ABSTRACT 
 
Title of Disertation: EFECT OF DYNAMIC FLEXURAL LOADING ON THE 
DURABILITY AND FAILURE SITE OF SOLDER 
INTECONECTS IN PRINTED WIRING ASEMBLIES 
 
 
Joseph Varghese, Doctor of Philosophy, 2007 
 
Disertation directed by: Profesor Abhijit Dasgupta 
     Department of Mechanical Enginering 
 
This disertation investigates the durability of solder interconnects of area aray 
packages mounted on Printed Wiring Asemblies (PWAs) subjected to dynamic flexural 
loads, using a combination of testing, empirical curve fiting and mechanistic modeling. 
Dynamic 4-point bend tests are conducted on a drop tower and with an impact 
pendulum. Failure data is collected and an empirical rate-dependent durability model, 
based on mechanistic considerations, is developed to estimate the fatigue failure 
envelopes of the solder, as a function of solder strain and strain-rate. The solder plastic 
strain histories are obtained from the PWA flexural strain and strain rate, using transfer 
functions developed from 3D transient Finite Element Analysis (FEA) with rate-
dependent solder material properties. The test data also shows the existence of multiple 
competing failure sites:  solder, copper trace, PWB under solder pads, and layers of 
intermetalic compound (IMC) betwen the solder and solder pads.  The failures in the 
IMC layers are found to be either in the bulk of the IMC layers or at the interface 
betwen diferent species of IMC layers.  The dominant failure site is found to be 
strongly dependent on the loading conditions. The empirical model is demonstrated for 
solder failures as wel as Cu trace failures, and the transition betwen their competing 
failure envelopes is identified.  
This disertation then focuses in detail on two of these competing failure sites: (i) 
the solder and (i) the interface betwen two IMC layers. A strain-range fatigue damage 
model, based on strain-rate hardening and exhaustion of ductility, is used to quantify the 
durability and estimate the fatigue constants of the solder for high strain rates of loading. 
Interfacial fracture mechanics is used to estimate the damage acumulation rates at the 
IMC interface.  
The IMC failure model and the solder failure model provide a mechanistic 
perspective on the failure site transitions. Durability metrics, based on the mechanics of 
these two failure mechanisms, are used to quantify the competing damage acumulation 
rates at the two failure sites for a given loading condition. The results not only identify 
which failure site dominates but also provide estimate of the durability of the solder 
interconnect. The test data shows good correlation with the model predictions. 
The test vehicles used in this study consist of PWAs with Sn37Pb solder 
interconnects. But the proposed test methodologies and mechanistic models are generic 
enough to be easily extended to other emerging lead fre solder materials. Wherever 
possible, suggestions are provided for the development of test techniques or 
phenomenological models which can be used for engineering applications. 
A methodology is proposed in the appendix to implement the findings of this thesis 
in real-world applications. Damage in the solder interconnect is quantified in terms of 
generic empirical metrics, PWA flexural strain and strain rate. It is shown that the 
proposed metrics (PWA strain and strain rate) can quantify the durability of the solder 
interconnect, irespective of the loading orientation or the PWA boundary conditions. 
 
 
 
EFECT OF DYNAMIC FLEXURAL LOADING ON THE DURABILITY !AND 
FAILURE SITE OF SOLDER INTECONECTS OF !PRINTED WIRING 
ASEMBLIES 
 
by 
Joseph Varghese 
 
 
Disertation submited to the Faculty of the Graduate School of the 
University of Maryland, in partial fulfilment 
of the requirement for the degre of 
Doctor of Philosophy 
2007 
 
 
 
Advisory Commite: 
 Profesor Abhijit Dasgupta, Chair/Advisor 
 Profesor Donald Barker 
 Profesor Bongtae Han  
 Profesor Hugh Bruck 
 Profesor Isabel Lloyd 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Copyright by 
 
Joseph Varghese 
 
2007 
 
 
i 
ACKNOWLEDGEMENTS 
When I first came to College Park, I did not want to do a PhD. The plan was to get 
out with a Masters, find a good job, and buy a BMW. I have been here a long time, and 
the last few years have been the most intelectualy rewarding period of my life. 
No one deserves more credit for shaping my years in UMD other than Prof. Abhijit 
Dasgupta, a scholar and a gentleman. The more I sink into the real world, the more I 
realize the importance of his actions. 
I would like to thank Dr. Bongtae Han, Dr. Hugh Bruck and Shiva Subbaraman, 
whose advice was instrumental at a very crucial time of my graduate studies. They went 
out of their way to bring out the best in me, and for that I am very grateful. 
I am also grateful to Dr. Barker and Dr. Lloyd who have advised and provided me 
with fedback on several occasions. 
What would grad school be without your lab-mates? From the binge-drinking 
sesions in Cornerstone and Town hal, to the chain-smoking sesions outside ITV, to 
slep-deprived discussions during the CALCE metings? Lab 0102 of Bldg 089 was a 
second family and home for me. I would specialy like to thank Dan, Gayatri, Moustafa, 
and Seungmin with whom I regularly discussed my thesis, and Lynn for geting my 
paperwork to graduate school on time.  
I would also like to thank those who enriched my grad-life experience. The Gubro 
fraternity and its energy-sapping ?sink?, the Malu club and its ?kappa? sesions, the 
CALCE students, both former and current, Berkley apartments and its house of sin, the 
ALE club, ze German students and their Berwyn house ? the list goes on! 
ii 
Special thanks also goes to Dr. Das, Rama, and Jahnavi, who always made me fel 
welcome at their abode. Whether it was the home cooked food, or intelectual discussions 
about politics and economy, Dr. Das and Rama always went out of their way to create a 
comfort-zone for the boys, especialy the ?scavengers?.  
While the thesis would have been incomplete without the people mentioned above, 
my life would have been incomplete without Prachi, my weaknes and strength. She 
stood by me when I almost dropped out of undergrad, lifted me up through the doldrums 
of grad school, and encouraged me to convert my dreams to reality. Words cannot do 
justice to my appreciation for her. 
. 
iv 
Table of Contents 
 
Chapter 1: Introduction 1 
1.1 Problem Statement 5 
1.2 Background and Motivation 6 
1.3 Aproach 9 
1.4 Overview of the Thesis 9 
Chapter 2: Literature Review 11 
2.1 Product Level Drop Testing 12 
2.2 Board Level Drop Testing 15 
2.2.1 Test Methods 15 
2.2.2 Experimental Data 20 
2.2.3 Simulation 27 
2.2.4 Durability Models 32 
2.3 Correlation Betwen Board and Product Level Drop Testing 34 
2.4 Interconnect Level Testing 35 
2.5 Sumary 39 
Chapter 3: Empirical Rate-dependent Failure Envelopes 42 
Nomenclature 43 
3.1 Introduction and Problem Statement 44 
3.2 Aproach 47 
3.3 Test Setup 48 
v 
3.4 Specimen Design 51 
3.5 Damage Model 52 
3.6 Results 54 
3.7 Discussion 60 
3.8 Conclusions and Future Work 63 
Acknowledgements 63 
Chapter 4: Solder Fatigue Model 64 
Nomenclature 65 
4.1 Introduction 66 
4.2 Aproach 68 
4.3 Specimen Design 70 
4.4 Test Results 71 
4.5 FEA Model 72 
4.6 Efect of Strain Rate Hardening 78 
4.7 Efect of Ductility Exhaustion 80 
4.8 Solder Fatigue Curves 82 
4.9 Discussion 85 
4.10 Conclusions and Future Work 88 
Acknowledgements 89 
Chapter 5: Intermetalic Fracture Model 90 
5.1 Introduction 91 
5.2 Aproach 94 
vi 
5.3 Experiment Details 95 
5.4 Macroscale Model 97 
5.5 Microscale Model 100 
5.6 Durability Model 108 
5.7 Discussion 110 
5.8 Sumary and Conclusions 111 
Chapter 6: Examples: Competing Failure Mechanisms in PWAs During Dynamic Flexural 
Loading 113 
6.1 Introduction 114 
6.2 Aproach 118 
6.3 Experimental Data 119 
6.4 Completing Failure Models 122 
6.5 Competing Failure Envelope 127 
6.6 Discussion and Conclusion 130 
Chapter 7: Discussions and Sumary 133 
7.1 Role of Solder 133 
7.2 . Role of IMC Interface 135 
7.3 Sumary and Conclusions 137 
7.4 Contributions 139 
7.4.1 Test Methodology 139 
7.4.2 Empirical Dynamic Durability Model for the Solder 140 
7.4.3 Mechanistic Insights into Solder Fatigue 140 
vii 
7.4.4 Mechanistic Insights into Interfacial IMC Fracture 141 
7.4.5 Mechanistic Insight into Failure Transition from Solder to IMC 141 
7.5 Limitations and Sugestions for Future Work 142 
7.5.1 Range of Validity of Study 142 
7.5.2 Sample Size 143 
7.5.3 Efect of Thermal Aging on Solder Microstructure 143 
7.5.4 Efect of Strain Rate on Fracture Toughnes 143 
7.5.5 Material Science Based Perspective to Interfacial IMC Fracture 144 
7.5.6 FEA proximations 144 
Apendix A 145 
References 181 
vii 
List of Figures 
Figure 1-1: Schematic of a typical Bal Grid Aray. Source: 
ww.practicalcomponents.com 3 
Figure 1-2: Competing failure sites in the solder interconnect[5] 3 
Figure 3-1: Test matrix. The circles represent the test conditions. 48 
Figure 3-2: Four-point bend test fixture on servo-hydraulic mechanical tester. 49 
Figure 3-3: Drop tower with four-point bend fixture. 50 
Figure 3-4: Schematic diagram of the instrumentation. 51 
Figure 3-5: Specimen configuration. 52 
Figure 3-6: Durability and failure site in terms of the damage metrics: PWA strain and 
strain rate. 55 
Figure 3-7: Failure in bulk solder. 55 
Figure 3-8: Failure in Coper trace. 56 
Figure 3-9: Crack in FR4 under the solder bal. 56 
Figure 3-10: Variation of durability with PWA flexural strain for diferent PWA strain 
rates. 57 
Figure 3-11: Contour plot of the average durability of the solder. The dots represent the 
test data. 59 
Figure 3-12: Comparison of durability model fit: model vs test data. 59 
Figure 3-13: Schematic plot of competing failure envelopes for solder and FR4/Cu-trace.
 61 
ix 
Figure 3-14: Failure map for the solder interconnect. 62 
Figure 4-1: Flowchart of the aproach 69 
Figure 4-2: Specimen configuration 71 
Figure 4-3: FEA model with symmetric boundary conditions on the vertical axis at center 
of model 73 
Figure 4-4: FEA model of the solder interconnect 73 
Figure 4-5: Rate-dependent properties of the Sn37Pb solder 76 
Figure 4-6: Distribution of plastic strain in the solder bals at PWA strain and strain rate 
of 8E-3 and 1E-2 sec-1, respectively. 76 
Figure 4-7: Cross-sectioning image of the outer most solder joint shows failure in the 
solder neck [73] 77 
Figure 4-8: Top view of the solder neck. The averaging area is about 5% of the total cross-
sectional area. 78 
Figure 4-9: Front view of the solder neck. The averaging area comprises of a single row of 
two elements. 78 
Figure 4-10: Log-log plot of average solder strain rate to the average PWA flexural strain 
rate 79 
Figure 4-11: FEA transfer function for diferent PWA strain rates and solder plastic strain 
rates. 79 
Figure 4-12: Log-normal plot of normalized failure strain versus solder strain rate. 
Estimated from [5]. 81 
x 
Figure 4-13: Log-normal plot of variation of failure strain versus solder plastic strain rate
 82 
Figure 4-14: Efect of loading rate on solder plastic strain, failure strain, and ratio of the 
two. 84 
Figure 4-15: Fatigue curve for dynamic loading of solder 85 
Figure 4-16: Family of Coffin-Manson curves for Sn37Pb solder at diferent plastic strain 
rates. 87 
Figure 5-1: Interface of two IMC layers at diferent thermal aging conditions [5] 93 
Figure 5-2: PWA specimen, showing location of components and strain gage. 96 
Figure 5-3: Fracture in the IMC layer on the package side of the solder [85][86] 97 
Figure 5-4: 2D model of PWA with symmetric boundary conditions 97 
Figure 5-5: The averaging area comprises of two elements each in the solder and the 
coper trace in the finely meshed outer solder bal. 99 
Figure 5-6: Variation of peeling and shear stres in the IMC layer with PWA strain 100 
Figure 5-7: Variation of bulk and interfacial Stres Intensity Factor with PWA strain 103 
Figure 5-8: Plot of bulk and interfacial phase angle with PWA strain shows almost no 
variation. Hence the mode mixity can be asumed to be constant 103 
Figure 5-9: 3D plot of the variation of G
t
/G with wavines and phase angle 105 
Figure 5-10: FEA transfer function for diferent interfacial morphologies. 106 
Figure 5-11: Typical ESEM picture of failure site 106 
Figure 5-12: Normalized interfacial strain energy release rate as a function of PWA strain, 
for diferent morphologies betwen the IMC layers. 107 
xi 
Figure 5-13: Plot of interfacial fatigue curve betwen the two examined IMCs. 109 
Figure 5-14: Variation of average crack propagation rate with G
t
/G
c
. 110 
Figure 6-1: Interface of two IMC layers at diferent thermal aging conditions 116 
Figure 6-2: PWA specimen, showing location of components and strain gage. 119 
Figure 6-3: ESEM image of the IMC layer betwen the solder and the Cu-pad of the 
unaged PWA [85] 120 
Figure 6-4: ESEM image of the IMC layer betwen solder and Cu-pad of the aged PWA 
[85]. 120 
Figure 6-5: Fracture in the solder on the package side of the interconnect [86]. 121 
Figure 6-6: Fracture in the IMC layer on the package side of the interconnect [86]. 122 
Figure 6-7: 2D model of PWA with symmetric boundary conditions 123 
Figure 6-8: Solder transfer function. 123 
Figure 6-9: Variation of peeling and shear stres in the IMC layer with PWA strain 124 
Figure 6-10: Normalized interfacial strain energy release rate as a function of PWA strain, 
for diferent morphologies betwen the IMC layers. 127 
Figure 6-11: Competing failure envelopes for solder and interface betwen the IMC layers
 128 
Figure 6-12: Comparison of predicted durability and experimental data. 128 
xii 
List of Tables 
Table 3-1: Experimental results. 57 
Table 3-2: Empirical damage constants. 58 
Table 4-1: Experimental results 72 
Table 4-2: Linear elastic material properties of the PWA 74 
Table 4-3: Bilinear material properties of coper 74 
Table 4-4: Quasi-static inelastic material properties of solder 75 
Table 4-5: Dynamic material properties of solder 75 
Table 4-6: FEA transfer function constants 80 
Table 4-7: Durability in terms of empirical [73] and mechanistic parameters 83 
Table 4-8: Rate-dependent durability constants for solder 85 
Table 4-9: Coffin-Manson Model constants for solder 87 
Table 5-1: Material properties of the IMCs and values of the interfacial parameters 102 
Table 5-2: Typical values of the interfacial wavines 107 
Table 5-3: Durability in terms of empirical [86] and mechanistic parameters 108 
Table 5-4: FEA material properties 118 
Table 6-1: Durability and failure sites of the PWAs 121 
Table 6-2: Material properties of the IMCs and values of the interfacial parameters 125 
Table 6-3: Typical values of the interfacial wavines for the aged PWA 126 
Table 6-4: Examples for methodology 129 
 
 
 1  
Chapter 1: Introduction 
Dynamic loading plays a crucial role in the performance and reliability of 
electronic devices. Portable electronic devices are often subjected to transient loads and 
vibration loading due to drop events during mechanical handling, acidental misuse, or 
shipping (transportation). Hence, they need to be rugged and sufficiently shock resistant. 
Furthermore, these products are typicaly densely packed with electrical and 
electromechanical components, have complex displays, heavy bateries, and are housed 
in thin-waled plastic cases. Many of the design features to reduce their weight and size, 
makes them susceptible to shock induced failure. Examples of such products include cel 
phones, laptops, Portable Digital Asistants (PDA), pagers, hand-held gaming products 
and portable audio-video entertainment devices. 
A common cause of failure in portable electronics is acidental drop by the user. 
Military applications often generate repetitive shocks (artilery fire), sudden high G 
loading (launching or maneuvering), or balistic impact. The final product has to be 
designed and tested for drop/shock loading in these environments. The main reliability 
chalenges are usualy mechanical failures like dislodging of the bateries, disengaging of 
the snap fits, contact damage in the casing, cracking of the Liquid Crystal Display (LCD), 
and fatigue of the electrical connections in the Printed Wiring Asembly (PWA), to name 
a few. Of al the potential failure sites in the product, this disertation focuses on PWA 
failure, specificaly in the solder interconnect betwen the component and the board. 
The PWA is connected to the housing of the product by using fasteners like screws, 
spring clips, etc. When the product is dropped, the PWA acts like a plate subjected to an 
aceleration pulse at the base. As expected, the structural response of the PWA depends 
 2  
on the distribution of components on the board, the boundary conditions imposed by the 
fasteners that connect the board to the product casing, and the drop orientation. The 
durability of solder interconnects of the components mounted on the PWA depends on 
this structural response. 
Area-aray components, like Bal Grid Arays (BGAs), are increasingly being used 
in portable devices because of their ability to acommodate a large number of I/Os for a 
given footprint. A substrate is used to redistribute the very fine pitch (as smal as 0.075 
m) peripheral pads on the chip to much larger pitch (1mm, 0.75mm and 0.5mm) area-
aray pads on the board [1]. As shown in the figure below, the die is atached with an 
adhesive to this substrate. The demand for increased device functionality has led to BGA 
designs with interconnects of finer pitch, which thereby shrinks the package dimensions. 
Hence the size of the solder interconnects is geting smaler, which can make it more 
sensitive to streses induced by dynamic flexure of the PWA. One of the most common 
failure sites due to dynamic loading of electronic products is in the surface mount solder 
interconnect betwen the board and the substrate of the component, commonly refered to 
as the second level interconnects. Researchers are trying to develop techniques to 
characterize, quantify, and predict the durability of the solder interconnect at high strain 
rates of loading. 
What complicates the proces of developing a generic test technique to quantify 
solder interconnect durability is the presence of competing failure sites. Researchers have 
reported multiple failure sites in the solder interconnect, depending on the solder type, 
plating material, specimen geometry and loading conditions [2-4]. For example: it was 
shown that interconnects with Electroles Nickel Imersion Gold (ENIG) finish have a 
 3  
tendency to fail either in the solder or the intermetalic layer at the solder ? copper pad 
interface during drop test conditions, while those with Organic Solderability Preservative 
(OSP) finish tend to fail either in the solder or in the PWB/ copper trace ().  Thermal 
aging, which changes the microstructure of Sn37Pb solders and the morphology of the 
intermetalic layer, was also found to afect the location of the failure site. Each failure 
site has a characteristic failure mechanism, and hence, a diferent influence on 
interconnect durability. The complex interactions betwen the competing failure 
mechanisms, especialy under diferent conditions of high strain-rate mechanical loading 
and thermal aging, have not yet been fully understood by the microelectronics reliability 
community. 
 
Figure 1-1: Schematic of a typical Bal Grid Aray. Source: ww.practicalcomponents.com 
 
Figure 1-2: Competing failure sites in the solder interconect[5] 
 
In summary, there is tremendous interest in extending the current state-of-art to 
quantify the durability and understand failure site transitions in the PWAs under drop 
testing conditions, for thre reasons: 
 4  
1. Existing testing methodologies do not provide adequate insight into the physics of the 
failure of the interconnect; and although useful from a statistical comparative 
perspective, have limited validity because they are conducted at the system level and 
they treat the test specimen as a ?black-box?. For example, durability is generaly 
quantified in terms of number of drops to failure, without conducting any analysis of 
the modal response of the board, location of component on the PWA, post-impact 
vibration, location of failure site, streses at the failure site, etc.  
2. There is a need for a systematic methodology, either empirical or mechanistic, to 
characterize the observed failure site transition from the solder to other parts of the 
PWA. 
3. Conducting drop tests on full products is a very costly and time-consuming proces, 
and the results are very dificult to post-proces. There is a need for a quicker, 
cheaper technique to replicate the loading experienced by the PWA during asembly 
and field conditions. 
This disertation presents a detailed study to characterize the drop durability of the 
solder interconnects in the PWA. The durability and failure site are characterized as a 
function of the load amplitude and loading rate (individualy or combined).  This study 
also shows that PWA flexural strain and strain rate can be used as empirical durability 
metrics for any drop orientation and PWA boundary condition. An empirical Failure Site 
Transition Zone (FSTZ) is characterized on the basis of the proposed durability metrics, 
to identify the transitions betwen competing failure mechanisms like solder fatigue and 
copper trace fatigue. Furthermore, detailed mechanistic analysis is conducted to provide 
insights into the failure site transition from the ductile solder to the britle interface 
 5  
betwen two IMC layers. Insights are developed to explain the complex interactions 
betwen the solder and the intermetalic layer. Durability and the failure site of the solder 
interconnect is characterized in terms of both the empirical and mechanistic parameters. 
1.1. Problem Statement 
The problem statement of this study is to understand the interactions betwen the 
solder and the intermetalic layer, in order to predict the durability and the failure site in 
surface mount interconnects during drop testing of the PWA. The focus of this study is 
limited to two common failure sites: the bulk of the solder joint and the interface betwen 
the two IMC layers at the interface betwen the solder and the bond pad. To conduct this 
analysis, the two competing failure modes in the interconnect and their respective root 
causes must be quantified. This raises a range of isues, listed below, that must be 
resolved before the stated problem statement can be addresed. 
1. The prevalent metric used to characterize drop durability is number of drops from a 
given height. Unfortunately, this metric is specific to the geometry of the PWA, 
orientation of drop, and boundary conditions of the PWA; and cannot be easily 
extrapolated or generalized to other architectures and loading configurations. Generic 
damage metrics that can quantify the durability, without being influenced strongly by 
the test setup or the specimen configuration, need to be identified. Furthermore, these 
metrics should serve as asesing parameters to capture the transition of failure sites 
during diferent loading conditions.  
2. A test setup has to be developed to help researchers understand the individual and 
combined efects of loading amplitude and loading rate on the interconnect. The 
design, fabrication, and instrumentation of an experimental setup for repeatable and 
 6  
acurate testing at high loading rates can be quite chalenging. Failure monitoring is 
an additional chalenge because the interconnect fracture during drop testing may last 
only for a few microseconds before the crack closes up again. 
3. Limited work has been done to characterize the failure site transitions or to 
understand the complex interactions betwen the solder and the intermetalic layer. 
Mechanistic parameters that can capture the physics of the problem, and are 
independent of loading condition and specimen geometry must be identified. 
4. A model must be developed using numerical and/or analytical techniques, to 
quantitatively explain the experimental results published in this thesis and other 
related experimental results published in the literature. 
1.2. Background and Motivation 
In general, drop testing is expensive and time-consuming, requiring much 
manpower in measurement and failure analysis. At present, manufacturers of electronic 
devices use the JESD22-B104-B standard for mechanical shock [6] to quantify reliability 
of the portable electronic product by the number of drops to failure. The electronic 
product is held in the desired orientation and atached to a drop cariage that is alowed to 
fal. The product is released just before it hits the ground to alow it to execute its natural 
rigid body motion and structural dynamics. But even a single drop event of an electronic 
product can produce a complex load history [7]. The structural response of the PWA is 
strongly dependent on the mas distribution of the internal electronics and the orientation 
of drop [8]. Hence, characterizing the drop durability of the interconnect by running tests 
or simulations at the product level is a very complex task. Drop testing the PWA is an 
 7  
easier solution to the same problem.  
Board level tests are usualy conducted on a Sub-asembly Drop Testing Machine 
based on the JEDEC JESD22-B111 Standards [9]. The PWA is screwed on to a drop 
cariage in the horizontal position at four or six points and dropped from diferent drop 
heights. Instrumentation includes acelerometers on the drop cariage, strain gages on the 
PWA and a high speed failure monitoring system. The drop durability is quantified in 
terms of the number of drops to failure. There are some isues with the existing technique 
that necesitate the development of an alternate test technique. These are briefly 
discussed below. A detailed description of these limitations is presented in the next 
chapter (Chapter 2) 
The durability of the solder interconnects is dependent on a variety of parameters: 
mas distribution in the PWA, drop height, dynamic material properties of the structure, 
boundary conditions, etc. The failed interconnect is usualy in the outermost row of the 
bal grid aray, implying that failure is driven by flexure of the PWA [10]. So far, 
researchers have developed an understanding damage acumulation in the interconnect, 
while focusing on a single failure mechanism. Researchers have also begun to explore 
the individual contributions of loading amplitude and rate on interconnect durability. The 
current state-of-art can be extended by characterizing and analyzing the efect of 
competing failure modes, under various dynamic loading conditions. 
For a given interconnect, the potential failure mechanisms are bond pad lift-off, 
copper trace failure, fracture of the britle intermetalic and fatigue failure of the ductile 
solder. Tests indicate that the failure site within the interconnect changes from solder bal 
to intermetalic or bond pad as the drop height increases [11].  Limited work has been 
 8  
done to understand the strain rate dependent transitions betwen these failure sites. 
Existing durability estimation models for drop testing are not generic in nature and 
are specific to the package mas, package design, and orientation. The parameters used to 
quantify durability (plastic strain or peeling stres) are based on bulk solder material 
properties, even though test data indicates that the failure site is not the solder bal [12]. 
This is primarily due to the fact that the damage constants are unknown for the other 
failure sites. 
Another factor that is geting increased atention is the transition to lead fre 
solders. The behavior of lead fre interconnects under vibration/shock loading conditions 
is largely unknown. The dynamic properties of many lead fre solders are stil being 
determined. Limited drop test results are available to compare the drop durability of 
leaded solders and Pb-fre solders. The empirical design rules for leaded solders may be 
no longer suitable for those with lead-fre solders. As a consequence, establishing new 
design rules for Pb-fre packages for drop durability has become an important topic in the 
electronic packaging industry. 
With this motivation, this disertation aims at addresing the above isues by 
providing generic empirical metrics to quantify durability and failure site, irespective of 
boundary conditions, and drop orientation, but dependent on the PWA geometry. The 
proposed empirical metrics have further been applied to Pb-fre and SnPb solder systems, 
in the as-reflowed and aged conditions, to provide a quantitative comparison of the 
durability under dynamic loading conditions, which are stil not wel-documented in 
literature. 3D transient Finite Element Analysis (FEA) has been used to extract empirical 
fatigue constants of the solders from high strain-rate tests.  Furthermore, interfacial 
 9  
fracture mechanics has also been used to provide a mechanistic insight into two 
competing failure sites: solder and the interface betwen the two IMC layers 
1.3. Aproach 
Acelerated reliability tests are used for conducting this study and correlating the 
laboratory and field loading conditions. A high-speed four point bend tester, built in-
house, is used to characterize the durability and the failure site transitions. A high speed 
data acquisition and resistance monitoring system is used to monitor failure in the solder 
interconnect. The test coupons used in this disertation have very simple designs to alow 
in-depth analysis with minimum complexity. Al test coupons used for in-depth analysis 
have Sn37Pb BGA components mounted on the board. Eutectic Sn37Pb has been chosen 
as the solder material because its dynamic properties have been wel characterized and 
documented in literature. Interfacial fracture mechanics, using linear elastic material 
properties, is used to develop a qualitative understanding of the failure site transitions 
within the solder interconnect. 3D transient finite element analysis, with rate-dependent 
solder material properties are combined with the interfacial fracture mechanics model to 
estimate the strain energy release rate of the non-planar interface within the IMC layer. 
The results of the analysis are used to provide insights into the failure site transition and 
the durability of the interconnect. This is compared with experimental results to verify 
the hypothesis made in the analysis. 
1.4. Overview of the Thesis 
This thesis includes manuscripts that have been either published in, or acepted by, 
or submited to scholarly journals. An exhaustive literature review about durability 
 10  
asesment and failure site transitions in the solder interconnects of PWAs is presented in 
Chapter 2. The test setup, instrumentation and failure monitoring schemes are discussed 
in detail in Chapter 3. PWA flexural strain and strain rate are used as empirical durability 
metrics to quantify the durability of the solder interconnects of a PWA supported in the 
four point bend configuration and subjected to out-of-plane bending. A ?Failure Map? is 
developed, in terms of PWA strain and strain rate, to plot the dynamic fatigue failure 
envelopes of the solder and identify the FSTZ. 3D transient FEA is used to understand 
the behavior of the solder at diferent loading conditions, and to determine the empirical 
fatigue constants for cyclic loading of the solder at high strain rates. Chapter 4 introduces 
a mechanistic model to understand individual and combined efects of load and loading 
rate on the failure of the solder. A new damage metric is proposed to quantify rate-
dependent durability of the solder. Chapter 5 characterizes failure in the interface 
betwen the IMC layers of the solder interconnect. FEA is used to conduct stres analysis 
at the macroscopic level and interfacial fracture mechanics is used at the microscopic 
level. Chapter 6 introduces a technique to predict the durability and failure site of solder 
interconnects of PWAs subjected to dynamic flexural loading. The proposed technique 
draws on the mechanistic models developed in Chapters 4 and 5. The predicted durability 
and failure site show good correlation with experimental data. 
 
