Interrogation of System State of Lead-Free Electronics Subjected to Mixed 
Sequential Steady-State and Cyclic Thermal Environments 
 
by 
 
Rahul Chandramohan Vaidya 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 13, 2010 
 
 
 
 
Keywords: PHM, Solder Joint Reliability, Life Prediction 
Prognostics, Electronic Packaging 
 
 
 
 
Approved by 
 
Pradeep Lall, Chair, Thomas Walter Professor of Mechanical Engineering 
 Jeffrey C Suhling, Quina Distinguished Professor of Mechanical Engineering 
Roy W Knight, Assistant Professor of Mechanical Engineering 
 
 
 
 
 
 
 
 iii 
 
 
 
 
 
Abstract 
 
 
Electronic assemblies deployed in harsh field environments may be exposed to 
single and multiple thermal environments during their service life. In real world setting it 
is often required to know during the service life of the system what is the amount of life 
consumed well before the actual failure occurs to schedule maintenance well in advance. 
The thermal conditions can change according to the change in the usage profile or also 
during redeployment from one field environment to another. For example in case of 
defense applications, military equipments come back from a particular field environment 
and are redeployed in different field environments after certain time intervals. Or in case 
of space missions the electronic systems embedded in the space equipments have to 
undergo different operational temperatures depending on the field conditions. It is 
important to note that different field environments have different magnitudes of damage 
incursions on electronic systems. Also electronic systems are often stored for a very long 
time before they are deployed in the intended environment. It is extremely important to 
quantify the expended life during storage especially for electronic systems used in 
mission critical applications. Although ambient temperature storage does not lead to any 
macro indicators of failure like cracks or de-lamination but it is well known that aging 
has an adverse effect on the life of electronics. Modern day electronic systems perform 
well when exposed to such multiple harsh environments and often times may not fail 
before their designed service life however the latent damage incurred at each stage can 
 iv 
not be neglected and has to be taken in to account to avoid catastrophic failures and 
system down time in the field. Quantification of thermal environments during use-life is 
often not feasible because of the data-capture and storage requirements, and the overhead 
on core-system functionality. Thus there is a growing need to develop and demonstrate 
technologies that can monitor and predict the remaining useful life (RUL) of electronics 
in single thermal environments and also assess operational readiness of the electronic 
system during redeployment. Proposed prognostic models are based on physics-of-failure 
based damage-proxies of second level solder interconnects found in today?s 
commercially available high I/O packaging architectures. Test vehicles have been 
carefully selected for the development and implementation of the models so that they are 
relevant to the current packaging trends. Prognostic framework involves the use of 
condition monitoring devices for gathering data on damage pre-cursors at periodic 
intervals. The presented Prognostic Health Management (PHM) framework lies in the 
pre-failure space without any knowledge of prior stress histories i.e. in the absence of 
macro-indicators like cracks or de-lamination. In this thesis, test cases have been 
presented to demonstrate the viability of the approach for assessment of prior damage, 
operational readiness, cyclic life reduction due to long-term storage and residual life for 
electronics. 
 iv 
Acknowledgments 
 
 
 I would like to express my deep gratitude to my research advisor Dr. Pradeep Lall 
for giving me the opportunity to work under his guidance and mentorship at NSF Center 
for Advanced Vehicle and Extreme Environment Electronics (CAVE3) as a Graduate 
Research Assistant at Auburn University. I would also like to thank my other committee 
members Dr. Jeffrey Suhling and Dr. Roy Knight for their support and guidance while 
completing this thesis. 
I would like to thank my parents Mr. C.T Vaidya and Mrs. Shailaja C Vaidya and 
my elder brother Rohan for having faith in me and providing endearing love, 
encouragement and moral support. I would also like to thank all my friends and 
colleagues for their priceless friendship and camaraderie all throughout my graduate 
studies. 
 v 
Table of Contents 
 
 
Abstract ............................................................................................................................... ii 
Acknowledgments ............................................................................................................. iv 
List of Figures .................................................................................................................. viii 
List of Tables .................................................................................................................... xii 
1 Introduction   .....................................................................................................................1 
 1.1 Electronic Packaging Overview .........................................................................1 
 1.2 Reliability Concerns...........................................................................................2 
            1.3 Prognostic Health Management Systems...........................................................6 
            1.4 Thesis Layout .....................................................................................................8 
2 Literature Review  ..........................................................................................................10 
             2.1 Solder Joint Reliability ...................................................................................10 
                    2.1.1 Reliability of BGA Packages ................................................................11 
                    2.1.2 Lead-Free (Pb-Free) Solders .................................................................12 
              2.2 Life Prediction Models ..................................................................................14 
                     2.2.1 Physics-of-Failure (POF) Models ........................................................15 
                     2.2.2 Finite Element Analysis (FEA) Models ...............................................16 
               2.3 Diagnostic Models ........................................................................................18 
               2.4 Applications of Prognostic Health Management Systems ............................21 
                     2.4.1 General PHM Applications ..................................................................21
 vi 
                     2.4.2 PHM for Electronics ............................................................................24 
3 Prognostic Model for Life Prediction of Electronics Subjected to Steady-State Thermal 
Environment  ..................................................................................................................28 
 
               3.1 Introduction  ..................................................................................................28 
               3.2 Test Vehicle  .................................................................................................28 
               3.3 Inter-Metallic Compound (IMC) Growth as Leading Indicator of Failure...31 
3.3.1 Formation of Different Inter-Metallic Compounds .............................32 
3.3.2 Inter-Metallic Compound (IMC) Measurement and Analysis .............33 
               3.4 Problem Definition and Prognostication Methodology ................................34 
               3.5 Levenberg-Marquardt Algorithm (LMA) .....................................................37 
               3.6 Case Study: Prognostication of Life Consumed  
                      due to Steady-State Aging  ..........................................................................41 
 
3.6.1 Inter-Metallic Compound (IMC) Growth  
          Measurement and Analysis .................................................................41 
3.6.2 Life Prediction using PHM Model .......................................................44 
3.6.3 Model Validation .................................................................................49 
               3.7 Conclusion  ...................................................................................................52 
4 Prognostic Model for the Quantification of Reduction in Cyclic Life Due to Long-Term 
Dormant Storage  ............................................................................................................53 
 
                4.1 Introduction  .................................................................................................53 
                4.2 Test Vehicle  ................................................................................................54 
4.2.1 Custom PCB Design ............................................................................56 
4.2.2 Test Conditions ....................................................................................61 
                4.3 Leading Indicators of Failure  ......................................................................62 
4.3.1 Phase-Growth as the Leading Indicator of Failure ..............................63 
 vii 
4.3.2 Phase-Growth Measurement ................................................................66 
                4.4 Concept of Sequential Thermal Aging and Thermal Cycling  ....................67 
                4.5 Concept of Damage Equivalency Based Mapping  .....................................69 
                4.6 Case Study: Prognostication of Life of Electronics Subjected to  
                      Sequential   Stresses .....................................................................................70 
 
4.6.1 Damage Equivalency Relationship between Thermal Aging and 
Thermal Cycling ..................................................................................71 
 
4.6.2 Prognostication of Life under Overlapping Stresses ...........................83 
                4.7 Prognostic Performance Metrics  .................................................................95 
                4.8 Conclusion .................................................................................................102 
5 Summary and Future Work  ..........................................................................................107 
Bibliography ....................................................................................................................111
 viii 
List of Figures 
 
 
Figure 1: Electronic Packaging Trends [Evans 2008, ELEC 6740]  ...................................2 
Figure 2: Typical Ball Grid Array (BGA) Electronic Package Architecture.......................3 
Figure 3: CABGA 100 Package Front and Back View .....................................................29 
Figure 4: Test Vehicle ........................................................................................................30 
Figure 5: Inter-metallic Compound (IMC) at Solder Ball, Copper Pad Interface .............31  
Figure 6: Problem Definition .............................................................................................35 
 Figure 7: Flowchart for Life Estimation of Electronics Subjected to Single Isothermal 
Aging Environment ............................................................................................................36 
 
Figure 8: Schematic of a Multidimensional Solution Space ..............................................38 
Figure 9: Schematic highlighting drawbacks of Steepest Descent Method .......................39 
Figure 10: SEM Back-scattered images of IMC Growth versus Thermal Aging for 
Sn1Ag0.5Cu (SAC 105) (Magnification 1000x)  ..............................................................42 
 
Figure 11: SEM Back-scattered images of IMC Growth versus Thermal Aging for 
Sn3Ag0.5Cu (SAC 305) (Magnification 1000x)  ..............................................................43 
 
Figure 12: IMC Growth, at various levels of time for CABGA 100 with Sn1Ag0.5Cu 
alloy (SAC 105)  ................................................................................................................44 
 
Figure 13: IMC Growth, at various levels of time for CABGA 100 with Sn3Ag0.5Cu 
alloy (SAC 305)  ................................................................................................................44 
 
Figure 14: Prognostication Approach ................................................................................45
 ix 
Figure 15: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn1Ag0.5Cu Solder Alloy Interconnects ...........................................................................47    
 
Figure 16: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn3Ag0.5Cu Solder Alloy Interconnects ...........................................................................47 
 
Figure 17: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn1Ag0.5Cu Solder Alloy Interconnects ...........................................................................48 
 
Figure 18: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn3Ag0.5Cu Solder Alloy Interconnects ...........................................................................48 
 
Figure 19: Computation of IMC Thickness (based on prognosticated y0 and k) vs. IMC 
from experimental values for 98.5Sn1.0Ag0.5Cu alloy ....................................................51 
 
Figure 20: Computation of IMC Thickness (based on prognosticated y0 and k) vs. IMC 
from experimental values for 96.5Sn3.0Ag0.5Cu alloy ....................................................51 
 
Figure 21: PBGA 676 Front and Back Side.......................................................................55 
 
Figure 22: PBGA 676 Component Side Daisy Chain Courtesy: Practical Components ...57 
 
Figure 23: 4 Daisy Chain Schematic .................................................................................57  
 
Figure 24: ExpressPCB Snapshot for PBGA 676 Daisy Chain Pattern.............................58  
 
Figure 25: Component Side Daisy Chain (BLACK) and Board Side Daisy Chain (GRAY) 
Overlaid to Show 4 Daisy Chain Patterns..........................................................................58 
 
Figure 26: Actual PCB with PBGA 676 Footprint Accommodating 4 Daisy Chain 
Patterns ...............................................................................................................................59 
 
Figure 27: Reflow Profile for SAC 305 Solder .................................................................60 
 
Figure 28: Test Vehicle ......................................................................................................60 
 
Figure 29: Thermal Cycling Profile ...................................................................................62 
 
Figure 30: IMC Growth as the Leading Indicator of Failure .............................................63 
 
Figure 31: Ag3Sn Grains in 95.5Sn4.0Ag0.5Cu solder microstructure ............................64 
 
Figure 32: SEM Image for Phase-Growth Analysis ..........................................................66 
 
Figure 33: Phase Size Measurement using NI-IMAQ .......................................................67 
 
 x 
Figure 34: Concept of Sequential Thermal Aging and Thermal Cycling ..........................68 
 
Figure 35: Mapping Reduction in Life Due to Dormant Storage. .....................................68 
 
Figure 36: Accrued Damage Due to Thermal Aging and Thermal Cycling respectively. 69 
 
Figure 37: Concept of Damage Equivalency and Mapping of Life Consumed Due to 
Storage. ..............................................................................................................................70 
 
Figure 38: SEM backscattered images of Phase growth versus number of cycles (Thermal 
cycling -55?C to 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, magnification 750x) 
............................................................................................................................................74                           
 
Figure 39: SEM backscattered images of IMC growth versus number of cycles (Thermal 
cycling -55?C to 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, magnification 1000x) 
............................................................................................................................................75 
 
Figure 40: Plot of Normalized Phase growth versus No. of Cycles for 96.5Sn3.0Ag0.5Cu 
solder, 676 PBGA, subjected to thermal cycling from -55?C to 125?C ............................75 
 
Figure 41: Plot of Normalized IMC growth versus No. of Cycles for 96.5Sn3.0Ag0.5Cu 
solder, 676 PBGA, subjected to thermal cycling from -55?C to 125?C ............................76 
 
Figure 42: SEM backscattered images of Phase growth at different aging time intervals 
(Thermal aging at 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, magnification 
750x)  .................................................................................................................................77  
 
Figure 43: SEM backscattered images of Intermetallic Thickness at different aging time 
intervals (Thermal aging at 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, 
magnification 1000x)  ........................................................................................................77 
 
Figure 44: Plot of Phase growth versus Aging Time for 96.5Sn3.0Ag0.5Cu solder, 676 
PBGA, subjected to thermal aging at 125?C .....................................................................78 
 
Figure 45: Plot of IMC growth versus Aging Time for 96.5Sn3.0Ag0.5Cu solder, 676 
PBGA, subjected to thermal aging at 125?C  ....................................................................78 
 
Figure 46: Combined plot Normalized Phase growth versus thermal aging time and 
thermal cycling...................................................................................................................80 
 
Figure 47: Combined plot Normalized IMC growth versus thermal aging time and 
thermal cycling ................................................................................................................. 81 
 
Figure 48: Combine plot of No of Cycles (N) versus Time in hrs, due to damage mapping 
from Phase growth and IMC thickness. .............................................................................82 
 
 xi 
Figure 49: Prognostication of Life Consumed Due to Aging in number of hours.  ..........84  
 
Figure 50: Prognostication of Life in Overlapping Environment ......................................84 
 
Figure 51: Schematic for Prognostication of Storage Time (for 48 hours Experimental 
Exposure)  ..........................................................................................................................88 
 
Figure 52: 3D plot of error versus aging time in hours for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 48 hours in isothermal aging at 125?C. 
............................................................................................................................................89                     
 
Figure 53: Schematic for Prognostication of Total Life in Sequential Stress Environment 
(for 48 hours+100 Cycles Experimental Exposure) ..........................................................90 
 
Figure 54: 3D plot of error versus number of cycles for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 48 hours in isothermal aging at 125?C 
followed by 100 cycles in -55?C to 125?C.  ......................................................................91 
 
Figure 55: Schematic for Prognostication of Storage Time (for 192 hours Experimental 
Exposure)  ..........................................................................................................................92 
 
Figure 56: 3D plot of error versus aging time in hours for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 192 hours in isothermal aging at 
125?C.  ...............................................................................................................................92 
 
Figure 57: Schematic for Prognostication of Total Life in Sequential Stress Environment 
(for 192 hours+100 Cycles Experimental Exposure) ........................................................93 
 
Figure 58: 3D plot of error versus number of cycles for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 192 hours in isothermal aging at 125?C 
followed by 100 cycles in -55?C to 125?C.  ......................................................................93 
 
Figure 59: ?-? curve for Prognostication using normalized phase-growth as the leading 
indicator of failure..............................................................................................................99 
 
Figure 60: ?-? curve for Prognostication using normalized IMC growth as the leading 
indicator of failure............................................................................................................100
 xii 
List of Tables 
 
Table 1: Thermal and Mechanical Attributes of Various Materials in BGA Package........3    
Table 2: Package Attributes (All Dimensions are in mm).................................................43 
Table 3: Comparison of computed values of t, y0 and k from prognostication model and 
experimental result.............................................................................................................49 
 
Table 4: Package Architecture Details...............................................................................55 
Table 5: Condition Monitoring Cells.................................................................................61 
Table 6: Damage Mapping from Leading Indicators of Failure........................................83 
Table 7: Error Estimation in Prognostication of Thermal Aging (Storage).......................94 
Table 8: Error Estimation in Reduction in Cyclic Life Due to Thermal Aging (Storage).94 
Table 9: Error Estimation in Prognostication of Overlapping Damage.............................95 
Table 10: Prognostic Metric Comparison........................................................................102
 1 
CHAPTER 1
INTRODUCTION 
 
1.1 Electronic Packaging Overview 
Electronic packaging is an inter-disciplinary field of study which deals with 
methods of construction and integration of diverse electronic circuits on a chip broadly 
referred to as IC?s (Integrated Circuits) or Packages. A single IC Package can fit multiple 
electronic circuits or devices thereby drastically reducing the size of a system as a whole. 
Nanotechnology has brought the microelectronic revolution over the last couple of 
decades. Wide scale research and development is carried out in this area in employing 
advanced techniques to further shrink the size of the individual packages to achieve 
higher component density per area. However it is extremely important to take into 
account the design considerations while scaling down the size like the mechanical or 
structural damage caused due to shock and exposure to extreme environments or the 
electrical constraints like electromagnetic interference, undesirable shorting of tracks and 
heat dissipation requirements. 
The Packaging techniques can broadly be classified into two main types? viz. 
Through-hole technology and Surface Mount technology. Through hole technology of 
mounting electronic components was in use from 1950?s ? 1970?s and is no longer 
employed for the manufacturing of commercial electronic products because although the 
through-hole mounting provides strong mechanical bonds and are more reliable and 
 2 
robust, the shrinkage of the component size is restricted which makes the overall 
electronic assembly bulky. In order to find the solution to the size constraints in through 
hole technology industry came up with the new mounting technology called surface 
mount technology which was invented in 1970?s and still finds its application in today?s 
electronic manufacturing. Components became much smaller and component placement 
on both sides of a board became far more common with surface-mounting than through-
hole mounting, allowing much higher circuit densities. It has evolved greatly in all these 
years with the current version requiring complete rethinking of design and production, 
along with new infrastructure to develop and sustain it. Figure 1 shows the schematic 
depicting evolution of electronic packaging over the years.  
 
