The Effects of Isothermal Aging on the Mechanical Behavior of  
Underfill Encapsulants 
 
by 
 
Chang Lin 
 
 
 
 
A dissertation submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Doctor of Philosophy  
 
Auburn, Alabama 
August 9, 2010 
 
 
 
 
Keywords:  Underfill, Encapsulant, Aging, Evolution 
Material Behavior, Creep 
 
 
Copyright 2010 by Chang Lin 
 
 
Approved by 
 
Jeffrey C. Suhling, Chair, Quina Distinguished Professor, Mechanic Department 
Pradeep Lall, Thomas Walter Professor, Mechanic Department 
Roy Knight, Assistant Professor, Mechanic Department 
Ruel A. Overfelt, Professor, Materials Department 
 
 
ii 
 
 
 
 
 
 
Abstract 
 
 
Underfill encapsulants are widely used in the microelectronics industry to improve the 
reliability of electronic components assembled to printed circuit boards.  In this work, the effects 
of isothermal aging on the stress-strain and creep behaviors of underfills have been 
experimentally characterized.  A novel method has been developed to fabricate underfill uniaxial 
test specimens so that they accurately reflect the encapsulant layer present in flip chip assemblies.  
Samples were subjected to various aging temperatures and aging times before testing.  The 
measured experimental data demonstrated that large changes (up to 100X) occur in the 
mechanical properties of the underfill.  Empirical and constitutive models have also been 
developed that describe the aging effects on the mechanical properties of the material. 
Furthermore, the effects of underfill cure temperature and JEDEC MSL preconditioning 
on underfill mechanical and strength properties, as well as flip chip assembly reliability, have 
been explored.  The failure mechanisms in the flip chip assemblies were studied using CSAM, 
X-ray and SEM analysis.  The results clearly indicate the advantages of the higher curing 
temperature.  These included improved mechanical properties, superior thermal cycling fatigue 
life, and enhanced resistance to detrimental effects from moisture exposure and solder reflow. 
 
 iii 
 
 
 
 
 
Acknowledgments 
 
 
I would like to express my sincere gratitude to my advisor Dr. Jeffrey C. Suhling for his 
support and guidance support throughout the course of this research.  Sincere gratitude and 
appreciation are also extended to Dr. Ruel A. Overfelt, Dr. Pradeep Lall and Dr. Roy Knight for 
serving on my Ph.D. committee as well as providing precious time, valuable instruction and 
recommendations. 
I would like to thank John Marcell for his kindness and help in maintaining all equipment.  
Special thanks are also extended to all my coworkers and friends, Kaysar Rahim, Jordan Roberts, 
Hongtao Ma, Yifei Zhang, and Zijie Cai for their encouragement and help. 
Finally, I would like to thank my family for their continuous support and encouragement 
during this time.  All of this would be impossible without their understanding and support.  
 
 
 
 
 iv 
 
 
 
 
 