 1  
Chapter 2: Literature Review 
This chapter starts by reviewing existing techniques to estimate the durability of 
portable electronic products subjected to drop tests. This is followed by a discussion of 
the drawbacks of these test methods specific to quantifying solder interconnect durability. 
Board level drop testing is then reviewed extensively, with a focus on the test technique 
and failure site transitions induced by loading rate and thermal aging. FEA simulation of 
board level drops and proposed durability models are also reviewed. Since this 
disertation studies failure site transition from the solder to the interface betwen the IMC 
layers, a literature review of dynamic testing of individual solder interconnects is also 
conducted. The test techniques and failure envelopes used to characterize failure in the 
intermetalic layer of the solder interconnect are reviewed. The drawbacks of the existing 
state-of-art and the need for a new study to characterize durability and failure site 
transitions are then presented. 
The problem of understanding the response of a structure to shock/vibration 
loading is not completely unknown. Much work has been done to understand the 
structural response during misile launch/gun fire [13, 14], occupant safety during vehicle 
collisions [15, 16], durability of casks under drop test conditions [17], random vibration 
induced fatigue of aircraft parts [18], dynamic response of human beings during road/rail 
transportation [19], etc. As described later on in this thesis, some of the tools used for 
analysis in the situations mentioned above have been implemented or modified in this 
study. 
 12  
2.1. Product Level Drop Testing  
At present, the trend among electronics manufacturers is to use the JEDEC 
JESD22-B104-B standard [6] to quantify reliability of the portable electronic product by 
the number of drops to failure. The electronic product is held in the desired orientation 
and atached to a drop cariage that is alowed to fal. The product is released from the 
drop cariage just before it hits the impact surface. This alows control of drop orientation 
before impact and also alows the electronic product to undergo its natural dynamic 
response after impact. Goyal, et al. [7, 20] used strings to control the orientation, while 
Lim, et al. [8] and Seah, et al. [21] used a gripper style mechanism. A load cel is used to 
determine the impact force. The drop cariage and the electronic product usualy have 
acelerometers and/or strain gages on them. The drop event is usualy recorded with a 
high speed camera to verify repeatability of orientation of impact. Published literature 
shows that a variety of failure sites and modes are possible for a given product level drop 
test. This includes cracking of the LCD scren, detachment of the batery case, damage in 
the plastic housing, etc. This study, and hence the literature review, focuses on solder 
interconnect failure in the area aray components mounted on the PWA, inside the 
product. 
A single drop event of an electronic device can produce a complex load history due 
to ?clatering?. Goyal, et al. [7, 22] used high-sped photography to show that during a 
single drop, one corner of the electronic product usualy touches down first and there is 
?clatering? as other corners strike repeatedly due to rebounds. During ?clatering?, the 
product can experience extremely high net velocity changes at each impact, thus inducing 
velocity shocks. Clatering of the product can also lead to alternating shocks that could 
 13  
cause resonance in suspended fragile components. Goyal, et al. [23, 24] also showed that 
the shock response of the electronic product is dependent on its mas distribution. Shock 
Response Spectrum (SRS) was used to correlate product response to the incident shock 
pulse and the natural frequency of the internal electronics and to define damage 
conditions in the suspended sub-asemblies by checking if the peak aceleration or peak 
displacement exceded some critical value. 
Work has also been done to characterize the drop durability of electronic products 
and sub-asemblies using dynamic 3D FEA. Low [25] simulated the drop an electronic 
product surrounded by a cushion bufer and showed that the cushion reduces the 
magnitude of the impact load. Hua, et al. [26] simulated the drop of a spindle fixation 
subasembly of an electronic product at various impact velocities and orientations to 
determine the G levels at which the spindle wil fail. Similar work has been done to 
characterize the impact force and drop response of 2 way radios [26], cel phones [26, 27] 
and audio systems [28]. Thus, it is very common to use FEA to identify the failure-prone 
zones in a portable product, or to identify critical values of the loading conditions under 
which the product may fail. 
Characterizing the drop durability of the interconnects by running tests or 
simulations at the product level is a very complex task. When a portable electronic device 
is dropped, part of the kinetic energy goes into the rigid body motion during rebound, 
part goes into the strain energy of deformation of the internal electronics and external 
housing, and the rest is lost to damping and friction. Only a portion of the energy 
absorbed by the internal electronics ends up causing damage to the interconnects. The 
amount of energy responsible for deformation of the interconnect depends on the loading 
 14  
conditions, boundary conditions, component architecture, housing structure, and 
materials. This was verified during drop tests conducted by Lim, et al. [8, 29] and Seah, 
et al. [21] that showed that the strains and acelerations in the PWA varied with the 
electronic device for the same orientation of drop, and varied with orientation for each 
device of the PWA. Even if the test condition is kept constant, the contact damage in the 
outer surface of the product wil change the dynamics of the PWA inside the housing. No 
study has been conducted so far to quantify the efect of contact damage in the housing 
on the internal behavior of the durability of the product.  
It is therefore not possible to create a generic test specification for drop durability 
of surface mount interconnects, which is based on the incident kinetic energy of drop or 
shock response spectrum damage estimation criteria. Instead, it is beter to relate the 
damage in the interconnects to the local response close to the failure site. This 
relationship is les dependent on the incident kinetic energy, boundary conditions, mas 
distribution and orientation of drop. 
Board level testing can be used to develop the failure envelopes for the 
characteristic damage causing mechanisms in the surface mount interconnects. From an 
industry perspective, testing the drop durability of the interconnect at the board level is 
easier and can be done by the OEM. However, this does not mean that product level drop 
testing can be neglected. Experimental work [30] indicates that constraining a sub-
asembly to behave as a single system and not alowing natural motion of the product 
during drop testing can lead to underestimating the damage potential of the drop and may 
even mis important failure mechanisms.  This is explained in detail in the following 
sections. 
 15  
2.2. Board Level Drop Testing 
JEDEC standards are generaly used by the portable electronics industry to quantify 
PWA durability. While following the existing standard has its own advantages, it is also a 
black box technique which offers no insight into the physics of the drop event. This has 
motivated many researchers to develop alternate techniques to quantify drop durability 
and understand the phenomenon. This section begins with a review of al the test setups 
developed to understand the behavior of solder interconnects at high loading rates, 
including the JEDEC board level drop tester. The experimental data and FEA simulations 
are then discussed to show the efect of material properties, loading rate and other 
parameters on the durability and the failure site of the interconnect. The section ends with 
a review of damage metrics that have been proposed by various researchers. 
2.2.1 Test Methods 
Board level tests are usualy conducted on a Sub-asembly Drop Testing Machine 
based on the JEDEC Standards [9]. The PWA is mounted on to the drop cariage in the 
horizontal position at four or six points. The drop cariage fals along two guide rods on 
to stationary stops, and induces out of plane displacement in the PWA on impact. The 
impact surface can be changed to vary the profile of the impact force. On impact, the 
PWA responds to the transient impact force applied to the base and then vibrates at its 
natural frequency. Instrumentation includes acelerometers on the drop cariage, strain 
gages on the PWA and a high speed failure monitoring system. The metric for 
characterizing durability is the number of drops to failure. 
The amplitude of the shock pulse depends on the height of the drop, but the 
 16  
duration of the pulse is strongly influenced by the material properties of the impact 
surface and the fixture. As explained by Wong, et al [31], the duration of the shock pulse 
during the drop test depends on the time it takes for the stres waves to bounce from the 
fre end and come back as tensile waves. Part of the compresive wave goes into the 
standoffs and gets converted from longitudinal waves to flexural waves in the PWA. The 
maximum aceleration is at the clamped ends of the PWA because that is directly 
connected to the drop fixture that experiences extremely high aceleration as it is stopped 
during drop. The highest aceleration is at time of impact and the other aceleration 
spikes are after a certain time gap depending on how much time it takes for the flexural 
wave to reach the center of the board. The wave at the center has lower amplitude and 
higher time period due to the damping of the wave. 
The dynamic response of the PWA to drop tests conducted acording to the 
JESD22-B104-B standards can vary depending on the robustnes of the test setup. Jing-
en, et al. [32] conducted JEDEC board level drop tests on PWAs populated with 
TFPBGA packages facing downwards. Acelerometers were atached on the fixture and 
the center of the PWA to measure the impact aceleration and the board response, 
respectively. Strain gages were also atached to the PWA, on the opposite side of the 
component. Fourier transforms of the data obtained from strain gages showed that the 
fundamental frequency of vibration varied with the tightnes of the screw holding the 
PWA to the fixture. As the number of drops increases, the screw tends to loosen, leading 
to a phase lag in the PWA response. Wearing out of the impact surface after repeated 
drops can change the coeficient of restitution, thus changing the nature of the input 
aceleration pulse. Similar drop tests were also conducted by Wang, et al. [33] on PWAs 
 17  
clamped at both edges, mounted with flip-chips of diferent sizes, with and without 
underfil. The drop height was maintained as 1 meter to obtain an input aceleration of 
about 1000 Gs. The PWA was instrumented with an acelerometer and strain gages and a 
high speed camera was used to measure the board displacement. These tests too, showed 
that the dynamic response of the PWA was strongly dependent on the impact surface. 
Thus, the same drop height may induce diferent levels of damage in the PWA. A source 
of testing variability that has not been studied so far is the change in the boundary 
condition due to damage in the PWA, near the mounting screws on the JEDEC fixture. 
Alternate techniques have also been proposed to quantify the durability of PWAs 
under dynamic loading conditions. This study used a pendulum style test setup [10] to 
impact a constrained PWA in the in-plane and out-of-plane orientations.  The kinetic 
energy of impact was varied by changing the mas of the stel sphere and/or the impact 
velocity. The impact velocity was varied by changing the pendulum release height. For 
out-of-plane impact, the specimen was oriented verticaly and clamped at its four corners. 
For in-plane impact, the specimen was oriented horizontaly and the two edges 
orthogonal to the impact axis are guided with leaf springs to remain in the impact plane. 
Horizontal motion of the impacted edge led to bending of the specimen. The PWA was 
instrumented with strain gages mounted near the edge of the component and a high speed 
failure monitoring system. Durability was quantified in terms of PWA strain obtained 
from the strain gage under the asumption that the efect of the boundary conditions is 
negligible. 
The asumption made in this study about the boundary conditions may not be valid 
al the time. Fong Kuan, et al. [34] placed strain gages on one side of a JEDEC standard 
 18  
PWA to correlate local PWA strains to solder joint durability. For a given loading 
condition and location on the PWA, the strain gages showed higher strains for the 6 
screw configuration than for the 4 screw configuration. This is because the strains 
measured on one side of the board are afected by the in-plane strains induced by the 
clamped boundary condition of the board and by the flexural strains due to the curvature 
of the board. Solder durability is a function of PWA flexure, and due care must be taken 
to eliminate the efect of boundary conditions from the strain gage data. This can be 
remedied by using strain gages on both sides of the PWA at the same location to 
eliminate the efect of the boundary conditions, or by using simply supported boundary 
conditions. 
Lal, et al [35] also developed an in-plane drop test method for PWAs. A glas tube 
with a diameter that is equal to the board edge length was used to guide the drop. High 
speed imaging was used to track the post-impact deflections of the PWA. Repeatability 
was measured by tracking the angle of the PWA before and after impact. Durability was 
quantified in terms of number of drops to failure. 
In spite of the work done by the researchers mentioned above, there was a growing 
need to develop a new technique due to two reasons: 
1. To understand the factors that afect drop durability, one needs to be able to closely 
control the input loading conditions. This includes the amplitude and rate of loading. 
This is not possible with the test setups mentioned above. 
2. A variety of Pb-fre solders are available that can replace SnPb solders. A variety of 
material combinations in terms of solder aloys and pad finishes are possible. The 
reliability of each material combination wil be diferent and the test setups 
 19  
mentioned above are very time and labor intensive. 
For most plastic encapsulated microelectronic systems, the mas of the component 
is very smal. Dynamic flexural tests to replace conventional drop/impact tests were 
developed after Wong, et al. [36] proved experimentaly that damage to the solder due to 
component inertia is negligible when compared that due to PWA curvature. They 
conducted drop tests on PWAs that were constrained from flexing so that the only failure 
driver was component inertia. The aceleration pulse due to drop was as high as 3000 Gs 
with a time period of 0.5 miliseconds. An additional mas was atached to the component 
to increase its inertia. The PWA did not show any failure, even with such high 
component inertia, thus leading to the conclusion that PWA flexure is the dominant 
parameter that drives solder interconnect failure. Hence, the efect of component inertia 
on solder durability can be neglected. 
Motivated by the work done above, this study used high-speed four point bend 
testing to quantify drop durability [37]. A commercialy available servo-hydraulic test 
machine was used at low loading rates. High loading rates were achieved by using a 
modified drop tower to drop stel spheres on a fixture holding the specimen in a four-
point configuration. The PWA was instrumented with strain gages and a high speed 
failure monitoring system. The PWA was simply supported and not clamped so that the 
strain gage measured only the flexural strain. This alowed a direct correlation betwen 
the sensor data and durability, without any post-procesing to remove the efect of 
clamped boundary conditions from the strain gage data. Durability was quantified in 
terms of PWA flexural strain and strain rate. 
The post-impact strain response of a PWA experienced the first mode of vibration 
 20  
resembles a damped sinusoidal wave. A conventional four point bend can induce cycling 
loading on a PWA, but can not capture the dynamic response of the PWA. Seah, et al. 
[38] developed a high-speed displacement-controlled bending machine where a cam was 
used to enforce a PWA strain profile that was similar to that sen during a JEDEC drop 
test. The PWA with a component at the center is clamped at four corners and atached to 
an anvil at the center, such that it resembles a four point bend setup. This leads to 
uniform bending moment around the component and a single rotation of the cam moves 
the anvil such that the PWA experiences a sinusoidal strain profile.  Durability was 
quantified in terms of PWA strain, at diferent values of loading frequency. Reif and 
Bradley [39] induced a similar type of damped sinusoid PWA response by conducting 
indirect impact tests. The PWA was clamped at the corners and loaded with an anvil in 
the region of interest. The anvil had had two knife edges that induced a four point bend 
condition. The mas was dropped from diferent heights on to the anvil. On impact, the 
PWA vibrated in its natural frequency and PWA strain was used as a metric to quantify 
durability. 
Marj?maki, et al. [40] used vibration to understand drop behavior of PWAs. They 
compared the failure sites observed in PWA vibration and drop tests. Specimens with 
Cu/OSP and Ni/Au asemblies tested with 10 replications. Solder cracking was observed 
at low amplitude vibration. Failure site transition from solder to the intermetalic layer 
and FR4/Cu trace was observed with increase in vibration amplitude. Similar failure sites 
observed for both drop and large amplitude vibration. 
2.2.2 Experimental Data 
Tan, et al. [41] explored the efect of loading rate on the overstres failures of 
 21  
solder interconnects. They conducted bend tests on PWAs mounted with Multi Chip 
Modules (MCMs) at displacement rates ranging from 0.1 m/sec to 10 m/sec and then 
drop tests from heights of 1 meter and 1.5 meters. As ramp rate increases, the deflection 
and load required for failure decreases. But at higher ramp rates, load and deflection 
don?t folow the same trends. Graph of PWA strain vs time tapers off as deflection is 
increased due to the yielding of the solder bal, which reduces the board curvature. Visual 
inspection also showed that solder bal deformation decreases with increasing loading 
rates. The failure site during bend was in the solder, while the dominant failure modes in 
drop testing were bond-pad lift off and intermetalic fracture. Similar studies were also 
conducted by Geng, et al [42] on PWAs mounted with eutectic Sn-Pb solders. Thre 
point bend tests were used to show that the solder failed at leser board deflections as the 
displacement rates increased. 
Yu, et al. [2] explored the efect of vibration mode shapes on the drop durability of 
PWAs. The test coupons were PWAs mounted with a single SnAgCu BGA component. 
The tests were conducted using a JEDEC style drop tester with a mas atached to the 
PWA, on the opposite side of the component. The location of the mas was varied to 
induce diferent mode shapes during the post-impact vibration of the PWA. As expected, 
drop tests conducted with the component and mas at the center of the board showed a 
decrease in durability with increasing drop height. For the same drop height, tests done 
with the mas and component at diferent locations showed a relative increase in 
durability when the chip is not at the location of the primary mode shape. They also 
noticed a change in the failure site from the bulk solder to the intermetalic layer with 
increasing drop height. 
 2  
Jing-en, et al. [43] used JEDEC board drop tests to conduct a Design of 
Experiments (DOE) study on durability of Systems in Package (SiP) components. The 
test coupon had 12 BGA components: 6 on each side of the center line. The BGA 
components had diferent package sizes, bal layouts, package layouts and die 
thickneses. The boards were supported at 4 points and failure site was found to be in the 
intermetalic layer of the outer most solder bal on the component side. The test data 
showed that durability decreases with increased solder bal height. Increase in diameter 
decreases durability because smaler solder bals are more compliant which reduces 
stres. However, when solder bal diameter is smaler than solder mask opening, the 
stres increases and durability is reduced. SnAgCu components were shown to have 
lower impact life than eutectic Sn-Pb components. This is because SnAgCu has a larger 
elastic modulus (46GPa) as compared to eutectic Sn-Pb (31.6GPa), so the streses are 
higher. For the same distance of the outer perimeter from the neutral point, drop 
durability was shown to increase with increase in the number of solder bal perimeter 
rows. Similar DOE studies using JEDEC drop standards were conducted by Yu and Jin 
[44] to reduce the interfacial peeling streses in Radio Frequency (RF) packages with 
Land Grid Aray (LGA) solder interconnects. LS-Dyna was used to relate the loading 
conditions to the solder streses. 
Le, et al [45] conducted board level drop tests to investigate the efect of diferent 
solder materials and peak reflow temperatures on the durability and failure site of the 
solder interconnects. The test coupon, a Plastic Bal Grid Aray (PBGA) component 
mounted on a 6 layer FR4 board with ENIG surface finish, was alowed to fal on to a 
stainles stel plate in the in-plane direction. It was found that eutectic Sn-Pb solder joints 
 23  
performed beter than Pb-fre solder joints. Thre failure sites were observed: within the 
bulk solder, the interface of the solder joint and copper pad, and fracture of the copper 
trace near the pad-trace junction.  Heaslip, et al. [46, 47] also compared the drop 
durability of Sn37Pb and Sn95.5Ag3.8Cu0.7 solders on JEDEC drop testers and showed 
that the failure sites and failure mechanisms change with drop height and solder type. 
Similarly, JEDEC level drop tests have been used to compare the durability of Pb-fre 
solders with diferent compositions [48], diferent underfil materials [49], diferent 
solder finishes [50], etc. 
The experimental work discussed above showed that both durability and failure site 
depends on a variety of parameters, including material properties and loading conditions. 
During the thesis work, Varghese and Dasgupta [4, 37] decoupled the efect of load 
amplitude and rate on the durability and the failure site by conducting high-speed bend 
tests on a PWA with a single SnPb/OSP BGA on it. They showed that there exists a 
FSTZ that can be characterized in terms of PWA strain and strain rate beyond which the 
failure site changed from solder to the FR4/Cu-pad. The developed technique was used in 
this study [11] to characterize the durability and failure site transitions for PWAs with 
SnPb/ENIG interconnects, where the failure site changed from the solder to the 
intermetalic layer.  Resistance monitoring showed that crack propagation in the solder 
failure takes longer, while britle failure in the intermetalic is instantaneous. Similar 
conclusions have been made by Seah, et al. [51] and Heaslip, et al. [47]. 
The sudden decrease in the durability due to the failure site transition prompted a 
study of how various solder and plating material combinations behave under dynamic 
loading conditions.  Chong, et al. [52, 53] compared the drop durability of leaded and 
 24  
lead fre BGA components with OSP, imersion tin and ENIG surface finishes by 
conducted JEDEC drop tests of PWAs supported at its corners. SnPb solders were found 
to have beter drop durability than Pb-fre solders, irespective of surface finish. For a 
given solder material, OSP finish provided beter drop durability than the other pad 
finishes. The solder interconnect strength was ranked as SnPb/OSP > SnPb/ENIG > Pb-
fre/OSP > Pb-fre/ENIG > Pb-fre/Imersion tin. The failure site for ENIG-based 
components was the intermetalic layer and that for OSP-based components was 
FR4/copper trace. Chai, et al. [54] studied the efect of board design, failure mechanism 
and durability of Quad Flat Package (QFP) and Chip Scale Package (CSP) components 
subjected to JESD22-B111 drop tests. Components with ENIG surface finish showed les 
durability than OSP surface finish, especialy when used with SnAgCu solder 
interconnects. Failure analysis showed copper trace failure for al OSP specimens and 
intermetalic failure betwen the Ni
3
Sn
4
 and Ni-P layers for al ENIG specimens.  
The authoritative work on the efect of isothermal and thermal cycling aging on 
intermetalic and kirkendal void growth was published in 2006 by Luhua and Pang [55]. 
They conducted JEDEC drop tests on thermaly aged PWAs mounted with SnAgCu BGA 
components with diferent plating materials to study the efect of intermetalic 
morphology and kirdendal void growth on board level durability. The PWAs were 
subjected to thermal cycling aging of 500, 1000 and 1500 cycles, with a profile of ?40
0
C 
to 125
0
C. The microstructure near the Intermetalic Compound (IMC) layer compared for 
isothermal and cyclic aging. The average grain size in the solder, near the intermetalic 
layer, was 20 microns before aging, 13 microns after 500 thermal cycles, and 5.8 microns 
after 1500 thermal cycles. The decrease in grain size means more number of grains, 
 25  
which leads to more grain boundaries. The authors suggested that the reduction in grain 
size at the solder/IMC interface was due to dynamic re-crystalization caused by the 
thermal streses induced by Coeficient of Thermal Expansion (CTE) mismatch. Some 
PWAs were also subjected to isothermal aging at 150
0
C for 120 hours, 240 hours and 390 
hours. The grain size at solder/IMC interface increased to 30 microns after 260 hours of 
aging, and some even reached 50 microns. In some PWAs, the grain boundaries 
disappeared and grains were combined together. 
The authors observed a significant decrease of drop durability was observed for 
both SnAgCu/ENIG and SnAgCu/Cu-OSP packages after thermal aging. SnAgCu/ENIG 
showed beter durability after aging than SnAgCu/Cu-OSP. Most of the interconnects 
failed at the intermetalic layer, though some also failed in the copper trace and the 
FR4/Cu-pad. In the as-reflowed SnAgCu/cu-OSP specimen, the intermetalic failure was 
either near the Cu
6
Sn
5
/Cu
3
Sn interface or near the SnAgCu/Cu
6
Sn
5
 interface or within the 
Cu
6
Sn
5
 layer. After 500 cycles of thermal aging, dominant cracks were sen within the 
Cu
6
Sn
5
. After 1000 hours, the crack was near the IMC/Cu pad, where a new layer of 
Cu
3
Sn had formed. The crack was found to be flater than the ones in les aged 
specimens. After 1500 hours of aging, the crack propagated through the bottom interface. 
For the SnAgCu/ENIG specimens, the crack was at the IMC/Ni(p) interface for al 
conditions of thermal cycling. At 1500 cycles, the Ni(P) layer was found to be very thin 
in some locations and voids could be sen in some spots. In some cases, a non-planar 
NiCuSn ternary layer was found to grow at the intermetalic layer. . 
The authors discussed the formation of Kirkendal voids in the SnAgCu/OSP solder 
joints that were subject to isothermal aging.  Unbalanced Cu-Sn interdifusion through 
 26  
interface creates atomic-level vacancies because the migrating Cu atoms on the bare Cu 
side are not filed by Sn atoms. These vacancies coalesce into the so-caled Kirkendal 
voids. No voids were observed for the as-reflowed specimens, but quite a lot voids 
formed at the Cu-IMC interface after 500 thermal cycles. The density of the voids area 
increased with number of thermal cycles. The voids finaly coalesced and generated 
micro-cracks at the interface. The authors noted that the voiding proces due to thermal 
cycling was faster than that in isothermal aging. This could be due to the dynamic 
recrystalization at the Solder/Cu
6
Sn
5
 interface which could acelerate the interdifusion 
of Cu atoms. The interdifusion rate in the Cu
6
Sn
5
/Cu
3
Sn/Cu interfaces kept the original 
rate, causing the unbalanced Cu-Sn interdifusion through interface to become even more 
significant. The growth of kirkendal voids could explain the efect of thermal cycling on 
drop durability of SAC/Cu-OSP samples. As the sub-micron level voids formed near the 
Cu/IMC interface and coalesced during thermal cycling and these cracks propagated 
much easier at the interface than in the IMC layer. 
Dewen, et al. [56] examined the evolution of the interfacial microstructure of 
SnAgCu solders bonded to Au/Ni/Cu pads for as-reflowed and aged conditions. One 
intermetalic compound with rough morphology and with needles penetrating into the 
solder was observed in the as-reflowed state. After aging, the authors observed that the 
solder/copper pad interface had two intermetalic compounds with a flat interface 
betwen them. Some parts of the IMC spaled into the bulk solder. Drop tests were 
conducted on the as-reflowed and aged PWAs. The as-reflowed PWA had cracks going 
through the solder and the intermetalic layer. The aged PWA failed completely in the 
intermetalic layer. Failure analysis showed that the crack weaved through the 
 27  
intermetalics and the interface betwen the two intermetalics. Analysis of the fracture 
surface showed that the crack was britle and no plastic deformation was found at the 
fracture surface. Thus, thermal aging influences the durability by providing alternate 
paths for crack propagation. 
Irespective of the test method used, the failure site dictates the failure mechanism 
and hence the damage model that is needed to predict durability. Appropriate damage 
metrics have to be chosen to quantify durability and develop failure envelopes. 
Researchers have used finite element simulations to gain an insight into the problem.  
2.2.3 Simulation 
Drop testing simulations have been conducted by modeling the solder as a rate 
independent elastic material [33], a rate dependent elastic material [2, 57, 58] and a rate 
dependent bilinear material [59]. The maximum strain rate in the solder bal during drop 
testing, calculated from FEA, varies from 200/sec [33] in Sn-Pb solders to 20/sec [2] in 
SAC solders. 
Yu, et al [2] conducted simulations of tests conducted on a JEDEC drop testing 
machine using rate-dependent elastic material properties to understand the efect of PWA 
orientation on drop durability. It was shown that a 2 degre and 10 degre drop 
orientation with respect to the horizontal can decrease maximum out-of-plane 
displacement of the PWA by 30%, when compared to that of a JEDEC style drop test. By 
using simple energy principles, an equivalent drop height was proposed to acommodate 
the efect of PWA orientation on the drop durability. 
Simulation of board level drop testing was also used to conduct parametric 
 28  
analyses. Wong, et al. [31] conducted a parametric study of board level drop test using 
FEA simulations and proposed that peeling stres in solder is the primary damage causing 
mechanism. It increases linearly with increasing impact velocity, increases monotonicaly 
(almost logarithmicaly) with decreasing bump height, decreases monotonicaly 
(asymptoticaly) with increasing solder bumps, and increases with increasing board 
length. The peeling stres in the solder is due to the curvature of the board and the inertial 
force of the component. For the same component, the peeling stres decreases with 
increasing PWA thicknes because the diferential stifnes decreases. But after a certain 
thicknes value, the PWA stifnes is so high that it does not flaten under the component 
and increases the peeling stres. Similar parametric studies were done by other 
researchers [60, 61] for JEDEC drop tests of PWAs. 
Irespective of whether strain-based or stres-based metrics are used to quantify 
durability, it is very clear that rate-dependent elastic-plastic solder material properties 
have to be used to realisticaly simulate the drop event. This necesitates the use of 
explicit finite element codes that are very time-consuming. Researchers have tried to 
develop techniques to reduce the simulation run time by first starting with implicit codes. 
Jie, et al. [62] created approximate models of the test specimens and compared that to the 
results obtained from an acurate FEA model. Diferent techniques were used to replace 
the solder joints, including equivalent beams and equivalent solder joint. One of the 
drawbacks of using beams to replace solders was the fact that only one node was used to 
represent the interface betwen the solder and the board. This afected the curvature at 
the solder/board interface, leading to eroneous results. In the equivalent solder joint 
model, one equivalent solder joint is used to represent a cluster of solder joints that are 
 29  
not critical to the analysis instead of using one beam per solder joint. The material 
properties of the equivalent solder joint was the same, but the dimensions were diferent. 
For example: the height of real solder joints was maintained, but the radius of the 
columns was increased to four times, such that mas of the solder column layer remained 
the same.  FEA simulations were run on single component PWA with 10,000 
interconnects using linear elastic material properties. The streses at critical solder joint 
for the equivalent solder joint model and actual model were found to be in good 
correlation. Significant reductions in model size and computational time were observed. 
Gu, et al. [63] also explored the feasibility of using an equivalent continuous layer of 
solder to replace the solder bals. Equivalent elastic modulus, poison?s ratio and shear 
modulus were used in the approximate FEA model. Diferent techniques were explored, 
including a fully smeared model and a partialy smeared model with solders at critical 
locations. The optimization of acuracy and computation time was done by comparing 
the simulation run time, total number of elements, size of critical element area, etc. 
Lal, et al. [35, 64] used explicit FEA code to model the in-plane drop of two 
PWAs to study the reliability of CSP and BGA packages, with eutectic Sn-Pb and Pb-fre 
solders. Two modeling approaches were used: reduced integration solid elements and 
continuum solid elements. Node to surface contact algorithm was used with rigid 
elements to model the floor. Smeared properties are used for the components. FEA 
results and test data were corelated using mode shapes captured by camera. 
Liping and Marcinkiewicz [59] used FEA to explore the feasibility of using von 
mises strain and plastic strain in the solder as the failure criterion. They conducted board 
level drop tests on PWAs mounted with Sn-Pb components using a JEDEC style drop 
 30  
tester and then simulated the tests using 3D explicit FEA. The solder was modeled as a 
rate-dependent bilinear material with strain rates up to 1E2 sec
-1
. An acelerometer 
atached to the fixture and two strain gages on the PWA were used to correlate the 
experiment and numerical model. The FEA used the shock pulse as input and tracked the 
von mises and plastic strains in the solder with respect to time. Both types of strains 
showed sinusoidal fluctuation that corresponded to the post-impact board vibrations, but 
the von mises strain showed elastic recovery and the plastic strains showed a logarithmic 
increase as the vibrations continued. They showed that test conditions that induced higher 
plastic strain in the solder (as calculated by FEA) also led to lower interconnect 
durability. Hence, plastic strain was proposed as a failure criterion. It was also shown that 
simulations using rate-independent solder material properties overestimate the solder 
plastic strain by as much as 50%, when compared to those using rate-dependent 
properties. This study underlined the necesity of using rate-dependent material 
properties for the simulation of PWA drop tests.  
Te, et al [65] explored the use of stres in the solder as the parameter to quantify 
drop durability when the failure site is the intermetalic layer. JEDEC style drop tests 
were conducted on PWAs instrumented with strain gages. The FEA model used 3D 
quarter symmetry of the component with linear elastic material properties. The shock 
pulse was used as input to the FEA model and the calculated PWA strains showed good 
correlation with the strain gage data. The shear, peeling, and principal streses in the 
solder were plotted with respect to time. They showed that shear streses in the solder 
were negligible compared to the peeling and principal streses and the magnitude of the 
peeling stres was more than that of the principal stres. The authors concluded that 
 31  
peeling stres was the primary criterion to quantify durability.  Luan, et al. [66] used 
peeling stres as the damage parameter to quantify the drop durability of system in 
package components. JEDEC drop tests were conducted and the measured impact pulse 
was used as input to a 3D FEA model with linear elastic material properties. Detailed 
package geometry, solder bals and pad design were included in the model. FEA shows 
high stres concentration at the failure site, which was the intermetalic layer on the 
component side of the outer most solder bal. As proposed by Te, et al [65], maximum 
peeling stres was considered to be the root cause of the britle failure. Power law fit was 
used to correlate average drops to failure from the test to maximum peeling stres of 
critical solder, obtained from the FEA. The authors noted that the value of the peeling 
stres is depends on element size, material models, etc., while the number of drops to 
failure depends on the test setup, failure criteria and other variables. Hence, the 
correlation constants are dependent on the failure model and drop tester. Te, et al. [67] 
also used peeling stres to characterize the drop durability of Thin and Fine-pitch Bal 
Grid Aray (TFBGA) packages with SnAgCu interconnects subjected to JEDEC drop 
tests. 3D FEA with linear elastic material properties was used and the stres concentration 
at the intermetalic layer in the outermost solder bal matched the failure site. The 
durability shows a power law relationship with peeling stres at the failure site. Pang and 
Che [68] used von-mises stres as the damage metric to understand the damage in the 
interconnects of SnAgCu PBGA components. The PWA was clamped at both edges and 
subjected to drop tests. FEA with rate-dependent elastic-plastic properties was used to 
compute the von-mises stres.  
Shah and Melo [69] proposed the use normal and shear forces in the solder to 
 32  
develop overstres failure envelopes for the solder interconnects. Mathematicaly, 
Z(F
normal
, F
shear
) = 0 is used to characterize failure, such that Z>0 implies failure. F
normal
 