Figure 1: Electronic Packaging Trends [Evans 2008, ELEC 6740] 
 
1.2 Reliability Concerns  
Microelectronic device integration has progressed to the point where complete 
systems-on-a-chip (SoC), Multi-chip Module (MCM) and 3D Stacking are being realized 
 3 
these days. It is inevitable to ensure product reliability to fully exploit the device 
shrinkage accomplished with the advent of Very Large Scale Integration (VLSI) and 
nanotechnology. Typically an electronic package consists of various materials (Figure 2) 
having different mechanical and thermal properties as shown in Table 1. The individual 
behavior and the interaction with other materials at different operating or field conditions 
raise mechanical, structural and electrical reliability issues in a package.  
 
Figure 2: Typical Ball Grid Array (BGA) Electronic Package Architecture 
  
Table 1: Thermal and Mechanical Attributes of Various Materials in BGA Package 
 
Color Material Elastic 
Modulus (E) 
(GPA) 
Coefficient 
of Thermal 
Expansion (CTE) 
(10-6 1/K) 
Black Mold 
Compound 
23.5 15 
Red Silicon Die 162.7 2.5 
Lavender Adhesive 6.8 52 
Yellow BT Substrate 18 12.4 
Blue Solder Balls 30.5 24.5 
Green Printed 
Circuit Board 
17 14.5 
 
Electronic assemblies undergo numerous unavoidable stresses and strains during 
their service life. The stresses are induced due to the different operational conditions. For 
example the electronic circuitry inside a commercial laptop undergoes power and or 
 4 
thermal cycling even during normal usage which induces thermal-structural stresses on 
electronic packages embedded inside. It is not unlikely that a portable electronic product 
like a cellular phone is accidently drop from a certain height. This typically is a high 
strain rate phenomenon which stresses various materials at different rates in a package 
and eventually after repeated drops the cellular phone stops working due to mechanical or 
electrical failures. Electronics used in automobiles have to undergo harsh thermal cycling 
environments (-55C to 125C) and demands high reliability for ideal functioning.  
Stresses are induced on an electronic system when it is exposed to one or more 
combinations of operating conditions like thermal cycling, isothermal aging, thermal 
shock, drop, shock, vibration, hazardous chemical exposure etc. It is important to identify 
the failure modes associated with different field conditions for ensuring long term 
reliability of the products. Some of the commonly encountered failures are solder joint 
fatigue, die fracture, chip delamination, silicon cratering, underfill cracking, pop-corn 
effect, corrosion etc. Some of these failures are attributed to as material and or processing 
defects like pop-corn failure which occurs during high temperature reflow due to the 
moisture absorbed by the package during storage. The presented work lies in the area of 
solder joint reliability under low cycle thermal fatigue and hence this has been discussed 
in great detail in the subsequent section. 
Electronic package design and development is a concurrent approach which takes 
into account many material and process variables. Solder is one of the crucial variables 
which has to be taken into account for reliable electronic performance. Solders used in 
surface mount technology not only have to serve the purpose of electrical connection but 
also has to ensure robust mechanical connection. Solder joint cracking is the most 
 5 
dominant failure mode in microelectronics. The coefficient of thermal expansion (CTE) 
of electronic package and the printed circuit board (PCB) are different as a result of 
which they expand and contract at different rates during power and thermal cycling. This 
CTE mismatch induced disparity in rates of expansion causes shear stress in the solder 
joints which leads to fracture in extreme cases and has been a major reliability concern. 
[Ye 2006, Abdulhamid 2008] have also reported on electro-migration and thermo-
migration in high temperature power electronic modules and its detrimental effect on 
solder joint reliability. Various techniques are used to reduce stress on the solder joints to 
improve solder joint reliability. Some of the techniques include developing substrates 
with matching CTEs thereby minimizing CTE differences in the substrate and package 
being mounted, developing substrates with compliant top layers that can absorb some 
stress and using underfill that provide stability to the solder joints during shearing thereby 
maintaining integrity of the joints.  
With the advent of Restriction of Hazardous Substances (RoHS) compliance and 
lead-free restrictions, electronics industry is looking into lead-free solders that can 
replace the universally accepted and widely used tin-lead solder. Research and 
development efforts are focused on the study of potential alloys that provide physical, 
mechanical, thermal and electrical properties similar to those of eutectic tin-lead solder. It 
has not been a smooth transition to switch from leaded to lead-free solders as the 
conventional eutectic Sn/Pb solder has been in use for almost half a century and all its 
properties pertaining to electronics assemblies is readily available. The biggest obstacle 
in switching to lead-free solders is the lack of material characterization data available for 
these solders for varied applications. Also the mechanical behavior of lead-free solder 
 6 
alloys is radically different from eutectic tin-lead which only compounds the 
sustainability and reliability issues of lead-free electronics. As a result electronic systems 
are not used to the desired degree in terms of life, especially in mission critical 
applications, in order to reduce the probability of failure in the field. Current tools and 
techniques can not perform reliability assessment of the system due to lack of sufficient 
information about the on going damage and its progression. The major problem in the 
industry today is the need to extend the useful life of such critical systems. Also the 
electronic components used in commercial applications like automotive safety systems 
are used to a lesser degree than desirable to avoid prospective malfunction in the long 
run. This is because the reliability associated with such safety equipments can not be 
compromised at any given point which forces the use of dependable components in such 
critical applications. Health monitoring of electronics is very relevant to such high 
reliability applications and there is a growing need to develop techniques that can 
evaluate the reliability of the system and provide information about the health of the 
system. The work presented in this thesis is based on health management of electronics 
using solder joint reliability and its associated damage proxies under thermo-mechanical 
loading. 
1.3 Prognostic Health Management Systems 
Health Management (HM) refers to the broad concept of assessing the on-going, 
in-service performance of a system using variety of measurement techniques. Prognostics 
can be thought of as a predictive diagnostics which includes determining the remaining 
life of the operational component. Prognostic Health Management (PHM) is the 
methodology of interrogation of state of a system based on computation of certain 
 7 
damage proxies to predict the Remaining Useful Life (RUL) of the system. The core 
function of any PHM model is to detect fault in the system and compute residual life at 
any given time. Typically fault detection involves interrogation of system state for 
physics-of-failure (POF) based damage proxies that provide information about the 
ongoing damage and impending failure. These damage proxies are classified as the 
leading indicators of failure and are used in PHM model development which directly or 
indirectly relates to the overall life of the system.  
Health monitoring of electronics has always gained utmost importance from the 
research community as it provides information about the current state of health of a 
system, identify faults and their behavior and assess accumulated damage thereby 
providing estimates of remaining life of the product [Lopez 2007]. Application of 
prognostic and health management (PHM) in electronics is still relatively at a nascent 
stage compared to its applications in other domains like aerospace, medicine, finance and 
weather [Saxena 2008].  
There is a growing need to develop techniques for reliability prediction of 
electronics that are exposed to sequential or overlapping multiple thermal environments. 
State-of-Art prognostic health management models are proposed in this thesis which 
helps in reliability assessment of electronics deployed in single and complex multiple 
thermal environments. The strength of the techniques lies in its ability to predict 
reliability of the electronic system without worrying about the previous usage profiles or 
materials used in the electronic component except for the solder joint. The models 
provide the decision framework for operational readiness of systems during redeployment 
and also account for reduction in cyclic life due to long-term dormant storage. The 
 8 
prognostic models have been developed based on micro-structural evolution of second 
level solder interconnects.    
1.4 Thesis Layout 
Chapter 2 encompasses literature survey on solder joint reliability and various life 
prediction models used in electronics. Since the presented work is for high I/O electronic 
packages, significant amount of literature has been reviewed pertaining to Ball Grid 
Array (BGA) packages. Reliability enhancement techniques for BGAs have also been 
discussed in detail. Transition from eutectic tin-lead solders to lead-free solders and its 
effect on solder joint reliability and overall package reliability has also been discussed in 
great detail. Life prediction models have been systematically classified into physics-of-
failure (POF) based models and finite element analysis (FEA) models for lucid 
understanding of the reader. To set the stage for Prognostic Health Management (PHM) 
systems, an overview of diagnostic models has also been presented in this chapter. Lastly 
vast literature on PHM systems and its application in various engineering domains has 
been discussed followed by its motivation and scope in electronics. 
Chapter 3 presents the prognostic model for life estimation of electronics 
subjected to steady-state aging. It involves in-depth discussion about test vehicle 
coverage, physics-of-failure based leading indicator of failure and implementation of 
novel non-linear least square (NLLSQ) method called Levenberg-Marquardt (LM) 
algorithm. Multiple case-studies have been presented wherein the life of the electronic 
system has been computed using the proposed prognostic model followed by model 
validation.  
 9 
Chapter 4 expands the realm of application of PHM systems for electronics from 
single environment to multiple thermo-mechanical environments. It provides the 
overview of multiple thermal environment scenarios and its complex nature of operation 
and why conventional life prediction models fail to predict life accurately. Specifically it 
addresses the issue of long-term dormant storage of electronics and its detrimental effect 
on the reliability. State-of-art prognostic model has been proposed in this chapter which 
quantifies the reduction in life due to storage. Multiple case-studies have been presented 
to investigate the effect of storage on cyclic life. Finally, Chapter 5 includes the 
conclusion of the presented prognostic health management models and briefly discusses 
the scope for future work. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
CHAPTER 2 
LITERATURE REVIEW 
 