Table of Contents 
 
 
Abstract........................................................................................................................................... ii 
Acknowledgments.......................................................................................................................... iii 
List of Tables ................................................................................................................................ vii 
List of Figures................................................................................................................................ ix 
Chapter 1  Introduction ....................................................................................................................1 
1.1 Electronic Packaging Technology .......................................................................................1 
1.2 Flip Chip Technology ..........................................................................................................2 
1.3 Solder Bump Connections ...................................................................................................4 
1.4 Underfill Technology...........................................................................................................8 
1.5 Underfill Flow Process ......................................................................................................11 
1.5.1 Capillary Underfill.................................................................................................11 
1.5.2 No-Flow Underfill .................................................................................................15 
1.5.3 Wafer Level Underfill............................................................................................15 
1.6 Underfill Materials.............................................................................................................17 
1.7 Thermal Aging Process......................................................................................................23 
1.8 Research Objectives...........................................................................................................30 
Chapter 2  Specimen Preparation and Uniaxial Testing ................................................................32 
2.1 Introduction........................................................................................................................32 
2.2 Experimental Underfill Material........................................................................................37 
2.3 Specimen Preparation Procedure .......................................................................................40 
2.4 Mechanical Testing System ...............................................................................................45 
2.5 Experimental Method and Mechanical Properties.............................................................47 
2.5.1 Tensile Stress Strain Properties .............................................................................47 
2.5.2 Creep Properties.....................................................................................................48 
Chapter 3  Effects off Temperature and Strain Rates on the Properties of Underfill ....................56 
3.1 Introduction........................................................................................................................56 
 v 
3.2 Objectives and Testing Program........................................................................................58 
3.3 Tensile Testing Data and Empirical Model .......................................................................59 
3.4 Experimental Results and Discussions ..............................................................................62 
3.4.1 Stress-Strain Curves...............................................................................................62 
3.4.2 Elastic Modulus .....................................................................................................63 
3.4.3 Ultimate Tensile Strength ......................................................................................67 
3.4.4 Elongation..............................................................................................................67 
3.5 Effects of Temperature and Strain Rate on Tensile Properties..........................................69 
3.6 Simultaneous Modeling of the Effects of Strain Rate and Temperature ...........................70 
Chapter 4  Effects of Aging on Stress-Strain Behavior and Mechanical Properties ....................77 
4.1 Introduction........................................................................................................................77 
4.2 Objectives and Testing Program........................................................................................79 
4.3 Experimental Results and Discussion................................................................................79 
4.3.1 Changes in Microstructure and Cure Properties ....................................................79 
4.3.2 Stress-Strain Data for Non-Aged Samples ............................................................81 
4.3.3 Stress-Strain Data for Aged Samples.....................................................................84 
4.3.4 Aging Time Effects and Comparisons...................................................................87 
4.3.5 Aging Temperature Effects and Comparisons.......................................................96 
4.3.6 Property Evolution with Aging Time ....................................................................96 
4.4 Combined Models for the Effects of Aging Temperature, Aging Time, and Testing 
Temperature .....................................................................................................................103 
4.5 Summary and conclusions ...............................................................................................115 
Chapter 5  Isothemal Aging Effects on The Creep Behaviors.....................................................116 
5.1 Introduction......................................................................................................................116 
5.2 Objectives and Test Program...........................................................................................120 
5.3 Experimental Results and Discussion..............................................................................121 
5.3.1 Stress Level and Test Temperature Effects and Comparison ..............................123 
5.3.2 Aging Time Effects and Comparison ..................................................................129 
5.4 Empirical Model for the Evolution of the Secondary Creep Rate ...................................129 
5.5 Empirical Model for the combined Effects of Aging Temperature, Aging Time,            
and Stress Level on the Secondary Creep Secondary Rate..............................................137 
5.6 Summary and Conclusions ..............................................................................................144 
 
 vi 
Chapter 6  Cure Profile Effects On The Mechanical Behavior And 
        Reliability Of Flip Chip On Laminate Assemblies....................................................145 
6.1 Introduction......................................................................................................................145 
6.2 Objectives ........................................................................................................................150 
6.3 Experimental Procedures .................................................................................................151 
6.4 Experimental Shear Strength Measurements...................................................................153 
6.5 Thermal Cycling Reliability Tests...................................................................................156 
6.6 Experimental Results .......................................................................................................159 
6.6.1 Mechanical Testing of Underfill Material ...........................................................159 
6.6.2 Shear Strength......................................................................................................167 
6.6.3 Thermal Cycling Reliability Tests.......................................................................169 
6.6.4 Microstructures ....................................................................................................170 
6.7 Summary and Conclusions ..............................................................................................175 
Chapter 7  Summary and Conclusions.........................................................................................176 
7.1 Literature Review for the Flip Chip Technology and Underfill Materials ......................176 
7.2 Unique Specimen Preparation Procedure ........................................................................176 
7.3 Strain Rate Effects ...........................................................................................................177 
7.4 Isothermal Aging Effects on the Underfill Tensile Properties.........................................177 
7.5 Isothermal Aging Effects on the Underfill Creep Behaviors...........................................178 
7.6 Moisture Effects and Reliability Tests.............................................................................179 
References....................................................................................................................................181 
Appendix      Additional Creep Data for Specimens Aged at 80, 125, and 150 ?C.....................187 
 
 
vii 
 
 
 
 
 