and F
shear
 are the normal and shear forces in the failure site, respectively. Z(F
normal
, F
shear
) 
can be defined as a linear function (Mohr-Coulomb) or non-linear function (Drucker-
Pager), depending on the physics of the loading and failure site. This technique, 
commonly used to characterize crack propagation in britle rocks, was applied to thre-
point bend tests of a PWA at diferent displacement rates. The component of interest was 
a single BGA chipset at the center of the PWA and the observed failure site was the 
intermetalic layer. The load-displacement curves obtained at diferent displacement rates 
show that the critical load to failure decreases with increasing loading rate. A detailed 3D 
FEA model, with elastic material properties, was used to determine the force state of the 
failure site by summing the internal forces in a layer of elements in the bal at diferent 
values of board curvature. Comparison with experiments showed that the bal with the 
force state closest to the failure envelope was the first to actualy fail. A case study, using 
a computer motherboard, was used to succesfully demonstrate the applicability of the 
proposed approach. 
2.2.4 Durability Models 
Durability models have been proposed over the last few years to quantify 
interconnect durability under board level impact testing conditions. In Feb 2003, 
Varghese and Dasgupta [70] introduced a test methodology (included in this thesis) to 
predict impact durability of surface mount interconnects. PWA flexural strain was used 
as the damage metric and the damage model was based on britle crack propagation 
because the failure site was in the britle intermetalic layer. A damage quantification 
 3  
algorithm was proposed, which used wavelet decomposition to decompose the PWA 
strain history into its constituent modal contributions, and rainflow cycle-counting to 
ases the damage at each frequency level. The test methodology was demonstrated for a 
PWA with a single Sn-Pb PBGA component, subjected to in-plane and out-of-plane 
impact on fixtures with diferent boundary conditions. Although the damage constants 
were verified to be independent of impact orientation, loading conditions and boundary 
conditions, the model constants were specific to the architecture of the PWA being tested. 
In Nov 2003 [10] the test methodology was modified to change the damage metric from 
PWA strain to solder strain by using FEA. This made the test methodology more generic, 
within the approximations of the analysis, because the model constants were a function of 
the material properties alone. Te, et al. [71] proposed a durability model in May 2003 
for out-of-plane drop testing of PWAs. Maximum peeling stres in the solder was used as 
the damage metric and the durability model was formulated using a power law 
relationship. The technique was demonstrated for boards mounted with TFBGA and Very 
Thin Profile Fine Pitch Bal Grid Aray (VTFBGA) components and subjected to drops 
on a JEDEC board level drop tester. In 2004, Liping and Marcinkiewicz [59] proposed 
the use of efective plastic strain in the solder bal as the damage metric and compared the 
component reliability at diferent loading conditions. Although a damage model was not 
developed, components with higher efective plastic strain were shown to fail earlier than 
those with lower values of plastic strain in the solder bal. In 2005, Lal, et al. [72] 
demonstrated the use of a damage quantification technique very similar to the one 
proposed in this study, on test vehicles mounted with BGAs and CSPs, subjected to in-
plane drop. Wavelets and cycle counting techniques were used to quantify the complex 
 34  
load history. PWA flexural strain was used as the damage metric and the damage model 
was based on the Coffin-Manson relationship because the failure site was in the solder. In 
2006, Varghese and Dasgupta [73] proposed an empirical rate-dependent durability 
model based on mechanistic considerations. The derivation and explanation are provided 
in this thesis. PWA strain and strain rate were used as metrics to quantify durability and 
identify a critical zone where the failure site changed from the solder to other parts of the 
PWA. The model was succesfully used quantify the behavior of PWAs with SnPb/OSP 
single chip BGAs and SnPb/ENIG stacked die BGAs.  
2.3. Correlation Betwen Board and Product Level Drop Testing  
It is generaly dificult to correlate the board level drop test results to product level 
drop test results. The PWA is clamped to the fixture during board level drop testing and 
is alowed to vibrate after a single drop event. Product level drop testing usualy involves 
multiple impacts and rotations after the first impact, termed as clatering. High-speed 
photography by Goyal and Buratynski [74] indicates that during a single product level 
drop event, one corner of the electronic product touches down first and there is 
"clatering" as other corners strike repeatedly. The product then bounces or comes to rest 
after undergoing these multiple impacts at its ends. It has been shown that during 
clatering, the product can experience velocity shocks that are several times higher than 
those experienced in a single drop event. The details of the clatering motion, and the 
various impact parameters of interest to the designer (change in velocities and impulses, 
the duration of the clater, et cetera) depend significantly on the mas distribution of the 
product and its efective coeficient of restitution at impact [23]. The mas distribution 
and boundary conditions of the PWAs used in the JEDEC board level drop tests is 
 35  
diferent from the PWAs mounted in an actual portable electronic device. 
One of the factors that make correlation of board level and product level JEDEC 
drop test data dificult is the use of damage metrics that are very structure-specific, for 
example: incident force, incident kinetic energy, incident velocity. This makes the 
damage constants strongly dependent of drop orientation and boundary conditions. 
Goyal, et al. [24] showed that the impulses asociated with individual clater impacts are 
very significant because it could lead to resonances in the internal components. This may 
not be captured by the board level drop tests. Experimental work by Goyal, et al. [30] 
also indicates that constraining the internal asembly to behave as a single system, as is 
done in board level drop tests, may even mis important failure mechanisms. 
2.4. Interconnect Level Testing 
During board level drop testing, the streses and strains in the solder and the 
intermetalic layer are influenced by the geometry and material properties of the board, 
die, overmold, etc. Motivated by the failure site transitions observed during drop, 
vibration and high-speed bend testing described in the earlier section, researchers 
developed techniques to characterize the fracture strength and failure site of the solder 
interconnect at diferent loading rates. Before reviewing the published literature in this 
field, it is important to discuss what intermetalics are used in the microelectronics 
industry and what role they play in a solder interconnect. 
Today's predominant PWA surface finishes include Hot Air Solder Level (HASL), 
OSP, ENIG, Imersion Silver (ImAg), Imersion Tin (ImSn), Reflowed Tin/Lead, 
Electrolytic Nickel Gold, and Electroles Paladium. The solder surface finish techniques 
 36  
mentioned above fal into two categories based on the composition of the intermetalic 
layer betwen the solder and the copper pad: Those with copper-tin intermetalics and 
those with nickel-tin intermetalics. The intermetalic compound bonds the solder to the 
copper pad and is a potential failure site. Techniques like HASL and OSP create the 
Cu
3
Sn and Cu
6
Sn
5
 intermetalic layers betwen the solder and the copper pad. Solder 
interconnects with copper-tin intermetalics have shown good durability under thermal 
cycling, vibration and drop testing conditions. Techniques like ENIG and Electrolytic 
Nickel Gold provide very good bonding betwen the solder and the copper trace by 
forming nickel-tin intermetalics. But the corosion of nickel by gold results in the 
formation of a thin black line that can not withstand dynamic loading. Gold 
embritlement, when the gold content is more than 0.3%, can also lower the reliability of 
the joint. Hence, manufacturers of portable electronic devices prefer to use OSP, HASL, 
or other techniques in their asembly proceses. Keping in mind the cost benefits of 
OSP, many mobile phone parts are finished with OSP on soldered areas, and with ENIG 
on touchpad surfaces. Hence, the fracture toughnes of the intermetalic layer strongly 
depends on plating material and the manufacturing proces.  
Darveaux, et al. [3] used a conventional tensile testing machine to characterize the 
strength and toughnes of a solder joint. The specimen was prepared by soldering 
together two substrates to form an area aray, like a BGA or a flip-chip. The sample was 
pulled in tension at diferent displacement rates til the joint failed. Stres in solder was 
calculated as the ratio of the applied force to the cross-sectional area of al solder bals in 
the area aray package. The strain rate was approximately calculated as the product of the 
applied displacement rate and the height of solder. The authors acknowledged that the 
 37  
actual strain rate in the solder joint was les than that given by the calculated value of 
strain rate because some of the displacement was taken up by the elastic response of the 
grips and the load train. The biggest advantage of this testing technique was that it took 
leser time to obtain statisticaly relevant data compared to bal shear or bal pull, which 
could only measure one interface at a time. In their first published paper itself, the 
authors had tested 990 samples with 566,251 solder bals. 
The authors studied the efect of pad metalization, solder aloy, reflow conditions 
and thermal aging on interfacial fracture of interconnects at high strain rates by 
subjecting BGA components to pull tests at high displacement rates. During the test, the 
whole BGA is lifted off the PWA and the solder strain rate is defined as the ratio of the 
displacement rate of tester to the height of solder bal. The authors reported thre failure 
modes: ductile solder fatigue, britle fracture of intermetalic layer and pad lift-off. They 
proposed the use of the Ductile to Britle Transition Strain Rate (DTBTSR) as a metric to 
quantify the performance of a package relative to interfacial failure. It was found that the 
failure site transition generaly occurred betwen strain rates of 0.1 sec
-1
 and 1 sec
-1
, with 
solder failure at the low strain rates and intermetalic failure at the high strain rates. In 
solder failure, failure site was observed to have a cone-cone or tafy pull type of failure. 
During intermetalic failure, the solder showed litle plastic deformation and the fracture 
surfaces were flat. The authors also showed experimentaly that the interfacial strength of 
the intermetalic layer decreases with increasing loading rate. This trend was observed for 
al solder aloys and for al aging conditions. Similar to the idea proposed in this thesis [4, 
37], the authors characterized the failure site transitions in terms of rate-dependent 
increase in the tensile strength of the ductile solder and decrease in the tensile strength of 
 38  
the britle intermetalic. 
Yeh and Lai [75] modified a drop tower to develop a Bal Impact Tester (BIT) that 
conducted high-speed shear tests on the solder interconnects of BGAs. A fixture was used 
to hold the component in a vertical position and a hamer was released from a specific 
height to fal along a guide rail. The hamer struck a pin which was in contact with the 
solder interconnect and the impact force was measured. The force-time plot was used to 
quantify certain parameters of the solder interconnect: Peak force was used as a measure 
of strength, which was a mix of normal and shear loading because the pin actualy caused 
mixed mode loading in the interconnect. The time taken to go from zero force to peak 
force was used as a measure of the ductility of the solder joint. The loading part of force-
time plot was used to measure joint toughnes by calculating area under the curve. Impact 
energy was calculated as a product of the toughnes and the impact velocity. The ratio of 
the slope of the force-time curve to the impact velocity was used to represent the stifnes 
of the joint. Tests showed that diferent fracture toughnes values and failure sites could 
be obtained by varying the impact force magnitude and rate. 
Yi-Shao, et al. [48] and Chang-Lin, et al. [76, 77] characterized transitions in the 
failure site on the basis of applied force and solder dynamic yield stres. Thre failure 
modes were observed: solder failure, fracture through solder and intermetalic, and 
intermetalic fracture. It as observed that at low force amplitudes and rates, the failure 
was in the solder. As the loading amplitude increases, the yield stres of the solder 
increases due to strain-rate hardening. For the same load amplitude, the failure site 
transitioned from pure solder to mixed solder and intermetalic and finaly purely 
intermetalic as the loading rate increased. The failure site was said to transition when the 
 39  
yield stres of the solder exceded a certain value. 
Yeh and Lai [78] used a force based failure envelope similar to that developed by 
Shah and Melo [69] to characterize intermetalic failure during bal impact tests.  The 
interfacial failure was characterized by 1
S
||f
sn
CC
!
"
#
$
%
&
?
+
"
#
$
%
&
?
, where subscripts f
n
 and 
f
s
 are the applied normal and shear forces, respectively, and S
n
 and S
s
 are the normal and 
shear force strengths of the intermetalic layer, respectively. A case study was presented 
using a single solder interconnect subjected to bal impact tests. A 3D FEA model with 
quarter symmetry was used with tetrahedral solid elements to eliminate hourglasing 
efects due to the localized streses at point of impact. Intermetalic fracture at the 
solder/Cu-pad interface was modeled using tiebreak nodes-to-surface contact which links 
adjacent meshes and confines the movements of nodes until the bond breaks. As a zero
th
 
order approximation, the values of C
s
 and C
n
 were asumed to be 2, thus making the 
failure envelope eliptical in nature. The normal force strength (S
n
) was calculated as the 
product of the tensile strength and contact area, and the shear force strength (S
s
) was 
asumed to be twice the value of S
n
. The area under the ascending part of the force-time 
curve obtained from the impact tests was used to determine the impact energy. It was 
shown that the plot of (f
n
-f
s
) with respect to applied force shows the same slope, 
irespective of solder composition.  
2.5. Sumary  
The literature review presented above can be summarized as follows 
? Many test setups have been proposed to quantify drop durability of PWAs. It has been 
 40  
demonstrated that component inertia has a negligible efect on the durability of PWAs 
mounted with low mas components (for example: PBGAs). Hence, board level drop 
tests can be replaced by high speed bending of the PWA, as discussed in Chapter 3.  
? There are many metrics to quantify durability of the PWA under dynamic flexural 
loading conditions. Some metrics, like PWA strain, make the results specific to the 
specimen tested, while others, like plastic strain in the solder at the failure site make the 
results much more generic. Al the prior durability models were rate-independent, even 
though the failure sites experience rate-dependent behavior.  
? Numerous studies report that under certain conditions of applied loading and thermal 
aging, the failure site changes from the solder to the intermetalic.  Some researchers 
have used empirical models to characterize the failure site transition. However, no 
study provides a qualitative or quantitative mechanistic explanation of the observed 
phenomenon. 
This disertation extends the state-of-art in the folowing manner 
? In Chapter 3, Failure Maps are developed in terms of PWA strain and strain rate to 
characterize failure site transitions from the solder to other parts of the PWA. A rate-
dependent empirical durability model based on mechanistic considerations is developed 
to quantify fatigue failure envelopes for the solder. The fatigue constants of the 
empirical model are used to identify the individual efect of loading amplitude and rate 
on the behavior of the solder interconnect. 
? In Chapter 4, mechanistic insights are provided into the strong dependence of the solder 
failure on load magnitude, and weak dependence on loading rate. A durability metric is 
 41  
introduced to quantify rate-dependent durability of the solder, in the strain rates 
observed during dynamic flexural loading of the PWA. 
? In Chapter 5, mechanistic insights are provided into the failure in the interfacial IMC 
layer of the solder interconnect. The efect of thermal aging on the morphology, and 
hence the durability of the interfacial IMC layer are understood and quantified. 
? In Chapter 6, interfacial fracture mechanics and exhaustion of ductility principles are 
used to characterize the durability and failure site transition in the solder interconnect in 
terms of mechanistic parameters, rather than empirical ones. 
 42 
Chapter 3: Empirical Rate-dependent Failure Envelopes
+
 
This chapter presents an experimental study to characterize the durability and 
failure site transitions in the solder interconnects of PWAs subjected to dynamic flexural 
loading. Depending on the loading conditions, the failure is found to be either in the 
solder joint or in the Cu trace on the PWB. PWA strain and strain rate are measured and 
used to develop a rate-dependent empirical durability model for the solder. It is observed 
that for the test conditions of this study, the durability of the solder is strongly dependent 
on loading amplitude and weakly dependent on loading rate. The transition to Cu-trace 
failures is charactierized in terms of competing failure envelopes and failure maps. The 
original draft of this chapter is a journal paper that is currently acepted for publication in 
Microelectronics Reliability.  The next chapter (Chapter 4) wil focus on developing 
mechanistic fatigue curves for the solder.  
An Experimental Aproach to Characterize Rate-dependent 
Failure Envelopes and Failure Site Transitions in Surface 
Mount Asemblies. 
J. Varghese, A. Dasgupta 
CALCE Electronic Packaging and Systems Center, University of Maryland, Colege Park, MD 20742 
Tel: 301-405-5251, Fax: 301-314-9269, Email: josephv@umd.edu, dasgupta@umd.edu 
This paper presents an experimental approach to identify the fatigue failure 
envelopes for solder damage in Printed Wiring Asemblies (PWAs) subjected to dynamic 
                                                
+
 Acepted for publication in Microelectronics Reliability. doi:10.1016/j.microrel.206.07.02. 
 
 43 
loading. An empirical, rate-dependent, power-law durability model, motivated by 
mechanistic considerations, is proposed to characterize the failure envelopes in terms of 
PWA flexural strain and strain rate, as damage metrics. It is further shown that there are 
critical combinations of these damage parameters, beyond which the failure site changes 
from the solder to other locations on the PWA. A case study, using a simple PWA 
specimen containing a single area aray component, is presented to demonstrate the 
proposed approach. Under certain loading conditions, the failure site changes from the 
bulk solder to the Cu-trace/FR4 interface. The proposed durability model is shown to 
succesfully describe the solder damage failure envelopes.  The concept of a ?Failure 
Map? is shown to provide a suitable framework to quantify the durability of the solder 
interconnect, determine its failure envelope, and identify the failure transition zone of the 
specimen.  The applicability of the proposed technique for comparing the durability of 
diferent packaging styles and for developing design guidelines for PWAs subjected to 
dynamic loading (for example: drop) is discussed. 
Keywords: drop test, four-point bend, failure site transition, strain rate, dynamic, 
durability model. 
Nomenclature 
b, : Coffin-Manson constants for solder (-) 
11
,,dca: Damage model constants (-) 
BA,: Damage model constants (-) 
p
!" : Plastic strain in the solder interconnect (-) 
 4 
f
! : Failure strain of the solder (-) 
PWA
 : PWA flexural strain (-) 
failure
! : PWA strain for overstres failure at quasi-static loading conditions (-) 
?
PA
 : PWA flexural strain rate (sec
-1
) 
?
0
! : Quasi-static PWA strain rate (sec
-1
) 
f
N : Average number of cycles to failure (-) 
3.1. Introduction and Problem Statement 
Dynamic loading plays a crucial role in the durability of solder interconnects in 
Printed Wiring Asemblies (PWAs). The trend toward decreasing solder bal diameter, 
pad diameter and I/O pitch makes the interconnect more susceptible to failure. This is 
often true for PWAs in portable electronic devices that are frequently subjected to 
dynamic loading during mechanical handling, acidental misuse and/or shipping 
(transportation). Examples include cel phones, laptops, and PDAs. PWAs used in 
military applications are often subjected to severe vibration, repetitive impacts and/or 
high G loading. Dynamic loading of the PWA during product asembly can also severely 
shorten the durability of the solder interconnect. Hence board level solder joint reliability 
under dynamic loading conditions is of critical concern to the microelectronics industry. 
Board level tests are usualy conducted on a sub-asembly drop testing machine 
based on a JEDEC Standard [9]. The PWA is screwed on to a drop cariage in the 
horizontal position at four or six points. The drop cariage fals along two guide rods and 
 45 
induces out-of-plane displacement in the PWA on impact. On impact, the PWA responds 
to the transient impact force applied to the base and then vibrates at its natural 
frequencies. Instrumentation typicaly consists of acelerometers mounted on the drop 
cariage and strain gages on the PWA. Recent work by Seah, et al. [38] proves that solder 
bal damage due to PWA flexure is much greater than that caused by inertial loading, thus 
making PWA flexural strain and strain rate the primary mechanisms which cause 
damage. Hence, bend tests can be used to focus the study on PWA flexural strain and 
strain rate and on its efect on interconnect durability. 
Much work has ben done to develop durability models and failure envelopes for 
solder interconnects under dynamic loading conditions. Empirical models have been 
developed to quantify durability as a function of PWA strain [9]-[70]  and PWA 
displacement [110]. In some cases, Finite Element Analysis (FEA) with rate-independent 
material properties has been used to quantify durability in terms of solder stres [35] 
[12][113] or solder strain [12][27] and to develop failure envelopes based on normal and 
shear forces in the solder [69]. 
However, the existing durability models and failure envelopes are rate-independent, 
even though tests show that the durability of the PWA varies with the loading rate 
[58][42]. There is a need to understand the combined efect of load amplitude and 
loading rate on the durability of the solder interconnects. Appropriate damage metrics 
have to be chosen to quantify durability and develop failure envelopes. 
This work is vital because load amplitude and loading rate can change the failure 
site from the solder to other locations on the PWA. The failure site dictates the failure 
mechanism and hence the damage model that is needed to predict durability. Yu, et al. [2] 
 46 
were the first to report a transition in the failure site from solder to the intermetalic with 
increasing drop height during drop testing of PWAs. Heaslip, et al. [47] compared the 
drop durability of Sn37Pb and Sn95.5Ag3.8Cu0.7 solders and showed that the failure 
sites and failure mechanisms change with drop height and solder type; while Varghese, et 
al. conducted high-speed bend tests and showed that the failure site transitions from the 
solder to the copper trace for specimens with Organic Solderability Preservative (OSP) 
finish [114][4]; and from the solder to the intermetalic compound (IMC) layer for 
specimens with Electroles Nickel/Imersion Gold (ENIG) finish [11]. Wong, et al. [36] 
showed that the failure sites and failure mechanisms change with solder and plating type. 
Despite the previous work described above, the transition of the failure site due to 
dynamic loading remains poorly quantified and understood. 
An experimental approach is presented to characterize the failure site transitions, 
develop failure envelopes for each component architecture and quantify the durability of 
the solder interconnects for PWAs subjected to dynamic loading. PWA flexural strain 
and PWA flexural strain rate are used as damage metrics. The proposed technique is 
demonstrated on a PWA with a single Plastic Bal Grid Aray (PBGA) mounted on it. 
The results of this study can be used by engineers as the basis of design guidelines for 
diferent surface mount component architectures and by researchers to develop damage 
models for surface mount interconnects. 
This paper is part of an ongoing efort to develop a generic test methodology for 
drop testing of PWAs. Earlier work by the authors [113] focused on the efect of loading 
amplitude, loading orientation and boundary conditions on the durability of the solder 
interconnects. The work presented in this paper adds the efect of loading rate on the 
 47 
durability and the failure site of the PWA, with an emphasis on solder failure. 
The experimental details are first explained, folowed by the test results. The 
subsequent sections discuss the failure envelope and the damage model. The applications 
of this technique and future work are discussed at the end of the paper. 
3.2. Aproach 
A test matrix, as shown in Figure 3-1, is developed to characterize the durability in 
terms of PWA flexural strain and strain rate. The test matrix spans four orders of 
magnitude of PWA flexural strain rate. Dynamic four-point bend tests are conducted to 
induce a nominaly uniform bending moment in the region of interest around the 
component. The tests are replicated once to verify the consistency of the data. A 
commercialy-available servo-hydraulic bend test machine is used for the low strain rate 
tests, and a drop tower is used for the high strain rate tests. A high-speed data acquisition 
system is used to obtain the strain history and durability of the specimen for each test 
condition. Failure analysis is performed after each test to identify the failure sites. A 
damage law and failure envelope are developed to quantify the durability of the solder 
interconnects. 
 48 
 
Figure 3-1: Test matrix. The circles represent the test conditions. 
The following simplifying approximations have been made in the development of 
the proposed technique. Interconnect damage due to inertial mas of the component and 
stres wave propagation in the solder bal is asumed to be negligible when compared to 
the rate-dependent damage due to PWA dynamic flexure. The solder bals are 
approximated as isotropic, homogenous and defect fre. The efect of initial defects and 
initial residual streses on drop durability is neglected. Damage acumulation is asumed 
to follow Miner?s rule. 
3.3. Test Setup 
A commercialy available servo-hydraulic test machine is used for four-point bend 
tests at PWA flexural strain rates below 0.1 sec
-1
, (Figure 3-2) and a drop tower is used 
for strain rates above 0.1 sec
-1
 and up to 2 sec
-1
 (Figure 3-3). The displacement of the 
LVDT in the servo-hydraulic machine can be varied from 0 to 100 m and displacement 
rate can be varied from 0 to 12.5 m/sec. The drop tower is used to drop stel spheres on 
the fixture holding the specimen in a four-point bend configuration to conduct high-speed 
bending tests (Figure 3-3). The fixtures holding the specimen are made of Delrin to damp 
 49 
out the high frequency ringing due to the impact of a stel sphere. These fixtures slide on 
hardened stel guide rods with linear bearings. The rigid base and the crossbar are made 
of aluminum. The guide rods are carefully aligned paralel to each other and 
perpendicular to the base. Both guide rods are torqued to increase their natural 
frequencies and thus decrease vibration during testing. The mas of the sphere can be 
varied from 65 g to 450 g and the impact velocity can be varied from 0 to 6 m/sec by 
changing the sphere drop height. 
 