2.1 Solder Joint Reliability 
In electronics the integrity of solder joints remains the backbone for ensuring 
quality of the product. A perfect joint is a joint showing complete wetting of solder to pad 
and this is a universal requirement that applies to surface mount as well as through-hole 
components. As suggested by [Woodgate 1987] the only acceptable joint is the perfect 
joint. In the pursuit of device shrinkage and circuit miniaturization, surface mount 
technology in itself has vastly evolved over the last couple of decades. With the potent 
need for small form factor packaging architectures, fine pitch packaging in the range of 
0.8mm-1.27mm became a reality which gave rise to the conception of ball grid array 
(BGA) packages. Manufacturing of fine pitch leaded chip carriers was a major issue 
which was one of the instrumental factors in pushing BGA packaging in the mainstream 
electronic manufacturing. BGAs appear to be the answer to the high pin count packaging 
trend since they can accommodate high I/O in a very small form. Fine pitch packages 
with their fragile leads pose serious handling problems and are difficult to place and 
solder. BGAs became popular because during placement and reflow, robust balls 
outperform fragile leads as they self align and provide better control during reflow at 
ultra-fine pitches. 
 11 
In surface mount devices (SMDs) like BGA packages, solder joints not only 
provide electrical connectivity but also ensure mechanical integrity between the package 
and the printed circuit board (PCB). The major reliability issue with BGA package is the 
thermal mismatch between the BT substrate and the printed circuit board (PCB). The 
difference in the coefficient of thermal expansion (CTE) of the BT substrate and the PCB 
induces shear stress in the second level solder interconnects due to disparity in the rate of 
expansion and contraction of the two materials when exposed to thermal loads. Repeated 
shearing of solder joints lead to cyclic stress or fatigue build-up in the solder joints 
causing them to fail eventually. Different techniques are employed to reduce cyclic 
thermal fatigue of solder joints as the solder joint reliability is directly proportional to the 
overall package reliability.  
2.1.1 Reliability of BGA Packages  
[Chiang 2000] proposed that a better reliability characteristic of BGA type 
packages can be achieved by using the 2nd reflow process. He showed 2X increase in the 
characteristic life of BGAs under thermal cycling due to significant reduction in 
equivalent plastic strain, the energy density and the Von-Mises stress of the solder joint. 
[Syed 1996] reported on package architecture variables affecting the solder joint 
reliability of BGA packages. He showed that perimeter array packages had a better solder 
joint reliability than full array packages. He also showed that the BT thickness had a 
direct impact on solder joint reliability with thicker BT substrate enhancing the solder 
join reliability.  
[Charles 1990] reported that increase in fatigue life under power cycling can be 
attained by fabricating solder joints with large fillets and low standoff heights. The large 
 12 
fillet geometry significantly reduces harmful stress concentrations while increasing the 
net cross-sectional area within the joint. Both factors tend to improve the fracture 
toughness of the joint. Temperature cycling studies indicate joints with slightly higher 
standoffs and low fillet angles are more resistant to cyclic fatigue than pillar type joints 
which tend to focus shear strains at the interfaces.  
Generally, for enhanced solder joint reliability of stacked die BGA, it is 
recommended to have smaller top and bottom dice sizes, thicker top or bottom die, 
thinner PCB, thicker substrate, higher solder ball standoff, larger solder mask opening 
size, smaller maximum ball diameter, smaller PCB pad size, smaller thermal cycling 
temperature range, longer ramp time, and shorter dwell time. It is possible to greatly 
enhance the solder joint performance through simple optimization in mold compound 
material and package thickness. The layout of solder balls is important as it affects the 
load distribution on critical solder ball [Tee 2004]. 
 [Zhong 1999] presented the effects of solder ball pad metallurgy, intermetallic 
compound (IMC) thickness and thermal cycling on the shear strengths of PBGA package 
solder balls. The study of the microstructures of solder balls revealed that only a very thin 
layer of intermetallic compound existed between solder balls and Ni or Ni alloy barrier 
layers immediately after ball placement and reflow. [Bradley 1996 and Suhling 2002] 
showed superior HASL pad finish thermal reliability performance over immersion nickel 
and palladium based pad finishes for BGA packages.  
2.1.2 Lead-Free (Pb-Free) Solders 
Recent global environmental projects like Restriction of Hazardous Substances 
(RoHS) and Waste from Electrical and Electronic Equipment (WEEE) has put a full stop 
 13 
on further use of tin-lead components in electronic manufacturing industry which gives a 
call for all the possible Pb-free alloys. There are hundreds of lead-free alloy compositions 
that are been studied for their applicability in electronics. The tin-silver-copper 
(Sn/Ag/Cu or "SAC") family of alloys is one of the leading contenders which have been 
accepted by electronics industry as a substitute for tin-lead solders.  
[Syed 2001, Zhang 2003 and Vandevelde 2004] have shown that the SAC alloy 
performance varies with different packaging architectures and has strong temperature 
dependence. The experimental studies have confirmed that the use of lead free solders 
with low Ag content significantly improves board level reliability during drop test when 
compared with high Ag content SAC alloys. On the contrary it has been reported by 
[Zhang 2008 and 2009] that higher Ag content SAC alloys enhance thermal reliability.  
[Schubert 2003 and Clech 2005] reported on the relative SAC solder alloy 
performance over conventional tin-lead solders. Their experimental studies have shown 
that there is significant enhancement in solder-joint reliability of second level 
interconnects with SAC alloys than tin-lead when used with compliant plastic substrates.  
As the SAC alloys are ternary system alloys the microstructure is pretty complex 
compared to binary system solder alloys. In case of eutectic tin-lead solders the intermetallic 
compound formation is so fast that the solder attains equilibrium condition quickly. The biggest 
problem with SAC alloys is that the intermetallic formation is very slow compared to eutectic tin-
lead due to high percentage of tin [Henderson 2004]. [Zhang 2003] reported that the fine 
microstructure of SAC alloys right after reflow help prevent grain boundary sliding and hence 
SAC alloys perform better than tin-lead in low stress regimes. [Dutta 2004] emphasized on the 
need for incorporating coarsening kinetics in the existing solder creep models as the 
microstructure of SAC alloys evolves rapidly during thermal cycling and creep behavior is related 
 14 
with microstrucure. [Liu 2004 and Tsai 2005] have reported on the difference in the mechanical 
behavior and characterization of intermetallic compounds found in SAC and Sn-Pb alloys and its 
effect on solder joint reliability. 
Apart from SAC alloys other potential metals that can be used as lead-free alloys 
are Indium, Zinc, Bismuth etc. [Seelig 2003] reported that Bismuth poses a potential supply 
problem since it is a by-product of lead mining, and also has embrittlement problems. 
Bismuth is also a poor conductor, both thermally and electrically. [Lung 2004] reported 
on potential Pb-free Sn-Zn and its relative performance with SAC alloys. [Shimizu 1995] 
showed that Indium-alloy solders have better mechanical properties for solder joints, and 
their flip-chip interconnection models showed a longer fatigue life than that of Pb-Sn 
solder in thermal shock tests between liquid nitrogen and room temperatures. He 
proposed lead-free solders such as indium (In)-alloy solders are a possible alternative to 
conventional lead-tin (Pb-Sn) solders and are suitable for fabricating reliable 
interconnections.  
2.2 Life Prediction Models 
Electronics is a fast paced industry and because the market life of individual 
commercial electronic product is typically 6-12 months it is impractical for any electronic 
manufacturing company to test every new product in the real field environment and 
evaluate mechanical reliability or life of the product. Instead, accelerated tests such as 
Highly Accelerated Life Tests (HALT) or Highly Accelerated Stress Tests (HAST) are 
used which impose harsher conditions on the electronic product causing them to fail in a 
shorter time to make reliability predictions in the actual field applications. There are 
number of life prediction techniques for electronics ranging from simple analytical 
 15 
methods to complex damage mechanics based finite elements models that are available in 
literature especially based on solder joint reliability mechanics.  
2.2.1 Physics of Failure (POF) Models 
Classical [Coffin 1954, Manson 1964 and Goldmann 1969] models have proposed 
physics of failure based life prediction equations that relate the plastic strain in the solder 
joints with failure life of the package. [Norris 1969, Lau 1995] studied the effect of 
cycling frequency and maximum temperature of cycling on fatigue failure of solder 
joints.  
[Wong 1990] proposed a mechanistic model for eutectic Pb/Sn solder life 
predictions wherein he studied crack initiation, crack propagation, microstructure 
coarsening and deformation kinetics models of the solder during thermal cycling.  By 
merging these models together he predicted the time to crack initiation and the time to 
failure of the solder joints.  
Low cycle fatigue testing of a eutectic alloy 63Sn/37Pb was carried out by [Shi 
1999] to study Morrow energy-based model, the frequency-modified Coffin-Manson 
model, and the frequency-modified energy-based model by [Solomon 1986] for life 
prediction.  
[Engelmaier 1982 and 1984] developed a surface mount solder joint reliability 
prediction model containing all the parameters influencing the shear fatigue life of a 
solder joint due to shear displacement caused by thermal expansion mismatch between 
component and substrate. [Wong 1988 and Yamada 1989] implemented fracture 
mechanics concept to study solder joint cracking and compute time to failure.  
 16 
[Choi 2003, Ye 2003 and Chiu 2006] studied the effect of joule heating, electro-
migration and thermo-migration on flip-chip solder joints. They proposed damage 
mechanics of flip-chip joints under high current densities and have related mean time to 
failure using Black?s equation. Overwhelming mechanical property degradation of solder 
joints was observed due to current stressing. Mass accumulation was reported to be 
primary reason for void formation and subsequent crack propagation in such high current 
density applications.   
[Lau 2002 and 2003] developed empirical equation for predicting the thermal-
fatigue life of wafer level chip scale package (WLCSP) solder joints. It is derived by 
combining the measured thermal-fatigue crack growth rate of the corner solder joint and 
the simulated nonlinear fracture characteristics i.e. average strain energy density per 
cycle around the crack tip of the corner solder joint with various crack lengths. 
2.2.2 Finite Element Analysis (FEA) Models 
Numerous researchers in the field of electronic packaging have used the power of 
finite element methods to make solder joint life predictions under different operating 
conditions like thermal and power cycling, drop and shock, vibration and bending. 
Majority of finite element life prediction models are based on accumulated field 
quantities and derivatives of field quantities like creep strain, inelastic strain energy 
density and nonlinear plastic work etc.  
[Amagai 1998 and Popelar 1997] proposed a viscoplastic constitutive model to 
analyze thermally induced plastic and creep deformation and low cycle fatigue behavior 
of the solder joints in Chip Scale Packages (CSP).  
 17 
[Frear 1997 and Vianco 1999] developed a finite element simulation methodology 
to predict solder joint mechanical behavior that includes micro-structural evolution. The 
micro-structural evolution was incorporated through a series of mathematical relations 
that describe mass flow in a temperature/strain environment.  
[Wang 2001] applied [Anand 1985] unified creep model to represent viscoplastic 
deformation behavior of solders. He concluded that inelastic deformation behavior 
calculated by the model can be applied for solder joint reliability predictions. [Zhang 
2000] proposed a novel life prediction model that takes into account the damage 
evolution to accurately predict solder joint reliability.  
[Darveaux 2000] established 63Sn37Pb eutectic alloy damage relationships 
correlating crack growth rate with inelastic strain energy density per cycle. This 
relationship is widely incorporated by other researchers in their life prediction 
frameworks to compute the characteristic life of ceramic BGAs on solder masked defined 
pads using finite element simulations. Later [Lall 2004] widened the scope of Darveaux?s 
work by updating damage relationship constants and applied that for life prediction of 
plastic BGAs with non-solder masked defined pads.  [Syed 2004] proposed accumulated 
creep strain and energy density based thermal fatigue life prediction models for lead-free 
SAC solder alloys using advanced finite element modeling and analysis. He used 
different constitutive equations proposed by [Wiese 2003, Schubert 2003, Zhang 2003 
and Morris 2003] to model solder creep and studied its effect on life prediction accuracy.  
[Zahn 2003] presented a three-dimensional finite element analysis methodology 
which explored global, sub-structure, and sub-modeling solution options using both slice 
and symmetry models for the purpose of deriving life prediction equations that determine 
 18 
the fatigue response of microelectronic package structures using both eutectic 
(63Sn37Pb) and lead-free (95.5Sn4Ag0.5Cu) solder materials. 
[Tee 2004] presented a life prediction model to estimate number of drops to 
failure for a package subjected to board level drop test. The maximum normal peel stress 
of the critical solder joint extracted from finite element simulation was used as the failure 
criteria to predict mean number of drops to failure. 
One of the potential causes for mechanical failure of component interconnects is 
the bending of the PCB. [Shetty 2003] demonstrated the application of three-point and 
four-point bending tests for evaluating the reliability of chip scale packages under 
curvature loads. He proposed deformation energy based empirical reliability model to 
calculate mean life time to failure of solder joints under mechanical bending. The 
relationship between average cycles to failure and average strain energy density is 
established in this reliability model by volume averaging the strain energy density over 
the top layer of the solder joint, volume average technique proposed by [Zhan 20003, 
Darveaux 1992 and 2000]. 
2.3 Diagnostic Models 
Life prediction models discussed in previous section are based on fear of failure, 
i.e. they provide estimate on failure life, which are only useful in making reliability 
predictions upfront i.e. before deployment in the intended field. Although these models 
help in benchmarking the overall life of electronics, they are of no use in the need of in-
field fault detection during the service life. This is especially important for hi-reliability, 
mission critical applications wherein the characteristic life of the component is important 
before deployment but also continuous monitoring of system is equally important. Thus 
 19 
condition monitoring leading to fault diagnosis has attracted researchers in the past few 
years because of its considerable influence on the operational continuation of many 
industrial processes. Correct diagnosis and early detection of incipient faults result in fast 
unscheduled maintenance and short downtime for the process under consideration. They 
also avoid harmful, sometimes devastating, consequences and reduce financial loss. An 
ideal diagnostic procedure should take the minimum measurements necessary from a 
machine and by analysis extract a diagnosis, so that its condition can be inferred to give a 
clear indication of incipient failure modes in a minimum time [Bellini 2008].  
The diagnostic methods can generally be classified into the three basic categories. 
The model-based diagnostics checks how the system responds to inputs. It relies on some 
model of correct behavior of the diagnosed system. Using the inputs the model makes 
predictions of correct outputs; the differences between the actual outputs and the 
predictions are diagnostic variables called residuals. The latter are usually compared with 
certain threshold values and the results of the comparisons are the basis for the ultimate 
diagnostic decisions. The reference-band diagnostics is only applicable to closed-loop 
control systems. As the closed-loop system outputs should follow the commanded values, 
excessive discrepancies between the outputs and commanded values can be indicative of 
faults. In other words, the reference-band diagnostics checks how the system tracks the 
reference values. The signal-based diagnostics disregards any input?output relationships 
and exploits the fact that the output signals themselves can convey information about the 
health of a system [Sleszynski 2009].  
The very first efforts in this area is the usage of Built- In-Self Test (BIST) circuit, 
which is an onboard hardware and software diagnostic means to identify and locate faults 
 20 
and includes error detection and correction circuits [Drees 2004]. BIST is a methodology 
that embeds additional functionality in the product to give it the ability to test and 
diagnose itself with minimal interaction from external test equipment [Chandramouli 
1996, Hassan 1992, Williams 1983, Zorian 1994]. BIST, when effectively designed in a 
chip / board / system, can yield an enormous amount of diagnostic information. BIST 
controllers can also output failure data that can be correlated to show exactly when the 
failure occurred. This data can then be interpreted by diagnostic software to analyze the 
cause of failure. For example, Pseudo-Random Binary-Sequence (PRBS) test pattern 
generators, apply input vectors to digital or analog [Al-Qutayri 1992] modules. Self-
Checking circuit designs provide on-line test for digital [Lala 1985] as well as for analog 
circuits [Kolarik 1993]. The obtained output is then compared with a golden response. 
The results obtained from BIST functions can generate diagnostic information which in 
turn provides additional confidence in the measurement result and confirm the device 
availability. 
Though BIST helps in minimizing the interaction with external automated test 
equipment (ATE) as well as provides the advantage of a more robust ?at-speed? test of 
the circuitry, the current form gives little insight about the system level reliability or the 
remaining useful life of the system. Also, several studies conducted [Allen 2003, Drees 
2004, Gao 2002, Rosenthal 1990] have shown that BIST can be prone to false alarms and 
can result in unnecessary costly replacement, re-qualification, delayed shipping, and loss 
of system availability. 
Also, Fuses and Canaries are mounted on the part to provide advance warning of 
failure due to specific wear out failure mechanism. The basic procedure here is to take 
 21 
some form of action, after an initial failure or malfunction, to prevent additional or 
secondary failures. By reducing the number of failures, techniques such as enhancing 
product reliability can be considered, although they also affect availability and product 
effectiveness. However, replacement of fuses and canaries does impact the maintenance, 
repair and part replacement making it difficult to integrate these systems with host 
system. 
Although diagnostic models are able to detect faults in the system but they are 
unable to provide any information about the ongoing damage such as damage initiation 
and damage progression. In other words a fault is detected or diagnosed only when 
failure occurs. It also lacks insight about the remaining useful life of the systems. There is 
a growing need to develop techniques that can provide information about the impending 
failure way before the system is about to fail and use this information to predict 
remaining useful life. Prognostic Health Management (PHM) systems have the ability to 
perform fault diagnosis before the actual failure occurs and compute remaining useful 
life, and hence its application is relevant especially in hi-reliability applications. 
2.4 Applications of Prognostic Health Management (PHM) Systems 
Maintenance has evolved over the years from corrective maintenance to 
performing time-based preventive maintenance. Future improvements in reduction of 
system downtime require emphasis on early detection of degradation mechanisms. 
Incentive for development of prognostics and health management methodologies has 
been provided by need for reduction in operation and maintenance process costs [Jarell 
2002].  New advances in sensor technology and failure analysis have catalyzed a 
broadening of application scope for prognostication systems to include large 
 22 
electromechanical systems such as aircraft, helicopters, ships, power plants, and many 
industrial operations. Current PHM application areas include, fatigue crack damage in 
mechanical structures such as those in aircraft [Munns 2000], surface ships [Baldwin 
2002], civil infrastructure [Chang 2003], railway structures [Barke 2005] and power 
plants [Jarrell 2002]. 
2.4.1 General PHM Applications 
Previously PHM of mechanical structures has been done by dynamic analysis 
based on natural frequencies, mode shapes, damping factors, and static analysis based on 
deformation or changes in structure orientation due to load or unexpected damage using 
innovative signal processing, new sensors, and control theory [Kok 2005].  
PHM systems for fault detection and characterization such as BEAM have also 
been proposed for spacecrafts which involves system characterization using all available 
observation followed by training of the characterization with respect to normal phase 
operation [Park 2002]. The use of multiple sources of information for the interrogation of 
system state and fault detection in aircrafts has been proposed in which predictions from 
various subsystems is used for fault diagnosis [Oza 2003]. 
Wayside detection involving fault identification using interrogating sensors 
placed along the sides of railway tracks has been used in the railway industry for 
gathering information about the vehicle performance. Information on the vehicle 
condition and performance over an extended period of time is recorded in an online 
database, which is interrogated for critical performance parameters to provide 
information on condition of in-service railway vehicles [Barke 2005].   
 23 
A model-based method has been used for the on-line identification of cracks in a 
rotor of aircraft engines which start and stop quite frequently and run at high speeds 
[Sekhar, 2003].   
Detection of surface corrosion has been used to reduce the maintenance required, 
and trigger preventive repair for increased aircraft availability and significantly reduced 
cost of ownership. Fluorescent fiber optic sensors that detect aluminum coating from the 
early stages of the corrosion process have been used for providing early warning of 
corrosion in susceptible areas of an aging aircraft [Maalej 2004].  
Crack modeling approach in beam has been used to demonstrate the structural 
HM using low frequency vibration; simple models of crack flexibility based on beam 
elements are adequate [Friswell 2002].  
Optical fiber based sensor system has been used on concrete structure to evaluate 
its performance for health monitoring [Fernando 2003]. Monitoring bridge performance 
has been done to answer questions on the performance of existing bridges, refine 
techniques needed to evaluate different bridge components, and develop approaches that 
can be used to provide a continuous picture of a bridge's structural integrity using 
structural health monitoring [DeWolf 2002]. These techniques help in detection of 
damage of bridges or building to avoid the economic and social effect of aging and 
deterioration [Chang 2003]. In other applications, signal feature analysis is used to detect 
abnormalities related to impending failure indication by an inference system using an 
historical database [Hess 2001]. 
 
 
 24 
 
2.4.2 PHM for Electronics 
Implementation of PHM algorithms in electronics for the interrogation of system 
state and residual life calculations is still relatively at a latent stage compared to its 
application in other domains. Prognostics based health monitoring of electronics require 
leading indicators in the system for fault detection and decision support. A prognostic 
feature provides an advanced warning of impending failure to predict remaining useful 
life (RUL). Prognostic features may be extracted from a combination of device, circuit, or 
system parameters sensitive to damage accumulation [Brown 2007]. 
Modern aircrafts are increasingly dependent on avionic systems for a variety of 
roles ranging from effective communication and navigation to flight control, engine 
control and fuel management. Most of the avionics are intended for flight safety and thus 
the reliability associated with it can not be compromised at any point of time. Routine 
maintenance of such high reliability equipments requires advance planning and high 
expertise. On board diagnostic systems are intended to identify and localize component 
failures but it is well known that electronic parts can fail in number of different modes at 
different times resulting in ambiguous diagnosis. There is a growing need to develop 
prognostic techniques for such high reliability applications which can provide early 
device degradation warning for maintenance with considerable reduction in variability. 
Some of the damage indicators that have been incorporated in the development of the 
prognostic techniques for avionics include power dissipation, output degradation and 
aging of semiconductors [Hecht 2006]. 
 25 
In case of mission critical applications like space explorations the reliability of the 
spacecraft is extremely important as they are away from the earth for considerably long 
periods of time. Effective on-board prognostic systems not only increase safety by 
detecting problems before they become serious and prevent major failures but also help 
schedule efficient maintenance [Schwabacher 2005]. 
Switch mode power supplies (SMPS) commonly used aboard aircraft for various 
electrical power requirements are susceptible to malfunction due to component failures. 
Previously prognostic approach dealing with SMPS health management has been 
developed in which components like switching transistors, filtering capacitors and 
rectifying diodes inside SMPS have been indentified as critical components for prognosis 
[Orsagh 2005]. 
Reliability of the electronic power modules used in vehicles has always been a 
concern as it consists of numerous electronic components which undergo thermal stresses 
and fatigue due to power dissipation during usage. The nature of the gradual degradation 
of these power modules has enabled the development of prognostic systems for the same. 
Some of the signatures of impending failures including increase in forward on-voltage, 
leakage current and thermal impedance have been used as the damage proxies for the on-
board prognostic system [Xiong 2008]. 
Field data from aircraft has been evaluated for the continuous health assessment 
of avionics and a prognostic software has been developed that involves mining of data 
from multiple sources, trending and ranking of anomalous indicators, development of on-
board built-in-test (BIT) data and automated advanced reasoning for reduced ambiguity 
[Dussault 2006]. 
 26 
For many years, commercial telecom systems have adopted many forms of 
reliability enhancements all intended to improve system up-time. While these changes 
have been effective, the surprise factor is still prevalent in systems carrying vitally 
important traffic over the network. Providers and technicians alike often wish there was 
some signal or other indicator of an upcoming problem in order to take some action in 
advance of a system shutdown [Wood 2006].  
Electronics systems may be subjected to prolonged periods of thermal exposure 
over wide temperature extremes and long periods of thermal aging at often high ambient 
temperatures.  High-rel systems may have very long operating life times with low 
downtime during operation.  Historical environmental conditions to which the systems 
may have been subjected may be often unavailable.  PHM for electronics has wide 
applicability spanning a number of different areas.  Electronics used in critical 
applications like space, military and avionics require multiple deployments with 
sequential thermal stresses.  Systems may also be subjected to long term dormant storage 
in uncontrolled thermal environments.  Ultra high reliability is needed to ensure 
predictable operation when needed and avoid any catastrophic damage during the service 
life. 
There is need for tools and techniques which will enable the spot-assessment of 
the system?s health and provide method for estimation of remaining useful life.  
Prognostication of sequential thermo-mechanical damage under thermal aging and 
thermal cycling based on damage pre-cursors is currently beyond the state of art. 
Previously [Lall 2005, 2006a,b, 2007a,b and 2008] has developed leading indicators 
based prognostic and health management methodologies for residual life computation of 
 27 
electronics subjected to single thermal environments comprising of isothermal aging and 
thermal cycling. Examples of damage pre-cursors include micro-structural evolution of 
second level solder interconnects, inter-metallic compound growth, stress and stress 
gradients.  Pre-cursors have been developed for both eutectic 63Sn37Pb and various lead-
free alloy compositions like Sn4Ag0.5Cu, Sn3Ag0.5Cu, Sn1Ag0.5Cu, Sn0.3Ag0.7Cu, 
Sn3Ag0.5Cu-Bi, Sn3Ag0.5Cu-Bi-Ni, 96.5Sn3.5Ag alloy systems on a variety of area-
array architectures. 
In this thesis, PHM models have been developed and implemented for the 
interrogation of system state and the estimation of remaining useful life of electronic 
systems subjected to single steady-state environment and multiple thermal environments 
of isothermal aging and thermal cycling. Data on damage pre-cursors has been collected 
and analyzed for both aging and cycling to develop a technique that can map aging time 
into number of cycles and thus account for reduction in life due to dormant storage. The 
methodology involves the use of condition monitoring devices which have been 
interrogated for aging, cycling and different combinations of aging + cycling for residual 
life predictions. Developed PHM technique is based on non-linear least-squares method 
called Levenberg-Marquardt (LM) algorithm which has been developed for two different 
damage proxies. Prognostic model performance based on standard prognostic metrics has 
also been evaluated for both the damage proxies to determine which leading indicator of 
failure can be employed for accurate life prediction. Results of interrogation of system 
state have been compared with a second set of experimental-matrix to validate the 
proposed methodology. 
 28 
CHAPTER 3
PROGNOSTIC MODEL FOR LIFE ESTIMATION OF ELECTRONICS SUBJECTED 
TO STEADY-STATE ISOTHERMAL AGING 
 
