests, other than the temperature range, the range of the strains, in particular the extent of the creep deformation should also be properly estimated.

10.2 Creep-strain-fatigue models

The creep-strain models are applied to account for the creep in solder-joint deformation. Early attempts to model the creep were made by isolating the elastic- and plastic-deformation mechanisms. Although creep phenomena have been studied exhaustively, few fatigue models fully capture the fatigue process due to an overlap of creep, plastic and elastic deformation. Some detailed studies have been conducted to evaluate the impact of microstructure, dislocation movement and grain boundary on the creep deformation, though the effects are yet to be integrated into the creep models [17,46]. The solder joint’s creep is commonly recognized as being related to grain-boundary sliding and/or matrix creep (dislocation movement). Knecht and Fox [16,51] have proposed a simple creep-fatigue model to relate the solder microstructure and the creep shear-strain range as follows.

C N f = , (10) γ mc

452 Advances in Fatigue, Fracture and Damage Assessment where the number of cycles Nf is related to a constant C, the value of which is dependent on the failure criteria and solder microstructure, ∆γmc is the creep- strain range.

The second creep mechanism, grain-boundary sliding, is incorporated into a fatigue model presented by Sayed [18]. In this model creep strain is partitioned into two parts as follows:

–1 Nf = ([0.22Dgbs]+[0.063Dmc]) (11)

Dgbs and Dmc in (11) are the accumulated equivalent creep strain per cycle for grain sliding and the matrix creep, respectively. Given that the thermal-cycling parameters dictate the solder-damage mechanism, the inclusion of creep strain into the fatigue models results in a more comprehensive model accounting for the effect of the dwell time, the strain amplitude and the solder microstructure, as well as the solder-joint geometry.

10.3 Energy-based models

The energy-based ones belong to the largest group of fatigue models. The models predict fatigue failure on the basis of hysteresis energy in terms of the volume-weighted average stress–strain hysteresis loop [11]. Dasgupta [19] indicated that the total strain energy, accounting for both the stress and strain information, should be a good indicator of the solder-joint damage. Akay et al. [20, 21] proposed a fatigue model as follows based on the total strain energy:

1 ∆W  /k N =  total  . (12) f W  o  − In (12) Nf is the mean cycles to failure, W total is the total strain energy, and W0 and k are fatigue coefficients. Liang et al. [22] reported a fatigue-life-prediction methodology that accounts also for the geometry of the solder joint based on elastic and creep analysis. The fatigue life is calculated using an energy-based fatigue-failure criterion as follows:

− −m NCWfss= () , (13) where Wss is the stress–strain hysteresis energy density, C and m are both material constants that are temperature dependent and derivable from low-cycle fatigue tests.

Another strain-energy-based model by Pang [23] is known as “Critical Accumulated Strain Energy” or CASE. The model assumes that as the strain energy accumulates during thermal cycling the fatigue failure occurs when the strain energy reaches a critical value C as follows:

Advances in Fatigue, Fracture and Damage Assessment 453

• • * C = N f (a E p + a E c). (14)

* In (14), Nf is the number of cycles to failure, C is defined as the critical strain- energy density with a given value of 4.55 MPa/mm3 for the range of the testing performed. The constant a and b are essentially determined from multiple linear regression of FEA results. And the creep and plastic energy, denoted as Ep and Ec, are also calculated via FEA modeling.

Energy-based models [12] are the first such models that attempt to include the hysteresis information. As with the strain-based (plastic and creep) ones, these models also account for the effect of the test conditions that dictate the solder fatigue life. Yet the energy-based models only predict the energy required to initiate a crack, not the occurrence of the final fatigue failure.

10.4 Damage-fatigue models

The damage-based fatigue models are founded on the basis of the fracture mechanics or the creep and fatigue mechanisms [24, 25, 26, 54]. The models calculate the total damage done by a thermal cycle to a solder joint. The model by Stolkarts et al. [27] is based on a constitutive derivation involving creep- plasticity to calculate the number of cycles to failure Nf as follows:

1− (1− d ) k−1 N = f . (15) f (k +1)L

In (15), df is the amount of damage at failure with a value of 0.5 given for the solder materials. K, defined as a material constant, is given a value of 2. L is defined by a time integral ∫ fdt that gives a nearly constant value. f in the integral is the initial rate of damage of the remaining undamaged material in the representative volume element. The essential parts of (15) encompass unified creep-plasticity models with an internal damage parameter. The stress–strain hysteresis loop is used to determine the amount of the damage. The damage at failure, df, introduced to allow the calculation of the number of cycles to failure. The loading (with or without hold times) is incorporated into the model, which made it capable of handling different cycling regimes with different dwell time and ramp rate.

11 Solder constitutive relation

The validity of an assessment for packaging reliability based on theories of fatigue failure relies much on the certainty in experimentally obtained constitutive relations [28–30]. The values of published constitutive parameters for Pb-Sn eutectic alloy show wide range variations [e.g. 7, 31, 32]. Table 4 lists the elastic modulus at different temperatures given by different sources.

454 Advances in Fatigue, Fracture and Damage Assessment

For Pb-Sn eutectic alloy assuming a steady-state creep mechanism, for instance, the investigation by Kashayap and Murty [6] showed that the flow stress is a unique function of strain rate, temperature [53] and grain size. The data listed in Table 5 include the grain-size exponent and the activation energy given in the temperature range between 298 and 443 K, the corresponding grain size ranging between 9.7 and 32.0 µm, and the strain rate between 10–7 and 10–2 s–1.