Figure 3-2: Four-point bend test fixture on servo-hydraulic mechanical tester. 
 50 
 
Figure 3-3: Drop tower with four-point bend fixture. 
A high-speed 4-channel data acquisition system, with a maximum sampling rate of 
5 MHz per channel, is used to track the PWA response and the solder bal failure in real 
time (Figure 3-4).  As the curvature of the board increases, the cracked surfaces of the 
failed interconnects are mechanicaly separated, thus causing an increase in the daisy 
chain resistance. Failure is defined as an increase in the electrical resistance of the 
interconnect by 1000 !.  As the curvature decreases, the fractured ends on the 
interconnect contact each other again, thus closing the electrical circuit. Due to this 
transient nature of the test, the opening of the circuit lasts for as litle as five miliseconds. 
As a consequence, an in-situ high-speed resistance measurement system, developed in an 
earlier study [9], is used for continuous failure monitoring during the test. The resistance 
monitoring system consists of a Wheatstone bridge, with the daisy chain resistance 
forming the quarter bridge. The bridge can be balanced and its sensitivity varied, by 
 51 
changing the values of the resistance of the other thre arms of the bridge.  
 
Figure 3-4: Schematic diagram of the instrumentation. 
3.4. Specimen Design 
The specimen (Figure 3-5) is a 256 I/O, full grid PBGA with 0.5 m diameter 
solder bals on a 1 m pitch.  This component is daisy chained for in-situ electrical 
continuity checks and is mounted at the center of a 140 m X 101.6 m X 1.6 m FR-4 
board. The board has one layer of copper traces on its surface at the component side to 
connect the daisy-chained component to the terminals. The solder bals are made of 
Sn37Pb eutectic solder. The pad finishes on the board and component side consists of an 
organic solderability preservative (OSP) and Sn15Pb, respectively. A 350 ! strain gage 
with 3.18 m gage length and 2.54 m grid width is atached to the board near the 
corner of the component (the site of maximum PWA curvature) to measure the flexural 
 52 
strain and the flexural strain rate. An electrical continuity tests is performed on each 
daisy-chained component to detect any opens or shorts. The purpose of choosing this 
simple specimen design is to alow an in-depth study of the drop event, without making 
the analysis too complex. The specimens are tested in as-soldered condition without any 
additional aging. The influence of aging on failures due to dynamic loading is discussed 
in an earlier paper [11]. The changes in the microstructure due to thermal aging can 
provide a low-energy path for crack propagation through the intermetalic layer which 
leads to a drastic reduction in the durability of the interconnect. 
 
Figure 3-5: Specimen configuration. 
3.5. Damage Model 
As explained earlier, existing damage models in literature [10][12][27][35][70] 
[110]-[113] do not addres the rate-dependence of durability, for dynamic loading of 
PWAs. We propose a new mechanistic, rate-dependent durability estimation model in 
this paper that focuses on solder failure. The model constants are architecture-dependent 
 53 
and are empiricaly determined from dynamic testing. 
During low-cycle fatigue, failure in the solder is dominated by plastic strain. The 
durability model, as proposed by Coffin and Manson [115] is: 
()
b
pf
N
!
"=#*         (3-1) 
 For overstres failure, 1=
f
N,
fp
!". Therefore, 
()
b
f
pf
!
=
#1
         (3-2) 
Solder is a rate-dependent ductile material [116]. For a given loading condition, the 
plastic strain and the failure strain (ductility) of a ductile material decrease with 
increasing strain rate due to a phenomenon caled strain-rate hardening. For a given PWA 
architecture, the solder plastic strain increases monotonicaly with PWA strain. 
Therefore, 
()
1
*,
1
b
PWAPAWp
af!!=
"
#
$
%
&
?
(
?
      (3-3) 
where, 
1
0
1
c
PA
?
"
#
%
&
(
 
Similarly: 
failure
PWA
failure
PAWf
k!!!*,
1
=
"
#
$
%
&
?
=
?
       (3-4) 
 where, 
1
0
1
d
PA
?
"
#
$
%
&
?
(
 
Substituting Eq. 3-3 and Eq. 3-4 into Eq. 3-2, 
 54 
)(*
0
*
1
1
)(
)(*
cdb
PWA
b
PAbfailure
PWA
f
d
c
N
!
?
!
!
"
#
$
%
&
?
"
#
$
%
&
?
=
     (3-5) 
Failure strain in the solder decreases with increasing strain rate [83]. Asuming that 
the failure strain is more rate-dependent than the plastic strain (ie. d
1
>c
1
), the equation 
takes the form 
C
PWA
B
failure
PA
f
N
!
?
!
"
#
$
%
&
?
%
&
?
=
0
*
(
(
       (3-6) 
The suitability of this model wil be tested in Section 5 on experimental data. 
3.6. Results 
Cyclic four-point bend tests are conducted for diferent combinations of PWA 
flexural strain and strain rate, as shown in the test matrix (Figure 3-1).  The testing is 
stopped as soon as a failure is detected and the specimen is cross-sectioned to determine 
the failure site. For al specimens, the failure is found to be in the outer rows of the 
component, paralel to the loading bars of the test fixture. Figure 3-6 shows the variation 
of durability and failure site with respect to PWA flexural strain and strain rate. A failure 
site transition zone exists for some critical combinations of PWA flexural strain and 
strain rate, below which the failure is in the bulk solder (Figure 3-7) and beyond which 
the failure site is in the FR4/copper trace (Figure 3-8, Figure 3-9). 
 5 
 
Figure 3-6: Durability and failure site in terms of the damage metrics: PWA strain and strain rate. 
 
Figure 3-7: Failure in bulk solder. 
 56 
 
Figure 3-8: Failure in Coper trace. 
 
Figure 3-9: Crack in FR4 under the solder bal. 
A brief summary of the test results is presented in Table 3-1. Figure 3-10 shows the 
variation of durability with respect to PWA strain and strain rate. For a given loading 
condition, solid trend lines are used for similar failure sites and dashed trend lines are 
used whenever there is a failure site transition. Irespective of the failure site, the 
durability has a power law relationship with PWA flexural strain (Figure 3-10). 
 57 
Table 3-1: Experimental results. 
Cycles to failure 
 Test num 
PWA strain 
(-) 
PWA strain 
rate (sec
-1
) 
Test 1 Test 2 
Failure Site 
1 2.5E-3 2.5E-3 639 1000 Solder 
2 5.0E-3 4.9E-3 31 39 Solder 
3 9.4E-3 2.5E-3 1 1 Solder 
4 2.5E-3 1.2E-1 691 651 Solder 
5 2.5E-3 2.5E-2 608 804 Solder 
6 4.9E-3 3.8E-2 71 50 Solder 
7 5.6E-3 2.2E0 7 5 FR4/ Cu-trace 
8 9.4E-3 9.5E-2 5 3 FR4/ Cu-trace 
9 1.2E-2 1.2E-1 2 2 FR4/ Cu-trace 
 
Figure 3-10: Variation of durability with PWA flexural strain for diferent PWA strain rates. 
 58 
The test data corresponding to failure in bulk solder are used to obtain the model 
constants. The values of overstres PWA strain (
filure
PWA
!) and static PWA strain rate (
?
0
!) 
are 9.4E-3 and 2.5E-3 sec
-1
, respectively. The values of the model constants, obtained 
from this test program, are listed in Table 3-2. A contour plot of the model (Figure 3-11) 
demonstrates its capability to quantify the durability of the solder within reasonable eror 
limits (Figure 3-12). The overstres failure envelope for the solder corresponds to those 
combinations of PWA strain and strain rate for which average cycles to failure is one. 
The solder failure envelopes are sen to have a strong dependence on strain level and a 
weak dependence on strain rate.  In the limit, when rate sensitivity is negligible (eg in 
intermetalic failures), this durability model simplifies to the strain-based power-law 
model proposed by Varghese and Dasgupta [12]. 
Table 3-2: Empirical damage constants. 
A(-) B(-) C(-) 
2.28 -4.43 -0.05 
 59 
 
Figure 3-1: Contour plot of the average durability of the solder. The dots represent the test data. 
 
Figure 3-12: Comparison of durability model fit: model vs test data. 
The simple mechanistic durability model proposed in Equation 5, is thus sen to 
describe the failure envelopes with reasonable acuracy.  The empiricaly obtained 
damage constants in Table 2 are valid only for the tested specimen architecture, because 
the damage metrics are structure-specific. Future work wil use non-linear explicit finite 
element analysis (FEA) to deduce solder stres from the PWA strain and strain rate. The 
 60 
corresponding model constants wil be reasonably independent of the specimen geometry 
and predominantly dependent on the dynamic material properties of the solder.   The 
values in Table 2 are presented for ilustrative purposes.  Additional data points are 
needed to achieve reasonable confidence in the damage constants. 
3.7. Discusion 
The phenomenon of transitions in the failure site during dynamic loading of PWAs, 
especialy during drop testing, has not received sufficient atention in the literature. As 
discussed earlier, the loading conditions can change the failure site from the solder to the 
intermetalic layer [2][11], copper trace [4], bond pad [36], etc. The strain energy of 
deformation is divided among competing failure sites, for example: solder, FR4/Cu-trace 
and intermetalic layer. Ductile materials, like eutectic Sn37Pb solder, have rate-
dependent material properties and show an increase in yield stres with strain rate [116]. 
For the same load amplitude, this phenomenon, caled strain-rate hardening, leads to a 
decrease in the plastic deformation of the solder bal at high strain rates, as confirmed by 
Tan, et al. [41]. This hardening of the solder interconnect increases the stres in the solder 
joint and in selected parts of the interconnect system.  Thus at high flexure rates, there 
exist certain loading conditions at which the stres is high enough to reach the cyclic 
failure limit in the FR4/Cu-trace or in the intermetalic layer, before the strain reaches the 
cyclic ductility limit in the ductile solder. This leads to a transition in the failure site from 
the solder to one of the other sites. This concept was schematicaly in an earlier 
publication [4]. 
A schematic 3D plot of the competing failure envelopes is shown in Figure 3-13, to 
ilustrate the notion of failure map and transition zone that marks the transition betwen 
 61 
the interconnect failure modes. Figure 3-14 presents the same data in the form of a 
contour plot. In the example presented in this study, we consider two competing failure 
sites: solder and FR4/Cu-trace. Each failure site has a fatigue failure envelope, which is 
quantified in terms of PWA strain and PWA strain rate. The material with the lowest 
durability for a given loading condition defines both the durability and the dominant 
failure site for that condition. The fatigue failure envelopes of the competing failure sites 
intersect along the failure site transition zone (defined by the PWA strain and strain rate), 
as shown in Figure 3-13 and Figure 3-14. At low values of strain and strain rate, the 
failure site is in the solder and the durability of the interconnect is defined by the solder 
failure envelope. Beyond the failure site transition zone, the failure site is in the FR4/Cu-
trace, and the interconnect durability is defined by the FR4/Cu-trace failure envelope.  
 
Figure 3-13: Schematic plot of competing failure envelopes for solder and FR4/Cu-trace. 
In this study, the failure in the FR4/Cu-trace is either bond-pad liftoff or a fracture 
of the trace betwen the two solder bals. In bond pad liftoff, the cracks start from the 
 62 
surface of the PWA on the solder side, grow through FR4 epoxy and finaly fracture the 
copper trace. No trends have been observed as to when one kind of FR4/Cu trace failure 
dominates over the other. 
The competition betwen the failure modes is strongly dependent on the PWA 
flexural strain and strain rate. The technique proposed in this paper alows the engineer or 
researcher to develop a failure map for a given PWA architecture, which defines the 
failure envelope for each failure mechanism and identifies the failure site transition 
zones, as shown in Figure 3-13 and Figure 3-14. This type of failure map is specific to the 
component geometry and dynamic properties of the materials used in this asembly. This 
makes the failure map an ideal experimental method to compare the durability of 
diferent PWA systems subjected to dynamic loading conditions. 
 
Figure 3-14: Failure map for the solder interconect. 
 63 
3.8. Conclusions and Future Work 
When a PWA is subjected to dynamic loading, there are competing failure 
mechanisms in action, each corresponding to a diferent failure site. The failure site 
depends on the loading conditions, the asembly architecture and the dynamic properties 
of the materials used in the PWA. This paper focuses on failure envelopes for dynamic 
failures in the solder. PWA flexural strain and strain rate are used as damage metrics to 
quantify the solder durability and to develop the fatigue failure envelopes. Failure maps 
are shown to be a convenient method for identifying these competing failure envelopes 
and their transition zones.  This failure map is an ideal tool for comparing the 
performance of diferent surface mount packages under dynamic loading conditions. 
Future work wil concentrate on demonstrating the use of the proposed technique as a 
tool to rank the durability of diferent material systems. PWA flexural strain and strain 
rate wil be used to compare the durability of Sn-Pb PWAs with Sn-Ag-Cu PWAs. 
Similarly, the proposed technique wil be used to compare the durability of unaged PWAs 
with that of aged PWAs, under dynamic loading conditions. Dynamic FEA wil be used 
to make the damage model constants independent of specimen geometry, and dependent 
only on the dynamic material properties of the solder.  Additional data points wil be 
presented to increase the confidence in the damage constants. 
Acknowledgements 
This work is sponsored by members of the CALCE Electronics Products and 
Systems Consortium at the University of Maryland. Discussions with Ed Tinsley of Del, 
Inc. and Simon Prakash of Apple Computer, Inc., are also gratefully acknowledged. 
64 
Chapter 4: Solder Fatigue Model
*
 
In this chapter, the test specimens are analyzed with 3D finite element analysis and 
rate-dependent solder properties, to quantify the fatigue failure envelopes of the solder. 
This provides failure envelopes in terms of mechanistic parameters, rather than empirical 
ones (as was done in Chapter 3). As observed in Chapter 3, for the test conditions of this 
study, the solder durability is strongly dependent on PWA strain and weakly dependent 
on PWA strain rate. It is hypothesized that the weak rate-dependence of solder durability 
is due to the competing efects of strain-rate hardening and exhaustion of ductility. The 
ratio of plastic strain to the failure strain is proposed as a non-empirical, mechanistic 
metric to quantify the solder durability and fatigue curves. The original draft of this 
chapter is a journal paper that is currently submited for peer-review to IEE 
Components and Packaging Technologies. 
Mechanistic Insights Into The Rate-Dependent Failure 
Envelopes of Solder Interconnects in Surface Mount 
Asemblies. 
J. Varghese, A. Dasgupta 
CALCE Electronic Packaging and Systems Center, University of Maryland, Colege Park, MD 20740, 
Tel: 301-405-5251, Fax: 301-314-9269, Email: josephv@umd.edu, dasgupta@umd.edu 
This paper characterizes the fatigue failure envelopes for solder damage in Printed 
Wiring Asemblies (PWAs) subjected to dynamic flexural loading. For a given PWA 
flexural strain, an increase in the PWA flexural strain rate decreases the plastic strain due 
                                                             
*
 Submited for per-review to IEE Transactions on Components and Packaging Technologies. 
65 
to strain rate hardening. The solder failure strain also decreases due to exhaustion of 
ductility. This study explores the efects of these two competing mechanisms on the rate-
dependent durability of the solder interconnect. The ratio of solder plastic strain to its 
failure strain is proposed as a metric to quantify the rate-dependent durability of the 
solder interconnect. Explicit transient non-linear finite element analysis (FEA) is used to 
derive damage constants that are independent of the specimen geometry and dependent 
only on solder material properties. A case study, using a simple PWA specimen 
containing a single area aray Sn37Pb Bal Grid Aray (BGA) component, is presented to 
demonstrate the proposed approach. 
Keywords: drop test, four point bend, BGA, solder failure, strain rate dependence, 
durability model 
Nomenclature 
b, : Mechanistic durability constants for solder (-) 
q,p : Failure strain constants for solder (-) 
1
c,b: Empirical durability model constants (-) 
p
! : Plastic strain in the solder (-) 
f
 : Failure strain of the solder (-) 
PWA
! : PWA flexural strain (-) 
p
?
 : Solder plastic strain rate (sec
-1
) 
0
?
! : Quasi-static PWA strain rate (sec
-1
) 
6 
PWA
?
! : PWA flexural strain rate (sec
-1
) 
f
N : Average number of cycles to failure (-) 
 
4.1. Introduction 
Dynamic loading plays a crucial role in the durability of solder interconnects in 
Printed Wiring Asemblies (PWAs). The trend toward decreasing solder bal diameter, 
pad diameter and I/O pitch makes the interconnect more susceptible to failure. This is 
often true for PWAs in portable electronic devices that are often subjected to dynamic 
loading during mechanical handling, acidental misuse and/or shipping (transportation). 
Hence board level solder joint reliability under dynamic loading conditions is of critical 
concern to the microelectronics industry. 
Board level tests are usualy conducted on a sub-asembly drop testing machine 
based on a JEDEC Standard [9]. Recent work by Seah, et al. [109] proved that in surface 
mount asemblies on compliant organic PWBs, solder bal damage due to PWA flexure is 
much greater than that caused by inertial loading or by stres wave propagation. Thus, 
PWA flexural strain and strain rate can be used as the primary metrics to quantify 
damage acumulation rates. Hence, bend tests can be used in lieu of drop tests to focus 
the study on PWA flexural strain and strain rate and on its efect on interconnect 
durability [73]. 
Much work has been done to develop durability models for solder interconnects 
under dynamic loading conditions. Empirical models have been developed to quantify 
durability as a function of PWA strain [110][117], PWA displacement [111], and PWA 
strain rate [10]. Al of the above mentioned damage metrics are structure-specific. Hence, 
67 
the damage constants are unique to the tested PWA geometry. FEA can be used to make 
the damage metrics relatively independent of PWA geometry, and solely dependent on 
the material properties at the failure site. 
FEA with rate-independent material properties has been used to quantify durability 
in terms of solder stres  [118] or solder strain [113]. Many researchers have also used 
rate-dependent material properties to quantify durability. Zhu and Marcinkiewicz [119] 
explored the possibility of using von-Mises strain and plastic strain as the damage metric 
for solders in PWAs subjected to drop tests. The von-Mises strain showed recoverable 
deformation, while the plastic strain showed steady acumulation during the post-impact 
vibration. Chong, et al. [120] used plastic strain as the damage metric and showed that 
plastic strain increases with time as the PWA vibrates. Chea and Pang [121] used plastic 
strain in the solder to quantify damage in PWAs subjected to four point bend and drop 
tests. Gu and Jin [63] used peeling stres in the solder as the damage criterion while 
optimizing the design of RF land grid aray packages. Shah and Melo [69] developed 
failure envelopes based on normal and shear forces on the solder bal to quantify the 
durability of the interconnects. 
This paper seks to extend the excelent work done by the researchers mentioned 
above. The ratio of solder plastic strain to its failure strain is proposed as a metric to 
quantify the rate-dependent durability of the solder interconnect. The proposed damage 
metric is motivated by mechanistic considerations. For a given load amplitude, an 
increase in the loading rate decreases the plastic strain and failure strain in the solder due 
to strain-rate hardening and exhaustion of ductility, respectively. The hypothesis of the 
proposed approach is that solder durability depends on the competing efects of these two 
mechanisms. 
68 
This paper is part of an ongoing efort to understand and quantify the damage 
experienced by solder interconnects during drop testing of PWAs. Earlier work [10][113] 
by the authors focused on the efect of load amplitude, impact orientation and PWA 
boundary conditions on interconnect durability. Later publications [73][118] added the 
efect of loading rate and thermal aging on the durability and failure site of the 
interconnect. The current study characterizes the rate-dependent durability of the solder 
in terms of the ratio of the plastic strain to the failure strain. 
The paper is aranged in the folowing format: The details of the FEA are first 
presented, followed by the FEA transfer functions that relate the plastic strain in the 
Sn37Pb solder to the PWA flexural strain at diferent loading rates. The variation of 
solder failure strain with PWA flexural strain is obtained and the fatigue failure envelope 
is presented.  
4.2. Aproach 
This paper uses experimental data from a previous study [73] in which a PWA of a 
simple design was subjected to high-sped four-point bend tests at diferent loading 
amplitudes and rates. The specimen design and test results are presented in this paper for 
the sake of completion. A 3D transient FEA  model of the PWA is used to relate the 
PWA strain to the plastic strain in the solder, for diferent PWA strain rates. Data 
available in literature [5] is extrapolated to quantify the decrease in solder failure strain 
with increasing strain rate. The power law relation is established betwen the proposed 
durability metrics (!
p
/!
f
) obtained from the FEA and cycles to failure, obtained from the 
experiments. A flow chart of the approach is shown in Figure 4-1. The left hand and right 
hand sides of the flowchart explain the quantification of strain-rate hardening and 
exhaustion of ductility, respectively. 
69 
The following simplifying approximations have ben made in the FEA model: The 
solder bal is asumed to be isotropic and homogenous, with no internal or external 
defects. It is asumed that the dynamic constitutive equations of the solder obtained from 
Split Hopkinson?s tests of macroscopic solder specimens can be used to represent the 
material behavior of the solder bals. In other words, the length scale efects on the 
material properties of the solder due to its microstructure are ignored. Al the materials in 
the PWA are modeled as isotropic homogenous. 
 
Figure 4-1: Flowchart of the aproach 
70 
4.3. Specimen design 
The specimen (Figure 4-2) is a 256 I/O, full grid PBGA with 0.5m diameter 
solder bals on a 1mm pitch.  This component is daisy chained for in-situ electrical 
continuity checks and is mounted at the center of a 140 m X 101.6 m X 1.6 m FR-4 
board. The board has one layer of copper (Cu) trace on its surface at the component side 
to connect the daisy-chained component to the terminals. The percentage coverage of 
copper on the board surface is negligible. Therefore, the material properties of the board 
are predominantly those of the FR4. The solder bals are made of Sn37Pb eutectic solder, 
which is solder mask defined on the component side, and non-solder mask defined on the 
board side. The pad finishes on the board and component side consists of an Organic 
Solderability Preservative (OSP) and Sn15Pb, respectively. A strain gage is atached to 
the board near the corner of the component (the site of maximum curvature) to measure 
the flexural strain and the flexural strain rate. An electrical continuity tests is performed 
on each daisy-chained component to detect any opens or shorts. The purpose of choosing 
this simple specimen design is to alow an in-depth study of the drop event, without 
making the analysis too complex. Sn37Pb solder also makes a beter baseline sample 
because it is a wel-studied material with numerous publications [5][116]about its 
behavior under high strain rate loading conditions. The specimens are tested in as-
soldered condition without any additional aging. Details of the test matrix, test setup, and 
the specimen can be found in an earlier publication [73]. 
 
71 
 
Figure 4-2: Specimen configuration 
4.4. Test results 
A brief summary of the test results is presented in Table 4-1. Since the focus of this 
study is on solder durability, failures in the FR4/Cu-trace are not addresed here. PWA 
flexural strain and PWA flexural strain rate are used as the empirical durability metrics. 
Non-linear transient finite element analysis (FEA) with an explicit solver is used to 
deduce the solder plastic strain for each test condition. 
 
 
72 
Table 4-1: Experimental results 
Cycles to failure 
 # 
PWA strain 
(-) 
PWA strain rate 
(sec
-1
) 
Test 1 Test 2 
Failure Site 
1 2.5E-3 2.5E-3 639 1000 Solder 
2 5.0E-3 4.9E-3 31 39 Solder 
3 9.4E-3 2.5E-3 1 1 Solder 
4 2.5E-3 1.2E-1 691 651 Solder 
5 2.5E-3 2.5E-2 608 804 Solder 
6 4.9E-3 3.8E-2 71 50 Solder 
7 5.6E-3 2.2E0 7 5 FR4/ Cu-trace 
8 9.4E-3 9.5E-2 5 3 FR4/ Cu-trace 
9 1.2E-2 1.2E-1 2 2 FR4/ Cu-trace 
 
4.5. FEA Model 
An explicit transient non-linear finite element model is generated using a 
commercialy available software to obtain the transfer function at diferent values of 
PWA strain rate. A 3-D strip model of the PWA is created, with a thicknes of one pitch. 
8-noded hexahedral elements are used to model the specimen. As shown in Figure 4-3, 
only one half length of the PWA is modeled because the test coupon is symmetric and the 
four point loading restricts its structural response to the first mode [73]. Symmetry 
boundary conditions are applied to the vertical axis in the center of the component. The 
copper trace connections betwen the solder bals and the copper trace that connects the 
daisy-chained component to the terminals are ignored in the FEA model (Figure 4-4). 
73 
The intermetalic compound (IMC) layer betwen the solder and the copper pad is also 
ignored. Al materials are modeled with isotropic homogenous properties. 
 
Figure 4-3: FEA model with symetric boundary conditions on the vertical axis at center of model 
 
Figure 4-4: FEA model of the solder interconect 
The mesh has 34992 elements and 40962 nodes, and is scaled to provide maximum 
mesh density at regions of high stres gradients, for example at the solder/Cu pad 
interface, and at the Cu pad/PWA interface. The solder and the copper pad are modeled 
with elastic-plastic properties, while al the other materials are modeled as linear elastic. 
The linear elastic properties of al the materials in the PWA are listed first (Table 4-2), 
followed by the rate-independent inelastic properties of copper (Table 4-3) and solder 
(Table 4-4). Since the tests were conducted over a large range of strain-rates, the solder 
has been modeled with rate-dependent properties obtained from literature [116]. The 
variation of solder yield stres with strain rate is listed in Table 4-5. Figure 4-5 shows the 
rate-dependent stres-strain curves of the Sn37Pb solder. 
74 
Table 4-2: Linear elastic material properties of the PWA 
Material Elastic modulus (GPa) Poison?s ratio (-) Density (kg/m
3
) 
FR4 17.2 0.39 1000 
Overmold 15.8 0.25 1900 
Substrate 22 0.3 1000 
Copper 120 0.34 8930 
Solder 29.9 0.35 8400 
 
Table 4-3: Bilinear material properties of coper 
Yield Stres (MPa) Post-yield Modulus (GPa) 
24 12 
 
75 
 
Table 4-4: Quasi-static inelastic material properties of solder 
Stres (MPa) Strain (-) 
0.00 0.0 
15.10 4.8E-4 
15.59 5.0E-4 
17.32 5.9E-4 
19.05 7.2E-4 
20.78 8.8E-4 
22.52 1.0E-3 
24.25 1.4E-3 
25.98 1.7E-3 
31.18 3.6E-3 
34.64 5.9E-3 
43.30 1.8E-2 
51.96 4.85E-2 
60.62 1.12E-1 
69.28 2.36E-1 
77.94 4.54E-1 
86.60 8.16E-1 
 
Table 4-5: Dynamic material properties of solder 
Yield Stres (MPa) 29.9 35.8 41.8 50.8 62.8 74.7 
Strain rate (-) 1E-3 1E-2 1E-1 1E0 1E1 1E2 
76 
 
Figure 4-5: Rate-dependent properties of the Sn37Pb solder 
FEA simulation at diferent loading rates shows that the region of maximum plastic 
strain is in the solder neck on the component side of the outermost solder bal. Figure 4-6 
shows a plot of the distribution of plastic strains in the outer most solder bal. This is in 
very good agrement with the test data, where the failure is in the neck of the outermost 
joint, on the component side (Figure 4-7). Hence, the results of the FEA can be viewed 
with a high degre of confidence. 
 
Figure 4-6: Distribution of plastic strain in the solder bals at PWA strain and strain rate of 8E-3 and 1E-2 
sec-1, respectively. 
7 
 
Figure 4-7: Cros-sectioning image of the outer most solder joint shows failure in the solder neck [73] 
The FEA transfer function is obtained by plotting the average equivalent plastic 
strain in the solder with respect to the PWA flexural strain averaged over the region of 
the strain gage. The averaging of the solder equivalent plastic strain decreases the 
dependence of the results on meshing approximation. The average technique is used 
extensively in the field of solder durability, but there are no standard averaging schemes. 
The averaging requires a trade-off betwen losing data resolution across a large region 
versus numerical erors in a very smal region. The authors have chosen a single row of 
elements, spread over 5% of the solder cross-sectional area in the region of maximum 
plastic strain, to provide a quantitative estimate of strains in the region. Figure 4-8 and 
Figure 4-9 show the cross-sectional area (which comprises of two elements) over which 
the plastic strains are averaged. The results of this study must be viewed within the 
context of this averaging scheme. 
78 
 
Figure 4-8: Top view of the solder neck. The averaging area is about 5% of the total cros-sectional area. 
 