3.1 Introduction 
Electronic systems may often be subjected to high temperature steady-state aging 
environments depending upon the usage profile or during storage. It is well known that 
even the steady-state temperature has a detrimental effect on life of electronics. The 
presented PHM model enables life estimation of electronics subjected to single 
isothermal aging environments. The proposed methodology enables spot assessment of 
life consumed due to isothermal aging environments in the pre-failure space, without any 
knowledge of prior stress histories. This technique eliminates the need for continuous 
monitoring of the system state to make life predictions, which considerable saves the 
overhead associated with data acquisition systems. The prognostic model is based on 
physics-of-failure of lead-free second level solder interconnects commonly found in 
today?s high I/O packaging architectures.   
3.2 Test Vehicle  
Two most popular lead-free solder alloy compositions viz. 98.5Sn1.0Ag0.5Cu 
(SAC 105) and 96.5Sn3.0Ag0.5Cu (SAC 305) on ball grid array packaging architecture 
have been used in this study. These two solder alloy compositions were chosen as 
industry has widely accepted these two solder alloy compositions as the drop-in 
 29 
replacement for eutectic Sn/Pb for drop/shock and thermo-mechanical applications 
respectively. The packaging architecture used for this study is chip-array ball grid array 
CABGA with 100 I/O. The primary motivation behind choosing this packaging 
architecture was that plastic ball grid arrays PBGAs are replacing leaded packages in the 
commercial sector due to its small form factor. The test vehicles were imported from 
practical components which consist of Amkor CABGA100 packages as shown in Figure 
3. The test board is a 132 mm X 77mm JEDEC drop test board as shown in Figure 4. 
SAC 105 and SAC 305 solder pastes were provided by Cookson Electronics. Table 2 
summarizes other package attributes. Test boards were subjected to single accelerated 
thermal aging environment only. The isothermal aging temperature chosen for this 
accelerated testing was 125?C so that substantial amount of damage is accrued in short 
period of time.  
   
                                        
Figure 3: CABGA 100 Package Front and Back View 
 
 
 
 
 
 30 
 
Figure 4: Test Vehicle 
 
Table 2: Package Attributes (All Dimensions are in mm) 
 
Bod
y 
Size
 
Sold
er 
Pac
kage
 
Typ
e 
Ball
 
Coun
t 
Ball
 
Pitc
h 
(mm)
 
Die
 
Th
ick
 
(mm)
 
Die
 
Size
 
(mm)
 
BT
 
Th
ickn
ess
 
(mm)
 
BT
 Pad
 
Typ
e 
Ball
 
Diam
ete
r 
 
10  SAC 305 CABGA 100 0.8 0.26 6.4 0.26 NSMD 0.50 
10  SAC 105 CABGA 100 0.8 0.26 6.4 0.26 NSMD 0.50 
 
Multiple sets of test vehicle have been used in this study for experimental and 
prognostication respectively. Two condition monitoring cells of test vehicles were 
created viz. CM#1 and CM#2 where, CM#1 was allotted for experimental part and was 
subjected to multiple of hours of aging at 125?C. Test vehicles in CM#2 were allotted for 
the development and implementation of the prognostic model.  
 
 
 31 
3.3 Inter-Metallic Compound (IMC) Growth as Leading Indicator of Failure 
The leading indicator of failure used for developing this prognostic model is 
called the inter-metallic compound (IMC) growth which is formed between the solder 
ball and board-side copper pad as shown in Figure 5. Typically in electronics 
manufacturing the solder paste is first printed on a copper pad footprint on a printed 
circuit board (PCB), components are placed on this solder print and the assembly is 
allowed to undergo high temperature reflow.  
 
Figure 5: Inter-metallic Compound (IMC) at Solder Ball, Copper Pad Interface 
 
During the soldering process when solder is in the molten stage, the formation of 
an inter-metallic compound between Sn-based solders and substrates is inevitable and 
then it continues to grow during solid-state aging. High temperature accelerates the 
diffusion of metal atoms across the interface, causing the formation of inter-metallics. 
The initial formation of these inter-metallic compounds at the interface between the 
solder and the substrate during soldering ensures a good metallurgical bond. However, 
the growth of these inter-metallic compounds influence the strength and can result in 
mechanical failure of the joints. 
Most lead free alloys are Sn-based. Eutectic alloy is preferred due to its single and 
low melting point. Eutectic Sn alloys have higher melting points than Sn-Pb. Hence the 
 32 
corresponding reflow temperatures are also higher, typically by about 30?C. This 
increases the rate of IMC formation with Cu. Furthermore it is not possible to develop a 
high temperature solder with SAC alloys as adding high percentages of Ag or Cu tend to 
have a large temperature gap between liquids and solidus points which is highly 
undesirable. 
Examining the microstructure of SAC alloys suggests that it is a mix of Sn and 
IMC, unlike eutectic Sn-Pb which has no equilibrium IMC. Also the Sn-Cu reaction rate 
during the high reflow temperatures is very intense; hence even the small amount of Ag 
leads to large amount of IMC formation. The properties and thickness of IMC?s formed 
at the solder pad interconnects directly affects the reliability of solder joints [Tz-Cheng 
2004, Tu 2002, Lehman 2005]. Understanding the effects of IMC formation in Pb-free 
solder joints and how this formation can be limited is crucial in obtaining solder joint 
reliability. 
3.3.1 Formation of Different Inter-metallic Compounds: 
 
Immediately after the flux reduces surface oxides and permits metallurgical 
contact of solder to Cu, the solid Cu starts to dissolve into the molten solder. The 
formation of Cu6Sn5 takes Cu out of the saturated solder and causes some further 
dissolution of Cu from the solid Cu pad. The Cu6Sn5 crystallizes and joins together to 
form a continuous layer on the Cu, blocking the channel for further liquid solder 
dissolution of Cu. However, Cu is not in equilibrium with Cu6Sn5. There is another IMC, 
Cu3Sn, between Cu and Cu6Sn5. This implies that the interface between the Cu6Sn5 
IMC and Cu pad is not stable. Consequently, the solder reaction will continue through 
solid state diffusion to form Cu3Sn IMC between Cu and Cu6Sn5 if the temperature is 
 33 
high enough to activate the reacting atoms of Cu and Sn. The Cu-Sn inter-diffusion 
process does not stop even after the Cu3Sn layer is in place. In the Cu-SnAgCu solder 
system, the diffusing Cu atoms arrive at Cu3Sn-Cu6Sn5 and Cu6Sn5- solder interfaces 
and result in the growth of both IMC layers towards the solder. Because of the 
unbalanced Cu-Sn inter-diffusion through interface, Cu atoms on the bare Cu side are not 
filled by Sn atoms. This result in the formation of something called as voiding at the IMC 
interface. The voiding process is initiated at as low as 100?C which is the main 
mechanism for joint strength degradation under thermal aging which can be detrimental 
in high temperature applications [Dunford 2004]. 
3.3.2 Inter-Metallic Compound (IMC) Measurement and Analysis 
The inter-metallic compound has been empirically observed to grow when the 
electronic assembly is subjected to high temperature isothermal aging for increasing time 
intervals [Lall 2004, 2005, 2006]. The compositions of the IMC layer closer to solder 
interconnect has been identified as Cu6Sn5 and that near to copper pad has been identified 
as Cu3Sn using energy dispersive X-ray (EDX). It has been observed that with the 
increasing aging time, the IMC layer thickens, and the local irregularities appear to 
gradually smooth out. 
Previously, empirical analysis of inter-metallic compound (IMC) thickness 
growth at various intervals of time has indicated a square root dependence of inter-
metallic thickness on aging time. 
tkyy(t) 0        (1)                              
Where y (t) is inter-metallic compound growth thickness during aging at time t, y0 is the 
initial thickness of inter-metallic compounds, k is the coefficient standing for the square 
 34 
root of the diffusivity at aging temperature, and t is the aging time. The exponent value, n 
= ? has been used in tkyy(t) 0        (1 above, which reveals a diffusion-
controlled mechanism during aging. The IMC growth data indicates that growth rate 
stays fairly uniform during the thermal aging. It is observed that for Sn-Ag solder 
systems, the inter-metallic compound thickens roughly as 2/1t  in a linear manner, where t 
is the aging time as expected for diffusion-controlled growth. This trend has been cross 
checked in the case study section for both SAC 105 and SAC 305 test vehicles. 
In order to measure the inter-metallic compound (IMC) growth, samples were 
withdrawn at various aging time intervals. The withdrawn samples were cross-sectioned, 
potted using epoxy resin and finely polished using grinding papers and collidal silica 
solution so that the inter-metallic layer was clearly visible under the microscope.  The 
inter-metallic thickness was measured using pictures taken from Scanning Electron 
Microscope (SEM), JEOL JSM-7000F operated at an accelerating voltage of 20V and 
magnification of 1000X. 
3.4 Problem Definition and Prognostication Methodology 
In real world setting it is often required to know during the service life of the 
system what is the amount of life consumed well before the actual failure occurs 
especially for mission critical applications. The problem defined in this chapter is a real 
world application problem wherein the electronic system is already deployed in some 
isothermal aging environment for unknown time period and one has to compute the life 
consumed in terms of hours of aging well before the failure takes place. Figure 6 depicts 
the problem definition. Here the timeline is defined by START and END or t=0 and 
t=FAILURE. It means that electronic system is deployed in isothermal aging 
 35 
environment (125?C) at t=0 and has an active field life until t=FAILURE. The primary 
objective of the prognostic model is to assess life consumed at any point of time between 
START and END. 
 
Figure 6: Problem Definition 
  
The framework adopted to compute the life consumed due to aging is shown in 
the form of a flowchart as shown in Figure 7. The prognostic model proposed in this 
chapter predicts the life in terms of aging based on inter-metallic compound growth as the 
leading indicator of failure discussed earlier in the chapter. A detailed case-study has 
been presented later in this chapter. 
The equation relating IMC growth of the solder interconnect with aging time ?t? 
the system has been exposed to a isothermal aging environment is given by, 
tkyy ( t) 0                   (2) 
 
Where, ?y(t)? is the IMC thickness measured after t hours of thermal aging, ?y0? is the 
IMC thickness measured after reflow, ?t? is the aging time the system is exposed to in a 
 36 
isothermal aging environment and ?k? is a constant. The damage incurred during aging is 
reflected in the IMC thickness of the solder which can be measured by cross-sectioning 
the sample. Thus in real time, without the knowledge of prior stress histories one can 
only find IMC thickness y(t) in the above equation while rest of the variables y0, k and t 
are unknowns.  
 
Figure 7: Flowchart for Life Estimation of Electronics Subjected to Single Isothermal 
Aging Environment 
 
The prognostic model has been developed to predict the aging time?t? the system 
has been exposed to in a isothermal aging environment based on the real time IMC 
measurement ?y?. In order to compute the aging time, the non-linear IMC growth 
equation (Equation 2) has been solved for the 3 unknown?s viz. t, k and y0. To solve 3 
 37 
unknowns we need 3 equations and therefore the system has to be subjected to known 
additional hours of aging (t + ?t, t + 2?t), followed by IMC thickness measurements yt+?t 
and yt+2?t for additional aging times respectively as depicted in the flowchart (Figure 7). 
The following 3 equations are solved to compute t, k and y0.  
tkyy(t) 0                                               (3) 
?ttky? t )y ( t 0                        (4) 
t2tkyt)2y ( t 0                   (5) 
 
As there exist a non-linear relationship between the IMC growth and time t, thus a 
non-linear least square technique has been employed to minimize error in the solution 
space. All the prognostic models proposed in this thesis are based on non-linear least 
square (NLLSQ) method called Levenberg-Marquardt algorithm which has been 
discussed in the next section. 
3.5 Levenberg-Marquardt Algorithm (LMA)  
A non-linear set of equations does not have a trivial solution which means that 
when non-linear equations like the three IMC growth equations are solved to compute 
three unknowns ( tkyy(t) 0                                               (3, 
?ttky? t )y ( t 0                        (4 and 
t2tkyt)2y ( t 0                   (5), we get multiple solutions for all 
the three unknowns. In order to find the exact solution from a multidimensional solution 
space or in other words to reduce multiple solutions to a single solution for each 
unknown a technique like Levenberg-Marquardt (LM) algorithm has to be implemented. 
 38 
Typical output from a LM algorithm is depicted in Figure 8. Each dot in the solution 
space represents a solution of non-linear equations. The algorithm iteratively minimizes 
error in each step and selects the final solution corresponding to the minimum error as 
shown by the red dotted lines. 
Levenberg-Algorithm is a higher order non-linear least square method which is a 
combination of Gauss-Newton method and Steepest Descent method. It is a hybrid 
method which combines the speed of the Newton algorithm with the stability of the 
Steepest Descent method. The primary reason for incorporating two non-linear least 
square methods into one algorithm is because it eliminates the individual weaknesses of 
Newton method and steepest descent method.  
 
Figure 8: Schematic of a Multidimensional Solution Space 
 
Solution of a non-linear system largely depends upon the guess values which vary 
according to the problem. The main obstacle in using steepest descent method alone is 
 39 
that if the error curvature is in different directions i.e. if the error envelope is zigzag, 
there is a high probability that the steepest descent method would get stuck in the local 
minima and would never converge to the global minima as shown in Figure 9. Or even if 
it does converge the entire process can be extremely inefficient and time consuming. On 
the contrary the disadvantage of using Gauss-Newton method alone is that it does not 
guarantee the convergence even to the local minima especially when we are away from 
the solution or at the start of the solution. If the initial guess value is far from the 
minimum there is a high probability that the Gauss-Newton method will not converge at 
all.  
 