The solder constitutive relation is the key to modeling the solder failure since it is involved in both the determination of solder-joint stress/strain and the solder fatigue-failure prediction. Yet the material-property characterization is hampered by technical difficulties, especially with respect to loading and measuring samples in the scale of microns. The available test data are mostly obtained using macro- scale samples, which results in so-called “bulk properties” that could deviate substantially from the actual properties of the solder in real joint dimensions.

Table 4: Elastic modulus of Sn63/Pb37 from different sources.

Elastic Elastic Elastic Elastic Elastic Elastic Temp (K) Temp (ºC) Th modulus modulus modulus modulus modulus modulus (MPa) [1] (MPa) [6] (MPa) [14] (MPa) [17] (MPa) [20] (MPa) [19]

218 –55 0.48 47 966 36 840 42 834 37 050.6 19 806.83 47 394

238 –35 0.52 46 892 35 080 39 794 35 284.6 18 826.83 46 054

258 –15 0.57 45 779 33 320 36 754 33 518.6 17 846.83 44 714

278 5 0.61 44 377 31 560 33 714 31 752.6 16 866.83 43 374

295 22 0.65 43 251 30 064 31 130 30 251.5 16 033.83 42 235

298 25 0.65 29 800 30 674 29 986.6 15 886.83 42 034

323 50 0.71 41 334 27 600 26 874 27 779.1 14 661.83 40 359

348 75 0.76 39 445 25 400 23 074 25 571.6 13 436.83 38 684

373 100 0.82 36 854 23 200 19 274 23 364.1 12 211.83 37 009

398 125 0.87 34 586 21 000 15 474 21 156.6 10 986.83 35 334

11.1 Solder-creep laws

The evolution of the study of solder creep has resulted in many similar creep laws yet with different mathematical expressions and indices. Among them, the sine hyperbolic law and power law are the most popularly used ones, as given in the following.

The hyperbolic creep law proposed by Darveaux and Banerji [55] is as follows:

Advances in Fatigue, Fracture and Damage Assessment 455

n dγ s  G  σ   − Q  = C1  sinh(α ) exp , (16) dt  T  G   kT  2 2 where G is the shear modulus in lbf/in , C1 = 0.198 (K/s/lbf/in ), α = 1300 n = 3.3 is the stress exponent, Q = 0.548 (eV) is the activation energy for deformation process and T is temperature in Kelvin.

Table 5: Experimental constitutive parameters for eutectic Pb-Sn at high temperature published in different sources. Reference Temperature Grain-size Activation (K) exponent energy kJ/mole Avery and Backofen 298 2 - [33] Martin and Backofen 298 2–4 - [34] Zehr and Backofen 299–443 2–3 - [35] Cline and Alden [36] 273–353 - 48 ± 10

Avery and Stuart [37] 223–353 4 47–75

Aldrich and Avery 273–323 1.7–5.4 32 – 50 [38] Baudelet and Suery 229–303 - 48.2 ± 2.1 [39] Geckinli and Barrett 268–344 3 45 ± 5 [40] Mohamed and 336~422 2.3 57.3 ± 0.5 Langdon [31] Lam et al. [32] 298–373 1.6 44.1 Grivas et al. [41] 273–433 1.8 48 Kashayap’s 298–443 3.34 ±0.23 44.7 ±1.1 (T < investigation [6] 408 K) 81.1 ±3.9 (T > 408 K)

Another hyperbolic creep law proposed by Pan is expressed as follows [47,48,50]

n m γcr = A(sinh Bτ ) (d) exp(−Q / RT) , (17)

456 Advances in Fatigue, Fracture and Damage Assessment

–1 where γcr in s is the shear strain rate, τ in MPa is the shear stress, A = 2.9524 ×108, B = 0.125938, n = 1.67, m = –3.011 are different constitutive coefficients, Q = 61417 joule/mole is the activation energy, d = 11 µm is the grain size and R = 8.31 Joule/mole K is the gas constant [48].

The power law has also different expressions. Dorn’s constitutive law [56] is expressed as follows:

p n A ⋅ G ⋅ B  b   σ  −(Q / R⋅T ) εs =   ⋅   ⋅ D0 ⋅ e , (18) k ⋅T  d   G 

where εs = steady-state strain rate, σ the applied stress (MPa), G the shear modulus (MPa), b = 3.23×10–7 mm is the Burger’s vector magnitude of a crystal dislocation, T the absolute temperature, k = 1.383 × 10-23 J/K is Boltzmann’s −3 2 constant, d = 5.53×10 mm is the grain size, D0=100 mm is the pre-exponential constant, Q = 44 kJ/mole is the activation energy for the rate-limiting diffusion process, R = 8.314 J/K mole is the gas constant, n = 2.4 is the stress exponent, p = 1.6 is the grain-size exponent and A = 40 is a dimensionless constant.

Lau et al. [57] used a creep law for eutectic tin-lead and lead-free solder materials as follows: −C ∂ε C3 4 = C1 [sinh()C2σ ]exp( ) , (19) ∂t kT 1 where C1 = 441000 (1/s), C2 = (1/Pa), C3 = 3.3 and C4 = 37.78×106 − 74414T 6360(K).