Figure 4-9: Front view of the solder neck. The averaging area comprises of a single row of two elements. 
4.6. Efect of Strain Rate Hardening  
The solder plastic strain increases monotonicaly with PWA flexural strain for al 
cases. For the same PWA flexure, the plastic strain in the solder decreases with 
increasing PWA strain rate. This is because the solder undergoes strain-rate hardening, 
which increases its yield stres and hence, delays the onset of plastic strain. Figure 4-10 
shows the plot of average solder plastic strain rate with respect to average PWA strain 
rate. The average strain rate is obtained by dividing the strain amplitude by the loading 
time. 
79 
 
Figure 4-10: Log-log plot of average solder strain rate to the average PWA flexural strain rate 
The curves shown in Figure 4-11 are the transfer functions needed to correlate 
PWA flexural strain to the average plastic strain at the failure site, for diferent values of 
PWA strain rates and corresponding solder plastic strain rates. 
 
Figure 4-1: FEA transfer function for diferent PWA strain rates and solder plastic strain rates. 
As proposed by the authors in an earlier study [73], the transfer function in Figure 
4-11 can be approximated as a power law relationship (Eq. 4-1). The values of the 
constants are listed in Table 4-6. 
80 
()
1
1
b
PWA
c
0
P
PWAp
,f !
"
#
$
%
&
?
=
"
#
$
%
&
?
!=!
?
?
         (4-1) 
Table 4-6: FEA transfer function constants 
C c
1
 b
1
 
7928 0.09 2.05 
 
Thus, the test data, obtained in terms of PWA strain and strain rate (Table 4-1) can 
be represented in terms of solder plastic strain and solder plastic strain rate Table 4-7. 
4.7. Efect of Ductility Exhaustion 
The failure strain of the solder is rate-dependent due to the exhaustion of ductility. 
Plumbridge and Gagg [5] conducted tensile tests at 20 ?C on Sn37Pb solders at strain 
rates ranging from 1E-3 to 1E-1 sec
-1 
and showed that the failure strain of the solder 
decreases monotonicaly with increasing strain rate. Here, we make a simplifying 
approximation that the failure strain follows the same slope at higher strain rates. On the 
basis of this approximation, the data published by Plumbridge and Gagg [5] is 
extrapolated to a strain rate of 1E1 sec
-1
 and normalized with respect to the quasi-static 
solder strain rate obtained from this study. For the solder strain rates of interest, the plot 
of normalized failure strain with solder strain rate follows a power law equation, as 
shown in Figure 4-12. 
81 
 
Figure 4-12: Log-normal plot of normalized failure strain versus solder strain rate. Estimated from [5]. 
The failure strain obtained from the macro-scale samples [5] may not be directly 
applicable for solder interconnects due to a variety of reasons, including length scale 
efects and microstructure. For the purpose of this study, we make a simplifying 
approximation that the failure strain of the micron-scale solder used in this study follows 
the trend reported in Figure 4-12. Further testing is needed to characterize the variation of 
failure strain with strain rate at the microscale. From the numerical simulations of the test 
specimens used in this study, the solder undergoes overstres failure at a plastic strain 
value of 5.93E-1 under quasi-static loading conditions. Using this data and the figure 
shown above, we can now estimate the solder failure strain for the strain rates of interest 
in this study. As expected, failure strain decreases monotonicaly with increasing solder 
plastic strain rate. As shown in Figure 4-13, the relationship can be approximated as a 
power law (Eq. 4-2). 
82 
 
Figure 4-13: Log-normal plot of variation of failure strain versus solder plastic strain rate 
q
pf
!
?
"
#
$
%
&
?
(=
    `         (4-2) 
where p = 0.5 and q = 0.09, from the data presented in Figure 4-13.  
4.8. Solder Fatigue Curves 
The rate-dependent durability of the solder is presented in terms of the ratio of the 
plastic strain to the failure strain. In other words, 
()
b
f
f
p
N
!
=
"
         (4-3) 
So, for a given PWA flexural strain, the solder plastic strain and the failure strain, 
both decrease with increasing loading rate. The decrease in the plastic strain due to strain-
rate hardening decreases the damage in the solder, thus increasing its durability. But the 
decrease in the failure strain due to ductility exhaustion in the solder has the efect of 
decreasing its durability. To fully understand the competing efects of these two 
phenomena, let us look at the available data in its entirety. Table 4-7 lists the durability of 
the solder in terms of the test parameters (PWA strain and strain rate), and mechanistic 
83 
parameters (plastic strain and failure strain). Let us consider the solder response to a 
constant PWA strain of 2.5E-3 and diferent PWA strain rates (Test numbers 3, 4, and 6 
from Table 4-7). It can be sen that as the PWA strain rate increases, the solder plastic 
strain and the failure strain decrease monotonicaly, but the ratio of the plastic strain to 
the failure strain shows a monotonic increase (Figure 4-14). This leads to a decrease in 
the durability of the solder 
Table 4-7: Durability in terms of empirical [73] and mechanistic parameters 
Cycles to 
failure Test 
num 
PWA 
strain  
(-) 
PWA 
strain 
rate 
(sec
-1
) 
Solder 
plastic 
strain  
(-) 
Solder 
plastic 
strain rate  
(sec
-1
) 
Solder 
failure 
strain  
(-) 
A B 
1 5.0E-3 4.9E-3 1.56E-1 4.66E-1 5.72E-1 31 39 
2 4.9E-3 3.8E-2 1.22E-1 1.59E0 5.13E-1 50 71 
3 2.5E-3 2.5E-2 3.30E-2 1.25E0 5.24E-1 608 804 
4 2.5E-3 2.5E-3 3.58E-2 3.15E-1 5.92E-1 639 1000 
5 9.4E-3 2.5E-3 5.93E-1 3.10E-1 5.93E-1 1 1 
6 2.5E-3 1.2E-1 3.14E-2 3.19E0 4.83E-1 651 691 
 
84 
 
Figure 4-14: Efect of loading rate on solder plastic strain, failure strain, and ratio of the two. 
For the loading rates observed in this study, the failure strain is more rate-
dependent than the plastic strain. In other words, exhaustion of ductility dominates, and 
the durability decreases with increasing PWA strain rate. Combining the results of the 
FEA with test data, we can now plot a fatigue curve for the solder (Figure 4-15). The 
solder durability is sen to follow a power law relation with the ratio of plastic strain to 
failure strain. The values of the rate-dependent constants of the durability model (Eq. 4-
3) are listed in Table 4-8. 
85 
 
Figure 4-15: Fatigue curve for dynamic loading of solder 
Table 4-8: Rate-dependent durability constants for solder 
a b 
1.13 0.43 
 
4.9. Discusion 
It has been shown in earlier studies [58][42][47]that the durability of the 
interconnect decreases with increasing loading rate during drop testing and high sped 
bending of PWAs. This study provides a mechanistic perspective into solder durability at 
plastic strain rates ranging from 1E-1 to 1E1 sec
-1
. These strain rates are too high for 
crep dominated deformation and too low for damage due to adiabatic heating. It is 
proposed that the variation of durability with strain rate depends on the competing efects 
of strain rate hardening and ductility exhaustion. The ratio of plastic strain to failure 
strain is proposed as a metric to quantify durability of the solder for the strain rates 
observed in this study. 
The proposed durability model is a modification of the Coffin-Manson relationship. 
Another modified Coffin-Manson model, proposed by Eckel [104], can be used to relate 
86 
the durability of the solder to loading frequency. Several studies, including the ones by 
Shi, et al. [105] and Kanchanomai, et al. [106] have used Eckels model to describe solder 
durability at various loading frequencies. One of the limitations of Eckel?s model is that 
the value of the exponent is dependent on the strain amplitude. The efect of frequency is 
higher when the strain range is higher and when the elastic modulus is lower. In 
comparison, the durability model proposed in this study is based on mechanistic 
concepts. Further work is needed to collect additional data to increase the robustnes of 
the model constants, and make it applicable to a wider range of strain rates.  
For the strain rates observed in this study, the durability of the solder varies 
strongly with solder plastic strain, and very weakly with solder plastic strain rate. This 
can be beter understood by substituting Eq. 4-2 into Eq. 4-3, and re-presenting the 
master-curve shown in Figure 4-15 by a family of Coffin-Manson curves, each 
corresponding to a diferent solder plastic strain rate (Figure 4-16). The values of the 
Coffin-Manson durability constants for each level of plastic strain rate are listed in Table 
4-9.  For a solder plastic strain rate of 1E0 sec
-1
, a 100% increase in the solder plastic 
strain from 0.1 to 0.2 decreases the durability by almost 83%. On the other hand, at a 
solder plastic strain of 0.1, an increase in the plastic strain rate by one order of magnitude 
from 1E0 sec
-1
to 1E1 sec
-1
 changes the durability by approximately 40%.  
87 
 
Figure 4-16: Family of Cofin-Manson curves for Sn37Pb solder at diferent plastic strain rates. 
Table 4-9: Cofin-Manson Model constants for solder 
Plastic strain  rate (sec
-1
) a b 
1E-1 0.7 0.43 
1E0 0.57 0.43 
1E1 0.46 0.43 
 
The rate-dependence of the solder is negligible at the PWA strain rates (1E-3 to 1E-
1) and solder strain rates (1E-1 to 1E1 sec
-1
) observed in this study, which is could be 
why the durability shows a weak dependence on strain rate. This could be atributed to 
changes in the deformation mechanisms at the microstructural level at these strain rates 
that can afect the rate-dependent material properties of the solder. For example: below a 
transitional strain rate of 1E-3 sec
-1
, Sn37Pb solder deforms due to wedge cracking 
induced by grain boundary sliding. The solder deforms due to cavitation on the colony 
boundaries when the strain rate is above the transitional strain rate [100]. Other studies 
have also reported that plastic deformation is dominated by dislocation motion at quasi-
8 
static loading rates, and by twinning at high strain rates [101][102]. This change in the 
deformation mechanism has been atributed to the strain rate hardening of the solder 
because it takes a higher value of the flow stres for nucleation of twins than dislocation 
motion [103]. Analysis at the microstructural level, which is beyond the scope of this 
study, can provide further insight into the behavior of the solder at the strain rates of 
interest.  
Depending on the geometry and material properties of the PWA, solder 
interconnects subjected to JEDEC board level drop tests [9] can experience strain rates 
close to those presented in this study and higher. Researchers have reported that solder 
interconnects can experience strain rates as high as 1E3 sec
-1
 during product level drop 
tests [122]. Hence, further work also needs to be done to increase the range of strain rates 
to include 1E3 sec
-1
. 
4.10. Conclusions and Future Work 
A mechanistic insight is offered to explain the dependence of solder durability on 
loading rate. For the test coupons used in this study, solder plastic strain varies strongly 
with the PWA flexural strain, and weakly with the PWA flexural strain rate. Solder 
failure strain is found to decrease exponentialy with increasing solder strain rate. In the 
range of strain rates observed in this study, the efect of strain rate hardening was weaker 
than that of ductility exhaustion. Hence, the damage metric, the ratio of solder plastic 
strain to solder failure strain, increased with increasing PWA flexural strain rate. 
Durability was shown to decrease exponentialy with increasing values of the damage 
metric. For the loading conditions used in this study, solder durability was strongly 
dependent on solder plastic strain, and weakly dependent on solder plastic strain rate. 
Future work needs to focus on characterizing the variation of failure strain with 
89 
strain rate for micron-scale solders. Work also needs to be done to increase the robustnes 
of the model constants, and make it applicable to a wider range of strain rates. 
Acknowledgements 
This work is sponsored by members of the CALCE Electronics Products and 
Systems Consortium at the University of Maryland, College Park. 
 
90 
Chapter 5: Intermetalic Fracture Model
#
 
This chapter presents mechanistic insights into the failure at the interface betwen 
the two IMC layers (Au0
.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4
) of a Sn37Pb/ENIG interconnect subjected 
to dynamic flexural loading. The original draft of this chapter is a journal paper that is 
currently submited for peer-review in Engineering Fracture Mechanics. The ratio of the 
interfacial strain energy release rate to the interfacial fracture toughnes is proposed as a 
mechanistic parameter to characterize the failure envelopes, instead of empirical metrics 
like PWA strain and strain rate, or drop height. For the test samples and test conditions 
used in this study, the non-planarity of the interface betwen the two IMC layers has a 
significant efect on the stres field at the crack tip. For a given PWA geometry and 
loading condition, the strain energy release rate at the interface is shown to increase with 
decreasing interfacial roughnes, thus increasing the chances of interfacial fracture. The 
proposed mechanistic durability metrics provide a suitable framework to quantify the 
durability of the interface, and have a power law relationship to the average cycles to 
failure obtained from the test data 
Failures in Intermetalic Layers of Solder Interconnects 
with ENIG Plating 
J. Varghese, A. Dasgupta 
CALCE Electronic Products and Systems Consortium, University of Maryland, Colege Park, MD 20742 
Tel: 301-405-5251, Fax: 301-314-9269, Email: josephv@umd.edu, dasgupta@umd.edu 
This study presents mechanistic insights into the interfacial failure betwen two 
                                                
#
 Submited for publication in Enginering Fracture Mechanics.  
91 
intermetalic layers (Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4
) of a Sn37Pb solder interconnect on a 
ENIG PWA, when subjected to dynamic flexural loading. Instead of empirical metrics 
(for example: PWA strain, drop height), the magnitude of the interfacial strain energy 
release rate (G
t
) normalized with respect to the interfacial fracture toughnes (G
c
) is used 
as a mechanistic parameter to characterize the failure envelopes. The efect of non-
planarity of the interface betwen the two intermetalic layers on the stres field at the 
crack tip is also quantified. The applicability of the proposed failure metrics for 
quantifying durability under dynamic loading (for example: drop testing) is discussed. 
5.1. Introduction 
Fracture at the interface of the intermetalic compound (IMC) of solder 
interconnects can have a significant efect on the durability of Printed Wiring Asemblies 
(PWAs). This is often true for PWAs with Electroles Nickel Imersion Gold (ENIG) 
plating and/or PWAs subjected to thermal aging for prolonged periods of time.  This 
failure mechanism is especialy relevant under dynamic flexural loading of the PWAs due 
to vibration and/or repetitive impacts during mechanical handling, acidental misuse and 
shipping (transportation). Hence, understanding of interfacial fracture at the IMC layer 
under flexural loading conditions is of critical concern to the microelectronics industry. 
Tests conducted by Luhua and Pang [5] showed that even within the IMC layer, the 
failure site can change with thermal aging (from the interface betwen the solder and the 
IMC, to the interface betwen the two IMC layers, to the interface betwen the IMC and 
the copper pad). In solder interconnects with Electroles Nickel Imersion gold (ENIG) 
finish, the most commonly reported failure site is in the thin black Ni(p) layer betwen 
the nickel plating and the Ni
3
Sn
4
 IMC [5]. Other failure sites observed in interconnects 
92 
with ENIG finish include the interface betwen the Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4 
IMC layers 
[86][87][88]. 
Failure in the intermetalic layer has been characterized in terms of empirical 
metrics, like drop height of a JEDEC board-level drop-tester [5][43][54], or PWA 
flexural strain and strain rate [86]. In al these studies, durability shows a monotonic 
decrease with increasing values of the drop severity, as measured by the empirical 
metric(s). The fracture toughnes of the IMC layer has been shown to decrease with 
loading rate [3] and with thermal aging [5]. 
FEA has been used by several authors to make the damage metrics les sensitive to 
PWA geometry, and more strongly dependent on the properties of the material(s) at the 
failure site. As an example, durability of the IMC layer has been characterized in terms of 
the peeling stres at the intermetalic layer [65][66][113] using FEA with rate-
independent material properties. The stres in the IMC layer is calculated by averaging 
the streses in the elements at the solder-copper interface. The morphology of the 
intermetalic layers was not explicitly considered in this study. Pang and Che [68] used 
FEA with rate-dependent elastic-plastic material properties to characterize IMC 
durability during JEDEC board level drop tests in terms of von Mises stres at the 
interface. However, von Mises stres is usualy not the best metric for britle failure 
mechanisms such as IMC fracture. Yeh and Lai [75] characterized intermetalic failure 
during high speed bal shear tests in terms of normal and shear forces in the IMC layer. 
The forces in the IMC layers were estimated with FEA by using ?tiebreak? nodes-to-
surface contact at the solder ? copper interface. This technique links adjacent meshes and 
confines the movements of nodes until the bond breaks.  Again, these authors did not 
93 
explicitly consider the morphology of the IMC layer(s). 
In al of these studies, FEA did not provide any insight into the efect of the 
interfacial morphology on the stres distribution in the IMC layer because the solder ? 
copper interface was asumed to be planar. However, studies by several researchers have 
shown that the interface betwen the two IMC layers is jagged and wavy 
[5][128][129][130]. The severity of wavines of the interfacial morphology depends on 
the manufacturing proceses and solder/plating material systems. The interfacial 
morphology varies constantly with time, even at room temperature, due to difusion 
betwen the plating material, copper trace and solder [130]. Figure 5-1 shows the 
variation in the morphology of Cu
6
Sn
5
/Cu
3
Sn interface of a SnAgCu interconnect with 
Organic Solderability Preservative (OSP) finish, at various conditions of thermal cycling 
[5]. The non-planar interface increases the efective fracture technique by crack-blunting 
and crack-shielding mechanisms at the crack tip. Closed-form analytical models, based 
on interfacial fracture mechanics, can be used to fil this gap. 
 
Figure 5-1: Interface of two IMC layers at diferent thermal aging conditions [5] 
This paper seks to extend the excelent work done by the researchers mentioned 
94 
above, by using a simple analytical model based on interfacial fracture mechanics, to 
develop an understanding of the failure in the interface betwen the two IMC layers. As a 
mechanistic interfacial fracture parameter, the energy release rate G
t
 (normalized by the 
fracture toughnes, G
c
), is used to characterize the failure envelopes.  This technique is 
les sensitive to specimen geometry, than empirical metrics like PWA strain and drop 
height. The proposed durability model is demonstrated on a Sn37Pb/ENIG component 
subjected to four point bend tests [85][86]. 
This paper is part of an ongoing efort to understand and quantify the damage 
experienced by solder interconnects during quasi-static as wel as dynamic flexural 
loading of PWAs. Earlier work by the authors focused on identifying empirical metrics to 
quantify interconnects durability [113] and to characterize failure site transitions from the 
solder to other parts of the PWA [73][123]. Recent work [124] established mechanistic, 
non-empirical, metrics to quantify the rate-dependent durability of the solder. The current 
study extends the previous work by proposing similar non-empirical metrics for 
interfacial fracture betwen the two IMC layers of solder-ENIG interfaces. 
The experimental details are first explained in brief, followed by the macroscopic 
and microscopic analysis of the test data. The subsequent sections discus the failure 
envelope and the durability model. Finaly, the applications of this technique and future 
work are discussed. 
5.2. Aproach 
The durability metrics and model proposed in this paper are based on experimental 
data from a previous study [85][86]in which a PWA of simple design was subjected to 
95 
four-point bend tests at diferent loading amplitudes and rates. The specimen design and 
test results are summarized in this paper for the sake of completenes. Details can be 
found in [85][86]. A macroscale to microscale approach is used to develop a mechanistic 
understanding of the observed failure. The macroscale model uses FEA to relate the 
PWA flexural strain to the peling and shear stres in the IMC layer. The microscale 
model estimates the interfacial strain energy release rate (G
t
) and mode mixity (!) at the 
interface betwen the two IMC layers, based on the streses obtained from the 
macroscopic model. This analysis takes into acount the non-planar (wavy) morphology 
of the IMC layer, and provides transfer functions betwen PWA strain and G
t
, for 
diferent magnitudes of interfacial wavines. The interfacial fracture toughnes (G
c
) is 
evaluated from the test data corresponding to overstres failure (N
f
=1) and failure is 
predicted to occur when the calculated value of G
t
 reaches G
c
. Durability is characterized 
in terms of the ratio of the interfacial strain energy release rate to the interfacial fracture 
toughnes (G
t
/G
c
). 
The following simplifying approximations have ben made: The PWA is asumed 
to be isotropic and homogenous, with no internal or external defects. The solder and the 
copper trace are modeled as elastic-plastic materials. Al other materials in the PWA, 
including the IMCs, have linear elastic properties. The wavy interface betwen the two 
IMC layers is idealized with a saw-tooth profile. This simplifying asumption can be 
justified on the basis of the jagged interfacial morphology observed by numerous 
researchers [5][126][28] . 
5.3. Experiment Details 
The component is a stacked die Bal Grid Aray (BGA) with 160 I/O, 0.44 m 
96 
diameter, 0.8 m pitch Sn37Pb eutectic solder bals. The pad finishes on the component 
and board side consist of electrolytic gold over nickel and ENIG, respectively. The 
PWAs are subjected to isothermal aging at 135?C for 168 hours. The IMC layer consists 
of Ni
3
Sn
4 
on the copper side and Au
0.5
Ni
0.5
Sn
4,
 on the solder side. The thicknes of the 
IMC layer is in the range of 2 to 3 microns. 
 
Figure 5-2: PWA specimen, showing location of components and strain gage. 
A 350 " strain gage with 3.18 m gage length and 2.54 m grid width is atached 
to the board near the corner of the component (Figure 5-2) to measure the flexural strain 
and the flexural strain rate. The PWA is subjected to 4 point bend tests. The failure site is 
found to be the interface betwen the Ni
3
Sn
4
 and the Au
0.5
Ni
0.5
Sn
4
 IMC layers, and is in 
agrement with other works in the literature [87][88]. Figure 5-3 shows the location of 
the crack. Details of the test matrix, test setup, specimen design and test results can be 
found in an earlier publication [86]. 
97 
 
Figure 5-3: Fracture in the IMC layer on the package side of the solder [86][85] 
5.4. Macroscale model 
A commercialy available software is used to generate a 2-D finite element model 
of the specimen with 4-noded plane stres elements. The elements are given an 
appropriate out-of-plane thicknes to reflect the geometry of the PWA. As shown in 
Figure 5-4, only one half length of the PWA is modeled because the the specimen is 
symmetric and its structural response is limited to the symmetric first mode [85][86]. 
Symmetry boundary conditions are applied about x=0, at the center of the model The 
copper trace connections are ignored in the FEA model. The IMC layer betwen the 
solder and the copper pad is also ignored in the FEA model, but it is addresed later in the 
microscale model. As mentioned earlier, al materials are modeled with isotropic 
homogenous properties. 
 
Figure 5-4: 2D model of PWA with symetric boundary conditions 
The mesh has 4126 elements and 4435 nodes, and is scaled to provide maximum 
mesh density at regions of high stres gradients, for example at the solder/Cu pad 
98 
interface, and at the Cu pad/PWA interface (Figure 5-5). The outermost solder bal has a 
higher mesh density than the inner solder bals because it is the location of the failure 
site. The solder and copper are modeled as rate-independent elastic-plastic materials. Al 
other materials are modeled as linear elastic. The material properties are listed in the 
section 4.5. 
The FEA results show that the maximum streses are in the outermost interconnect, 
at the solder neck near the component termination. This is in very good agrement with 
the test data, where the failure is at the interface of the two IMC layers betwen the 
component copper-pad and the solder bal. Hence, the results of the FEA macroscale 
model can be treated with a reasonable degre of confidence. 
The average stres in the intermetalic layer is obtained by dividing the local 
interconnect force by a local efective load-bearing area.  The averaging decreases the 
dependence of the results on meshing approximation, and requires a trade-off betwen 
losing data resolution across a large region versus FEA discretization erors in a very 
smal region. Because of the lack of industry standards for averaging, a logical scheme is 
chosen in this study. The averaging zone consists of a sufficient number of elements in a 
single row on each side of the solder-copper interface, near the critical location (in the 
neck of the solder joint), such that averaging zone is approximately 5% of the solder joint 
cross-sectional area. Figure 5-5 shows the area (which comprises of four elements: two 
each from the solder and copper) over which the streses are averaged. The results of this 
study must be viewed within the context of this averaging scheme. 
9 
 
Figure 5-5: The averaging area comprises of two elements each in the solder and the coper trace in the 
finely meshed outer solder bal. 
 
Figure 5-6 is the FEA transfer function that relates the PWA strain to the peeling 
and shear stres in the intermetalic layer. The PWA strain is obtained by averaging the 
longitudinal strains (along the x-axis) over the elements on the board surface located 
under the foot-print of the strain gage. However, this macroscale transfer function does 
not include the the efect of the morphology at the interface betwen the two IMC layers. 
This necesitates the use of the microscale model. The next section describes how the 
output of the macroscale (FEA) model is used to quantify the stres distribution in the 
interface. 
10 
 
Figure 5-6: Variation of peling and shear stres in the IMC layer with PWA strain 
5.5. Microscale model 
The micro-scale model, based on interfacial fracture mechanics, uses the data in 
Figure 5-6 to ases the durability of the IMC interface. Let us asume the existence of a 
smal crack that initiates at the interface of the Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4
 layers. For 
purposes of ilustration, we asume a crack length of 1% of the diameter of the solder bal 
at the neck. However, the theory is equaly applicable for other asumptions of crack 
length. The material at this location in the interconnect structure undergoes mixed mode 
loading. Using simple approximations, the stres distribution is first used to define the 
stres intensity factors (K) for bulk materials, K
I
 and K
II
. Details of this technique are 
available in the literature [90]. 
2K
pI
!"=
                         (5-1) 
a
I
                         (5-2) 
Where, 
a
is the crack length (asumed here to be 1% of the solder bal diameter at the neck) 
101 
p
!
is the peeling stres (mode I) obtained from the FEA macro-model 
is the shear stres (mode I) obtained from the FEA macro-model 
 
!
"
#
$
%
&
=?
(
I
1
K
tan
 is the phase angle, indicating the mode mixity in the bulk material 
In a homogeneous material, the crack propagates along a trajectory at which K
II
 is 
zero [91]. However, at a bi-material interface, the trajectory of the crack depends both on 
the fracture energy and the phase angle [92]. The diferences in the material properties of 
the two IMC layers change the value of the efective mode I and mode I stres intensity 
factors at the interface. As proposed by Suo and Hutchinson [93], we can now relate the 
bulk stres intensity factors (K
I
 and K
II
) to the interfacial stres intensity factors (K
1
 and 
K
2
). 
!"
+
#
$
%
&
?
(
)*
=+
i
I
2
1
21
eL)iK(iK
            (5-3) 
Where 
# and $ are the non-dimensional Dundurs parameters [94] that relate the properties 
of the two materials at the interface. 
L is the characteristic length of the stres field, whose value in this study is the 
thicknes of the IMC layer: 3?m 
% is a non-dimensional parameter that represents the oscilatory nature of the stres 
field at the tip of the interfacial crack [125] 
& is the phase shift in the mode mixity due to the mismatch in the material 
properties at the interface, whose values are provided in [92] 
102 
The stres intensity factor exhibits an oscilatory behavior near the crack tip due to 
the complex eigen-values obtained as part of the solution of the above equation [98]. The 
oscilatory field implies that the material in the smal zone behind the crack tip 
interpenetrate even when the crack is subjected to far-field tensile loads. They also imply 
that K
1
 and K
2
 are coupled and do not have the same meaning (or units) as the stres 
intensity factor for homogenous materials [95]. 
Studies [95][97][99] have indicated that $ makes a negligible contribution to the 
solution of the above equation and to the value of &. Hence it is a justifiable 
approximation to take the value of $ = 0. In addition to simplifying the solution, it also 
decouples interfacial stres intensity factors, K
1
 and K
2
, thus making them as 
representative of the stres field as the bulk stres intensity factors, K
I
 and K
I
. As shown 
in Figure 5-1, the material properties of the intermetalic compounds (obtained from 
literature [96]) can be used to estimate the Dundurs parameters and the phase angle of the 
interfacial crack. 
Table 5-1: Material properties [96] of the IMCs and calculated values of the interfacial parameters 
Au
0.5
Ni
0.5
Sn
4
 Ni
3
Sn
4
 
E (GPa) ? (-) E (GPa) ? (-) 
# 
(-) 
& (#, 0) 
(?) 
13.3 0.3 48 -0.47 -0.47 3.25
0
 
 
Figure 5-7 and Figure 5-8 show the variation of the stres intensity factors and the 
corresponding phase angles with PWA strain, respectively. While the interfacial and bulk 
stres intensity factors increase monotonicaly and non-linearly with PWA strain, the 
mode mixity is almost independent of PWA strain. 
103 
 
Figure 5-7: Variation of bulk and interfacial Stres Intensity Factor with PWA strain 
 
Figure 5-8: Plot of bulk and interfacial phase angle with PWA strain shows almost no variation. Hence the 
mode mixity can be asumed to be constant 
Asuming $=0, the strain energy release rate for the interfacial crack can be 
calculated using the following equation [97]. 
()
2
1
NiSnNiAu
K
E2
G+=
!
        (5-4) 
The above equation asumes a flat interface betwen the two IMC layers. Let us 
introduce the efect of non-planarity at the interface. As mentioned in the literature 
review, the jagged interface betwen the two IMC layers acts as a crack tip blunting 
mechanism. In this study, we approximate the wavines of the interface betwen the IMC 
104 
layers with a triangular wave-form. The facet angle () in a wavy IMC interface can be 
expresed in terms of the pitch ()) and height (h) of the triangular profile. As proposed by 
Evans and Hutchinson [91], the efective stres intensity factors for non-planar interfaces 
is given by  
())CosKSinefiKK
21
i
12
t
1
t
2
!+"#+=
$
      (5-5) 
where 
* is the size of the characteristic length on the crack surface, whose value in this 
study is 1% of the crack length.  
f(*) is a non-dimensional scaling factor for the stres intensity factors whose value, 
as obtained from [91], is 0.2  
!
"
#
$
%
&
?
(=)
h
tan
1
 is the facet angle of the non-planar interface.  
t
i
K
 is the stres intensity factor of the non-planar interface at the i
th
 mode. 
The variation in the interfacial strain energy release rate due to the non-planarity of 
the interface, when compared to a planar interface, is given by the following equation 
[91]. 
)(tan1
)(CostanSin)(f2
1
G
2
2t
!+
""#
=
       (5-6) 
Where 
t
 is the strain energy release rate due to crack propagation along a wavy interface 
and G is the baseline for a smooth, flat interface 
105 
!
"
#
$
%
&
=?
(
t
1
2
K
tan
 is the efective mode mixity at the non-planar interface 
Figure 5-9 is a 3D plot of the above equation and shows that G
t
/G decreases 
monotonicaly with increasing interfacial wavines and phase angle. The changes in the 
value of h/) reflect the changes in the interfacial morphology from rough (h/) = 5) to 
smooth (h/) =0). The rough interface clearly provides beter resistance to crack 
propagation, and hence has a lower energy release rate for a given loading condition. For 
a given level of mode mixity at the interface, the value of the interfacial strain energy 
release rate decreases with increasing non-planarity. For the same !, G
t
/G decreases with 
increasing h/), and for a given h/), G
t
/G decreases with increasing !. 
 