 
Figure 9: Schematic highlighting drawbacks of Steepest Descent Method 
 
Levenberg-Marquardt algorithm has been developed to exploit the advantages of 
both the methods at the same time and eliminate the individual drawbacks of the two 
methods. It effectively switches between these two methods using a learning parameter or 
 40 
a damping parameter. When the solution is away from the minima it becomes steepest 
descent method and switches to Gauss-Newton when it is close to the final solution. The 
equation used to minimize the multidimensional solution space is given by, 
eJh? I)J(J TT                       (6) 
 
Where J is the Jacobian matrix which is used to minimize the error in the each iteration 
step, ? is the damping parameter which governs the switching of the two methods, I is the 
identity matrix, h is the descent direction which controls the step size in each iteration 
and e is the error vector. Jacobian is a partial derivative of the governing equation with 
respect to each unknown. The governing equation for this problem is given by 
tkyy ( t) 0                   (2. It relates IMC growth with the aging time. Thus the 
partial derivatives of tkyy ( t) 0                   (2 with respect three unknowns 
viz. y0, k and t is given by, 
1yy
0
                   (7) 
 
tky                   (8) 
 
tk21ty
              (9) 
 
As we have 3 unknowns the size of the Jacobian matrix is 3X3 as shown below, 
 41 
t
y
k
y
y
y
t
y
k
y
y
y
t
y
k
y
y
y
J
33
0
3
22
0
2
11
0
1
                              (10) 
 
3.6 Case Study: Prognostication of Life Consumed Due to Steady State Aging 
The primary objective of this case study was to develop and implement the 
prognostic model for the life prediction of electronics subjected to isothermal aging 
environments. The model has been implemented on the test vehicle discussed in the 
previous section. Case study has been divided into two parts viz. IMC growth 
measurement and analysis followed by implementation of the PHM model for 
prognostication of life using IMC growth as the leading indicator of failure.  
3.6.1 Inter-Metallic Compound (IMC) Growth Measurement and Analysis 
For this a condition monitoring cell was created consisting of 100 CABGA 
packages with SAC 105 and SAC 305 solder alloys. This condition monitoring cell was 
subjected to several hours of isothermal aging at 125?C to study the damage progression 
in steady state thermal environments. The aged components were withdrawn at regular 
intervals of aging time to measure the intermetallic compound growth at board side 
copper interface. The withdrawn samples were cross-sectioned, potted using epoxy resin 
and finely polished using grinding papers and collidal silica solution so that the inter-
metallic layer was clearly visible under the microscope. Figure 10 and Figure 11 show 
SEM backscattered images exhibiting examples of IMC growth with aging time for 100 
I/O, BGA solder ball for SAC 105 and SAC 305 solder alloys respectively. The IMC 
 42 
thickness has been measured in commercial image processing software using these SEM 
images. It is evident from the SEM images that the IMC thickness tends to grow as the 
electronic packages are exposed to long durations of thermal aging. The IMC growth has 
been plotted against aging time for both SAC 105 and SAC 305 solder alloys as shown in 
Figure 12 and Figure 13. The trend analysis does show a square root dependence of IMC 
growth over time as mentioned in the previous section.  
 
Figure 10: SEM Back-scattered images of IMC Growth versus Thermal Aging for 
Sn1Ag0.5Cu (SAC 105) (Magnification 1000x) 
 
 43 
 
Figure 11: SEM Back-scattered images of IMC Growth versus Thermal Aging for 
Sn3Ag0.5Cu (SAC 305) (Magnification 1000x) 
 
 44 
Time, hr^0.5
0 10 20 30 40 50 60 70
IMC Thickn
ess (y-y
0
) (in 
m)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
SA C 10 5
(y -y
0
)=k (t)
0 .5
k = 0.022 6
 Figure 12: IMC Growth, at various levels of time for CABGA 100 with Sn1Ag0.5Cu 
alloy (SAC 105) 
 
Time ,  hr^0. 5
0 10 20 30 40 50 60 70
IMC Thic
kness
 (y-y
0
) 
(in 
m)
0
1
2
3
4
5
SA C 305
(y -y
0
) = k( t)
0.5
k = 0.079 4
 
 Figure 13: IMC Growth, at various levels of time for CABGA 100 with Sn3Ag0.5Cu 
alloy (SAC 305) 
 
3.6.2 Life Prediction using PHM Model 
Test assemblies were subjected to unknown hours of isothermal aging and the 
consumed life was predicted using the framework summarized in Figure 14. Two aging 
times have been prognosticated to prove the viability of the PHM model.  
 45 
 
Figure 14: Prognostication Approach 
 
As IMC growth has been used as the leading indicator of failure in the model, we 
need 3 equations to solve 3 unknown?s viz. y0, k and t as explained in the earlier section. 
In order to solve 3 unknowns we need 3 equations and hence the test assembly has to be 
subjected to additional (known) hours of aging at 125?C. Therefore to prognosticate two 
unknown aging time t1 and t2, some of the 100 CABGA packages from the condition 
monitoring cells were subjected to additional 667 hours and 1333 hours of aging as 
shown in Figure 14. The packages were cross sectioned for IMC growth measurement at 
each interval and the following sets of equations were solved using Levenberg-Marquardt 
algorithm to compute t1 and t2 respectively. 
 46 
101 tky)y ( t                                        (11) 
667tky667)y ( t 101         (12) 
1 3 3 3tky1 3 3 3 )y ( t 101     (13) 
 
202 tky)y ( t                                       (14) 
6 6 7tky6 6 7 )y ( t 202         (15) 
1333tky1333)y ( t 202     (16) 
 
Figure 15 and Figure 17 shows the model outputs for t1 and t2 respectively for 
SAC 105 CABGA 100 test vehicle. Similarly Figure 16 and Figure 18 show the model 
outputs for t1 and t2 respectively for SAC 305 CABGA 100 test vehicle. It?s a 2D plot of 
error Vs aging time in hours. Each and every blue dot in the solution space represents the 
solution of a non-linear set of equations. Levenberg-Marquardt algorithm iteratively 
minimizes the error in the solution space and selects the final solution corresponding to 
the minimum error indicated by red dotted line in all the figures. Thus for the 
experimental value of 667 hours, proposed prognostic model predicts 621 hours for SAC 
105 CABGA 100 test vehicle (Figure 15) and 625 hours for SAC 305 CABGA 100 test 
vehicle (Figure 16). It should be noted that similar 2D plots can be graphed for the rest of 
the unknown?s y0 and k respectively. However as aging time is the most important 
unknown of all and as life prediction has been the chief scope of this thesis only plots 
pertaining to aging time are retained, although model results for other unknowns have 
been documented in the subsequent validation section. 
 47 
 
Figure 15: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn1Ag0.5Cu Solder Alloy Interconnects 
 
 
 
Figure 16: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn3Ag0.5Cu Solder Alloy Interconnects 
 48 
 
Figure 17: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn1Ag0.5Cu Solder Alloy Interconnects 
 
 
 
 
Figure 18: Global Minima for IMC based History Calculation for 100 I/O CABGA, 
Sn3Ag0.5Cu Solder Alloy Interconnects 
 
 
 49 
3.6.3 Model Validation 
Life predicted from the proposed prognostic model has to be checked to study the 
errors associated with the model. For this model predictions have been correlated with the 
actual experimental data in this section. Although only the plots corresponding to aging 
time t are presented in the previous section, but, all the three unknowns have been 
compared with the experimental values to check individual errors. Two different aging 
time intervals have been prognosticated and correlated with the experimental data to 
examine the robustness of the prediction model. Table 3 correlates the model results with 
the experimental values for all the three unknowns. Error has been computed for all the 
three unknowns with respect to the experimental values to gain more insight on how 
individual unknowns are predicted by the prognostic model. 
Table 3: Comparison of computed values of t, y0 and k from prognostication model and 
experimental result 
 
Solder 
Interconnect 
Aging Time t (hrs) Initial IMC y0 (?m) Constant k 
EXPT MODEL ERROR EXPT MODEL ERROR EXPT MODEL ERROR 
SAC 105 667 621 6.9 % 2.89 2.82 2.4 % 0.0226 0.0258 14.2 % 
1333 1395 4.7 % 2.89 2.69 6.9 % 0.0226 0.0215 4.8 % 
SAC 305 667 625 6.3 % 2.68 3.03 13 % 0.0794 0.0790 0.5 % 
1333 1320 0.98 % 2.68 2.28 14.9 % 0.0794 0.0781 1.6 % 
 
The model predictions for unknown t for both the time intervals and solder 
interconnect lay in the range of 1 % to 7 % which is very good from a life prediction 
model perspective. Initial IMC y0 predicted by the model for SAC 105 interconnects is 
better than that for SAC 305 solder interconnects which is in the range of 13 % to 15 %. 
As for constant k error envelope is in the range of 1.6 % to 15 % for both the solder 
 50 
interconnects. As the model results are directly dependent on the input guess values for 
each unknown, one way of reducing the individual errors is by expanding the guess 
values for each unknown. However this has a direct impact on the computational 
efficiency. So like any other life prediction model it is a trade off between the appetite for 
risk and computational capability. 
The other interesting finding was that the IMC thickness calculated from the 
prognosticated values of y0 and k correlate well with the measured experimental value. 
The primary reason for this correlation was to find out how well the extrapolated IMC 
thickness match with the actual experimentally measured IMC thickness so that the 
extrapolated value can be used for further life predictions. This by passes the need to 
cross section the samples in real time for IMC measurement which can be thought of as a 
big leap forward in the implementation of the proposed PHM model. Figure 19 and 
Figure 20 shows the correlation plots for SAC 105 and SAC 305 solder interconnects 
respectively. 
 51 
IM C Thic kness Vs T im e  f or  SAC  1 05  
Ti m e  ( hour s)
0 500 1000 1500 2000 2500 3000 3500
IM
C 
Thic
kness 
(i
n 
m
)
0
1
2
3
4
5
Expe rim en tal
Algo rith m
 
Figure 19: Computation of IMC Thickness (based on prognosticated y0 and k) vs. IMC 
from experimental values for 98.5Sn1.0Ag0.5Cu alloy 
IM C Thic kness Vs T im e  f or  SAC  3 05  
Ti m e  ( hour s)
0 500 1000 1500 2000 2500 3000 3500
IM
C 
Thic
kness 
(m
ic
r
ons)
0
2
4
6
8
Expe rim en tal
Algo rith m
 Figure 20: Computation of IMC Thickness (based on prognosticated y
0 and k) vs. IMC 
from experimental values for 96.5Sn3.0Ag0.5Cu alloy 
 
 
 52 
3.7 Conclusion 
In this chapter a prognostic health management model was developed and 
successfully implemented on electronic components exposed to single isothermal aging 
environments for accurate life prediction. It has been shown that the physics-of-failure 
based damage proxy identified as inter-metallic compound (IMC) growth, formed 
between the second level solder interconnect and copper pad at the board side interface 
can be used as a leading indicator of failure. Levenberg-Marquardt algorithm which has 
been as used as a non-linear least square method in this model has been explained in 
detail followed by its application to this particular problem. A comprehensive 
methodology has been explained through prognostication equations at each step for easy 
understanding. The practicality of this model has been demonstrated in the form of a 
detailed case study on the commercially available packaging architecture with lead-free 
SAC solder interconnects. The model predictions have been compared with the 
experimental results for multiple aging time intervals to study the robustness of the 
proposed model.  The correlations indicate that the proposed PHM model can be used to 
interrogate the system state and thus estimate the residual life of a electronic component. 
The prognostic model finds its application in a real world setting where one has to 
find the remaining useful life of the electronic system in the same isothermal 
environment well before the actual failure occurs i.e. in the pre-failure space without any 
knowledge of prior stress histories. In such scenario the proposed prognostic model can 
be implemented using condition monitoring devices which would be used to interrogate 
the damage progression in the form of IMC growth data. This data can be fed to the 
Levenberg-Marquardt algorithm developed for this model for accurate life predictions.  
 53 
CHAPTER 4
PROGNOSTIC MODEL FOR THE QUANTIFICATION OF REDUCTION IN CYCLIC 
LIFE DUE TO LONG-TERM DORMANT STORAGE 
 
4.1 Introduction 
Electronic systems are often stored for a very long time before they are deployed 
in the intended environment. It is extremely important to quantify the expended life 
during storage especially for electronic systems used in mission critical applications. 
Although ambient temperature storage does not lead to any macro indicators of failure 
like cracks or de-lamination but it is well known that aging has an adverse effect on the 
life of electronics. Thus the primary objective of the presented PHM framework is to 
account for the damage incurred during dormant storage and map this damage in terms of 
life in the intended environment without any knowledge of prior stress history. 
Applications for the presented PHM framework include defense applications such as 
avionics systems, naval electronic warfare systems wherein the electronics is subjected to 
thermo mechanical loading after long term dormant storage.   
In this chapter a PHM model has been developed and implemented for the 
interrogation of system state and life estimation for sequential thermo-mechanical 
stresses. Dormant storage has been simulated by isothermal aging environment as 
typically electronics are stored in a temperature controlled storage facilities before field 
deployment. Field application has been simulated by a conventional harsh thermal cyclic 
 54 
environment used for reliability qualification under accelerated stress testing. Two 
physics-of-failure based damage proxies of second level solder interconnect have been 
examined and incorporated in this prognostic model. Damage proxies have been 
extracted and analyzed for isothermal aging, thermal cycling and combination of aging + 
cycling to study their dame progression in single and sequential thermo-mechanical stress 
scenarios. Measured damage proxies have been identified as the leading indicators of 
failure and have been used for damage mapping as well as prognostication of life in 
multiple thermal environments of thermal aging and thermal cycling. Life has been 
prognosticated using Levenberg-Marquardt algorithm discussed in the previous chapter. 
Model predictions have been validated using another set of experimental results. As this 
model incorporates two damage proxies, standard prognostic metrics such as (?-?) curve 
have also been evaluated to study the relative performance of both the damage proxies 
with respect to life prediction. 
4.2 Test Vehicle  
Test vehicle used for the development and implementation of the prognostic 
model is plastic ball grid array (PBGA) type area array package with 676 I/O?s assembled 
on a FR4 printed circuit board with Sn3.0Ag0.5Cu (SAC 305) solder paste. PBGA 676 
package was chosen for this study because typically this kind of high I/O packaging 
architecture serves as the primary component on the commercially offered electronic 
systems such as engine control unit installed in today?s automobiles. PBGA 676 
electronic package with SAC 305 solder balls was imported from practical components. 
It is a AMKOR dummy component as shown in Figure 21. The package attributes have 
been summarized in Table 4. SAC 305 solder alloy composition was selected as it has 
 55 
been a major contender for interconnecting small form factor type components due to its 
acceptable mechanical properties in harsh thermal applications and ready availability. 
SAC 305 solder paste was imported from Multi-CoreTM. Test vehicle was assembled at an 
in-house SMT laboratory at Auburn University. The novelty in this test vehicle is that 
custom PCB?s were designed to accommodate 4 daisy chain patterns instead of 
conventional 1 daisy chain pattern for resistance monitoring. The primary reason for 
incorporating this change was for effective fault detection and isolation followed by 
systematic failure analysis.  
     
Figure 21: PBGA 676 Front and Back Side 
 
 
Table 4: Package Architecture Details 
 
Solder Sn3Ag0.5Cu 
Package Size (mm) 27 x 27 
Package Type PBGA 
I/O Count 676 
I/O Pitch (mm) 1 
Ball Diameter (mm) 0.63 
Mold thickness (mm) 1.17 
Substrate Pad  SMD 
 
 
 
 56 
4.2.1 Custom PCB Design 
The first step in PCB footprint design to create 4 daisy chains was to check the 
component side daisy chain pattern. For this PBGA 676 daisy chain pattern was 
downloaded from practical components website as shown in Figure 22. The 4 daisy 
chains were laid out into 4 quadrants as shown in Figure 23. As we do not have any 
control over the component side daisy chain pattern the only way of creating 4 daisy 
chain patterns was to route copper traces on the PCB footprint such that we get 4 daisy 
chain quadrants as shown in Figure 24. If the component side daisy chain and the board 
side daisy chain are overlaid the 4 daisy chain pattern is vividly seen as shown in Figure 
25. PCB footprint was created in ExpressPCB software for JEDEC size board 132 mm X 
77 mm. This design was sent out to a PCB manufacturing vendor for manufacturing. The 
actual PCB with PBGA 676 footprint for 4 daisy chain patterns is shown in Figure 26. 
The printed circuit board pads were solder mask defined (SMD) with immersion silver 
finish. 
 57 
 
Figure 22: PBGA 676 Component Side Daisy Chain Courtesy: Practical Components  
                                        
  
Figure 23: 4 Daisy Chain Schematic 
 58 
 
 
 
Figure 24: ExpressPCB Snapshot for PBGA 676 Daisy Chain Pattern 
 
 
  
Figure 25: Component Side Daisy Chain (BLACK) and Board Side Daisy Chain (GRAY) 
Overlaid to Show 4 Daisy Chain Patterns 
 59 
 
  
Figure 26: Actual PCB with PBGA 676 Footprint Accommodating 4 Daisy Chain 
Patterns 
 
Once the custom PCBs were manufactured multiple sets of test vehicles were 
assembled in-house at NSF CAVE3 SMT laboratory. Stencil for solder printing was 
obtained from practical components. Manncorp SP-5500 machine was used for SAC 305 
solder paste printing, manual pick and place was used for placing PBGA 676 package 
onto PCB (Manncorp optical Mounter (FP-100)) and the assembly was reflowed in a 
single stage lead free convection reflow oven (X-Reflow 306 LF). Different reflow 
profiles were designed and tested on dummy assemblies to ensure high quality finished 
boards. After multiple trials the profile shown in Figure 27 was used to reflow multiple 
sets of test vehicles. The final board after reflow is shown in Figure 28. The daisy chain 
resistance was measured on all the 4 quadrants after reflow to check for manufacturing 
failures and defects such as warpage during high temperature reflow and misalignment 
 60 
during print and place. Also solder joints were inspected under optical microscopes after 
each reflow to check the integrity of the joints. 
R e f l o w  P r o f i l e
0
50
100
150
200
250
300
0 5 10 15 20
T i m e  i n  m i n u t e s
T
e
m
p
e
r
a
t
u
r
e
 i
n
 ?
C
 