11.2 Determining constitutive parameters for solder alloys

The concern about the scale dependency of the properties justifies the effort to characterize the solder properties on solder joints in real packages. A slice cut from a BGA assembly, for instance, can serve as a test specimen that is constituted of a row of the solder balls connecting a strip of the component package (including the silicon die and the substrate) on one side, and another strip of the PCB on the other. The variation of the environment temperature will subject the solder joints to thermal stress even with the absence of mechanical loads. Changing the rate of temperature variation will result in a different stress rate. The simplicity of the sample structure makes the evaluation of the solder- ball stress and strain an easy task using finite-element modeling. The modeling will yield results of acceptable credibility provided that reliable material-property parameters are implemented for die, substrate and PCB, along with a suitable solder constitutive law and coefficients. The uncertainties in silicon die, plastic substrate and PCB properties are assumed to be low given that the values published in the open literature show better consistency. Besides, these properties can be measured with sufficient accuracy on macro-scale specimens using

Advances in Fatigue, Fracture and Damage Assessment 457 standard 3-point or 4-point beam-bending tests. The solder constitutive relation must be carefully chosen to fit the test condition under which the solder strains are to be measured. The coefficients of the selected constitutive law can be determined inversely using an iterative approach that will progressively improve the values until the FEA-calculated solder strains match the experimentally measured ones.

11.3 Solder activation energy

As previously mentioned, the steady-state creep predominates the solder deformation at temperatures above 0.5Tm. With the assumption that creep is a singly activated process the Arrhenius-type rate equation can be expressed as: • ε = A⋅exp(−Q / RT ), (20) • where ε is the strain rate, Q the activation energy, R the universal gas constant and A is the pre-exponential complex constant. A temperature-differential creep test is often used to measure the creep activation energy. Within a small temperature interval the change in creep mechanism is considered minimal. The results from an extensive correlation of creep and diffusion data for pure metals show that the activation energy for high-temperature creep equals the activation energy for self-diffusion. Under the assumption of the steady-state deformation, the flow stress is a unique function of strain rate, temperature and grain size. A study of the values for the parameters used in the constitutive relations for Pb-Sn eutectic alloy shows that in applications of the creep laws, the values taken for the constitutive parameters greatly affect the final results for stress or energy density. It is noted that while the index of grain size has only a minor direct impact on the estimated solder life, the solder microstructure affects the creep- strain fatigue to a much greater degree. This is understood from the mathematical expressions of the creep laws (e.g., (14) and (15)), in which a few different constitutive parameters are microstructure dependent, including the activation energy, the stress exponent and grain-size exponent, etc. Yet the activation energy is the most important parameter since its value has the greatest impact on the creep-life estimates. An example presented below shows that corresponding to a 10% variation of the activation energy from different sources, a several times difference in predicted number of cycles to failure for solder can result (see Fig. 9). Figures 10 and 11 give the charts from which the activation energy and grain-size exponent can be determined, respectively, for a given temperature. Figure 12 shows the shear stress vs. shear strain curve for a corner area in a solder joint. Stress is calculated based on strain and strain-rate measurements in that area applying the sine hyperbolic creep law. The different curves are obtained corresponding to a 10% variation of the value taken for the activation energy. The example is an application of creep law in calculating the solder-joint shear stress from the measured strain and strain-rate data [45]. The experiment employs a test vehicle that is a power package consisting of a copper-tungsten device connected to a copper substrate with a eutectic Pb-Sn solder layer. With temperature cycling at –25oC to 125oC at a rate 3oC/min, the solder-joint shear strain at different time and temperature level was measured at

458 Advances in Fatigue, Fracture and Damage Assessment a site of known stress concentration. The stress calculation based on the creep law results in a looped area of the stress versus strain curve that corresponds to the thermal cycle, and in turn, the energy density per cycle in the corner of the solder joint. By adopting the accumulated strain-energy-density criterion, the application can reach the fatigue-life estimate for the solder joint.

1200 1000 800 600 400 200

No. of Cycles to Failure, N Cycles to Failure, No. of 0 42 44 46 48 50 52 Activation Energy, Q (kJ/mole)

Figure 9: The value for activation energy shows a 10% increase from the lowest to the highest in the range. Correspondingly the predicted number of cycles to failure is decreased by almost five-fold.

Figure 10: Arhenius plot for determination of activation energy (the grain size in the chart is in units of µm) [6].

Advances in Fatigue, Fracture and Damage Assessment 459 s

Figure 11: Plot for determination of grain-size exponent at different temperatures [6]. The unit of grain size is µm.

14.000

Q=43.6 KJ/mole 12.000 Q=44.7 KJ/mole Q=45.8 KJ/mole

Q=47.6 KJ/mole 10.000 Q=48.7 KJ/mole Q=49.8 KJ/mole

8.000 s

6.000 Shear Stress (MPa)

4.000

2.000

0.000 -0.0020 0.0050 0.0055 0.0300 0.0500 0.0700 0.1000

Shear Strain

Figure 12: Shear stress vs. shear strain in a corner of a solder joint. Stress is calculated based on measured strain and strain-rate applying the sine hyperbolic creep law. The different curves correspond to up to 10% variation in values for activation energy used in the stress calculation.

460 Advances in Fatigue, Fracture and Damage Assessment 12 Accelerated thermal-cycle testing

Unless some more reliable new methodologies are found, the reality is that the industry will continue to rely heavily on the so-called accelerated thermal-cycle testing for routine reliability assessment of new products. The accelerated testing is designed to complete the assessment in a much shorter time period than the actual field life of the product. This is mainly realized by reducing the temperature-ramp time and dwell time in thermal cycling, though occasionally enhancing the CTE mismatch between the components and the circuit board of test vehicles is used as an alternative to serve the same purpose. To properly interprete test data and correlate the data with product field reliability is always a crucial task. One obvious reason is that the failure modes and damage mechanisms that occurred in the tested pieces can significantly differ from what are actually present in a real assembly under service condition, especially with regard to the surface-mounted solder attachment. To model the assembly under conditions of both accelerated testing and service has been an effort aimed to correlate the test data with the field life via physics-based failure analysis.