Figure 5-9: 3D plot of the variation of G
t
/G with wavines and phase angle 
Figure 5-9 can be combined with the equations discussed above to obtain the FEA 
transfer functions betwen the interfacial strain energy release rate and PWA strain for 
diferent facet angles. The FEA transfer function for diferent amounts of interfacial 
wavines is shown in Figure 5-10. 
106 
 
Figure 5-10: FEA transfer function for diferent interfacial morphologies. 
Environmental Scanning Electron Microscopy (ESEM) is used to obtain images of 
the failure site. (Figure 5-11) and quantify the wavines of the crack (Table 5-2). The 
average value of h/) is approximately 0.5, with a variance of 0.13. This corresponds to a 
( of approximately 168
0
.  The wavines often reduces with thermal aging due to 
difusion, thus reducing the efective interfacial fracture toughnes. 
 
Figure 5-1: Typical ESEM picture of failure site 
107 
Table 5-2: Typical values of the interfacial wavines 
h (?m) 1.2 0.9 0.8 1.1 1.0 0.8 1.0 
! (?m) 3.1 1.7 1.9 3.0 2.9 1.2 1.6 
h/! (-) 0.39 0.53 0.42 0.37 0.35 0.67 0.63 
 
Failure occurs when G
t
 reaches a critical value (G
c
), which is a material property. 
The value of G
c
 may also change with strain rate and with aging, but that is beyond scope 
of this study. For quasi-static loading, test data shows that the overstres failure of the 
intermetalic layer ocurs at a PWA strain value of 4E-3. The FEA transfer function 
developed in Figure 5-10 can be used to estimate the G
c
 value of the interface at that 
mode mixity. Hence, by combining the FEA plot and the test data, we can obtain the 
variation of the normalized G
t
/G
c
 as a function of PWA strain, for the facet angle 
calculated from the fracture site (Figure 5-12). 
 
Figure 5-12: Normalized interfacial strain energy release rate as a function of PWA strain, for diferent 
morphologies betwen the IMC layers. 
 
108 
5.6. Durability model 
The test results presented in an earlier publication [86] quantified the durability of 
the IMC interface in terms of the empirical metrics: PWA strain and strain rate. In view 
of the weak rate-sensitivity revealed in [86], the rate efects are ignored in the present 
study. In other words, durability is considered to be a function only of the PWA strain, 
and not of the PWA strain rate. Using the analysis conducted above, we can represent the 
durability data in terms of the mechanistic parameter: G
t
/G
c
 (Table 5-3) 
Table 5-3: Durability in terms of empirical [86] and mechanistic parameters 
Board Num PWA strain (-) G
t
/G
c
  (-) Avg cycles to failure (-) 
1 3.04E-6 0.82 15.75 
2 2.06E-6 0.58 133 
3 2.01E-6 0.56 204.25 
4 1.06E-6 0.3 1735 
 
The durability of the IMC interface can be related to Gt/Gc with a power law 
relationship as given below. 
 
! 
G
t
=p(N
f
)
q
         (5-7) 
where p = 1.64 and q = -0.18 are the durability constants. Figure 5-13 shows the 
fatigue curve for this IMC interface, in terms of the normalized durability parameter 
(G
t
/G
c
). 
109 
 
Figure 5-13: Plot of interfacial fatigue curve betwen the two examined IMCs. 
Failure analysis of the tested specimens revealed that the crack path was limited to 
the interface betwen the two IMC layers [86]. Normalizing the diameter of the solder 
neck with the durability for a given loading condition gives us the average crack 
propagation rate for each loading condition. As shown in the equation below and in 
Figure 5-14, Gt/Gc follows a power law relation with the average crack propagation rate. 
! 
da
dN
=m
G
t
" 
# 
$ 
% 
& 
? 
n
         (5-8) 
where m=0.05 and n=4.5 are the constants of the equation for this intermetalic 
system.  
10 
 
Figure 5-14: Variation of average crack propagation rate with G
t
/G
c
. 
In the above figure, the calculated values of the abscisa (Gt/Gc) are based on the 
existence of a crack at the IMC interface, and does not take crack propagation into 
acount. Also, the ordinate represents the crack propagation rate averaged over the solder 
bal neck. The values of m and n must be viewed within the context of this 
approximation. 
5.7. Discusion 
The efective strain energy release rate (G
t
) has been used in many studies to 
understand crack propagation in interfaces. Examples include de-cohesion of thin film on 
substrates [91], delamination of underfil/solder mask interface in electronic packages 
[107], delamination of epoxy/silicon interfaces[108], among others. 
In this study, the crack path was completely through the interface. However, this 
need not be the case al the time. Mixed-path cracks, where the propagation is through the 
IMC layers and the solder, have been observed during bal impact tests [75] and uniaxial 
vibration of solder interconnects [126]. Similar mixed-path cracks have also been 
observed during decohesion of thin film on britle substrates [127]. The tendency of the 
11 
crack to either remain at the interfaces or deviate away into the bulk material depends on 
the sign and magnitude of the phase angle [91]. This is specialy true for ductile/britle 
interfaces. As shown in Figure 5-8, the phase angle at the crack tip depends on the 
geometry and material properties of the PWA. Hence, it is possible to design the PWA in 
a manner in which the crack follows a pre-planned trajectory. 
In general, adhesion betwen two IMC layers is due to a combination of 
mechanical interlocking at the interface (analyzed in this study) and interatomic forces 
across the interface, which is in a state of constant evolution even at room temperature. 
The difusion of Sn and Ni leads to a steady change in the thicknes and morphology of 
the two IMC layers. Studies have also shown that the residual stres in the IMC layer, 
caused by negative volume changes, increases with aging time. The residual stres can 
change the value of the mode I and mode I stres intensity factors at the site of the 
micro-crack, and hence the value of the phase angle at the crack tip [91]. This wil not 
only afect the durability of the joint, but also the path of the crack as it could be diverted 
away or toward the interface. 
5.8. Sumary and Conclusions 
To the best knowledge of the authors, this is the first study that provides a 
mechanistic perspective on the efect of interfacial morphology on interfacial fracture 
betwen the two IMC layers of a solder-ENIG interconnect system.  
The durability of the joint has a power law dependence on the normalized energy 
release rate (Gt/Gc). For a given mixed mode loading condition, Gt/Gc decreases with 
increasing slope of the facet. This provides a mechanistic explanation as to why a jagged 
12 
interface (asociated with unaged PWAs or certain reflow profiles) rarely ses failure in 
the IMC layer during flexural testing, while a relatively smoother interface (asociated 
with aged PWAs) is more prone to interfacial failure. 
For the test coupon used in this study, the mode-mixity did not vary with the 
applied load. Hence, the results of the overstres failure (Nf=1) were used to determine 
the fracture toughnes of the interface, Gc(!), at that phase angle. Characterizing the 
fracture toughnes of the interface by using a brazil-nut or a double cantilever beam 
specimen could greatly enhance the acuracy of the proposed approach. 
The average crack propagation rate is found to have a power-law dependence on 
the normalized crack energy release rate (Gt/Gc). The technique and insight developed in 
this study can be used to quantify the efect of thermal aging on the fracture in the 
interfacial intermetalic layer. This study can also be used to understand the widely 
reported [5][86][3][75][123] failure site transitions  observed during flexural loading of 
unaged and aged PWAs, from the solder and the interface betwen the IMC layers. This 
wil be the focus of future studies. 
 
13 
Chapter 6: Examples: Competing Failure Mechanisms in 
PWAs During Dynamic Flexural Loading
%
 
This chapter presents a technique to ases the competition betwen competing 
failure mechanisms in the solder interconnect, and to ases the resulting durability. The 
failure mechanisms of interest are cyclic fatigue in the solder material and interfacial 
fracture betwen IMC layers.  Mechanistic metrics, developed in Chapters 4 and 5, are 
used to quantify damage in the solder and IMC interface, respectively. The applicability 
and the limitations of the proposed metrics are also discussed. The original draft of this 
chapter is a journal paper that is currently submited for peer-review to ASME Journal of 
Electronic Packaging. 
 A Technique to Predict the Failure Site and Durability in the 
Solder Interconnect During Flexural Loading of the Printed 
Wiring Asembly  
J. Varghese, A. Dasgupta 
CALCE Electronic Packaging and Systems Center, University of Maryland, Colege Park, MD 20742 
Tel: 301-405-5251, Fax: 301-314-9269, Email: josephv@umd.edu, dasgupta@umd.edu 
A methodology is presented to predict the durability and the dominant failure site 
in the interconnects of a Printed Wiring Asembly (PWA) subjected to flexural loading, 
in the presence of competing failure mechanisms. This study focuses on two widely 
reported failure sites: solder bals and interfacial intermetalic layers. The failure 
                                                
%
 Submited for review to ASME Journal of Electronic Packaging 
14 
envelope for each of these sites is examined in terms of mechanistic metrics (based on 
interfacial strain energy release rate and plastic strain), instead of empirical metrics (such 
as drop height, PWA aceleration, or PWA flexural strain). Thre examples are presented 
to demonstrate the technique. The predicted failure site and durability are found to agre 
with experimental data.  
Keywords: Interfacial fracture, solder, intermetalic compound, thermal aging, 
competing failure envelopes, damage 
6.1. Introduction 
The importance of dynamic loading to the durability of SMT solder interconnects 
in modern portable electronic products has received much atention in the recent literature 
[9][105][116][129][131]. Up until a few years ago, it was common to group al failure 
mechanisms in the interconnect system under a common category.  However, recent 
research [3][54][73] has documented the major competing failure sites to be in the solder, 
copper trace, intermetalic layer, and the interface betwen the copper pad and the PWB. 
Failures in the intermetalic compound (IMC) can be further sub-divided into the 
bulk IMC, the interface betwen IMC species, and the interface betwen solder and IMC. 
However, very few researchers [55][86] have made such detailed distinctions betwen 
failure mechanisms, and instead provided more qualitative comparisons of drop 
durability of emerging technologies. Further research on this topic is waranted because 
load amplitude and loading rate can change the failure site from the solder to other 
competing failure sites in the interconnect. The failure site and the associated failure 
mechanism govern the proper choice of damage model for predicting durability. 
15 
In recent years, researchers have reported on the change in failure site within the 
solder interconnect under diferent loading conditions. Yu, et al. [2] were the first to 
report a transition in the failure site from solder to the IMC layer with increasing drop 
height during JEDEC level drop testing of PWAs. Heaslip, et al. [47] compared the drop 
durability of Sn37Pb and Sn95.5Ag3.8Cu0.7 solders and showed that the failure sites and 
failure mechanisms change with drop height and solder type. Bary, et al [126] conducted 
mode I cyclic loading on single solder interconnects and observed a change in the failure 
site from the solder to the IMC layer, as the crack progresed through the cross-section. 
Song, et al. [86] conducted high-speed four point bend tests and reported on failure site 
transitions from the solder to the interface betwen the IMC layers for specimens with 
Electroles Nickel/Imersion Gold (ENIG) finish. A Failure Site Transition Zone 
(FSTZ), in terms of PWA strain and strain rate, was proposed to characterize the failure 
site transitions. Chai, et al. [54] and Darveaux [3] characterized the fracture strength and 
failure site of solder interconnects with diferent combinations of solder aloy and plating 
material. In general, solders with ENIG finish showed failure site transition from solder 
to the IMC layer with increasing loading rate and thermal aging. Yeh and Lai [132] ran 
charpy style impact tests on single solder interconnect asemblies. Depending on the 
loading rate, the failure was found to be in the solder, IMC layer, or mixed mode (crack 
traveling through the solder and the IMC layer). The failure site transitions were 
characterized in terms of the normal and shear forces in the solder. 
This paper seks to extend the excelent work done by the researchers mentioned 
above by providing a mechanistic insight into the failure site transitions. Despite the 
previous work described above, the transition of the failure site in the solder interconnect 
16 
due to flexural loading of the PWA remains poorly quantified and understood. Most 
metrics used to characterize the failure site transitions are empirical in nature, and are 
specific to the tested PWA. Studies that have used numerical simulation do not consider 
the efect of the interfacial morphology on the stres distribution in the IMC layer 
because the solder ? copper interface was asumed to be planar. 
However, studies by several researchers have shown that the interface betwen the 
two IMC layers is jagged and wavy [55][87][88][130]. The severity of wavines of the 
interfacial morphology depends on the manufacturing proceses and solder/plating 
material systems. The interfacial morphology varies constantly with time, even at room 
temperature, due to difusion betwen the plating material, copper trace and solder [130].  
Figure 6-1 shows the variation in the morphology of Cu
6
Sn
5
/Cu
3
Sn interface of a 
SnAgCu interconnect with Organic Solderability Preservative (OSP) finish, at various 
conditions of thermal cycling [9]. The non-planar interface increases the efective 
fracture toughnes by crack-blunting and crack-shielding mechanisms at the crack tip. 
 
Figure 6-1: Interface of two IMC layers at diferent thermal aging conditions [5] 
This study aims to provide a mechanistic perspective on the failure site transitions 
17 
from the solder to the interface betwen the IMC layers. Fatigue curves using mechanistic 
durability metrics for both competing failure sites are used to predict the durability and 
the failure site of the solder interconnect. The proposed technique is demonstrated on a 
Sn37Pb/ENIG component subjected to four point bend tests. 
This paper is part of an ongoing efort to understand and quantify the damage 
experienced by solder interconnects during quasi-static as wel as dynamic flexural 
loading of PWAs. Earlier work by the authors focused on identifying empirical metrics to 
quantify interconnects durability [113] and to characterize failure site transitions from the 
solder to other parts of the PWA [73][118]. Recent work established mechanistic, non-
empirical, metrics to quantify the rate-dependent durability of the solder [124] and the 
rate-independent durability of the interface betwen the intermetalic layers [133]. The 
current study extends the previous work by proposing a technique to combine models of 
these two competing failure modes, to predict which one wil dominate under diferent 
stres conditions. 
The paper is aranged as follows: the experimental data taken from earlier work 
[85][86], to validate the proposed asesment of  competing failure modes, are first 
summarized. The mechanistic failure models, presented earlier by the authors for relating 
the applied load to damage in the solder [124] and in the interfacial IMC layers [133] are 
also summarized for completenes. The subsequent section demonstrates how the 
dominant failure mode is picked from these competing candidates. Finaly, the technique 
is demonstrated using thre examples. 
18 
6.2. Aproach 
The durability metrics and model proposed in this paper are based on experimental 
data from a previous study [85][86] in which a PWA of simple design was subjected to 
four-point bend tests at diferent loading amplitudes and rates. The specimen design and 
test results are summarized in this paper for the sake of completenes. An FEA model of 
the PWA is developed to relate the input loading conditions to the plastic strain in the 
solder and the streses in the IMC layer. Interfacial fracture mechanics is used to estimate 
the interfacial strain energy release rate (G
t
) and mode mixity (!) at the interface betwen 
the two IMC layers, based on the streses obtained from the FEA model. Damage in the 
solder is characterized in terms of the ratio of plastic strain to the failure strain ("
p
/"
f
) of 
the solder material. Damage in the IMC layer is characterized in terms of the ratio of the 
interfacial strain energy release rate to the interfacial fracture toughnes (G
t
/G
c
) for the 
IMC interface. Of these two possible failure sites, the one with the highest acumulated 
damage is predicted to dominate for a given loading condition. Thre examples of this 
approach are presented in this paper. 
The following simplifying approximations have been made in the damage 
modeling efort: The PWA is asumed to be isotropic and homogenous, with no internal 
or external defects. The solder and the copper trace are modeled as elastic-plastic 
materials. Al other materials in the PWA, including the IMCs, have linear elastic 
properties. It is asumed that the constitutive equations of bulk solder obtained from 
literature can be used to represent the behavior of the solder bals. In other words, the 
length scale efects on the material properties of the solder due to its microstructure are 
ignored. The wavy interface betwen the two IMC layers is idealized with a saw-tooth 
19 
profile. This simplifying asumption can be justified on the basis of the jagged interfacial 
morphology observed by numerous researchers [55][86][130]. 
6.3. Experimental Data  
Four stacked-die Bal Grid Aray (BGA) packages with 160 Sn37Pb eutectic solder 
bals each, are mounted on each FR-4 board, as shown in Figure 2. The pad finishes on 
the component and PWB consist of electrolytic and electroles gold over nickel, 
respectively. The PWA is subjected to 4 point bend tests at diferent load amplitudes and 
loading rates. The flexural strain and strain rate are monitored with suitably placed strain 
gages. The purpose of choosing this simple specimen design is to alow an in-depth study 
of the failure site transition, without making the analysis too complex. Sn37Pb solder also 
makes a beter baseline sample because it is a wel-studied material with wel 
documented [5][82][83] behavior under high strain-rate loading conditions. Details of the 
test matrix, test setup, and the specimen can be found in earlier publications [73][86].  
 
Figure 6-2: PWA specimen, showing location of components and strain gage. 
Solid state difusion at the solder-copper interface of the interconnect leads to 
formation of Ni
3
Sn
4
 and Au
0.5
Ni
0.5
Sn
4
 intermetalic compounds on the copper and solder 
120 
sides, respectively. Some PWAs are tested in the unaged (as-reflowed) condition, while 
others are tested after isothermal aging at 135?C for 168 hours. The thicknes of the IMC 
layer is les than 0.3 microns for the unaged specimens, and in the range of 2 to 3 
microns for the aged specimens. The IMC growth betwen the metal pad and the bulk 
solder on the component side of the as-reflowed and aged solder joints are ilustrated in 
Figure 6-3 and Figure 6-4. 
 
Figure 6-3: ESEM image of the IMC layer betwen the solder and the Cu-pad of the unaged PWA [85] 
 
Figure 6-4: ESEM image of the IMC layer betwen solder and Cu-pad of the aged PWA [85]. 
The results of the four point bend test are characterized in terms of cycles to failure 
and the failure site, for diferent PWA flexural strain and PWA flexural strain rate.  A 
brief summary of the solder and IMC failure data are presented in Table 6-1. Failures in 
the FR4/Cu-trace are not presented here as they are not relevant for the current study. 
121 
Table 6-1: Durabilty and failure sites of the PWAs 
Num(-) 
PWA Strain 
(?!) 
PWA Strain 
Rate (?!/sec) 
Aging 
Avg. cycles to 
failure (-) 
Failure Site 
1 2397 1067 No 838.7 Solder 
2 3040 1002 Yes 15.7 IMC 
3 2060 1015 Yes 133 IMC 
4 2010 990 Yes 204.2 IMC 
5 1060 1055 Yes 1735 IMC 
6 326 40750 Yes 2423.3 IMC 
7 2060 338 Yes 269.2 IMC 
8 2000 10000 Yes 102 IMC 
 
Figure 6-5 and Figure 6-6 show typical cross-sectional images of the solder and 
IMC failures listed in Table 6-1. The failure site in the IMC is found to be at the interface 
betwen the Ni
3
Sn
4
 and the Au
0.5
Ni
0.5
Sn
4
 layers, and is in agrement with other works in 
the literature [87][88]. 
 
Figure 6-5: Fracture in the solder on the package side of the interconect [86]. 
12 
 
Figure 6-6: Fracture in the IMC layer on the package side of the interconect [86]. 
6.4. Completing Failure Models 
The models for the competing failure modes are summarized here for the solder 
failure and IMC failure.  In order to use the failure models, transfer functions are first 
needed to deduce the stres levels at the failure site, for the given PWB deformation. 
A numerical model is used to create transfer functions that relate the loading 
condition to the durability metrics at the two failure sites of interest: !
p
/!
f
 and G
t
/G
c
 for 
the solder and IMC interface, respectively. A commercialy available software is used to 
generate a 2-D finite element model of the specimen with 4-noded plane stres elements. 
The elements are given an appropriate out-of-plane thicknes to reflect the geometry of 
the PWA. As shown in Figure 6-7, only one half length of the PWA is modeled because 
the specimen is symmetric and it?s structural response is limited to the symmetric first 
mode [86]. Symmetry boundary conditions are applied about x=0, at the center of the 
model The copper trace connections are ignored in the FEA model. The IMC layer 
betwen the solder and the copper pad is also ignored in the FEA model, but it is 
addresed later in the analytical model. 
123 
 
Figure 6-7: 2D model of PWA with symetric boundary conditions 
 The FEA transfer functions are obtained by plotting the average value of the stres 
at the britle IMC layer and the maximum plastic strain in the solder, with respect to the 
PWA flexural strain. The solder transfer function is normalized with respect to failure 
strain in the solder. The failure strain is the solder plastic strain estimated from the PWA 
strain corresponding to overstres failure (N
f
=1). Details of the technique are presented in 
[124]. 
 Figure 6-8 shows the normalized solder transfer function for this specimen. One 
can se that the solder deformation is in the elastic regime til a PWA strain value of 
approximately 1E-3.  Beyond that, the normalized solder plastic strain follows a power 
law relation with PWA strain. 
 
Figure 6-8: Solder transfer function. 
Figure 6-9 is the FEA transfer function that relates the PWA strain to the peeling 
and shear stres in the intermetalic layer of this specimen.  Once again, the modeling 
124 
details are presented elsewhere [133]. However, this transfer function is not capable of 
quantifying the efect of the morphology at the interface betwen the two IMC layers. 
This necesitates the use of an analytical fracture model. The next paragraph summarizes 
how the transfer function is used in the interfacial fracture mechanics model to obtain a 
more detailed transfer function that relates the normalized strain energy release rate at the 
wavy IMC interface to the PWA strain. Details are presented elsewhere [133]. 
 
Figure 6-9: Variation of peling and shear stres in the IMC layer with PWA strain 
Let us asume the existence of a smal crack that initiates at the interface of the 
Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4
 layers. Let us also asume that the crack length is 1% of the 
solder bal diameter at the neck. The mixed-mode stres intensity factors (K
t
) and the 
energy release rate (G
t
) at the wavy interface betwen the Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4
 IMC 
layers are given by [93][95][99]:  
())CosKSinefiKK
21
i
12
t
1
t
2
!+"#+=
$
     (6-1) 
! 
G
t
=
E
Au"NiSn
+E
Ni"Sn
2
Au"NiSnNiSn
K
1
t
()
2
+K
2
t
()
2
[ ]
      (6-2) 
where: 
# is the size of the characteristic length on the crack surface, whose value in this 
125 
study is 1% of the crack length.  
f(#) is a non-dimensional scaling factor for the stres intensity factors whose value, 
as obtained from [91], is 0.2  
!
"
#
$
%
&
?
(=)
h
tan
1
 is the facet angle of the non-planar interface.  
K
i
 are the interfacial stres intensity factors for a straight interface, derived [93] in 
terms of the bulk stres intensity factors, the Dundur?s parameter ($) for the interface, a 
parameter " that quantifies the oscilatory stres field at the interfacial crack tip, a 
parameter " that gives the phase shift in the mode mixity due to the mismatch in the 
material properties at the interface, and the characteristic length (which in this case is the 
IMC thicknes).  In turn, the bulk stres intensity factors are derived from the crack 
length and the interfacial peeling and shear streses shown in Figure 11. Details of these 
relationships are wel established in literature [133] and are omited here for brevity.  
As shown in Table 6-2, the material properties of the intermetalic compounds 
(obtained from literature [96]) can be used to estimate al the relevant parameters in this 
derivation. 
Table 6-2: Material properties [96] of the IMCs and calculated values of the interfacial parameters 
Au
0.5
Ni
0.5
Sn
4
 Ni
3
Sn
4
 
E (GPa) % (-) E (GPa) % (-) 
$ 
(-) 
& ($, 0) 
(?) 
133.3  0.33 48 -0.47 -0.47 3.25
0
 
 
126 
The above equations can be used to obtain a family of transfer functions betwen 
the interfacial strain energy release rate and PWA strain for diferent interfacial wavines. 
Environmental Scanning Electron Microscopy (ESEM) is used to quantify the wavines 
of the interfacial crack for the unaged and aged PWAs in this study. As noted earlier, the 
combined thicknes of Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4 
in the unaged PWA is approximately 0.3 
microns, which is too thin for acurate measurement of the interfacial wavines. Here, we 
make an approximation that the value of h/? is 5 for the unaged PWA. For the aged PWA 
(Table 6-3), the average value of h/? is approximately 0.5 with a variance of 0.13. The 
wavines often reduces with thermal aging due to difusion, thus reducing the efective 
interfacial fracture toughnes. 
Table 6-3: Typical values of the interfacial wavines for the aged PWA 
h (?m) 1.2 0.9 0.8 1.1 1.0 0.8 1.0 
" (?m) 3.1 1.7 1.9 3.0 2.9 1.2 1.6 
h/" (-) 0.39 0.53 0.42 0.37 0.35 0.67 0.63 
 
Failure occurs when G
t
 reaches a critical value (G
c
), which is a material property. 
Overstres failure of the IMC interface occurs at a PWA strain value of 4E-3, which can 
be used to estimate the value of G
c
 at that mode mixity. Figure 6-10 shows the 
normalized FEA transfer function for the IMC interface for diferent facet angles. 
127 
 
Figure 6-10: Normalized interfacial strain energy release rate as a function of PWA strain, for diferent 
morphologies betwen the IMC layers. 
6.5. Competing Failure Envelopes 
As shown in the following equations, the durability of the solder and the IMC 
interface have a power law relationship with "
p
/"
f
 [124] and G
t
/G
c 
[133], respectively. 
! 
"
p
"
f
=m(N
f
)
n
         (6-3) 
where m= 1.13 and n= -0.43 are the durability constants for the solder material. The 
above equation characterizes the competing rate dependent mechanisms on the durability 
of the solder interconnect: strain rate hardening and exhaustion of ductility. Experimental 
data combined with explicit transient non-linear finite element analysis (FEA) was used 
to derive the damage constants. The ratio of solder plastic strain to its failure strain is 
used to quantify the rate-dependent durability of the solder interconnect, thus making the 
damage constants independent of the specimen geometry and dependent only on solder 
material properties. Details can be found in [124]. 
! 
G
t
c
=p(N
f
)
q
         (6-4) 
where p= 1.64 and q = -0.18 are the durability constants for the interfacial IMC 
128 
layer. The above equation characterizes the durability of a crack at the interface of 
(Au
0.5
Ni
0.5
Sn
4
 and Ni
3
Sn
4
). This equation also takes in to acount the efect of non-
planarity of the interface betwen the two intermetalic layers on the stres field at the 
crack tip. The use of mechanistic parameters to quantify durability makes the damage 
constants independent of the specimen geometry and dependent only on the properties of 
the materials that form the crack and the mode mixity of loading. Details can be found in 
[133]. 
Figure 6-11 shows the resulting failure envelopes of the competing failure sites in 
the solder and the IMC interface. 
 