Figure 27: Reflow Profile for SAC 305 Solder  
 
 
Figure 28: Test Vehicle 
 
 
 
 61 
4.2.2 Test Conditions 
Three different condition monitoring cells were created viz. CM#1, CM#2 and 
CM#3 as summarized in Table 5. Test vehicles in CM#1 were subjected to air to air 
thermal cycling (AATC) from ?55?C to 125?C and the damage proxies were extracted at 
different cycling intervals. Thermal cycling profile is shown in Figure 29. It is a hundred 
minutes cycle with 15 minute dwells at each extreme. The ramp up time is 25 minutes 
and is less than ramp down time which is 45 minutes as in AATC the thermal chamber 
takes more time to attend sub-zero temperatures. In CM#2 test vehicles were subjected to 
isothermal aging at 125?C and the damage proxies were extracted at different aging 
times. Test vehicles in CM#3 were subjected to some combination of isothermal aging 
and thermal cycling for the assessment of residual damage in sequential thermo-
mechanical environments followed by prognostication of life in such complex 
environments.  
Table 5: Condition Monitoring Cells 
 
Condition 
Monitoring Cell 
Thermal Cycling 
(-55?C to 125?C) 
Isothermal Aging 
(125?C) 
Isothermal Aging 
 +  
Thermal Cycling 
CM # 1 ? ? ? 
CM # 2 ? ? ? 
CM # 3 ? ? ? 
 62 
 
Figure 29: Thermal Cycling Profile 
 
4.3 Leading Indicators of Failure 
The change in solder microstructure and its derivatives have been used as the 
leading indicators of failure for electronics subjected to multiple thermal environments of 
thermal aging and thermal cycling. The core function of any prognostic health 
management model is to detect fault in the system and compute residual life at any given 
time. Typically fault detection involves interrogation of system state for physics-of-
failure (POF) based damage proxies that provide information about the ongoing damage 
and impending failure. These damage proxies are classified as the leading indicators of 
failure and are used in a PHM model development which directly or indirectly relate to 
the overall life of the system. There are two damage proxies used in this model which are 
based on the micro-structural evolution of second level solder interconnects. The first 
damage proxy has already been discussed in the previous chapter called the IMC growth 
which is formed at the board-side copper pad solder ball interface as shown in. This 
damage proxy has been used as the leading indicator of failure for the prognostic model 
development in Chapter 3. The same proxy has also been used in this model. The damage 
proxy extraction and analysis details can be referred in Chapter 3.3. 
 63 
 
Figure 30: IMC Growth as the Leading Indicator of Failure 
 
4.3.1 Phase-Growth as the Leading Indicator of Failure 
 
Temperature excursions during operation of an electronic circuit are due to both 
power-cycling and variations in ambient conditions resulting in thermo-mechanical cyclic 
stresses and strains induced primarily by thermal expansion mismatch between the 
package and the board assembly.  Previous researchers have studied the micro structural 
evolution of ternary SnAgCu alloys at elevated temperatures using bulk real solder joints 
with different designs, geometry and process conditions. The SnAgCu microstructure 
comprises Ag3Sn and Cu6Sn5 dispersed within the tin matrix as shown in Figure 31. The 
relatively low percentage of alloying elements, 1-4% for Ag and 0.5% for Cu results in 
phases which comprise a small percentage of the total volume within the solder joint. The 
microstructural evolution of SnAgCu alloys over time has been found to affect the 
thermo-mechanical properties and damage behavior [Ye 2000, Allen 2004a, b, Kang 2004, 
Xiao 2004, Henderson 2004, Kang 2005, Korhonen 2006, Jung 2001].  
 64 
 
Figure 31: Ag3Sn Grains in 95.5Sn4.0Ag0.5Cu solder microstructure 
 
Micro-structural coarsening during thermo-mechanical deformation is attributed 
to the generation of excess vacancies caused by the combined effect of local hydrostatic 
state of stress, and the instantaneous inelastic strain rate [Dutta 2003a, 2003b, 2004; Jung 
2001].  Evolution of solder microstructure in 63Sn37Pb and lead-free chip resistor solder 
joints due to thermal fatigue have been studied previously by previous researchers 
[Sayama, et al. 1999, 2003] and thermal fatigue correlated with occurrence of micro-
structural coarsening in the fatigue damaged region in of 63Sn37Pb solder interconnects 
[Frear 1990, Morris 1991].  Correlation of grain coarsening with thermal fatigue has also 
been established for high-lead solders [Bangs 1978, Wolverton 1987, Tribula 1989].  
Previously the phase-size evolution and derivatives of phase growth rate have been 
investigated and classified as prognostics parameters on a wide range of leaded and 
Sn4Ag0.5Cu devices in underhood applications [Lall 2004b, 2005, 2006a,b, 2007a,b]. 
Phase growth under thermal cycling and thermal aging has been identified as the 
damage precursor to compute the residual life.  The relation between phase growth 
parameter and time for polycrystalline material is given by [Callister 1985]. 
 65 
Ktgg n0n                                          (17) 
Where g is the average grain size at time t, 0g  is the average grain size of solder after 
reflow, K and n (varies from 2 to 5) are time independent constants. Senkov and Myshlev 
[1986] applied the theory of phase growth process in a super plastic alloy and validated 
the theory for Zn/Al eutectic alloy. They expressed the phase growth parameter S as: 
 
KtggS 404                                   (18) 
The exponent value of 4 indicates that the phase coarsening kinetics is primarily due to 
grain boundary sliding under thermo-mechanical loading studied by [Allen 2004]. 
Previously, it has been shown that the rate of change in phase growth parameter 
[d(lnS)/d(lnN)] is valid damage proxy for prognostication of thermo-mechanical damage 
in solder interconnects and assessment of residual life [Lall 2004a, 2005a, 2006c,d, 
2007c,e, 2008c,d, 2009c,d]. The damage proxy [d(lnS)/d(lnN)] is related to the micro-
structural evolution of damage by the following equation: 
b404 a ( N )ggS                                  (19) 
Where g is the phase size measured after N number of thermal cycles, g0 is the phase size 
measured after reflow, a and b are the constant and exponents respectively. The log-plot 
of the equation provides a straight line relationship between the phase growth parameter 
and the number of cycles. 
l n ( N ) b aln)ggl n (l n ( S ) 404       (20) 
 
bd[ln(N)]d[ln(S)]                                                           (21) 
 
 66 
b404 a( t)ggS           (22) 
 
It should be noted that the same equation is valid for the solder alloys subjected to 
thermal aging as shown in b404 a( t)ggS           (22 since the fundamental physics 
of phase coarsening remains the same. 
4.3.2 Phase-Growth Measurement  
The phase size is measured by cross-sectioning the samples after thermal cycling 
or thermal aging. The cross-sectioned samples are potted using resin and hardener to 
form an epoxy. The samples are finely polished using different levels of grinding papers 
and colloidal silica solution so that the Ag3Sn phases are clearly visible. Cross-sectioned / 
polished samples are then gold sputter coated so as to take SEM images at 750x 
magnification to measure the growth rate of tin and Ag3Sn phases. Phase size is 
measured using SEM and image analysis. For this the SEM images are cropped in a 
60?m X 45?m window (Figure 32) and are converted into a gray scale images as shown 
in Figure 33. Image processing software called NI-IMAQ Vision Builder is used to 
measure the average phase size. 
 
Figure 32: SEM Image for Phase-Growth Analysis 
 67 
 
Figure 33: Phase Size Measurement using NI-IMAQ 
 
4.4 Concept of Sequential Thermal Aging and Thermal Cycling 
In the real world application not all the electronics that is manufactured on SMT 
assembly line is deployed in the field right away. Most electronic systems are often 
stored for some amount of time before their application in the field environment. As 
aging has an adverse effect on the life of electronics it is extremely important to account 
for the damage incurred due to storage before the deployment to determine the 
operational readiness of the system and compute remaining useful life in the intended 
field. In thermal cyclic field applications, life of the electronic system is measured in 
terms of number of thermal cycles it has been exposed to. However life in thermal aging 
environment is always measured in time scale i.e. number of hours, days, weeks or 
months. So it becomes all the more difficult to relate two different measuring scales, i.e. 
time for aging and number of thermal cycles for thermal cycling to quantify and map the 
life consumed due to aging onto the thermal cyclic field. 
Figure 34 depicts the concept of storage and deployment encountered in the real 
world application. Here the storage and field application have been replicated by 
isothermal aging and thermal cycling respectively. In order to account for life expended 
due to aging, the life in terms of number of hours ?t? has to be converted to life in terms 
of number of cycles ?N? due to the difference in the life measuring scales for two 
 68 
environments as shown in Figure 35. Therefore in order to develop the damage mapping 
relationship between number of hours and number of cycles, test vehicles have been 
subjected to isothermal aging and thermal cycling respectively to plot damage vs number 
of hours and damage vs number of cycles as shown in Figure 36. 
 
Figure 34: Concept of Sequential Thermal Aging and Thermal Cycling 
 
 
Figure 35: Mapping Reduction in Life Due to Dormant Storage. 
 69 
  
Figure 36: Accrued Damage Due to Thermal Aging and Thermal Cycling respectively. 
 
4.5 Concept of Damage Equivalency Based Mapping 
Figure 37 shows the schematic of damage equivalency based mapping of life 
consumed due to aging in terms of number of cycles. It is a combined plot of normalized 
phase growth (SN) as a damage parameter on the vertical axis vs. life on the horizontal 
axis (in terms of time?t? for aging and in terms of number of cycles ?N? for cycling). The 
relationship between time t and number of cycles N can be developed based on the 
concept of damage equivalency by keeping the damage parameter S constant. It should be 
noted that the difference in the slopes of the two lines (S vs. t and S vs. N) is because of 
the different magnitudes of damage incurred due to thermal cycling and thermal aging. It 
has been previously observed that the phase growth parameter increases more rapidly in 
thermal cycling than in thermal aging. 
In the schematic, point ?A? can be thought of as the cross-over point where the 
electronic system comes out of storage and is ready for deployment. Thus it is essential to 
find the life consumed during this storage i.e. until point ?A?. The damage parameter viz. 
phase growth parameter SA can be measured at point A or in other words at the end of 
storage. This damage parameter SA can be mapped back on the thermal cycling curve 
 70 
(marked by point B) that corresponds to SB to find the equivalent number of cycles NB. 
The horizontal projection of damage parameter from point A to point B marked by black 
solid line does not incur any new damage which implies that SA = SB which is also 
evident from the schematic. Thus NB is the life consumed due to storage in terms of 
number of cycles based on the concept of damage equivalency. In other words it takes NB 
number of cycles in thermal cycling environment to accrue same amount of damage (SA) 
that was incurred due to tA hours of thermal aging. 
 
Figure 37: Concept of Damage Equivalency and Mapping of Life Consumed Due to 
Storage. 
 
4.6 Case-Study: Prognostication of Life of Electronics Subjected to Sequential 
Stresses 
 
The case study has been divided into two sections for lucid understanding. The 
first section is an experimental part where the damage equivalency based relationships 
have been established to account for life consumed due to storage using two damage 
 71 
proxies. In the later prognostication section the life consumed in sequential thermo-
mechanical environments of thermal aging and thermal cycling has been computed and 
validated using the developed experimental relationships to study how close the model 
accounts for the life expended due to thermal aging. 
4.6.1 Damage Equivalency Relationship between Thermal Aging and Thermal 
Cycling 
The test vehicles have been subjected to thermal aging and thermal cycling 
respectively to establish damage mapping relationship between number of cycles and 
aging time. Later in the prognostication section test vehicles have been exposed to some 
combination of aging + cycling. The function of each condition monitoring cell has been 
summarized in Table 5. One test vehicle was cross-sectioned and polished right after 
reflow to measure damage proxies in the pristine condition i.e. un-aged / un-cycled or 0 
hours of aging / 0 number of cycles. 
It should be noted that as it is a multiple thermal environment problem wherein 
the damage mapping relationships have been established based on two damage proxies 
the fundamental equations for phase-growth and IMC growth have been normalized with 
respect to initial phase-size and initial IMC respectively. This has been done for better 
representation of equations. If we look at the equation of phase-growth the only variable 
which is independent of thermal cycles N or aging time t is the initial phase-size g0 as 
shown in b404 a ( N )ggS      (23 and b404 a( t)ggS        (24.  
b404 a ( N )ggS      (23) 
 
b404 a( t)ggS        (24) 
 
 72 
Similarly for the IMC equation y0 is the only variable which does not depend on aging 
time t or thermal cycles N as shown in m0 k(t)yy               (25 
and m0 k(N )yy            (26. 
m0 k(t)yy               (25) 
 
m0 k(N )yy            (26) 
 
As both the damage proxies have been extracted and analyzed for both thermal 
cycling and thermal aging normalization of these equations with respect to g0 / y0 
eliminates any ambiguity about the damage proxies in thermal aging and thermal cycling 
environments. The normalized equations used for the damage mapping as well as 
prognostication of life in sequential thermal environments of thermal aging and thermal 
cycling are of the form shown in 
TNbTN
4
0
TN ( N )a1g
gS
  (27, 
NtbNt
4
0
Nt ( t )a1g
gS
              (28, 
NtmNt
0
t)(k1yy
                                  
(29 and
TNmTN
0
( N )k1yy
                       (30. 
 TNb
TN
4
0
TN ( N )a1g
gS   (27) 
 
Where SN?T: Normalized phase-growth parameter during thermal cycling 
 73 
                 g: Phase-Size measured after N number of thermal cycles 
                g0: Initial phase size 
            aN?T: Normalized phase-growth coefficient during thermal cycling 
           bN?T: Normalized phase-growth exponent during thermal cycling    
NtbNt
4
0
Nt ( t )a1g
gS               (28) 
Where SNt: Normalized phase-growth parameter during thermal aging 
               g: Phase size measured after t hours of thermal aging 
             g0: Initial phase size 
            aNt: Normalized phase-growth coefficient during thermal aging 
           bNt: Normalized phase-growth exponent during thermal aging 
 
NtmNt
0
t)(k1yy                                   (29) 
Where y: IMC growth measured after t hours of thermal aging 
          y0: Initial IMC growth 
       kNt: Normalized IMC growth coefficient during thermal aging 
      mNt: Normalized IMC growth exponent during thermal aging (mNt=0.5) 
 
TNmTN
0
( N )k1yy                        (30) 
Where y: IMC growth measured after N number of thermal cycles 
          y0: Initial IMC growth 
       kN?T: Normalized IMC growth coefficient during thermal cycling 
      mN?T: Normalized IMC growth exponent during thermal cycling 
 
Analysis of Damage Proxies in Thermal Cycling 
 74 
Condition monitoring cell CM #1 was populated with 7 custom designed PBGA 
676 test vehicles which were subjected to thermal cycling from -55?C to 125?C. Each of 
the 7 test vehicles were withdrawn at an interval of 100 cycles for damage proxy 
measurement and analysis. After every 100 cycles the packages were cross-sectioned and 
polished to measure two damage proxies? discussed in Chapter 4.3 viz. inter-metallic 
compound (IMC) and phase-growth. The primary objective of analyzing 7 samples was 
to study the damage progression of each damage proxy in thermal cycling. Figure 38 and 
Figure 39 show phase-growth and IMC growth evolution over number of cycles. It is 
evident from these figures that as the packages are exposed to more number of thermal 
cycles both the damage proxies evolve over time. The phase growth coarsens from 0 
cycles to 700 cycles while there is an obvious increase in IMC growth from 0 cycles to 
700 cycles.  
Normalized phase-growth and IMC growth have been plotted against number of 
cycles to study the damage progression. The log plots shown in Figure 40 and Figure 41 
indicate linear relationship between the individual damage proxies with respect to 
number of thermal cycles. The actual equations are shown below. 
0 . 7 8TN N)(015.0S                          (31) 
 
0 . 8 1
0
0 .0 1 9 9 ( N )1yy          (32) 
 75 
 
Figure 38: SEM backscattered images of Phase growth versus number of cycles (Thermal 
cycling -55?C to 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, magnification 750x) 
 
 
Figure 39: SEM backscattered images of IMC growth versus number of cycles (Thermal 
cycling -55?C to 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, magnification 1000x) 
 
 
 76 
 
Figure 40: Plot of Normalized Phase growth versus No. of Cycles for 96.5Sn3.0Ag0.5Cu 
solder, 676 PBGA, subjected to thermal cycling from -55?C to 125?C 
 
 Figure 41: Plot of Normalized IMC growth versus No. of Cycles for 96.5Sn3.0Ag0.5Cu 
solder, 676 PBGA, subjected to thermal cycling from -55?C to 125?C 
 
Analysis of Damage Proxies in Thermal Aging 
 77 
To study damage progression in isothermal aging environment condition 
monitoring cell CM #2 was created consisting of 7 PBGA 676 test vehicles similar to CM 
#1. The test vehicles were placed in a thermal oven and were allowed to age at steady-
state 125?C. The packages were withdrawn after every 48 hours interval for damage 
proxy analysis. Packages were cross-sectioned and polished followed by SEM imaging 
for the extraction of both the damage proxies. The extracted damage proxies were 
analyzed to examine their behavior in isothermal aging environment. Figure 42 and 
Figure 43 show the damage progression of phase-growth and IMC growth respectively as 
a function of aging time. It is quiet evident from these figures that both the damage 
proxies evolve due to isothermal aging. The micro-structure coarsens in the bulk solder 
while the inter-metallic thickness at the board side copper interface grows rapidly as a 
function of aging time. 
 