12.1 Modeling accelerated testing

A few different approaches have been reported regarding the modeling of solder- interconnect deformation in responding to temperature-cyclic change. The “dwell creep” method proposed by Chong and Low neglects the creep deformation during temperature ramps, thus is relatively simple to implement. While applying creep analysis only to the dwell periods (e.g., at 125oC and – 55oC) of the cycle, the method implants the time-independent elastic-plastic model in simulating the temperature-ramp periods. The so-called “full creep” method proposed by Pang et al. [42] that models the creep deformation for the entire cycle. While the pure-creep model is applied to the dwell periods, for the temperature ramp up and down periods the method implants both time- independent elastic-plastic deformation and time-dependent creep deformation models and calculates deformation alternately in small time increments. The full creep analysis accounts for the accumulation of the creep deformation of solder during the entire thermal cycle, thus it is supposed to better represent the actual solder-joint response to thermal cycling. Figure 13 shows the temperature profiles for both “dwell creep” and “full creep”.

High maximum temperature Tmax or a wide range of temperature cycle ∆T results in significant solder creep deformation. By applying the “full creep” method two cases are compared. One with ∆T of 25ºC, with temperature varying between 75–50ºC and the other with ∆T of –55ºC and the temperature varies between 125–175ºC. The application is aimed at evaluating the effect of Tmax and ∆T on the solder-joint plastic strain and creep strain. The modeling application proved that the ramp-rate and dwell time are the most important parameters of thermal cycling. Both parameters have significant impact on the solder creep and stress relaxation. Pang and Chang [43] have earlier shown that at slower ramp rates, more creep exposure occurs at the temperature-ramp

Advances in Fatigue, Fracture and Damage Assessment 461 periods. Shiratori and Yu [44] determined that the creep deformation became significant only in the early part of a dwell period and diminished in the second half of the dwell due to the stress relaxation. A conclusion was drawn that a dwell time longer than five minutes was not all necessary since five minutes are sufficient for solder stress to relax to a lower level where creep-strain accumulation becomes no longer significant. Pang and Chang also studied the fatigue lives by applying the creep-fatigue modeling. It was shown that a higher ∆T resulted in a lower fatigue life owing to higher creep-strain range per cycle. A reduced fatigue life is predicted for the case of high maximum temperature by similar calculation, while ∆T remains constant.

Temp (oC) Temp (oC)

Elasto-Plastic Elasto-Plastic Creep

125 125

25 25 Time Time

Creep Creep -55 -55

st st 1 Cycle 1 Cycle (a) (b)

Figure 13: (a) “Dwell Creep” model; (b) “Full Creep” model [42].

12.2 Modeling for interpreting accelerated test results

As previously presented the accumulation of the solder-joint damage is equivalent to the energy density accumulated in the solder during accelerated testing, which can be modeled based on the physical laws governing the solder deformation and failure. Implementation of a proper constitutive relation is the key to determining the solder stress–strain curve. In order to correlate the accelerated temperature cycle with a real service cycle, the solder damage per cycle in an accelerated testing is compared with what occurred in the real, slower cycle. The scope of the correlation is to reach an “acceleration factor,” which can be obtained simply by comparing the energy density per cycle in the two cases based on the respective curves of stress–strain hysteresis. As long as the acceleration factor is determined, the failure data obtained from an accelerated testing can be transformed to the real field life on the basis of failure physics. It,

462 Advances in Fatigue, Fracture and Damage Assessment however, should be noted that, first, the models have to be validated due to the reason as previously discussed; and secondly, the correlation and the test-data interpretation are only valid if the dominant damage-storage mechanisms in both cases match. The model validation involves experimental verification of the modeling results. A recommended flow diagram for the validation of an iterative process model is mapped in Fig. 14 [61, 63, 66, 69, 70]. To inspect and identify the failure mechanisms requires extended failure analysis employing various experimental techniques and the product field returned failure data where possible.

Prepare/modify test vehicles and boundary conditions Test/Re-test

Iterating

Compare Compare No good! Good! results results

Prepare /modify Solve/Re-solve

Numerical/Theoretical Model Validation Completed!

Figure 14: Flow diagram for an iterative process-model validation/selection.

Advances in Fatigue, Fracture and Damage Assessment 463 Part D: Digital speckle correlation, a new technique for solder-joint strain measurement

13 Computer vision measurement techniques

A successful physics-based assessment, by modeling or experimental measuring, cannot be achieved without obtaining accurate strain measurements at failure- prone interconnects. The measurement techniques should meet the requirement on spatial resolution to match the solder layer’s geometric scale as well as that of the damage initiation. Also, since an evaluation usually involves a large amount of data collected at different times and temperatures, to adopt computer- automated techniques is necessary for the efficiency of the assessment. Digital Speckle Correlation (DSC) can meet the requirements as it is realized with a computer vision system as schematically shown in Fig. 15 [58, 59]. The system integrates the functions of image acquisition, digitizing, recording, processing, data post-processing and displaying, etc. The technique requires that the surface to be measured exhibits a random or speckle- like pattern. What is essentially needed is a variable light reflectivity across the area to be measured. A surface’s natural texture may sufficiently fit a proper application as long as it possesses a certain degree of light reflectivity variation. Otherwise, a black and white speckle coating can always be spray-painted to cover a monochromatic surface.