Figure 6-1: Competing failure envelopes for solder and interface betwen the IMC layers 
For a given loading condition, damage can be estimated at each failure site by 
combining the transfer function with the failure envelope. Failure is predicted to occur 
at the site with the maximum damage (lowest value of N
f
).  This methodology is 
ilustrated below for thre selected examples.  
129 
Table 6-4: Examples for methodology 
Cycles to 
failure 
(from Figure 
6-11) 
PWA 
strain 
(-) 
PWA 
strain 
rate 
(sec-1) 
aging 
(-) 
h/# 
(-) 
G
t
/G
c
  
(from 
Figure 
6-10) 
!
p
/!
f
 
(from 
Figure 
6-8) 
IMC Solder 
Predicted 
cycles to 
failure 
Test 
cycles to 
failure 
2.4E-3 1E-3 no 5 0.25 0.06 4806 833 
N
f
=833 
Solder 
N
f
= 839 
Solder 
2E-3 1E-3 yes 0.5 0.58 0.042 110 2115 
N
f
=110 
IMC 
N
f
=133 
IMC 
3.26E-4 4E-2 yes 0.5 0.06 3.2E-4 3E6 1.7E8 
N
f
=3E6 
IMC 
N
f
=2434 
IMC 
 
The thre examples tabulated above correspond to case numbers 1,3, and 6 of Table 
6-1. The predicted durability for each failure site and the test data show very good 
correlation, as shown in Table 6-4 and Figure 6-12. In example 3, the PWA strain is 
almost one order of magnitude lower than those of examples 1 and 2, while the PWA 
strain rate is higher by one order of magnitude. Earlier studies have shown that the 
durability of the IMC interface [133] and the Sn37Pb solder [124] are only weakly 
dependent on the loading rate. Hence, as a simplifying step, we can use the failure 
envelopes shown in Figure 6-11. 
130 
 
Figure 6-12: Comparison of predicted durability and experimental data. 
These examples show how the durability of the IMC interface can decrease as the 
wavines at this interface decreases (due to aging, for example).  This is observed in 
experiments [86], where aging reduces the interface wavines and moves the failure site 
from the solder to the IMC interface.  There may also be an aging-induced degradation 
of the intrinsic fracture toughnes of this interface and this is the subject of future work. 
6.6. Discusion and Conclusion 
Published literature [2][3][47][54][55][73][86][126][132] shows that depending on 
the specimen geometry, material properties and loading conditions, the generaly 
observed failure sites during flexural loading or drop testing of PWAs are solder, copper 
trace, and the IMC layer. This study focused on the solder and the interface betwen the 
two IMC layers and proposed an approach to quantify and understand the interplay 
betwen the competing failure mechanisms. To the best knowledge of the authors, this is 
the first study that provides a mechanistic insight into the failure site transitions in the 
interconnect during flexural loading of the PWA. 
The examples used in this study are quite simple because the crack path is limited 
131 
to either the solder to the IMC interface. Mixed-path cracks, where the propagation is 
through the IMC layers and the solder, have been observed during bal impact tests [132], 
uni-axial vibration of solder interconnects [126], and during drop testing of PWAs [2]. 
Similar mixed-path cracks have also been observed during decohesion of thin film on 
britle substrates [127] and debonding failure of FRP-reinforced concrete beams [134]. 
The fracture strength of the IMC interface is in a state of constant evolution even at 
room temperature because the interfacial morphology and the inter-atomic forces across 
the interface are changing with time. While this study analyzes the efect of mechanical 
interlocking at the interface, it does not provide any materials-based insight into the 
competing failure sites. For example, a simplifying approximation has been made that the 
failure strain ("
f
) of the solder and critical strain energy release rate (G
c
) of the IMC 
interface do not change with thermal aging. This may be a valid approximation for the 
limited amount of aging conducted in this study. An in-depth analysis of the efect of 
thermal aging on "
f
 and G
c
 are beyond the scope of this study. 
For the test coupons used in this study thermal aging, and hence the interfacial 
morphology of the IMC layer, was found to have a strong influence on the failure site of 
the solder interconnect. The strain energy release rate, calculated at the interfacial crack 
tip for a given loading condition, decreases with increasing wavines of the intermetalic 
interface. This could be why a jagged interface (asociated with unaged PWAs or certain 
reflow profiles) rarely ses failure in the IMC layer during flexural testing, while a 
relatively smoother interface (asociated with aged PWAs) is more prone to interfacial 
failure. The technique and insight developed in this study can be used to quantify the 
efect of thermal aging on solder to interfacial IMC failure site transitions for a variety of 
132 
solder and plating material combinations that have been reported in literature 
[3][116][126]. 
This focus of this study is limited to understanding damage initiation, which is why 
the crack length was asumed to be constant. Hence, the mode-mixity at the crack tip did 
not vary with the applied load, thus enabling the use of a single value for the fracture 
toughnes of the interface, G
c
(!), at that phase angle. Future work needs to focus on 
characterizing the interfacial fracture toughnes of the IMC layers as a function of aging. 
Characterizing the fracture toughnes of the interface by using a brazil-nut or a double 
cantilever beam specimen could greatly enhance the acuracy of the proposed approach. 
 
13 
Chapter 7: Summary 
The focus in this thesis is on the durability of surface mount area-aray solder 
interconnects under dynamic loading of the PWA, and on the phenomenon of resulting 
transitions in the failure site, that has recently started receiving atention in literature. As 
discussed in the literature review in Chapter 2, the failure site can be in the bulk solder, in 
the interfacial intermetalic layers, in the copper traces or in the PWB under the bond-
pad.  Many factors can afect the transition of the failure site from the solder to the 
remaining sites listed above. This includes load amplitude, loading rate, material 
properties of the solder and the intermetalic compound, and thermal aging.  
This study focuses in particular, on competing failures due to fatigue within the 
solder and at the interface betwen two IMC layers, and proposes an approach to quantify 
the competing mechanics. Detailed mechanistic understanding of damage acumulation 
in the solder and in the IMC interface are discussed in sections 7.1 and 7.2, respectively. 
An overal discussion about the disertation is provided in section 7.3. Finaly, sections 
7.4 and 7.5 list the contributions and limitations of the disertation. 
7.1. Conclusions: Role of Solder 
As discused in Chapter 4, the test coupons used in this study generaly experience 
PWA flexural strain rates ranging from 2.5E-3 sec-1 to 2.2E0sec-1, which corresponds to 
solder plastic strain rates ranging from 1E-1 to 1E1 sec
-1
. These strain rates are too high 
for crep-dominated deformation and too low for damage due to adiabatic heating. The 
durability of the solder varies strongly with solder plastic strain, and very weakly with 
solder plastic strain rate. For a plastic strain rate of 1E0 sec
-1
, a 100% increase in the 
134 
solder plastic strain from 0.1 to 0.2 decreases the durability by almost 83%. On the other 
hand, at a solder plastic strain of 0.1, an increase in the plastic strain rate by one order of 
magnitude from 1E0 sec
-1 
to 1E1 sec
-1
 changes the durability only by 40%.  
A possible explanation for the weak dependence of solder durability on loading rate 
could be that the strain-rate hardening of solder at the strain rates encountered in this 
study (1E-1 to 1E1 sec
-1
), is negligible. This could be atributed to changes in the 
deformation mechanisms at the microstructural level at these strain rates. For example: 
below a transitional strain rate of 1E-3 sec
-1
, Sn37Pb solder deforms due to wedge 
cracking induced by grain boundary sliding, while it deforms due to cavitation on the 
colony boundaries when the strain rate is above the transitional strain rate [100] . Other 
studies have also reported that plastic deformation is dominated by dislocation motion at 
quasi-static loading rates, and by twinning at high strain rates [102][103], which can be 
atributed to the strain rate hardening of the solder because nucleation of twins requires a 
higher flow stres than dislocation motion does [103]. Analysis at the microstructural 
level, which is beyond the scope of this study, can provide further insight into the 
behavior of the solder at the strain rates of interest.  
The weak dependence of durability on loading rate can also be explained by the 
competing efects of strain-rate hardening and ductility exhaustion. This study proposes 
that the ratio of plastic strain to failure strain be used as a metric to quantify durability of 
the solder for the strain rates observed in this study. The proposed durability model is a 
modification of the Coffin-Manson relationship. Another modified Coffin-Manson 
model, proposed by Eckel [104] is used to relate the durability of the solder to loading 
frequency. Several studies, including the ones by Shi, et al. [105] and Kanchanomai, et al. 
135 
[106] have used the Eckel model to describe solder durability as a function of loading 
frequency. One of the limitations of Eckel?s model is that the value of the exponent is 
dependent on the strain amplitude. The efect of frequency is higher when the strain 
range is higher and when the elastic modulus is lower. In comparison, the durability 
model proposed in Chapter 4 of this disertation is based on mechanistic concepts. 
Further work is needed to collect additional data to increase the robustnes of the model 
constants, and make it applicable to a wider range of strain rates.  
A direct result of the strain-rate hardening described above is an increase in the 
yield stres of the solder, which in turn increases the stres in the intermetalic layer 
during dynamic PWA flexure. The efect of this stres increase is discused in Chapter 5 
and summarized in Section 7.2 below. 
7.2. Conclusions: Role of IMC Interface 
In the test coupons used in this study, and described in Chapter 5, the difusion of 
Sn and Ni leads to a steady change in the thicknes and morphology of the two IMC 
layers of the interconnect. The intermetalic layer itself is made up of layers of diferent 
intermetalic compounds formed by the difusion of Sn from the solder, Cu from the 
copper trace, and the plating material. Adhesion betwen the IMC layers is due to a 
combination of mechanical interlocking at the interface and inter-atomic forces across the 
interface, which is in a state of constant evolution even at room temperature. The 
following section discuses the efect of the IMC interfacial morphology on failure site 
transition and durability of the interface. Results show that as the interconnect is aged, 
the interface betwen diferent IMC species becomes les and les wavy (decreasing facet 
angles).  Experimental results further suggest that the durability of the interface can be 
136 
described as a power-law function of the normalized energy release rate (G
t
/G
c
). For a 
given mixed-mode loading condition, G
t
/G
c
 decreases with increasing slope of the facet. 
This provides a mechanistic explanation as to why a jagged interface (asociated with 
unaged PWAs or certain reflow profiles) rarely ses failure in the IMC layer during 
flexural testing, while a relatively smoother interface (asociated with aged PWAs) is 
more prone to interfacial failure. 
The efective strain energy release rate (G
t
) has been used in many studies to 
understand crack propagation in interfaces. Examples include de-cohesion of thin film on 
substrates [91], delamination of underfil/solder mask interface in electronic packages 
[107], delamination of epoxy/silicon interfaces [108] among others. In this study, the 
crack path was completely through the interface. However, this need not be the case al 
the time. Mixed-path cracks, where the propagation is partly through the IMC layers and 
partly through the solder, have been observed during bal impact tests [75] and uniaxial 
vibration of solder interconnects [109]. The tendency of the crack to either remain at the 
interfaces or deviate away into the bulk material depends on the sign and magnitude of 
the phase angle. This is specialy true for ductile/britle interfaces. As shown in Chapter 
5, the phase angle at the crack tip depends on the geometry and material properties of the 
PWA. Hence, it is possible to design the PWA in a manner in which the crack follows a 
pre-planned trajectory. 
Studies have also shown that the residual stres in the IMC layer, caused by 
negative volume changes, increases with aging time. The residual stres can change the 
value of the mode I and mode I stres intensity factors at the site of the micro-crack, and 
hence the value of the phase angle at the crack tip [91].  This wil not only afect the 
137 
durability of the joint, but also the path of the crack as it could be diverted away or 
toward the interface. 
This disertation therefore provides mechanistic insights as wel as related 
methodologies to ases the relative durability of two competing failure modes: fatigue 
cracking through the solder or at the interface betwen diferent IMC species at the bond 
pad.  Fatigue failure in the solder is addresed with an exhaustion-of-ductility model and 
failure in the IMC interface is addresed with interfacial fracture mechanics. This study 
does not addres the materials-based aspects of the competing failure sites. For example, 
the value of !
f
 for the solder and G
c
 of the interface are asumed to not change with 
thermal aging. This may be an aceptable simplifying asumption for the limited amount 
of aging conducted in this study. An in-depth analysis of the efect of thermal aging on !
f
 
and G
c
 are beyond the scope of this disertation. 
7.3. Discusion 
This disertation presents a systematic approach to characterize the durability and 
failure site transitions of solder interconnects due to dynamic flexural loading of PWAs. 
Failure Maps are used to characterize the failure site transitions from the solder to other 
parts of the interconnect. Of al the potential competing failure sites within the 
interconnect (solder, Cu-trace, FR4, bulk IMC layer, IMC interfaces, etc), this study 
focuses on the solder and the interface betwen two IMC layers. Exhaustion of ductility 
and interfacial fracture mechanics are used to provide a mechanistic perspective to the 
failure site transitions betwen these two selected failure sites. 
The failure mode with the lowest durability for a given loading condition governs 
138 
the durability and defines the dominant failure site for that condition. The fatigue failure 
envelopes of competing failure mechanisms at competing sites intersect along the failure 
site transition zone. As an example, for the test coupons and loading conditions used in 
this study, the failure site at low load amplitudes and loading rates is in the solder and the 
durability of the interconnect is defined by the solder failure envelope. 
Empirical and mechanistic metrics are identified to understand and quantify the 
rate-dependent failure site transition betwen the two failure sites of interest: solder and 
IMC interface. 3D explicit numerical simulations with rate-dependent material properties, 
conducted as part of this disertation, show that strain-rate hardening of the solder during 
dynamic flexural loading of the PWA increases the stres in the remaining failure sites 
while decreasing the plastic strain in the solder. The resultant loading conditions cause 
the interface betwen the IMC layers to reach their fatigue failure limit before the solder 
reaches its own. This leads to a transition in the failure site from the solder to IMC 
interface. This concept is discussed in detail in Chapter 6, along with examples of failure 
site transitions betwen the solder and the interfacial IMC. 
While many researchers have observed failure site transitions from the solder to the 
IMC layer under dynamic flexural loading conditions, only some have tried to understand 
it from the materials perspective and very few have tried to characterize it 
experimentaly. Surprisingly, there has been no study where a detailed mechanistic 
analysis of the failure site transitions and durability damage metrics in terms of 
mechanistic parameters has been conducted. This is partly because the dynamic behavior 
of IMC interfaces is unknown and partly because this is a very recent problem. Each 
aspect of solder interconnect durability investigated in this disertation is a separate 
139 
research field in its own right and no single work can do justice to al these aspects. 
However, progres was made in asimilation, extension and development of al the 
aspects mentioned in this disertation. A detailed description of the contributions of the 
disertation is provided in the next section. 
7.4. Contributions 
As summarized in the earlier section, this disertation provides a mechanistic 
perspective to the durability and failure site transition in the solder interconnects of a 
PWA. It is expected that development of new Pb-fre solders wil benefit from the 
insights provided in this disertation. The findings of this thesis can also be used in other 
engineering applications; for example: competing failure mechanisms during the de-
bonding of composite-plated concrete beams and loosening at the glenoid component at 
the bone-cement interface during treatment of osteoarthritis, among other problems. A 
detailed description of the contributions of the disertation are discussed below 
7.4.1 Test Methodology 
A new test methodology was developed to quantify the durability of the solder 
interconnect of a PWA subjected to board level drop testing, irespective of its boundary 
conditions and loading orientation. Compared to the existing techniques to conduct board 
level drop tests, the proposed methodology alows researchers to understand the 
individual and combined efects of load amplitude and rate on the durability of the solder 
interconnect. Empirical failure maps were also developed as part of the test methodology 
to characterize failure site transitions betwen the solder and other parts of the PWA. 
The test methodology was demonstrated for PWA strains ranging from 2E-3 to 
140 
1.2E-2 strains, and PWA strain rates ranging from 2.5E-3 to 2.2E0 sec
-1
. Although the 
test methodology was demonstrated on PWAs with Sn37Pb solder interconnects (which 
is a wel-characterized material at high strain rates), the technique can easily be extended 
to Pb-fre interconnects whose behavior under dynamic loading conditions is relatively 
unknown. 
7.4.2 Empirical Dynamic Durability Model for the Solder 
An empirical rate-dependent durability model, based on mechanistic principles, 
was developed to obtain fatigue failure envelopes for the solder under dynamic loading 
conditions. The model has been succesfully used to compare the durability of solder 
interconnects with diferent material properties (Sn37Pb vs SnAgCu), and aging 
conditions (as-reflowed vs aged for 100 hours at 150
0
C) for PWA strains ranging from 
2E-3 to 1.2E-2 strains, and PWA strain rates ranging from 2.5E-3 to 2.2E0 sec
-1
.  The 
model showed good correlation with experimental data. 
7.4.3 Mechanistic Insights into Solder Fatigue 
For the test samples (Sn37Pb solder interconnects) and conditions used in this 
study, the experimental data showed that solder durability had a high dependence on 
PWA strain amplitude (which ranged from 2E-3 to 1.2E-2 strains) and a very weak 
dependence on the PWA strain rate (which ranged from 2.5E-3 to 2.2E0 sec
-1
), even 
though the loading rate was varied over four orders of magnitude. The empirical rate-
dependent durability model developed in this disertation was combined with rate-
dependent FEA to provide an insight into this atypical behavior, for the solder strain rates 
sen in this study (3E-1 to 3.2E0 sec
-1
). Guidelines can be developed to optimize the 
141 
competing efects of strain?rate hardening and exhaustion of ductility to reduce the 
plastic deformation in the solder at high strain rates, thereby increasing solder durability. 
7.4.4 Mechanistic Insight into Interfacial IMC Fracture  
This thesis combines, for the first time, microstructural aspects of the interfacial 
IMC layer, as provided by Xu and Pang [55], and the fundamentals of non-planar 
interfacial fracture, as developed by Evans and Hutchinson [91], to understand the 
evolution of interfacial strength of the IMC layer as a function of thermal aging, material 
systems, and interfacial morphology. The insights provided in this study are limited to 
ENIG-Sn37Pb solder systems that have been isothermaly aged at 135
0
C for 168 hours. 
The PWA strains ranged from 3.25E-4 to 2.4E-3, and PWA strain rates ranged from 1E-3 
to 4E-2 sec
-1
. The approach developed in this study can easily be implemented for other 
material systems and thermal aging profiles. 
7.4.5 Mechanistic Insight into Failure Site Transitions from Solder to IMC  
A phenomenological model was proposed to characterize the failure site transitions, 
observed in this study, betwen the solder and the interface betwen the IMC layers. The 
proposed model takes into acount, the efect of strain rate hardening and exhaustion of 
ductility in the solder due to high loading rates, the efect of interfacial morphology in the 
IMC interface due to manufacturing proces and thermal aging, and the efect of mode 
mixity due to PWA geometry and loading orientation. The model was demonstrated for 
PWAs with ENIG-Sn37Pb solder interconnects, for PWA strains ranging from 3.25E-4 to 
2.4E-3, and PWA strain rates ranging from 1E-3 to 4E-2 sec
-1
. The mechanistic failure 
criteria proposed in this work can now be utilized for defining solder and IMC failure, as 
142 
opposed to empirical criteria used so far. To the best knowledge of the author, this is the 
first model that provides a mechanistic perspective on the failure site transitions betwen 
the solder and the IMC layer. 
The contributions of this disertation are expected to gain importance as solder 
interconnects become smaler, thus making them more susceptible to streses during 
dynamic flexure of the PWA. However, there are many limitations in this disertation 
that can be addresed in the future. The relevant ones are discussed in the following 
section. 
7.5. Limitations and Suggestions for Future Work 
The following suggestions are made for improvement and extension of the current 
work. 
7.5.1 Range of Validity of Study 
The test methodology developed in this study was demonstrated for PWA strains 
ranging from 2E-3 to 1.2E-2 strains, and PWA strain rates ranging from 2.5E-3 to 2.2E0 
sec
-1
.  The phenomenological model developed in this study to understand and 
characterize failure site transitions from the solder to the interfacial IMC layer was 
demonstrated for PWA strains ranging from 3.25E-4 to 2.4E-3, and PWA strain rates 
ranging from 1E-3 to 4E-2 sec
-1
.
 
The material system of the solder interconnect was 
limited to Sn37Pb. While the proposed methods are generic because of its mechanistic 
foundations, their actual applicability outside of the parametric range requires further 
study.  
143 
7.5.2 Sample Size 
The smal sample sizes used in the test program in this study alow qualitative 
conclusions but the confidence in quantitative model constants is limited. This 
disertation used only two data points per test condition to determine the solder fatigue 
properties at high strain rates. A larger sample size wil strongly enhance the confidence 
in the solder fatigue properties determined in this thesis. 
7.5.3 Efect of Thermal Aging on Solder Microstructure 
The macroscopic (continuum mechanics) to microscopic (fracture mechanics) 
phenomenological model asumes that the microstructure of the solder for the given 
thermal aging condition (168 hours at 125
0
 C) has a negligible efect on the results, when 
compared to the efect of interfacial morphology. Such an asumption may be valid for 
short durations of isothermal aging, as was the case in the tests conducted. However, 
changes in the solder material properties induced by the long-term thermal aging could 
play a definitive role in the failure site transition and durability under high strain rates. 
This needs to be investigated. 
7.5.4 Efect of Strain Rate on Fracture Toughnes 
As shown in Chapter 5, the fracture toughnes of the interfaces betwen two IMC 
layers of interest is unknown, especialy at high strain rates. This is stil an open field of 
research and the current lack of understanding in this area may prove to be a major 
bottleneck in the future. This is especialy true because many of the solder compositions, 
plating materials and manufacturing proceses for Pb-fre solders are stil in a state of 
evolution. 
14 
7.5.5. Material Science Based Perspective to Interfacial Fracture 
Relatively few studies have been conducted to understand the failure site transitions 
from the solder to the IMC layer. This disertation only considers the mechanistic aspects 
of the observed phenomenon for the load amplitudes, loading rates and test coupons used 
in this study. The disertation does not consider the material aspects of interfacial IMC 
fracture. For example, it is not known if (and by how much) thermal aging weakens the 
adhesive bonds betwen the two interfaces of the IMC layer. It is also not known if the 
fracture toughnes of the interface varies with loading rate. These material properties of 
the interface can have a very dominant efect on the failure site transitions, and must be 
investigated in detail. 
7.5.6 FEA proximations 
The rate-dependent 3D numerical analysis conducted in this study uses dynamic 
material properties of the solder that were obtained using macroscopic specimens. The 
Hal-Petch efect on solder material properties is very wel documented in literature and 
hence the length scale dependent material properties are required. Future studies should 
focus on acurate characterization of length scale dependent material properties of the 
solder. This wil strongly enhance the results and conclusions provided by the numerical 
analysis. 
 
145 
Apendix A: Durability Estimation Methodology 
1
 
This chapter proposes a methodology to quantify durability of the solder 
interconnect of a PWA subjected to transient loading. The original draft of this chapter is 
published in the Microelectronics Reliability journal. The methodology, which uses 
experimentation, signal procesing and numerical analysis, is presented to quantify the 
interconnect durability. It is shown that the proposed methodology can quantify 
durability, irespective of the loading orientation and PWA boundary conditions. A case 
study, using a PWA of a simple design, is used to demonstrate the approach. 
Test Methodology for Durability Estimation of 
Surface Mount Interconnects under Drop Testing Conditions 
J. Varghese, A. Dasgupta 
CALCE Electronic Packaging and Systems Center, University of Maryland, Colege Park, Maryland 20742 
Tel: 301-405-5251, Fax: 301-314-9269, Email: josephv@umd.edu, dasgupta@umd.edu 
This paper presents a generic methodology to determine the durability of surface 
mount interconnects in electronic asemblies, under drop loading conditions. Damage 
acumulated in the interconnects due to repeated drops is quantified in terms of local 
Printed Wiring Asembly (PWA) response (flexural strain, strain rate, aceleration, 
number of flexural cycles), rather than the loading (total impact energy, orientation and 
number of drops). The advantage is that the results are more generic and can be 
extrapolated to diferent asemblies and diferent loading/orientation conditions. A 
damage estimation model, based on the observed failure mechanism and mode, is used to 
                                                