List of Tables 
 
 
1.1 Properties of Materials Used in Flip Chip Packaging..........................................................5 
1.2 Historical Underfill General Performance .........................................................................16 
1.3 The General Desirable Characteristics and Advantages of an Underfill Material.............20 
2.1 Underfill Material Composition.........................................................................................38 
2.2 Underfill Material Characteristics and Cure Procedure.....................................................38 
2.3 Comparison of the Specimen Preparation Methods...........................................................44 
2.4 Models for the Mechanical Properties of Epoxy Underfills ..............................................49 
2.5 Table of Constant Values for the Parameters ....................................................................55 
2.6 Constitutive Models for Epoxy Creep Behavior................................................................55 
3.1 Table of Sample Test Temperatures and Strain Rates.......................................................60 
3.2 Mechanical Properties of Underfill Material at Different Strain Rates .............................71 
3.3 Logarithmic Model Fitting Constants................................................................................73 
3.4 Power Law Model Fitting Constants .................................................................................73 
3.5 Fitting Constants for Empirical Models in Equations 3.12 and 3.13.................................76 
4.1 Test Matrix for Tensile Test Sample Aging Exposures.....................................................80 
4.2 Elastic Modulus and Ultimate Strength vs. Temperature                                                  
for Samples Aged at 80 ?C ................................................................................................99 
4.3 Elastic Modulus and Ultimate Strength vs. Temperature                                                   
for Samples Aged at 100 ?C ..............................................................................................99 
4.4 Elastic Modulus and Ultimate Strength vs. Temperature                                                   
for Samples Aged at 125 ?C ............................................................................................100 
4.5  Elastic Modulus and Ultimate Strength vs. Temperature                                                  
for Samples Aged at 150 ?C ............................................................................................100 
4.6 Parameter Values for the Elastic Modulus Empirical Model ..........................................111 
4.7 Parameter Values for the UTS empirical Model..............................................................114 
 
viii 
5.1 Matrix of Aging Exposures for Creep Tests....................................................................122 
5.2 The Slope of Secondary Creep Rate vs. Aging Time for Long Term Aging ..................136 
6.1 Sample Preconditioning Exposures .................................................................................152 
6.2 Calculated Weibull Parameters........................................................................................172 
 
 
 
 
 
 
 
ix 
 
 
 
 
 
List of Figures 
 
 
1.1 Typical Electronic Packaging Configuration.......................................................................3 
1.2 Schematic of a Flip Chip Assembly.....................................................................................3 
1.3 Solder Joint Fatigue During Thermal Cycling.....................................................................7 
1.4 Major Markets for Thermoplastic Resins ............................................................................9 
1.5 Solder Joint Strain Prediction for Different Underfill Properties ......................................11 
1.6 Schematic of a Flip Chip Assembly with Underfill Material ............................................12 
1.7 Underfill Capillary Flow Process [9].................................................................................12 
1.8 Underfill Capillary Flow Process Parameters....................................................................14 
1.9 No-Flow Underfill Process [9]...........................................................................................16 
1.10 Wafer Level Underfill Process...........................................................................................18 
1.11 Relaxation Modulus for A: Crystalline Polystyrene; B: Lightly Cross                            
Linked Polystyrene; C: Amorphous Polystyrene [5].........................................................22 
1.12 Variation of Initial Tensile and Shear Strength for (D, L-lactide-co-glycolide)              
with Aging Time [22] ........................................................................................................25 
1.13 Creep Compliance Curves for Syndiotactic Polystyrene (SPS140A) [24]........................27 
1.14 Creep Compliance Curves for DGEBA/400 Diamine Epoxy Glass                                 
with 0.05% Mass Fraction CTBN Rubber [23] .................................................................27 
1.15 Variation of the Creep Response of Epoxy with Aging Time [13] ...................................28 
1.16 Combination of TTSP and TSSP to Form a Master Curve [5, 24]....................................29 
2.1 Samples Used by Qian and coworkers [26].......................................................................34 
2.2 Samples Used by Rao, et al. [27].......................................................................................34 
2.3 Mold and Samples used by Shi, et al. [28] ........................................................................36 
2.4  Fabrication Process and Samples used by Kuo, et al. [29] ................................................36 
2.5 Microstructure of the Underfill Material with Silica Filler ...............................................39 
 