CCD Camera Desk Top Computer with AutoStrain Micro- Zoom Lens Light Source

Specimen Vertical Movement

Horizontal Movement

Micro positioning Stage

Figure 15: Schematic of DSC vision system for thermal-strain measurement.

14 Solder-strain measurement by DSC

DSC for strain measurements is based on an iterative algorithm evaluating the cross-correlation between a pair of images of the same object recorded under different conditions. A factor S is defined as follows to relate the images:

464 Advances in Fatigue, Fracture and Damage Assessment

Σfxyg(, ) *(*,*) x y (21) S(u,v,∂∂∂∂∂∂∂∂ u/ x, u/ y, v/ x,)1 v/ x =− . ΣΣf 22(,xy ) g *(*,*) x y As shown, S is a function of six independent variables, namely two in-plane displacement components and four partial derivatives of the displacements. S characterizes the degree of decorrelation or dissimilarity between a pair of the subsets of the recorded image patterns. In (21) f(x,y) represents an originally recorded image subset that serves as a reference, which is usually recorded represents an artificial (٭y,٭x)٭when a surface is in an un-deformed state. g (٭y,٭image subset that is modified based on another originally recorded g(x corresponding to a deformed state. A point (x,y) in the subset is related to in the counterpart subset according to the laws of deformation kinematics (٭y,٭x) when digitized, are ,(٭y,٭x)٭via the six deformation parameters. f(x,y)and g and give the grayscale ٭y,٭discrete functions of the position variables x,y and x values at grid points in the respective subset. It is worth noting that the deformation parameters obtained at the end of the image processing are for the centre point of the subset f(x,y). The processing involves the method of Newton– Raphson for progressive approximation in solving for the six parameters. The initial estimates of these parameters are needed to initiate the iterative process. As the iteration goes on, the parameters are upgraded along with the improved image correlation, which is evidenced by the convergence of S to zero. The process is finally terminated based on a preset criterion for a minimal value of S, indicating the deformation parameters have been optimized. To obtain whole field deformation measurement in a finite area, the above process simply needs to be repeated at each predetermined grid point of the area. For problems involving temperature changes, the obtained measurements are the so-called “total strain,” namely the sum of the mechanical and the thermal strains. If the materials being measured are thermally isotropic and respond linearly to temperature change ∆T, the mechanical strain components can be extracted from the measured displacement gradients via the following equations:

2 2 ∂u  ∂u   ∂v  ε x = 1+ 2 +   +   −1−α∆T ∂x  ∂x   ∂x  2 2 ∂v  ∂v   ∂u  (22) ε y = 1+ 2 +   +   −1−α∆T ∂y  ∂y   ∂y  ∂u ∂v ∂u ∂u ∂v ∂v + + + ∂y ∂x ∂x ∂y ∂x ∂y γ xy = arcsin . ()1+ ε x ()1+ ε y

For small deformation, the following approximate forms of (22) can be used:

∂u ∂v ∂u ∂v ε x = −αT ε = −αT γ = + . (23) ∂x y ∂y xy ∂y ∂x

For applications involving no temperature changes (22) and (23) are reduced respectively to

Advances in Fatigue, Fracture and Damage Assessment 465

2 2 ∂u  ∂u   ∂v  ε x = 1+ 2 +   +   −1 ∂x  ∂x   ∂x  2 2 ∂v  ∂v   ∂u  (22) ε y = 1+ 2 +   +   −1 ∂y  ∂y   ∂y  ∂u ∂v ∂u ∂u ∂v ∂v + + + ∂y ∂x ∂y ∂y ∂x ∂y γxy = arcsin , ()()1+ εx 1+ εy and ∂u ∂v ∂u ∂v (23) εx = , εy = , γxy = + . ∂x ∂y ∂y ∂x

The experimentally measured strain terms are independent of any prior knowledge of the material’s constitutive relations and the structural constraints. DSC can be applied to large/small-scale flat surfaces or be used in measuring an interested point in a highly magnified element of the curved surfaces. The flexibility comes from the convenience in adjusting from macro-to-micro the spatial resolution by using different optical imaging systems. Some additional technical features including being non-contact, non-coherent and remote sensing allow DSC to extend the applications to surfaces that are soft, fragile, or in- accessible (e.g., confined in environmental chambers). The accuracy of the strain measurement is around 100–200 µε. Given that the magnitude of solder strains can be one or several orders of magnitude higher than that of the uncertainty, the measurements are considered sufficiently reliable. The chart in Fig. 16 recommends the procedures for a model validation using DSC.

15 Typical application examples involving DSC technique

15.1 Measurement of shear strain in a solder attachment

The example [60, 62, 67] shown in Fig. 17 is an experiment conducted on a test vehicle that is placed in a programmable thermal chamber. The test vehicle is a power package consisting of a copper-tungsten device interconnected with a layer of eutectic Pb-Sn solder to a copper substrate. To measure the solder strain, the vision system was focused on the corner of a cross section of the sample that exposes the solder interface. The sample temperature was made to vary between –25˚C and 125˚C at a rate of 3˚C/min. A series of images of the sandwich area was recorded corresponding to different times and temperatures. Upon subsequent digital image processing, the strain measurements of the targeted area were obtained. Typical strain results are given in Fig. 18. The strain rate was further determined from the curve of strain versus time.