Figure 42: SEM backscattered images of Phase growth at different aging time intervals 
(Thermal aging at 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, magnification 
750x) 
 
 78 
 
Figure 43: SEM backscattered images of Intermetallic Thickness at different aging time 
intervals (Thermal aging at 125?C, 96.5Sn3.0Ag0.5Cu solder, 676 I/O PBGA, 
magnification 1000x) 
 
Normalized plots of phase-growth and IMC growth have been plotted against 
aging time as shown in Figure 44 and Figure 45. The log plots have been plotted to 
indicate a linear relationship between the damage progression and aging time for both the 
damage proxies. 
 79 
 
Figure 44: Plot of Phase growth versus Aging Time for 96.5Sn3.0Ag0.5Cu solder, 676 
PBGA, subjected to thermal aging at 125?C 
 Figure 45: Plot of IMC growth versus Aging Time for 96.5Sn3.0Ag0.5Cu solder, 676 
PBGA, subjected to thermal aging at 125?C 
 
The equations of normalized phase growth and IMC growth as a function of aging 
time are shown below. 
 80 
0 .4 9Nt t)(0 2 9 7.0S              (33) 
 
0 . 5
0
0 .0 4 4 ( t )1yy    (34) 
 
Relationship between number of cycles N and aging time t 
The relationship between the aging time and number of cycles has been derived 
using both normalized phase growth and normalized inter-metallic compound (IMC) 
growth. Both the damage proxies have been used to establish this relationship to capture 
the true life consumed due to aging and thus eliminate any error contribution from 
individual damage proxies. 
In Figure 46 normalized phase-growth has been plotted against aging time and 
number of cycles. The plot has two x-axes viz. time in hours and number of cycles. It 
should be noted that aging time is for isothermal exposure of 125?C while the number of 
cycles are corresponding to the thermal cycle ranging from -55 ?C to 125 ?C. It is evident 
from Figure 46 that same amount of phase coarsening or phase-growth can be obtained 
by exposure to either thermal cycling or thermal aging. This is the underlying theory of 
damage equivalency which enables to establish a relationship between two different time 
scales i.e. number of cycles and aging time. Thus if we equate 0 . 7 8TN N)(015.0S                          
(31 and 0 .4 9Nt t)(0 2 9 7.0S              (33 based on the concept of damage equivalency 
for the same normalized phase-growth parameter we get the relationship between number 
of cycles and aging time ( 0.63t)(40.2N                                  (37) as follows, 
NtTN SS                                      (35) 
 81 
0 . 490 . 78 t)(0 2 9 7.0N)(0 1 5.0        (36) 
 
0.63t)(40.2N                                  (37) 
 
 
Figure 46: Combined plot Normalized Phase growth versus thermal aging time and 
thermal cycling 
 
Similar relationship can be derived using normalized IMC growth as the damage 
proxy. The primary reason for deriving the relationship using both the damage proxies is 
to validate the relationship and also examine if the fundamental damage mechanics holds 
true in complex thermal environments. To derive the relationship the normalized IMC 
thickness has been plotted for thermal cycling and thermal aging as shown in Figure 47. 
It is a combined plot of normalized IMC thickness vs. aging time and number of cycles 
where normalized IMC thickness in on y-axis while time in hours and number of cycles 
have been plotted on dual x-axes. 
 82 
 
Figure 47: Combined plot Normalized IMC growth versus thermal aging time and 
thermal cycling 
 
As the concept of damage equivalency holds true for this damage proxy as well 
same amount of IMC thickness can be achieved by either thermal cycling or thermal 
aging. Therefore if we equate 0 . 8 1
0
0 .0 1 9 9 ( N )1yy          (32) 
and
0 . 5
0
0 .0 4 4 ( t )1yy
   (34) we get a relationship between number of cycles and 
aging time ( 0 .6 2t)(6 7 5.2N                             (39) using normalized IMC thickness as 
the damage proxy. 
0 . 50 . 8 1 t)(0 4 4.0N)(0 1 9 9.0       (38) 
 
0 .6 2t)(6 7 5.2N                             (39) 
 
 83 
One of the vital observations that can be made from the combined plots of both 
the damage proxies vs. thermal cycling and thermal aging (Figure 46 and Figure 47) is 
the difference in the slopes for thermal cycling and thermal aging. It is evident from the 
combined plots that the damage accumulation and progression in thermal cyclic 
environment is faster than isothermal aging environment for both the damage proxies. 
This is because in thermal cycling the temperature ramps-up and down continuously 
which causes shearing of the solder joints due to CTE mismatch. Although creep which is 
a thermally activated phenomenon governs the plastic deformation in viscoplastic 
materials such as solders thermo-mechanical deformations due to low cycle thermal 
fatigue are dominant in thermal cyclic environments as compared to steady state 
isothermal aging environment. As the micro-structural evolution is directly proportional 
to these thermo-mechanical deformations both the damage proxies evolve relatively 
faster in thermal cyclic environments than in steady state thermal aging. 
 
Figure 48: Combine plot of No of Cycles (N) versus Time in hrs, due to damage mapping 
from Phase growth and IMC thickness. 
 
 84 
0.63t)(40.2N                                  (37and 0 .6 2t)(6 7 5.2N                             
(39 are plotted are in Figure 48. It is a plot of number of cycles vs. aging time using 
normalized IMC growth and normalized phase-growth. Both the curves marked by blue 
and red line follow similar exponential trend which help us conclude that the damage 
mapping is correct and can be used to computer life expended due to storage. It shows the 
influence of dormant storage on thermal cyclic life. Table 6 summarizes the cyclic life 
consumed in -55?C to 125?C thermal cycle due to isothermal aging 125?C for different 
aging time intervals using both the leading indicators of failure. Last row in the table 
indicates that the cyclic life reduces by 100 cycles when the electronics is stored for 336 
hours i.e. 14 days. This is a considerable amount of reduction in life due to storage which 
can not be neglected and have to be taken into account in the life prediction models for 
such complex environments.  
Table 6: Damage Mapping from Leading Indicators of Failure 
 
Time in 
Hrs 
Reduction in life 
from 
Normalized 
Phase Growth 
Reduction in 
life from 
Normalized 
IMC thickness 
growth 
48 28 29 
96 43 45 
144 55 58 
192 67 69 
240 77 80 
288 86 89 
336 93 98 
 
4.6.2 Prognostication of Life under Overlapping Stresses 
Condition monitoring cell CM #3 (Table 5) was created consisting of multiple 
PBGA 676 test vehicles and was subjected to two different combinations of thermal 
 85 
aging and thermal cycling viz. 48 hours in isothermal aging at 125?C followed by 100 
cycles in -55?C to 125?C thermal cycle and 192 hours in isothermal aging at 125?C 
followed by 100 cycles in -55?C to 125?C. Prognostication of life for two combinations 
of aging + cyclic exposure has been presented to demonstrate the viability and prove the 
robustness of the proposed prognostic model.  
The life in the sequential stress environment has been prognosticated in two ways 
to show the significance of dormant storage and its effect on the cyclic life. Life has been 
prognosticated at the end of storage as shown in Figure 49 and also after overlapping 
exposure as shown in Figure 50. Life in terms of number of hours in aging i.e. after 
storage has been computed using normalized IMC growth as the leading indicator of 
failure while total life consumed in overlapping environment has been computed using 
normalized phase-growth as the leading indicator of failure. 
 
Figure 49: Prognostication of Life Consumed Due to Aging in number of hours. 
 
 
 
Figure 50: Prognostication of Life in Overlapping Environment 
 
Normalized equation relating IMC growth with aging time is shown in Equation. 
3 equations are needed to solve 3 unknown?s y0, kNt and t. Thus to get 3 equations 
packages have been subjected to known additional hours of aging (t+?t and t+2?t) at 
 86 
125?C as depicted in Figure 49 followed by IMC growth analysis at each time interval 
(yt, yt+?t and yt+2?t). Levenberg-Marquardt algorithm explained in Chapter 3 has been 
used to solve the set of non-linear equations below (
tk1yy Nt
0
t
                    
(40, ttk1y
y
Nt0 tt       (41and t2tk1y
y
Nt0 t2t   (42). 
tk1yy Nt
0
t                     (40) 
 
ttk1yy Nt
0
tt       (41) 
 
t2tk1yy Nt
0
t2t   (42) 
 
Similarly normalized phase-growth parameter has been used as the leading 
indicator of failure to prognosticate total life in the overlapping stress environment i.e. 
aging followed by cycling. Levenberg-Marquardt algorithm explained in Chapter 3.5 has 
been used for the life prediction using normalized phase-growth as the leading indicator 
of failure. LM algorithm has been modified to take the phase-growth equations. As 
discussed earlier (Chapter 4.3) the generalized equation relating phase growth of the 
solder interconnect with number of cycles it has been subjected to is given by, 
b404 a(N )gg         (43) 
 
 87 
Where, ?g? is the grain size measured after N number of thermal cycles, ?g0? is the grain 
size measured after reflow, ?N? is the number of cycles the system is exposed to in a 
thermal cycling environment, and ?a? and ?b? are the constant and exponent respectively 
which take into account material and temperature reliant factors. The damage incurred 
after each cycle is reflected in the grain size of the solder which can be measured by 
cross-sectioning the sample and analyzing it using the image processing software. Thus 
in real time, without the knowledge of prior stress histories one can only find g in the 
above equation while rest of the variables g0, a, N and b are unknowns. 
The prognostic model predicts the number of cycles ?N? the system has been 
exposed to in a thermal cycling environment based on the real time grain size 
measurement ?g?. In order to compute number of cycles, the non-linear normalized phase 
growth equation has to be solved for the 4 unknowns viz. N, a, b and g0. To get 4 
equations to solve 4 unknowns the system has to be subjected to known additional 
number of cycling (N+?N, N+2?N and N+3?N) depicted in Figure 50, followed by 
grain size measurement gN+?N, gN+2?N and gN+3?N after each additional cycling 
respectively. 4 normalized equations solved using LM algorithm to compute N, g0, aN?T 
and bN?T are shown below. 
 88 
TNbTN
4
0
N ( N )a1gg                                   (44) 
 
TNbTN
4
0
NN N)(Na1gg                (45) 
 
TNbTN
4
0
N2N N)2(Na1gg            (46) 
 
TNbTN
4
0
N3N N)3(Na1gg            (47) 
 
The LM algorithm equation that iteratively minimizes the error in a multi-
dimensional solution space is given by, 
E-JhIJJ TT       (48) 
 
Thus the Jacobian matrix J ( 
 
b
g
N
g
a
g
g
g
b
g
N
g
a
g
g
g
b
g
N
g
a
g
g
g
b
g
N
g
a
g
g
g
J
444
0
4
333
0
3
222
0
2
111
0
1
             (53) for phase-growth as the leading indicator 
will be a (4X4) matrix as there are 4 unknowns. As Jacobian is a partial derivative of the 
 89 
governing equation with respect to each unknown sample individual components of the 
Jacobian matrix J are evaluated below. 
4
3b4
0
3
0
0 a ( N )g
g
g
g            (49) 
 
4
3b4
0
b
a ( N )g4
N
a
g            (50) 
 
4
3b4
0
b
a ( N )gN4
a b ( N )
N
g     (51) 
 
4
3b4
0
b
a ( N )g4
NNa l o g
b
g            (52) 
 
 
b
g
N
g
a
g
g
g
b
g
N
g
a
g
g
g
b
g
N
g
a
g
g
g
b
g
N
g
a
g
g
g
J
444
0
4
333
0
3
222
0
2
111
0
1
             (53) 
 
Prognostication Results and Validation 
Two combinations of sequential aging and cycling have been presented and 
prognosticated to demonstrate the influence of aging time on the cyclic life. The first 
combination is 48 hours in isothermal aging followed by 100 cycles in thermal cycling as 
shown in. Here the storage time or aging time is prognosticated using normalized IMC 
 90 
growth as the leading indicator of failure. For this some of the packages from CM #3 
after storage were subjected to known additional hours of aging to get 3 equations to 
solve 3 unknowns as shown in Figure 51. The IMC growth was extracted and analyzed 
after each additional aging interval respectively. 
 
Figure 51: Schematic for Prognostication of Storage Time (for 48 hours Experimental 
Exposure) 
 
Following three normalized IMC growth equations were solved using Levenberg-
Marquardt algorithm to compute t, kNt and y0. 
tk1yy Nt
0
t                   (54) 
 
48tk1yy Nt
0
48t   (55) 
 
96tk1yy Nt
0
96t   (56) 
 
Figure 52 shows the prognostication output for the life consumed due to storage. 
It is a 3D plot of number of hours in aging i.e. t, normalized IMC y/y0 and error. The 3D 
plot has been graphed to present how the error varies with respect to the two unknowns. 
 91 
It can be seen that Levenberg-Marquardt algorithm iteratively minimizes the error in the 
solution space. Each and every blue dot is a solution to the non-linear set of equations but 
only the solution corresponding to the minimum error marked by red dotted line is 
selected as the final answers. Thus for experimental value of 48 hours in isothermal 
aging, prognostic model predicted 46 hours in storage.  
 
Figure 52: 3D plot of error versus aging time in hours for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 48 hours in isothermal aging at 125?C. 
 
Total life in sequential stress environment of 48 hours in thermal aging followed 
by 100 cycles in thermal cycling has been prognosticated using normalized phase-growth 
as the leading indicator of failure. As Levenberg-Marquardt algorithm has to solve 4 
unknowns for phase-growth as the damage proxy some of the packages from CM #3 after 
were subjected to known additional number of cycles as shown in Figure 53 to get 4 
equations. 
 92 
 
Figure 53: Schematic for Prognostication of Total Life in Sequential Stress Environment 
(for 48 hours+100 Cycles Experimental Exposure) 
 
The set of normalized phase-growth equations solved to compute N, aN?T, bN?T and g0 are 
shown below,  
TNbTN
4
0
N ( N )a1gg                          (57) 
 
TNbTN
4
0
1 00N )1 0 0(Na1gg      (58) 
 
TNbTN
4
0
002N )2 0 0(Na1gg      (59) 
 
TNbTN
4
0
003N 00)3(Na1gg      (60) 
 
Figure 54 shows the prognostication output for total life consumed in the 
sequential stress environment. It is a 3D plot of number of cycles N, normalized phase-
growth g/g0 and error. Similar to previous output the 3D plot helps to comprehend the 
iterative minimization of error scheme adopted by LM algorithm for two unknowns. Thus 
in the sequential stress environment prognostic model predicted 143 cycles when 
 93 
experimentally packages were subjected to a combination of 48 hours in storage + 100 
cycles in operation.  
 
Figure 54: 3D plot of error versus number of cycles for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 48 hours in isothermal aging at 125?C 
followed by 100 cycles in -55?C to 125?C. 
 
Similar prognostication was carried out for packages subjected to 192 hours in 
isothermal aging followed by 100 cycles in cyclic thermal environment. The 
prognostication schematics for the life consumed due to storage and total life 
computation has been shown in Figure 55 and Figure 57. It should be noted that the 
prognostication equations solved to compute life in storage are similar to 
tk1yy Nt
0
t
                  (54
48tk1yy Nt
0
48t
  
 94 
(55
96tk1yy Nt
0
96t
  (56 while prognostication equations solved to 
compute total cyclic life are similar to 
TNbTN
4
0
N ( N )a1gg
                         
(57,
TNbTN
4
0
1 00N )1 0 0(Na1gg
     
(58,
TNbTN
4
0
002N )2 0 0(Na1gg
     
(59
TNbTN
4
0
003N 00)3(Na1gg
     (60. Prognostication outputs for life 
consumed due to storage and total life after sequential stress environments are shown in 
Figure 56 and Figure 58 respectively.  
 
Figure 55: Schematic for Prognostication of Storage Time (for 192 hours Experimental 
Exposure) 
 
 95 
 Figure 56: 3D plot of error versus aging time in hours for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 192 hours in isothermal aging at 
125?C. 
 
Figure 57: Schematic for Prognostication of Total Life in Sequential Stress Environment 
(for 192 hours+100 Cycles Experimental Exposure) 
 
 96 
 
Figure 58: 3D plot of error versus number of cycles for 676 PBGA 96.5Sn3.0Ag0.5Cu 
solder interconnects for experimental exposure of 192 hours in isothermal aging at 125?C 
followed by 100 cycles in -55?C to 125?C. 
 