x 
2.6 Thermo-Expansion TMA Test Results for the Underfill Material ....................................39 
2.7 Specimen Mold Assembly .................................................................................................41 
2.8 Underfill Uniaxial Specimens and Final Dimensions........................................................41 
2.9 CAM/ALOT System 3700 and Underfill Material Dispensing.........................................42 
2.10 Underfill Material Curing Oven.........................................................................................44 
2.11 Temperature Profile During the Underfill Material Curing Process .................................44 
2.12 Testing System and Environment Chambers.....................................................................46 
2.13 A Typical Creep Curve ......................................................................................................51 
3.1 A Typical Temperature Dependent Underfill Stress-Strain Curve                                     
(T = 100 ?C, and ?&  = 1 x 10-3 sec-1)................................................................................61 
3.2 Hyperbolic Tangent Model Fit to Underfill Stress-Strain Curves                                         
(T = 100 ?C, and ?&  = 1 x 10-3 sec-1)................................................................................61 
3.3 Stress-Strain Curves for Different Temperatures at a Constant Strain                             
Rate: (a) 0.001 (1/sec), (b) 0.0001 (1/sec), (c) 0.00001 (1/sec).........................................64 
3.4 Comparison of Stress-Strain Curves Tested at the Same Testing Temperature                     
for Different Strain Rates...................................................................................................65 
3.5 Temperature Effects on the Underfill Elastic Modulus .....................................................66 
3.6 Temperature Effects on the Underfill Ultimate Tensile Strength......................................68 
3.7 Strain Rate Effects on the Underfill Elongation ................................................................68 
3.8 Linear Dependence of the Elastic Modulus on the Logarithmic Strain Rate ....................72 
3.9 Linear Dependence of the UTS on the Logarithmic Strain Rate .......................................72 
3.10 Strain Rate and Temperature Effects on the Elastic Modulus ...........................................75 
3.11 Strain Rate and Temperature Effects on the UTS                                                               75 
4.1 Aging Effects on Underfill Microstructure........................................................................82 
4.2 Aging Effects on Underfill Thermal Properties.................................................................83 
4.3 Typical Temperature Dependent Underfill Stress-Strain Curves (No Aging)...................85 
4.4 Underfill Effective Elastic Modulus vs. Temperature .......................................................85 
4.5 Average Stress-Strain Curves (No Aging).........................................................................86 
4.6 Stress-Strain Curves for Specimens Aged at 100 ?C for 10,                                              
30 100, 200 and 300 Days..................................................................................................88 
 
xi 
4.7 Stress-Strain Curves for Specimens Aged at 100 ?C                                                            
(T = 25, 50, 75, 100, 125 and 150 ?C) ...............................................................................89 
4.8 Stress-Strain Curves for Specimens Aged at 80 ?C for 10,                                                
30 100, 200 and 300 Days..................................................................................................90 
4.9 Stress-Strain Curves for Specimens Aged at 80 ?C                                                              
(T = 25, 50, 75, 100, 125 and 150 ?C) ...............................................................................91 
4.10 Stress-Strain Curves for Specimens Aged at 125 ?C for 10,                                               
30 100, 200 and 300 Days..................................................................................................92 
4.11 Stress-Strain Curves for Specimens Aged at 125 ?C                                                            
(T = 25, 50, 75, 100, 125 and 150 ?C) ...............................................................................93 
4.12 Stress-Strain Curves for Specimens Aged at 150 ?C for 10,                                              
30 100, 200 and 300 Days..................................................................................................94 
4.13 Stress-Strain Curves for Specimens Aged at 150 ?C                                                                
(T = 25, 50, 75, 100, 125 and 150 ?C) ...............................................................................95 
4.14 Effective Elastic Modulus and UTS vs. Temperature for Aging at 80 ?C.........................97 
4.15 Effective Elastic Modulus and UTS vs. Temperature for Aging at 100 ?C.......................97 
4.16 Effective Elastic Modulus and UTS vs. Temperature for Aging at 125 ?C.......................98 
4.17 Effective Elastic Modulus and UTS vs. Temperature for Aging at 150 ?C.......................98 
4.18 Aging Temperature Effects on Elastic Modulus and UTS (Aged for 10 Days) ..............101 
4.19 Aging Temperature Effects on Elastic Modulus and UTS (Aged for 30 Days) ..............101 
4.20 Aging Temperature Effects on Elastic Modulus and UTS (Aged for 100 Days) ............101 
4.21 Aging Temperature Effects on Elastic Modulus and UTS (Aged for 200 Days) ............102 
4.22 Aging Temperature Effects on Elastic Modulus and UTS (Aged for 300 Days) ............102 
4.23 Strength Evolution with Aging Time...............................................................................104 
4.24 Empirical Fit to Material Property Evolution Data..........................................................104 
4.25 Effective Elastic Modulus and UTS vs. Aging Time for Aging at 80 ?C........................105 
4.26 Effective Elastic Modulus and UTS vs. Aging Time for Aging at 100 ?C......................105 
4.27 Effective Elastic Modulus and UTS vs. Aging Time for Aging at 125 ?C......................106 
4.28 Effective Elastic Modulus and UTS vs. Aging Time for Aging at 150 ?C......................106 
4.29 Elastic Modulus vs. Aging Effects for Testing at T = 100 ?C.........................................109 
4.30 3D Visualization of Elastic Modulus vs. Aging Effects for Testing at T = 100 ?C ........109 
 