466 Advances in Fatigue, Fracture and Damage Assessment

Digital speckle correlation

In-plane εx, εy, γxy , u, v as functions of T, t

γ max

Strain rate dγ /dt , … xy

Creep theory

Shear stress τ, …

Strain-energy density

Life prediction by critical Maximum shear Strain-energy density criterion,… -strain criterion

Figure 16: A recommended experimental physics-based procedures for reliability prediction and design-concept evaluation.

15.2 Evaluation of residual stress in wireless micro-power package [67, 68]

The geometric dimensions of the wireless micro-power assembly unit are in the range of microns. The high heat generated during the power-on period causes the IC die and solder link to crack, constituting a main threat to the structural integrity of the assembly. The targeted evaluation includes the determination of soldering process-induced residual strain/stress that remains in the GaAs die and gold-tin solder joint at room temperature. The “residual stress” is referred to as the stress “locked” in the assembly under room temperature conditions due to die bonding, encapsulating and soldering processes. In general, the existence of residual stress in a chip-on-board or a die-on-leadframe assembly elevates the level of mean stress, and thus reduces the assembly’s fatigue life. According to theory, the assembly is assumed stress free before the solder joints

Advances in Fatigue, Fracture and Damage Assessment 467

Device PWB

A Board A

320 µm 10m

78m 210 µm

Component Speckle coated εx A - A Solder γ xy

Board

Figure 17: Test vehicle and targeted area for strain measurement. The test vehicle is a power package consisting of a copper-tungsten device connected to a copper substrate with eutectic Pb-Sn solder layer.

Solder

ZE ZE ZE

Figure 18: Typical strain measurement in targeted area.

solidify during reflow process. Since the solidification is not a uniform process, inter-grain stresses develop at the microscopic level. Upon completion of the solder solidification, the cooling of the solder resumes and the stress continues to increase at a larger rate due to the mismatch between coefficients of thermal expansion of the materials on both sides of the solder joints. The stress in the

468 Advances in Fatigue, Fracture and Damage Assessment power assembly is assumed higher than that in most other type packages owing to the higher melting temperature (356oC) of the eutectic gold solder used in the die bonding. Based on the above theory, the main step in the assessment of solder joint residual stress for the assembly is to measure the solder joint deformation corresponding to a heating process that brings the sample from room temperature up to the solder’s melting point. This is but a reversed process of the solder solidification and cooling during reflow. If the de-solidification at the high temperature would result in a full release of the residual stress, the measured strain (referred to as the “apparent strain”) may be viewed as equal with opposite sign to the room-temperature deformation of the solder joint. Precisely speaking, the re-heating induced deformation recovery cannot be a simple reversal of the deformation due to soldering process. In particular, the time-dependent stress relaxation that takes place during the assembly’s life-time would cause some change of the solder joint deformation. However, given that the solder permanent (plastic and creep) strains dominate the solder-joint deformation, the measured apparent strain should largely represent the reversed solder deformation at the room temperature. And the stress evaluated based on the theory and the measured apparent strain is assumed to be very close to the residual stress of the assembly at the time of the evaluation. Furthermore, the solder solidification is known to be a non-synchronized process. The residual stress in the solder joint is expected to be non-uniform both microscopically and macroscopically. The actual assessment was conducted by applying, separately, the DSC measurement and FEA simulation. Fig. 19 shows the patterns of distribution of the measured and the modeled apparent shear strains in a section of the assembly.

0 0005 0 0005 0001 0002 0001 0002 0003

DSC-measured strain FE–calculated strain

Figure 19: Comparison of DSC and FEA results. Temperature load = –331°C.

15.3 Validation of a FE model for a CSP [64, 65, 70,72]

Modeling solder-interconnect stress often faces uncertainties for adopting suitable constitutive laws and proper values of model parameters. The difficulty can be coped with by experimentally validating the solder-joint strain results obtained from applying different material models in finite-element analysis. The example presented as follows involves a chip-scale package. By using a diamond precision cutting wheel, the sample is cut into two halves to expose the

Advances in Fatigue, Fracture and Damage Assessment 469 largest ball cross section of the mid-row solder balls. The surface is then deposited with fine white-and-black speckles. Shown in Fig. 20 are the contour maps of the measured shear strain, with the background showing the images of a corner ball. The sample results are selected from a dozen such contour maps that are obtained from processing a series of images recorded following a temperature vs. time profile. It is seen that the patterns of shear-strain distribution at different temperatures remain similar, with the location of strain concentration staying near the upper-right and lower-left corners of the solder ball. For achieving the purpose of model verification, three-dimensional FE models are made to simulate the half-package sample both in structure and in boundary conditions, as Fig. 21 shows.

33°C58°C

350µm

80°C 102°C

Figure 20: Solder-joint shear strain measured by DSC.

Cu-PbSn Interface 0.04 0.05 18 m 0.03 µ 0.02 0.03 Area Measured

Figure 21: Maximum shear strain measured at a corner of pad- solder ball interface for a CSP by DSC.

Owing to the high resolution of DSC the strain measurements are obtained at the node points of a fine grid covering the measured area of the solder joint. (The capacity of the DSC technique actually is still underused in this application as a separate test demonstrates, as seen in Fig. 21, that the strain in the area of 18 µm scale is resolved.) The FE model mesh density for the same area does not match the DSC grid due to limitations of computing capacity. The comparison is made

470 Advances in Fatigue, Fracture and Damage Assessment between the modeled shear strain at the mid-nodal point and the average of the measured shear strains at the grid points in an area the size and the location of which match the FE model element. The validation involves four FE analyses each implemented with a different solder constitutive model and/or slightly altered solder-joint dimensions. The diagram in Fig. 22 demonstrates that one of the four sets of FE modeling results finds the best correlation with the DSC measured shear strain. The generality of the material model is proved by further applications, in which the same modeling and testing procedures are repeated for another test vehicle of the same solder material and similar design but slightly different material and geometry configuration. The agreement obtained in the subsequent application indicates that the FE modeling and the material law used is deemed non-package specific.