Life computed at each stage i.e. after storage and after sequential stresses have 
been validated with the experimental values to study the errors associated with the 
prognostic model. Model predictions after storage for both the aging times have been 
validated in Table 7. Error is the in the range of 4 % to 7 % which is very good from a 
life prediction stand point. Error associated with the prognosticated reduction in cyclic 
life due to storage and experimental reduction in cyclic life due to storage has been 
tabulated in Table 8. Here the error ranges from 3 % to 5 % which is acceptable. From 
both these tables it can be concluded that the proposed prognostic model performs well 
for the life computation after storage as the model predictions correlate really well with 
the experimental values. 
 97 
Table 7: Error Estimation in Prognostication of Thermal Aging (Storage) 
 
Storage Time (Isothermal Aging Time) 
Experimental Model % Error 
48 hours 46 hours 4.2  
192 hours 178 hours 7.3  
 
Table 8: Error Estimation in Reduction in Cyclic Life Due to Thermal Aging (Storage) 
 
Experimental 
Aging Time 
(hrs) 
Equivalent 
Reduction in 
Cyclic Life 
0.63t)(40.2N                                  
(37) 
(A) 
Prognosticated 
Aging Time 
(hrs) 
Equivalent 
Reduction in 
Cyclic Life 
0.63t)(40.2N                                  
(37) 
(B) 
% Error, 
(A) and (B) 
48 28 46 27 3.6 
192 66 178 63 4.5 
 
 
Prognosticated total life in overlapping environment of thermal aging and thermal 
cycling has been correlated with the experimental values in Table 9. For prognostication 
of total life error envelope is in the range of 8 % to 12 % which is quite good from a life 
prediction perspective. The total life has also been systematically split into aging time, 
reduction in cyclic time due to aging and only cyclic life for experimental as well as 
 98 
prognosticated results for better understanding of life consumption in such complex 
sequential or overlapping thermal environments of thermal aging and thermal cycling.  
Table 9: Error Estimation in Prognostication of Overlapping Damage 
 
Stre
ss His
tory
 
Experimental Prognostication 
% Er
ror
 
(V
+W
) a
nd (
X)
 
Cyc
lic
 Life
 
Re
duc
tion due
 to 
Aging (
Cyc
les)
, 
Colum
n (A
), Ta
ble
 6 
(V
) 
Impose
d The
rma
l 
Cyc
les
 
(W
) 
Tota
l C
yc
lic
 Life
 
(V
+W
) 
Tota
l C
yc
lic
 Life
 
(X
) 
Cyc
lic
 Life
 
Re
duc
tion Due
 to 
Aging 
(Cyc
les)
 
Colum
n (B)
,Ta
ble 
6 
(Y
) 
Cyc
lic
 Life
 Alone
 
Cyc
les, (
X-
Y)
 
48 
Hours  
+  
100 
Cycles 
28 100 128 143 27 116 -11.7 
192 
Hours  
+  
100 
Cycles 
66 100 166 180 63 117 -8.4 
 
4.7 Prognostic Performance Metrics 
Prognostics is an emerging concept in condition based maintenance (CBM) of 
critical systems, where it is desired to predict residual life left in the system before any 
catastrophic failure takes place and so it is extremely important to check the validation of 
such prediction algorithms. Since these prognostics concepts are relatively new they lack 
standard definitions and there is an inconsistency in their interpretations. The lack of 
standards is in part due to the wide variety of end user requirements for different 
application, wide range of time scales involved, available domain information, domain 
dynamics etc. So there is actually very little means of comparing different prognostics 
approaches based on a common ground. Further in order to evaluate prognostics 
 99 
approach in real world condition a rigorous testing of variety of parameters is required 
before they can be used in any critical system. So to serve this purpose performance 
metrics were established. Performance metrics help establish design requirements that 
must be met for comparison. In the absence of standardized metrics it has been difficult 
to quantify acceptable performance limits and specify crisp and unambiguous 
requirements to the designers. These metrics allows comparing different algorithms and 
also yields constructive feedback to further improve these algorithms. There are various 
performance metrics which have been used in domains like Aerospace, Electronics, 
medicine, Finance, Weather prediction, Nuclear and Automotive [Saxena 2008]. 
In this chapter two separate prognostication models based on two leading 
indicators of failure viz. normalized phase-growth and normalized inter-metallic 
compound (IMC) growth of second level solder interconnects have been proposed and 
implemented for the life prediction of electronics. The sole purpose of evaluating various 
performance metrics was to relatively compare the two models and see which leading 
indicator of failure accurately predicts life. For this seven different performance metrics 
viz. ?-? curve, accuracy, precision, Mean Squared Error (MSE), and Mean Absolute 
Percentage Error (MAPE), relative accuracy (RA) and cumulative relative accuracy 
(CRA) have been computed to compare the two models. 
Terms and Notations: 
 UUT is unit under test 
 )(il  is the error between the predicted and the true RUL at time index i for UUT l. 
 EOP (End-of-Prediction) is the earliest time index, i, after prediction crosses the 
failure threshold. 
 100 
 EOL represents End-of-Life, the time index for actual end of life defined by the 
failure threshold. 
 P is the time index at which the first prediction is made        by the prognostic system. 
   )(irl is the RUL estimate for the lth UUT at time ti as   determined from 
measurement and analysis. 
  )(* irl is the true RUL at time ti given that data is available up to time ti for the lth 
UUT. 
   ? is the cardinality of the set of all time indices at which the predictions are made, 
i.e. ?  = (i | P  i  EOP). 
    Error (i)?l = (i)r(i)r ll*                                   
Average Bias: 
Average bias method averages the error in predictions made at all subsequent 
times after prediction starts for the lth UUT. The metric can be extended to average bias 
over all UUTs to establish overall bias. 
1PEOP
(i)?
B
EOP
Pi
l
l                     (61) 
 
 
Sample Standard Deviation (S): 
Sample standard deviation measures the dispersion/speed of the error with respect 
to the sample mean of the error. This metric is restricted to the assumption of normal 
distribution of the error. It is, therefore, recommended to carry out a visual inspection of 
error plots.  
 101 
1n
M( i)?S ( i) 2n 1l l               (62) 
 
Where M is sample mean of the error 
Mean squared error (MSE): 
Mean squared error averages the square prediction error for multiple UUTs at the 
same prediction horizon. A derivative of MSE is root mean square error (RMSE). 
L
1i
2l (i)?L1M S E (i)             (63) 
 
Mean absolute percentage error (MAPE): 
MAPE averages the absolute error in the predictions of multiple UUTs at the 
same prediction horizon. Instead of the mean, median can be used to compute Median 
absolute percentage error (MdAPE) in similar fashion. 
L
1l l*
l
( i )r ( i )100 ?L1MA P E ( i )
          (64) 
 
?-? accuracy: 
Conventionally the primary purpose of plotting ?-? curve for any prognostic 
health management (PHM) model is to find the prognostic horizon point. The detailed 
technical definitions and discussion can be found in [Saxena 2008]. However it also helps 
visually understand the model performance at different intervals of time. In this paper the 
?-? curve has been plotted for both the models as shown in Figure 59 and Figure 60. It is 
a normalized plot of Remaining Useful Life (RUL) Vs Life which is compared against 
the ground truth and the error bounds. In this case the ground truth is the experimental 
 102 
data obtained from accelerated testing shown by blue line in the plots and ? 10% error 
bounds are imposed shown by dotted lines. It should be noted that the selection of error 
bounds is application specific and typically tighter bounds are imposed as the criticality 
of the system increases. 
 
Figure 59: ?-? curve for Prognostication using normalized phase-growth as the leading 
indicator of failure 
 103 
 Figure 60:
 ?-? curve for Prognostication using normalized IMC growth as the leading 
indicator of failure 
 
In this chapter the main idea to plot ?-? curves for the two models was not to find 
the prognostic horizon point but to compare the relative performance of the models 
visually. It is clear from the plots that although the red curve in Figure 59 diverges and 
goes outside error bounds at the end but still relatively it remains close to the blue line 
compared to the green curve in Figure 60. It helps conclude that the prognostication 
model developed using phase-growth parameter as the leading indicator of failure 
performs better than the prognostication model developed using IMC for the current field 
conditions.  
Also ?-? curve does not provide absolute value based comparison but it provides 
useful information about the model at different intervals. For example visually it is 
evident from both the plots that the IMC model works better than the phase growth model 
until 50% of the life and then the IMC model diverges more than the Phase-growth 
 104 
model. Thus this information can be used to modify the model by tweaking certain 
critical parameters and also check the factors affecting the variability. 
Relative accuracy (RA): 
Relative prediction accuracy is a notion similar to ?-? accuracy where, instead of 
finding out whether the predictions fall within a given accuracy levels at a given time 
instant, we measure the accuracy level. The time instant is again described as a fraction 
of actual remaining useful life from the point when the first prediction is made. An 
algorithm with higher relative accuracy is desirable.  
)(tr )(tr)(tr1RA ?* ?
l?*                     (65) 
 
Where t?= P + ? (EOP ? P)  
Cumulative Relative Accuracy (CRA): 
Relative accuracy can be evaluated at multiple time instances. To aggregate these 
accuracy levels, we define Cumulative Relative Accuracy as a normalized weighted sum 
of relative prediction accuracies at specific time instances. 
E O L
Pl RA1PE O P
1C R A         (66) 
 
Where w is a weight factor as a function of RUL at all time indices. In most cases it is 
desirable to weigh the relative accuracies higher closer to the EOL. 
Table 10 summarizes all the prognostic metrics discussed above for both the PHM 
models viz. using normalized phase-growth and normalized IMC-growth respectively. 
From these metric values it can be concluded that both the damage proxies perform well 
and can be used as leading indicator of failures in the PHM models. 
 105 
Table 10: Prognostic Metric Comparison 
 
Prognostic 
Metrics 
PHM Model for 
Phase-Growth 
PHM Model for 
IMC Growth 
Average Bias -0.82316 2.225578 
Sample 
Standard 
Deviation (S) 
220.6121 292.8947 
MSE 54181.35 130216.3 
MAPE 0.065839 0.177259 
RA (?=0.5) 0.9732 0.7836 
CRA 0.007713 0.0074246 
 
4.8 Conclusion 
State-of-art prognostic health management (PHM) model for electronics exposed 
to a combination of dormant storage and field application was proposed and implemented 
on commercial test vehicle. Dormant storage was simulated by isothermal aging 
environment while cyclic field application was replicated by thermal cyclic environment. 
Custom test vehicle was designed to accommodate 4 daisy chain patterns as against 
conventional 1 daisy chain for effective fault detection and isolation. Mathematical 
relationship between storage time and corresponding reduction in cyclic life was 
successfully established based on two physics-of-failure based damage proxies viz. 
phase-growth and inter-metallic compound (IMC) growth of second level solder 
interconnects. Life after storage and sequential stress application was prognosticated to 
show the influence of dormant storage on the cyclic life. Prognostication results were 
carefully studied to see if it captures the life expended during storage in thermal cyclic 
environment. It is clear from the prognostication results and damage equivalency 
 106 
relationship that the effect of dormant storage can not be neglected as it considerably 
reduces the cyclic life and its effect has to be taken into account for accurate life 
predictions. 
The viability of the proposed prognostic model was demonstrated for multiple 
combinations of overlapping stress environments to prove the robustness of the model. 
Correlation between the prognosticated damage and the actual accrued damage displays 
that the proposed PHM model can be used to assess damage accrued under overlapping 
thermo-mechanical stresses of thermal aging and thermal cycling. In addition, 
prognostics metrics have been used to quantitatively evaluate the performance of the 
prognostic algorithms using both the leading indicators. Results demonstrate that both 
damage proxies work well in estimating accrued damage and estimating residual life.
 107 
 
CHAPTER 5
SUMMARY AND FUTURE WORK 
 
Electronics from a reliability perspective can be thought of as a function of three 
primary variables viz. materials, process, and application. There is a ton of literature 
available on reliability enhancement techniques specifically addressing materials and 
compliant processes. However even after employing all the reliability enhancement 
schemes it is well known that the deployed parts are observed to have erratic failure 
behavior and characteristics in the field even after rigorous qualification tests. 
Conventional life prediction models used for measuring electronics reliability are based 
on fear of failure whose decisions are based on pristine state and lack insight about the 
ongoing reliability of the system. The work presented in this thesis is an effort to address 
the growing need to develop techniques that can monitor in-field system state during the 
service life and make life predictions based on interrogation of system state. Although 
this technique requires condition monitoring it still eliminates the need for continuous 
monitoring of the system state to make life predictions which considerable saves the 
overhead associated with data acquisition systems. Two prognostic health management 
(PHM) models were presented for single and multiple thermal environments respectively. 
 
 
 108 
5.1 PHM Model for Single Thermo-Mechanical Environment 
Novel prognostic health management (PHM) model was developed for electronics 
exposed to steady-state temperature profiles. The proposed model was implemented on 
commercially relevant test vehicle to demonstrate its applicability in real field deployed 
electronics. The PHM model allowed life estimation of electronics subjected to single 
isothermal aging environments. The proposed methodology enabled spot assessment of 
life consumed due to isothermal aging environments in the pre-failure space, without any 
knowledge of prior stress histories. The prognostic model was based on physics-of-failure 
of lead-free second level solder interconnects commonly found in today?s high I/O 
packaging architectures. It has been shown that the physics-of-failure based damage 
proxy identified as inter-metallic compound (IMC) growth, formed between the second 
level solder interconnect and copper pad at the board side interface can be used as a 
leading indicator of failure. Higher learning algorithm theory like Levenberg-Marquardt 
algorithm was used a non-linear least square (NLLSQ) method and was employed for the 
first time in evaluating electronics reliability. 
The prognostic model proposed in Chapter 3 finds its application in a real world 
setting where one has to find the remaining useful life of the electronic system in the 
same isothermal environment well before the actual failure occurs i.e. in the pre-failure 
space without any knowledge of prior stress histories. In such scenario the proposed 
prognostic model can be implemented using condition monitoring devices which would 
be used to interrogate the damage progression in the form of IMC growth data. This data 
can be fed to the Levenberg-Marquardt algorithm developed for this model for accurate 
life predictions. 
 109 
5.2 PHM Model for Sequential Thermal Environments of Thermal Aging and 
Thermal Cycling 
In Chapter 4 a PHM model was developed for prognostication of accrued prior 
damage in electronics subjected to overlapping sequential environments of thermal aging 
and thermal cycling. Mathematical relationship between storage time and corresponding 
reduction in cyclic life was successfully established based on two physics-of-failure 
based damage proxies viz. phase-growth and inter-metallic compound (IMC) growth of 
second level solder interconnects. Life after storage and sequential stress application was 
prognosticated to show the influence of dormant storage on the cyclic life. 
Prognostication results were carefully studied to see if it captures the life expended 
during storage in thermal cyclic environment. It is clear from the prognostication results 
and damage equivalency relationship that the effect of dormant storage can not be 
neglected as it considerably reduces the cyclic life and its effect has to be taken into 
account for accurate life predictions. 
The viability of the proposed prognostic model was demonstrated for multiple 
combinations of overlapping stress environments to prove the robustness of the model. 
Correlation between the prognosticated damage and the actual accrued damage displays 
that the proposed PHM model can be used to assess damage accrued under overlapping 
thermo-mechanical stresses of thermal aging and thermal cycling. In addition, 
prognostics metrics have been used to quantitatively evaluate the performance of the 
prognostic algorithms using both the leading indicators. Results demonstrate that both 
damage proxies work well in estimating accrued damage and estimating residual life. 
 
 110 
5.3 Scope for Future Work 
 Prognostic model performance has been evaluated using standard prognostic 
metrics available in the literature. It would be interesting to relate these metrics for the 
model enhancement in the future. For example ?-? curve for both the leading indicator 
based models indicate that the models diverge at the end of life where it is critical to get 
tighter results. It would be worth to study various model parameters and check the 
sensitivity of each individual parameter with respect to the model outputs. The studied 
sensitivities can be incorporated in the models for accurate life predictions in the future. 
Prognostic models in this thesis are based on non-linear least square (NLLSQ) 
method called Levenberg-Marquardt algorithm. It will also be interesting to apply other 
higher order learning algorithms to solve the set non-linear physic-of-failure based 
equations for life computation. Various models can then be compared using prognostic 
metrics and ranked for specific application. 
In future prognostic models can be developed for more complex environments 
such as multiple combinations of thermal aging and thermal cycling. Also sequential low 
cycle thermal fatigue and transient drop event can be studied for prognosis. It would be 
valuable to study the effect of thermal aging and thermal cycling on the drop reliability of 
electronics. Complex overlapping environment such as thermal fatigue and high strain 
rate drop testing can be studied to extract damage proxies which can be incorporated as 
leading indicators of failure in future prognostic models.
 111 
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