1
 Acepted for publication in Microelectronics Reliability (IF=0.724), In Pres and available online 31 
March, 206, htp:/dx.doi.org/10.1016/j.microrel.206.07.02 
146 
determine the durability of the surface mount interconnects under the applied loading 
history. The same model can be used to extrapolate the results to field conditions. A case 
study, using a simple specimen, is presented to demonstrate the proposed methodology. 
Failures are observed in the interfacial intermetalic layer of the component bond pad in 
the corner solder joint. The generality of the method is demonstrated by calibrating the 
model constants with in-plane drop tests and then succesfully predicting the durability 
for an out-of-plane drop test. Thus, the approach and model constants are shown to be 
independent of impact orientation and boundary conditions.  
Keywords: Drop testing; Impact testing, Interconnect damage, Intermetalic 
fracture, Durability, Electronic Packaging. 
Nomenclature 
A
i
: Mode shape dependent constant at the i
th
 mode 
C
1
, C
2
: Constants in damage model 
D:  Damage in the intermetalic 
N:  Number of cycles to failure 
W
i
: Weight function of the i
th
 mode 
a:  Crack length 
a
i
:  Crack length before the loading cycle 
a
f
:  Crack length after the loading cycle 
m:  Total number of modes 
n
ij
:  Number of cycles of the j
th
 bin at the i
th
 mode 
147 
p:  Slope of Paris? curve 
r:  Number of bins at each mode 
!:  Crack tip angle 
"K: Cyclic range of stres intensity factor 
"#: Cyclic stres range 
("#
peling
 )
ij
: Range of peeling stres at the failure site at the j
th
 bin at the i
th
 mode 
A - 1. Introduction 
Electronic devices in a variety of applications are often subjected to drop and 
vibration loading. Military electronics are subjected to repetitive shocks (artilery fire), 
sudden high G loading during launching or maneuvering of projectiles or during balistic 
impact. Other electronic products may experience costly drop events during 
transportation and handling. Portable electronics may se similar drop events throughout 
the life cycle due to acidental abuse.  These transient events can cause damage to the 
external housing, internal components, internal plastic mounts and snaps, and 
component-to-board interconnects, among others. 
Electronic products subjected to this type of dynamic loading are expected to be 
rugged. However, the need for reduction in product weight and size leads to design 
features that make the products susceptible to failures induced by drop and impact. The 
drive towards finer pitch and high density packages exacerbates the risk of interconnect 
failure. This paper therefore focuses on design and testing of electronic interconnects for 
drop/impact loading. 
148 
At present, manufacturers of hand-held electronic devices use the JEDEC JESD22-
B104-B standard for mechanical drop testing [1].  The drop-durability of portable 
electronic products is quantified and ranked by the number of drops to failure. The 
product is held in the desired orientation on a drop cariage that is alowed to fal on to a 
fixed target. But characterizing the drop durability of interconnects by running tests or 
simulations at the product level is a very complex task. Goyal and Buratynski [2] showed 
that even a single drop event of an electronic product can produce a complex multi-modal 
transient response history. Lim and Low [3] showed that the structural response of the 
PWA is strongly dependent on the mas distribution of the internal electronics, the 
mounting of the PWA, and the orientation of drop. Consequently, conventional testing 
approaches that atempt to correlate drop durability to loading parameters (total impact 
energy, orientation and number of drops to failure), typicaly report dificulties in 
correlating with drop durability under field conditions.  
When a portable electronic product is dropped, part of the kinetic energy goes into 
the rigid body motion during rebound, part goes into the strain energy of deformation of 
the internal electronics and external housing, and the rest is lost to damping and friction. 
Only a portion of the energy absorbed by the internal electronics causes damage to the 
interconnects. The amount of energy responsible for the deformation of the interconnect 
depends on the loading conditions, component architecture, PWA mounting details 
(boundary conditions), housing structure, and material properties. 
Drop tests conducted by Lim, et al. [3][4] and Seah, et al. [5] showed the extent of 
variation in PWA strains and acelerations, for diferent electronic devices and diferent 
drop orientations. Therefore, test specifications for drop durability of surface mount 
149 
interconnects, which are based on loading specifications (such as incident kinetic energy 
or shock response spectrum), are bound to be case-specific and wil lack the generality 
for extrapolation across diferent product styles and diferent drop conditions. It is beter 
to relate the damage in the interconnects to the local response of the PWA, close to the 
failure site, because the relationship betwen the local response and the damage amount 
is les sensitive to test conditions. 
The test vehicle recommended by the JEDEC Standard JESD22-B111 [6] for 
studying interconnect durability is a daisy-chained PWA of standard form, with standard 
fixturing (i.e. with standard boundary conditions), in order to minimize some of the 
complexities discussed above.  PWA level testing can be used to develop failure 
envelopes for the characteristic damage mechanisms in surface mount interconnects. 
From an industry perspective, testing the drop durability of the interconnect at the board 
level is easier and can be done by the component supplier.  
In the JEDEC Standard [6], the PWA with daisy-chained components is mounted 
on to a drop cariage in the horizontal position, at four or six points. The drop cariage 
fals verticaly along two guide rods on to a stationary impact surface and induces out-of-
plane displacement in the PWA on impact. The impact surface can be changed to vary the 
profile of the impact force and deceleration histories. On impact, the PWA responds to 
the transient impact force applied to the base and then vibrates at its natural frequency. 
Instrumentation includes acelerometers on the drop cariage, strain gages on the PWA 
and a high speed data acquisition and failure monitoring system. 
Durability of the interconnects is strongly dependent on the strain and strain rate of 
deformation. Tests conducted by Yu, et al. [7] and Juso, et al. [8] indicated that the 
150 
number of cycles to failure decreased as the PWA strain and strain rate increased. 
Varghese and Dasgupta [9] ran impact tests on PWAs in the in-plane and out-of-plane 
orientations and showed that the number of impacts to failure decreased with increasing 
PWA strain. The failure site for both impact orientations was the interfacial intermetalic 
layer. Researchers have also reported diferent failure sites for diferent loading 
conditions. Yu, et al. [7] observed a transition in the failure site from the solder to the 
interfacial intermetalic beyond a critical drop height. Varghese and Dasgupta [10] 
subjected PWAs to flexural strain rates ranging from 10
-3
 sec
-1
 to 10
1 
sec
-1
 and observed a 
failure site transition from the solder to the copper trace beyond a critical PWA strain 
rate. This change in failure site and in the failure mechanism caused the durability to vary 
non-monotonicaly with PWA strain rate, although it stil varied monotonicaly with 
PWA strain amplitude.  Heaslip, et al. [11] compared the drop durability of Sn-Pb and 
Pb-fre solders and showed that the failure sites and failure mechanisms change with 
drop height and solder type. 
Damage modeling methodologies have been proposed over the last few years to 
quantify interconnect durability under board level impact testing conditions. In Feb 2003, 
Varghese and Dasgupta [9] introduced a test methodology to predict impact durability of 
surface mount interconnects. PWA flexural strain was used as the damage metric and the 
damage model was based on britle crack propagation because the failure site was in the 
britle intermetalic layer. A damage quantification algorithm was proposed, which used 
wavelet decomposition to decompose the PWA strain history into its constituent modal 
contributions, and rainflow cycle-counting to ases the damage at each frequency level. 
The test methodology was demonstrated for a PWA with a single Sn-Pb Plastic Bal Grid 
151 
Aray (PBGA) component, subjected to in-plane and out-of-plane impact on fixtures with 
diferent boundary conditions. Although the damage constants were verified to be 
independent of impact orientation, loading conditions and boundary conditions, the 
model constants were specific to the architecture of the PWA being tested. In Nov 2003 
[12] the test methodology was modified to change the damage metric from PWA strain to 
solder strain by using Finite Element Analysis (FEA). This made the test methodology 
more generic, within the approximations of the analysis, because the model constants 
were a function of the material properties alone. Te, et al. [13] proposed a durability 
model in May 2003 for out-of-plane drop testing of PWAs. Maximum peeling stres in 
the solder was used as the damage metric and the durability model was formulated using 
a power law relationship. The technique was demonstrated for boards mounted with Thin 
Profile Fine Pitch Bal Grid Aray (TFBGA) and Very Thin Profile Fine Pitch Bal Grid 
Aray (VTFBGA) components. In Nov. 2003, Heaslip and Punch [14] demonstrated the 
use of wavelet analysis to understand the complex spectral response of an unpopulated 
board subjected to drop tests. In 2004, Zhu and Marcinkiewicz [15] proposed the use of 
efective plastic strain in the solder bal as the damage metric and compared the 
component reliability at diferent loading conditions. Although a damage model was not 
developed, components with higher efective plastic strain were shown to fail earlier than 
those with lower values of plastic strain in the solder bal. In 2005, Lal, et al. [16] 
demonstrated the use of a damage quantification technique very similar to the one 
proposed by Varghese and Dasgupta [9][12], on test vehicles mounted with BGAs and 
CSPs, subjected to in-plane drop. Wavelets and cycle counting techniques were used to 
quantify the complex load history. PWA flexural strain was used as the damage metric 
152 
and the damage model was based on the Coffin-Manson relationship because the failure 
site was in the solder. 
In summary, the literature shows that existing drop testing standards are not generic 
in nature. The durability of interconnects depends on a variety of parameters, such as the 
mas distribution on the PWA, drop height, drop orientation, impact surface, dynamic 
material properties of the structure and boundary conditions. The failed interconnect in 
most bal grid aray (BGA) components is usualy in the outermost row, implying that 
failure is driven by flexure of the PWA [13]. On the other hand, interconnects of heavy 
BGA components can also fail in the inner rows, implying that failure in this case may be 
primarily driven by inertial forces generated by the component mas [17].  The 
partitioning of the contribution of PWA flexure and component inertia to the damage in 
the interconnects under drop testing conditions is component-specific and has not yet 
been quantified. The damage parameter (plastic strain or peeling stres) is usualy 
monitored in the bulk solder, even when experimental data indicates that the failure site 
under drop testing conditions could be not only in the solder, but also in the PWA under 
the bond pad, in a nearby copper trace, or in the intermetalic layer. The distribution of 
strain energy in the PWA must be understood to improve the test methodology for drop 
durability of interconnects. 
To consider drop durability proactively in the design phase, there is a need for a 
methodology based on an understanding of the fundamental mechanics of the problem. 
The method developed in this study, is as follows: 
? Establish an acurate and repeatable test methodology for diferent 
specimens, boundary conditions and loading conditions. 
153 
? Develop a generic & unified basis for damage estimation, which is 
independent of product geometry, loading & boundary conditions. 
The organization of this paper is as follows: The proposed test methodology is first 
discussed in generic terms.  A specific case study is then presented in the subsequent 
section to demonstrate the approach. The correlation of board and product level drop 
testing is discussed at the end of the paper. 
A - 2. Aproach 
This work proposes a test methodology that characterizes the resulting interconnect 
failure in terms of the local structural response at the failure site. A summarized version 
of the test methodology, presented in [9], is repeated below, for completenes. Figure 1 
presents the flowchart and the details are presented in the following sub-sections. 
Step 1: Obtain the strain gage and acelerometer data for each test condition. 
Step 2: Observe the number of drops to failure for each test condition. Conduct failure 
analysis and group the results acording to the failure site and the failure 
mechanism. 
Step 3: Identify modal participation of PWA transient response by wavelet decomposition 
of the strain and aceleration signatures. 
Step 4: Obtain amplitude distribution functions (number of cycles at each amplitude) by 
using cycle counting analysis, to quantify the load history at each mode. 
Step 5: Use FEA to obtain stres at the failure site for a given PWA strain, strain rate and 
component aceleration.  
Step 6: Relate stres amplitude at failure site to damage, using relevant damage model. 
154 
Step 7: Repeat Step 4 and Step 6 to quantify damage for every mode decomposed by the 
wavelet transforms (D
mode_i
). 
Step 8: Sum the results for al modes to quantify the cumulative damage from al the 
response modes for a given drop event. (D
drop
) using the results of Step 3 and Step 
7. 
The following simplifying approximations have been made in the development of 
this test methodology. The solder bals are approximated as isotropic, homogenous and 
defect fre. The efect of initial defects and initial residual streses on drop durability is 
neglected. Damage due to stres wave propagation in the solder bal is asumed to be 
negligible when compared to the damage induced by PWA flexure, flexural rate and 
component aceleration. It is also asumed that damage acumulation is linear and 
follows Miner?s rule. The non-linear efects of load sequencing are beyond the scope of 
this paper. 
 
15 
 
Figure A-1: Flowchart for quantifying damage in drop testing. 
A - 2.1 Test Matrix 
The response parameters of interest at the site of each failed interconnect are the 
local PWA flexural strain, flexural strain rate and average aceleration of the component. 
A test matrix is developed to systematicaly vary these thre parameters, by varying the 
loading parameters such as incident kinetic energy, boundary conditions and impact 
orientation. The tests can be clasified in to thre types: 
156 
? Flexural tests: The specimen is impacted in diferent orientations, but constrained to 
prevent any rigid body aceleration. Durability of the interconnect is thus afected only 
by flexural strain and flexural strain rate of the PWA. 
? Inertial tests: Specimen is dropped in diferent orientations, but constrained to prevent 
any curvature in the PWA. Durability of interconnect is afected only by inertia forces 
exerted by the component on the interconnect.  
? Combined tests: The specimen is dropped in diferent orientations, but neither flexure, 
nor rigid-body acelerations are constrained. Interconnect durability is afected by both 
flexural and inertial loads.  
The various combinations are shown in Table A-1 and Figure A-2. Each test 
condition is repeated to explore the consistency of the data 
Table A-1: Test Matrix. X and 0 represent the active and inactive test variables respectively. 
Test Curvature Curvature rate 
Component 
aceleration 
Drops to failure (N) 
Flexural X X 0 
?
=),(!f 
Inertial 0 0 X 
aN 
Combined X X X 
),(f
?
=! 
157 
 
Figure A-2: Test matrix. Component aceleration is zero for flexural tests and PWA flexure is zero for 
inertial tests. Combined tests represent actual drop conditions. 
A - 2.2 Test Setup and Instrumentation 
A 6 ft tal pendulum-style impact test setup is designed and fabricated in-house for 
conducting in-plane and out-of-plane impact tests (Figure A-3). The kinetic energy of 
impact can be varied by changing the mas of the stel sphere and/or the impact velocity. 
The mas of the stel sphere can be varied from 25 grams to 450 grams. The impact 
velocity, which can reach a maximum value of 6m/sec, is varied by changing the 
pendulum release height. 
 
Figure A-3: Pendulum test setup for conducting flexural tests. 
 
158 
The out-of-plane and in-plane fixtures, shown in Figure A-4 and Figure A-5, 
respectively, are made of aluminum. A schematic diagram of the fixtures is shown in 
Figure A-6. For out-of-plane impact, the specimen is oriented verticaly and clamped at 
its four corners. The sphere impacts the center of the PWA, causing out-of-plane 
displacement. For in-plane impact, the specimen is oriented horizontaly and the two 
edges orthogonal to the impact axis are guided with leaf springs to remain in the impact 
plane. Horizontal motion of the impacted edge translates into bending of the specimen. 
The PWA is given a smal initial flexure while mounting it to the in-plane fixture to 
induce bending toward the component side. This ensures the repeatability of the direction 
of PWA deflection. The value of the initial flexure is recorded by the strain gage mounted 
on the PWA. Ensuring repeatability of the test setup is a critical step in developing the 
drop test methodology and is discussed below, after the description of the 
instrumentation.  
 
 
Figure A-4: Out-of-plane fixture.  
159 
 
Figure A-5: In-plane fixture.  
 
 (a) 
 
(b) 
Figure A-6: Schematic diagram of the (a) out-of-plane fixture (b) in-plane fixture. 
A 350 ohm resistance strain gage with 3.18 m gage length and 2.54 m grid 
width is atached to the PWA near the corner of the component (the site of maximum 
curvature) to measure the flexural strain and the flexural strain rate along the longitudinal 
axis of the PWA. Failure is defined as the increase in the resistance of the interconnect by 
1000 ohms. Due to the transient nature of the test, the resistance spike can last for les 
than one milisecond. So, an in-situ high speed resistance measurement system is 
developed in-house for continuous failure monitoring. The high speed data acquisition 
system (Figure A-7) consists of a 4 channel, 16 bit DAQ card with a maximum sampling 
rate of 5MHz per channel. The sampling frequency during the tests is maintained at 
25kHz. 
160 
 
Figure A-7: In-situ resistance monitoring system. 
The entire test setup is tested for repeatability.  PWA strain histories of 10 
consecutive impacts are compared to verify the repeatability of the out-of-plane and in-
plane fixtures. The typical out-of-plane strain response looks like a damped sinusoidal 
wave, as shown in Figure A-8. The typical strain history of the in-plane impact looks like 
an impulse signal, as shown in Figure A-9.  The first mode dominates the structural 
response of the PWA for both impact orientations. Repeatability of the test setup is 
quantified by calculating the mean and the standard deviation of the strain history at the 
point of maximum strain. The values are tabulated in Table A-2. Both fixtures show very 
good repeatability. 
 
161 
 
Figure A-8: Comparison of the strain histories of ten out-of-plane impacts to verify repeatability. 
 
Figure A-9: Comparison of the strain histories of ten in-plane impacts to verify repeatability. 
Table A-2: Repeatability of test setup. 
Maximum Strain  
Out-of-plane (?!) In-plane (?!) 
Mean 796.7 823.1 
Std. Deviation 18.4 48.1 
A - 2.3 Signal Post-Procesing 
The problem of decomposing the structural response of a body to shock/vibration 
loading is not new. Much work has been done to understand the structural response 
162 
during misile launch/gun fire [18][19], occupant safety during vehicle collisions 
[20][21], durability of casks under drop test conditions [22], fatigue of aircraft parts [23], 
dynamic response of human beings during road/rail transportation [24], et cetera. A PWA 
subjected to drop testing vibrates in a non-stationary random manner. One way to 
decompose the complex signal is to use Discrete Wavelet Transform (DWT). Alternate 
techniques for temporal and spectral decomposition of transient and random signals 
include Fast Fourier Transform (FT) or Short Term Fourier Transform (STFT). The 
relative advantages and disadvantages of DWT over FT and STFT are described below. 
The FT, using sinusoidal basis functions, gives the average frequency spectrum of 
a signal, with no information about temporal variation. FT is best suited for the analysis 
of stationary signals, or signals whose spectrum remains constant. The STFT is a 
windowed FT that alows analysis of non-stationary signals. The STFT performs an 
FT sequentialy on smal windowed sub-sections of data to obtain the frequency 
spectrum of the signal for that section. However, STFT requires a design tradeoff 
betwen time and frequency resolution. For an STFT to yield useful results, only smal 
frequency changes can occur during the short sampled period, thus limiting its use for 
applications with transient signals. 
DWT uses various types of functions with adjustable compact support, as basis 
functions in software filters, to separate a signal into frequency bands. DWT can be used 
to analyze non-stationary signals with greater flexibility than the STFT. Diferent basis 
functions, or mother wavelets, may be used in wavelet analysis to achieve the best results 
for a specific application. The windowing proces for the DWT is variable, alowing for 
good time resolution of high frequency components and good frequency resolution of low 
163 
frequency components in the same analysis. Thus, wavelet analysis can show how 
frequency content changes with time. This makes DWT an ideal tool for decomposition 
of drop test data. Detailed information about signal procesing of transient loading and 
random vibration signals can be found in the text by Newland [25].  
The acuracy of the wavelet decomposition technique needs more investigation for 
narow-band signals, as is the case in dynamic structural response, especialy when the 
response frequencies are not very close to the frequencies corresponding to each wavelet 
levels. Dujari, et al. [26] discussed these isues in the context of complicated vibration 
response histories, and similar investigations for drop testing wil be reported in a future 
paper.  
In the present study, DWT is combined with cycle counting methods to quantify 
damage for relatively simple signals in drop testing, as proposed earlier by Varghese and 
Dasgupta [9][12], and demonstrated by Lal, et al. [16].  For demonstration purposes, 
Figure A-10 shows the DWT decomposition of the strain response of a loosely clamped 
PWA subjected to out-of-plane impact. The input signal can be described as a noisy 
damped sinusoidal wave. Daubechies 5 wavelets are used because the shape of this 
wavelet basis function best matches the input signal. The decomposition is conducted for 
four levels, beyond which, there is significant loss of temporal resolution. The high 
frequency component, caled ?detail? and the low frequency component, caled 
?approximation?, are obtained for each level. The contribution of each level can be 
clearly observed in Figure A-10. Levels 1, 2 and 3 cary the low amplitude, high strain 
rate part of the signal; while Level 4 caries the high amplitude, low strain rate 
component. 
164 
The strain history at each level is then quantified by using a cycle-counting 
technique to expres the signal as a superposition of many constant-amplitude signals, 
each with a specific number of cycles.  Each of the selected amplitude levels is 
designated as a ?bin?. The result is a range-distribution function (RDF) for strain at each 
wavelet level.  
 
Figure A-10: Wavelet decomposition of PWA strain history. 
165 
A - 2.4 Finite Element Transfer Function 
The local PWA response, obtained from the strain gage and acelerometer signals 
discussed in Section 2.2, has to be related to the stres history at the failure sites, so that 
the damage can be estimated using suitable damage models.  In this study, a finite 
element model is used to obtain this transfer function.  Wong, et al. [27] conducted a 
parametric study of board level drop test using FEA simulations and showed that peeling 
stres in the solder is the primary damage-inducing mechanism. The peeling stres in the 
solder is due to the curvature of the board and the inertial force of the component. Peling 
stres increases linearly with increasing impact velocity, increases almost logarithmicaly 
with decreasing bump height, decreases asymptoticaly with increasing number of solder 
bumps, and increases with increasing PWA length. 
In this study, the FEA transfer function is obtained by plotting the average peeling 
stres at the failure site with respect to the average PWA strain evaluated over the region 
of the strain gage. The averaging of the peeling stres decreases the dependence of the 
results on meshing approximation. The averaging technique is used extensively in the 
field of solder durability, but there are no standard averaging schemes. Various authors 
have reported diferent schemes for averaging the FEA results over a finite region. The 
averaging requires a trade off betwen loosing data resolution across a large region 
versus numerical erors in a very smal region. The authors have chosen 20% of the 
solder cross-sectional length at the failure site to provide a qualitative estimate of streses 
in the region. An ideal averaging scheme for solder streses is a subject for future papers. 
The results of this study must be viewed within the context of this averaging scheme. 
This FEA transfer function is then combined with the PWA strain RDF described 
16 
in section 2.3, to obtain the RDF of the peeling stres at the failure site. 
A - 2.5 Durability Estimation Methodology 
A simple, first-order failure model is proposed to quantify the damage in the 
interconnects. Since the failure in this study is by incremental crack propagation in the 
britle intermetalic, the damage model has been motivated by Paris? law for cyclic 
fatigue crack propagation [28]: 
p
KC
dN
da
)(
1
!= 
where, )()(
1
!"#$=$fa 
Integrating for Number of cycles to failure: 
p
pp
i
p
f
C
A
a
!
+!+!
"==)(
)()12/(
1
2/
1/
#
$%
 (A-1) 
Normalized damage in the solder for each cycle is related to the peeling stres by: 
p
eling
f
CD)(
1
2
!"= (A-2) 
The RDF of the peeling stres, discussed in Section 2.4, is described as: 
=
""
r
j
ijpelingipelng
1
])([)(## (A-3) 
Substituting Equations (3) in Equation (2), damage caused by the i
th
 response mode 
can be expresed as: 
!
=
"
r
j
p
jpelingii
i
AD
1
])([# (A-4) 
167 
Therefore, total damage per impact is given by: 
!
=
"
r
j
p
ijelngi
i
itoal
WD
1
)(# (A-5) 
Failure is asumed to finaly occur when D
total
 reaches 1. 
A - 3. Case Study 
The methodology described above is demonstrated on a  PWA test specimen. A 
simple test specimen is used to alow detailed study of the failure modes and failure 
mechanisms. The test vehicle is a 74mm $ 40mm $ 1.4mm FR4 board mounted with a 
256 I/O, 0.88 m diameter, 1.2 m pitch PBGA (Figure A-11). The PBGA has a 27mm 
x 27mm x 0.5 m FR4 substrate and a 24mm x 24mm x 1.1mm epoxy overmold, with 
eutectic Sn-Pb solder bals.  The pad finish on the board side of the solder bals is 
Electroles Nickel Imersion Gold (ENIG) and that on the substrate side is 63Sn-37Pb.  
 
Figure A-1: Test specimen with component of interest. 
The specimen is impacted using the pendulum test setup in the in-plane and out-of-
plane orientations. The results of the flexural tests, as described in the test matrix, are 
discussed in this paper. The strain histories for out-of-plane and in-plane impacts are 
shown in Figure A-12 and Figure A-13 respectively. The strain histories are quite simple 
and lack the high frequency content sen in Figure 10. 
168 
 
Figure A-12: PWA strain vs time for out-of-plane impact. 
 
Figure A-13: PWA strain vs time for in-plane impact. 
The test is repeated at each test condition to explore the consistency of data. The 
results, presented in Table A-3 and Figure A-14, show that the average number of 
impacts to failure has a monotonic relation to PWA flexural strain. The PWA flexural 
strain rates are around 10
0
 sec
-1
. Future papers wil discuss the rate dependent efects of 
durability using tests conducted over wider range of PWA flexural strain rates. 
Table A-3: Experimental results. 
Case 
number 
Impact 
Orientation 
Peak PWA 
strain (?!) 
Average impacts 
to failure 
1 In-plane 785 7 
2 In-plane 1962 4 
3 Out-of-plane 60 9 
4 Out-of-plane 5613 1 
169 
 
 
Figure A-14: Average number of impacts to failure for in-plane and out-of-plane impact testing shows a 
monotonic relationship to PWA strain. 
The failure mechanism for al tests is fracture in the intermetalic layer on the PWA 
side (Figure A-15). This could be because the specimens were aged for nearly 24 months 
at room temperature.  Aging causes the intermetalic thicknes to increase to 
approximately 5 microns due to solid state difusion. Studies by Jang, et al. [29] and 
Prakash and Sritharan [30] have shown that aging causes the failure site to change from 
the solder to the intermetalics. 
 
170 
 
Figure A-15: Cros-sectioning picture shows that the failure site is at the intermetalics. The red arows 
indicate the location and path of the crack. 
Wavelet analysis and rainflow cycle counting is conducted on the test data. The 
resulting damage at each wavelet level is discused later. The signals are dominated by 
mode 1 deformation.  
A 2-D finite element model is generated using a comericaly available software to 
obtain the FEA transfer function. 4-noded plane stres quadratic elements are used to 
model the specimen. The model is symmetric about the vertical axis, with 7408 elements 
and 8530 nodes. The mesh in the outermost interconnect is denser than in the iner 
interconnects (Figure A-16). 
 
171 
 
 
Coarse mesh 
 
Fine mesh 
Figure A-16: 2D model of PWA with coarse mesh for iner solder bals and fine mesh for the outermost 
solder bal. Al dimensions are in milimeters. 
The mesh is scaled to provide maximum mesh density at regions of high stres 
gradients, for example at the solder/Cu pad interface, and at the Cu pad/PWA interface. 
Mesh convergence tests are conducted to optimize the mesh density for best results in the 
least computational time. Since our tests are conducted over a smal range of strain-rates, 
the solder and copper trace are modeled as rate-independent bilinear materials. In future 
papers, where tests wil be conducted over wider range of strain-rates, rate-dependent 
material properties wil be used. Al other materials are modeled as linear elastic. The 
material properties are listed in Table A-4. 
172 
Table A-4: Material Properties. 
ELASTIC MATERIAL PROPERTIES 
Material Elastic Modulus (GPa) Poison?s Ratio (-) Density (kg/m
3
) 
FR4 17.2 0.39 100 
Overmold 15.8 0.25 190 
Die 191 0.3 230 
Substrate 2 0.3 280 
Coper 120 0.34 8930 
Sn-Pb solder 29.9 0.35 840 
PLASTIC MATERIAL PROPERTIES 
Material Yield Stres (MPa) Tangent Modulus (GPa) 
Coper 240 12 
Solder 32.7 2 
 
Figure A-17 shows a contour plot of the peeling streses in the solder bals. The 
maximum streses are in the outermost interconnect, at the interface betwen the solder 
and the copper pad on the PWA side. This is in agrement with the failure site obtained 
from the experiment. The curve shown in Figure A-18, is the transfer function needed to 
correlate PWA strain to the average peeling stres at the failure site. 
173 
 
Figure A-17: Contour plot of peling stres in the solder bals. The solder bal to the extreme right is the 
outermost solder bal. The region of maximum peling streses (encircled above) matches with the failure 
site from the experiments. 
 
Figure A-18: Transfer function betwen peling stres at the failure site and 
 local flexural strain in the PWA. 
As discused in Section 2.5, damage per impact is given by Equation 5. The values 
of the unknown damage constants in Equation 5 are obtained from the results of the in-
plane impact tests (cases 1 and 2 of Table A-3). The value of ?W? is 80.13 and that of 
?p? is -0.611. For this approach to be generic, these constants should be independent of 
loading orientation and boundary conditions. This is verified in this study by evaluating 
their ability to predict the observed damage acumulation rate for a diferent type of 
loading (out-of-plane impact). In other words, the damage constants are used to calculate 
the durability for the out-of-plane impact tests, specificaly, case 3 of Table A-3. Case 4 
is an overstres failure and not used for the fatigue calculations. The calculated value of 
number of impacts to failure is 8.29, which agres wel with the experimental value of 9 
impacts, as shown in Table A-3. Thus, the methodology and the damage constants are 
174 
independent of boundary conditions and impact orientation. 
The damage calculations show that in the out-of-plane strain history, 94.3% of the 
interconnect damage is due to response in the first structural response mode. Although 
this is expected for the simple loading profile used in this study, it may not be so for 
complex loading histories. 
The test data can be plotted in terms of peeling stres at the failure site and number 
of impacts to failure (Figure A-19). The durability shows a power law fit with the average 
peeing stres at the failure site. This verifies the generic nature of the damage constants 
and the use of peeling stres as a damage metric. 
 
Figure A-19: Durability shows a power-law fit with the average peling stres at the failure site. 
A - 4. Discusion 
It is generaly dificult to correlate the board level drop test results to product level 
drop test results. The PWA is clamped to the fixture during board level drop testing and 
is alowed to vibrate after a single drop event. Product level drop testing usualy involves 
multiple impacts and rotations after the first impact, termed as clatering. High-speed 
photography by Goyal and Buratynski [2] indicates that during a single product level 
drop event, one corner of the electronic product touches down first and there is 
175 
"clatering" as other corners strike repeatedly. The product then bounces or comes to rest 
after undergoing these multiple impacts at its ends. It has been shown that during 
clatering, the product can experience velocity shocks that are several times higher than 
those experienced in a single drop event. The details of the clatering motion, and the 
various impact parameters of interest to the designer (change in velocities and impulses, 
the duration of the clater, et cetera) depend significantly on the mas distribution of the 
product and its efective coeficient of restitution at impact [31]. The mas distribution 
and boundary conditions of the PWAs used in the JEDEC board level drop tests is 
diferent from the PWAs mounted in an actual portable electronic device. 
One of the factors that make correlation of board level and product level JEDEC 
drop test data dificult is the use of damage metrics that are very structure-specific, for 
example: incident force, incident kinetic energy, incident velocity. This paper quantifies 
damage in terms of the streses at the failure site, caused by the local PWA response 
during the impact event. This makes the damage constants in Figure 19 independent of 
drop orientation and boundary conditions. Wavelet analysis, in conjunction with rainflow 
cycle counting analysis, can be used to decompose the complex PWA response 
asociated with clatering. Thus, for a given failure mechanism, the proposed test 
methodology and damage constants can be used to extrapolate the board level test results 
to field conditions. 
However, there are certain limitations to the application of the proposed drop test 
methodology. Goyal, et al. [32] showed that the impulses asociated with individual 
clater impacts are very significant because it could lead to resonances in the internal 
components. This may not be captured by the board level drop tests. Experimental work 
176 
by Goyal, et al. [33] also indicates that constraining the internal asembly to behave as a 
single system, as is done in board level drop tests, may even mis important failure 
mechanisms. The proposed drop test methodology is not a replacement for product level 
drop testing. Rather, it is a tool to bring about a beter correlation betwen board and 
product level drop testing. 
A - 5. Conclusion and Future Work 
A generic methodology is presented to determine the drop durability of surface 
mount interconnects of PWAs. The proposed method combines impact testing, 
measurement of local PWA response, time-frequency decomposition to quantify the 
response histories, finite element simulations to ases the stres history at the failure site 
under the given response, and a damage model to predict durability for the given failure 
mechanism. A case study is presented for a PBGA asembly. Test data are presented for 
both in-plane and out-of-plane loading.  The methodology and the resulting damage 
constants are demonstrated to be independent of boundary conditions and impact 
orientation, thus making the methodology quite generic. 
In addition to estimating the durability of electronic packages under test conditions, 
the proposed methodology can also be used to extrapolate results to field conditions, and 
to quantitatively compare and rank the impact resistance of diferent styles of surface 
mount interconnects.  
Future work wil focus on the influence of PWA flexural strain rate on the 
durability and failure site of surface mount interconnects. The efectivenes of the 
wavelet signal procesing technique for characterizing drop structural response wil also 
17 
be investigated. 
Acknowledgements 
This work is sponsored by the members of the CALCE Electronics Products and 
Systems Consortium at the University of Maryland, College Park. 
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