Correlation found 30000 meas linear, tall 25000 linear, short

20000 bkin, tall bkin, short 15000 10000

micro-strain 5000

0 0 20 40 60 80 100 120 ∆T°C

Shear strain vs. temperature at mid-point of a CSP solder joint

Figure 22: Comparison of solder shear strain obtained by FEA and DSC.

Advances in Fatigue, Fracture and Damage Assessment 471 Part E: Solder-joint strain ratcheting in a temperature cycle [71,73]

16 Creep vs. stress relaxation in solder joint of real packages

Many previous modeling studies are based on an assumption that the creep dominates the solder deformation in temperature-dwell periods of a thermal cycle. Such an assumption is rarely subject to scrutiny by direct experimental measurement of solder deformation in real packages. The study presented here subjects test vehicles to temperature cycling while the solder-joint deformation is evaluated by using DSC. Two types of ceramic-resistor package are involved: one with eutectic Pb-Sn solder joints and the other of Pb-free solder joints. The primary objective is to resolve the thermal-mechanical strains of the real solder joints in the scale of about 20 microns in thickness. The results obtained include full-field in-plane displacement as well as strain components. Since shear deformation is known to dominate the solder-joint deformation, the analysis focuses on the variation of shear strain in responding to different temperature vs.

8 mm

7 mm SOLDER 0.5mm Ts Tc CERAMIC

L CU 1.15 mm FR4

Figure 23: Geometric dimensions of ceramic resistor packages for test.

Solder Ceramic

FR4

(A) (B)

Figure 24: Resistor package of lead-based and lead-free solder joints. Thermal-strain measurement aim at (A) the corner of right fillet (Test-1 and Test-2) and (B) corner of left fillet (Test 3 and Test 4) using DSC technique.

472 Advances in Fatigue, Fracture and Damage Assessment time profiles. The four tests presented below involve four test samples the dimensions of which are given in Fig. 23. The samples used in Test-1, 2 and 3 are of PbSn eutectic solder joints and that for Test-4 has Pb-free solder joints. The strains are measured at the corner of the solder fillet. The schematic in Fig. 24 indicates the fillet corner of the solder joint where the measurements are taken.

17 Testing temperature profiles and strain results

The temperature cycles in these tests are made different to explicitly show the effect of creep and stress relaxation in responding to different testing parameters (e.g., ramp rate, dwell time, high and low dwell temperature, etc.). The maximum temperature in these tests goes up to 120 oC. The temperature vs. time and the shear strain vs. time curves are as given in Figs. 25–32.

140 120 100 80 60 Temp(C) 40 20 0 0 20 40 60 80 100 120 Time (min)

Figure 25: Temperature profile for Test-1.

9.00E-03

8.00E-03

7.00E-03

6.00E-03

5.00E-03

4.00E-03 Shear Strain Strain Shear 3.00E-03

2.00E-03

1.00E-03

0.00E+00 0 20 40 60 80 100 120 140

Time (min)

Figure 26: Shear strain vs. time at right corner in lead-based solder joint of Test-1 sample.

Advances in Fatigue, Fracture and Damage Assessment 473

140 120 100 80 60 Temp(C) 40 20 0 0 102030405060

Time (min)

Figure 27: Temperature profile for Test-2.

4.50E-03 4.00E-03 3.50E-03 3.00E-03 2.50E-03 2.00E-03

Shear Strain Shear 1.50E-03 1.00E-03 5.00E-04 0.00E+00 0 10203040506070 Time (min)

Figure 28: Shear strain vs. time at right corner in lead-based solder joint of Test-2 sample.

474 Advances in Fatigue, Fracture and Damage Assessment

90 80 70 60 50 40 Temp(C) 30 20 10 0 0 1020304050 Time (min)

Figure 29: Temperature profile for Test-3.

4.000E-03 3.500E-03 3.000E-03 2.500E-03 2.000E-03 1.500E-03 Shear Strain Strain Shear 1.000E-03 5.000E-04 0.000E+00 0 1020304050

Time(min)Time (min)

Figure 30: Shear strain vs. time at left corner in lead-based solder joint of Test-3 sample.

Advances in Fatigue, Fracture and Damage Assessment 475

160 140 120 100 80

Temp(C) 60 40 20 0 0 20 40 60 80 100 120 140 160 180 Time (min)

Figure 31: Temperature profile for Test-4.

7.00E-03

6.00E-03

5.00E-03

4.00E-03

3.00E-03 Shear Strain Strain Shear 2.00E-03

1.00E-03

0.00E+00 0 20 40 60 80 100 120 140 160 180

Time(min)Time (min)

Figure 32: Shear strain vs. time at left corner of lead-free solder joint of Test-4 sample.

476 Advances in Fatigue, Fracture and Damage Assessment

In analyzing the data, the shear strain vs. time and shear strain vs. temperature curves are compared in the following. The strain ratcheting with the time is shown in all the four test results. Dissimilarities exist and are clearly noticeable between the strain variation obtained from the Pb-free package (Test-4) and those from the eutectic PbSn solder. In particular, during the temperature ramp- down period, the shear strain in the solder joint of Pb-free material experiences a faster recovery from its peak value. Meanwhile the variation of shear strain exhibits some distinct features at different stages of a thermal cycle. The strain ratcheting is considered to be caused by the competition between strain creep and stress relaxation in responding to the temperature variation with time. Test-1 and Test-2 involve the same type of samples with eutectic solder joints and have nearly the same dwell temperature except that Test-1 has a longer dwell time. Consistency is demonstrated by the similarity in the trend of strain variation as well as in the order of strain magnitude. In the early part of the temperature ramp-up, shear strain rises with the temperature mainly due to the rise of elastic stress. The high-temperature dwell both causes extended creep and induces the stress relaxation. During the ramp-down period, the lowered thermal mismatch results in reduced elastic stress, resulting in the recovery of the elastic strain. The magnitude of the highest strain in the sample of Test-1 is higher than that in the Test-2 sample. This may be attributed to the longer high-temperature dwell time in Test-1. The extended dwell period allows greater creep strain to accumulate, but as the results show that the accumulation decelerates and eventually diminishes as the stress relaxation goes. It is not difficult to imagine that in an accelerated thermal-cycling test, the solder-joint stress should rise during ramp up faster than the pace that the strain creep tries to relax the stress, resulting in a net increase in the effective stress. Conversely, in a slow cycle the stress relaxation should dominate, resulting in lower effective stress. A prolonged dwell under constant high temperature (Test-1) tends to stabilize the strain, whereas a relatively low high-temperature dwell (Test-3) results in a larger portion of elastic strain in the measured total strain, and thus shows a decreasing trend of strain during low-temperature dwelling. Test-4 sample has lead-free solder joints and the results show a similar trend as those from Test-3. Figs. 33−36 plot the shear strain vs. temperature for the four tests. The plots show the part of the shear strain that remains as the temperature cools down. A noticeable dissimilarity in the Test-4 results (Figures 32 and 36) as opposed to the other tests is, when the temperature ramps down, the lead-free solder apparently experiences a faster recovery from its peak and thus less permanent deformation remains at cooling down. A logical explanation may be that the lead-free solder is less creepy due to its higher melting point (~230oC). A higher proportion in the measured total strain is elastic strain and that recovers when the solder cools down.

Advances in Fatigue, Fracture and Damage Assessment 477

9.00E-03 8.00E-03 7.00E-03 6.00E-03 5.00E-03 4.00E-03

Shear Strain 3.00E-03 2.00E-03 1.00E-03 0.00E+00 0 20 40 60 80 100 120 140

TempTemp (ºC) (C)

Figure 33: Shear strain vs. temp (oC) at right corner in lead-based solder of Test-1 sample.

4.50E-03 4.00E-03 3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03 Shear Strain Shear 1.00E-03 5.00E-04 0.00E+00 0 20 40 60 80 100 120 140

TempTemp (ºC) (C)

Figure 34: Shear strain vs. temp (oC) at right corner in lead-based solder joint of Test-2 sample.

478 Advances in Fatigue, Fracture and Damage Assessment

4.000E-03 3.500E-03 3.000E-03 2.500E-03 2.000E-03 1.500E-03 Shear Strain 1.000E-03 5.000E-04 0.000E+00 0 20406080100

TempTemp (ºC)(C)

Figure 35: Shear strain vs. temp (oC) left corner in lead-based solder joint of Test-3 sample.

7.00E-03

6.00E-03

5.00E-03

4.00E-03

3.00E-03 Shear Strain Strain Shear

2.00E-03

1.00E-03

0.00E+00 0 20 40 60 80 100 120 140

TempTemp (ºC)(C)

Figure 36: Shear strain vs. temp (oC) right corner in lead-based solder joint of Test-4 sample.

Advances in Fatigue, Fracture and Damage Assessment 479 18 Concluding remarks

As previously discussed, there are numerous solder-fatigue models proposed and applied, including several very popular ones. One aim of the modeling is to correlate the package thermal-fatigue lives with different statistics-based life testing hoping to reduce the dependence on the cost- and time-inefficient testing. Each of these models may have some advantage over others in dealing with a particular aspect of the package reliability. Yet none is perhaps truly adequate to cover all actual failure mechanisms crucial to the solder interconnects. Many early models, while focusing on strain due to thermal-expansion mismatch, literally ignore the effect of creep. Recent ones have placed emphasis on creep as a main damaging deformation considering the low- temperature creep nature of the solder material. A key concern about the physics-based modeling is how to appropriately choose a solder constitutive relation and how to determine exact values for constitutive parameters in a particular application. In this regard, the multiple and inter-related factors and their uncertainties, high sensitivity of some factors to failure prediction and multiple non-linearity contribute to the complexity of physics-based analysis and curb the practicality of model execution. Shortage of first-hand data and lack of experimental model verification further make the modeling application a much more subtle task. Despite all this, credible applications supported by solid experimental validations are seen to gain momentum in the area of research.

Acknowledgement

The authors wish to express their appreciations for the financial support given to the research by NSERC (Natural Science and Engineering Research Council) of Canada, DARPA (Defense Advanced Research Program Agency) of US and many industrial partners (Motorola, Inc. and Onsemi-conductors, in particular). They are also grateful to the contributors to the research projects mentioned in the chapter, including Dr. Chaoyuan Liu, Tim Luise, Ming Zhou, Guihua Shi, Muhamod Ajmal of Ryerson, Jesse Zhou and Garry Moi of Motorola, and Roger Stout and Dr. Yong Xu of Onsemi, etc.

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480 Advances in Fatigue, Fracture and Damage Assessment

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