xii 
4.31 Empirical Model Fit for Elastic Modulus vs. Aging Effects                                              
for Testing at T = 100 ?C .................................................................................................109 
4.32 Model Fitting for E vs. Aging Effects at All Test Temperatures.....................................110 
4.33 Elastic Modulus Empirical Model Parameters vs. Testing Temperature ........................111 
4.34 Model Fitting for UTS vs. Aging Effects at All Testing Temperatures ..........................113 
4.35 Ultimate Tensile Strength Empirical Model Parameters vs.                                        
Testing Temperature ........................................................................................................114 
5.1 Typical Creep Strain vs. Time Response.........................................................................118 
5.2 Typical Secondary Creep Strain Rate vs. Time Response...............................................118 
5.3 Creep Curves for Non-Aged Specimens Tested at 100 ?C..............................................124 
5.4 Isochronous Stress-Strain Curves for Non-Aged Specimens Tested at 100 ?C ..............124 
5.5 Creep Curves for Various Stresses (Samples Aged at 100 ?C                                              
for 0 and 1 Day, Tested at 80, 100, 125 ?C) ....................................................................125 
5.6 Creep Curves for Various Stresses (Samples Aged at 100 ?C                                              
for 3 and 10 Days, Tested at 80, 100, 125 ?C).................................................................126 
5.7 Creep Curves for Various Stresses (Samples Aged at 100 ?C                                            
for 30 and 100 Days, Tested at 80, 100, 125 ?C).............................................................127 
5.8 Creep Curves for Various Stresses (Samples Aged at 100 ?C                                                  
for 200 and 300 Days, Tested at 80, 100, 125 ?C)...........................................................128 
5.9 Creep curves for Various Aging Times (Samples Aged at 100 ?C,                                  
Tested at 80, 100 ?C) .......................................................................................................130 
5.10 Creep Curves for Various Aging Times (Samples Aged at 100 ?C,                            
Tested at 125 ?C) .............................................................................................................131 
5.11 Secondary Creep Rate vs. Aging Time (Samples Aged at 100 ?C).................................133 
5.12  Secondary Creep Rate vs. Aging Time (Samples Aged at 100 ?C).................................134 
5.13 Secondary Creep Rate vs. Aging Time (Samples Aged at 80, 125 and 150 ?C).............135 
5.14 Secondary Creep Rate vs. Aging Time (Samples Aged at 80 ?C)...................................139 
5.15 Secondary Creep Rate vs. Aging Time (Samples Aged at 100 ?C).................................140 
5.16 Secondary Creep Rate vs. Aging Time (Samples Aged at 125 ?C).................................141 
5.17 Calculated Parameters C0, C1 and C2 vs. Stress and Temperature.................................142 
5.18 Calculated Parameters C0, C1 and C2 vs. Stress Level...................................................143 
 
xiii 
6.1 Moisture Absorption of Underfill under Normal Lab Environment                              
(Sample Thickness: 2 mm) [54].......................................................................................147 
6.2 Fracture Strength as a Function of Different Displacement Rate,                       
Preconditioning Condition and Specimen Type [29].......................................................147 
6.3 Moisture Absorption of a 2 ? 2 ? 50 mm Long Orthogonal Bar of G25                        
Underfill during 85/85 Aging [57]...................................................................................149 
6.4 Adhesion Strength of G25 on SiN vs. Aging Time [57] .................................................149 
6.5 The MSL3 + 245 Reflow Process Temperature Profile...................................................152 
6.6 Schematic of the Underfill Adhesion Shear Test.............................................................155 
6.7 Assembled Shear Test Coupons Before and After Die Attaching...................................155 
6.8 Cured Underfill Dot After Shear Test..............................................................................155 
6.9 Flip Chip Thermal Cycling Test Board ...........................................................................158 
6.10 (a) Die Site (b) Finger Design for I/O..............................................................................158 
6.11 Underfill Stress-Strain Curves for Curing at 150 ?C and 165 ?C                                          
(No Preconditioning) .......................................................................................................160 
6.12 Comparison of Stress-Strain Curves for Curing at 150 ?C and 165 ?C (No 
Preconditioning)...............................................................................................................161 
6.13 Mechanical Properties Comparisons for Underfill with Two Cure Conditions                    
(No Preconditioning) .......................................................................................................162 
6.14 Underfill Stress-Strain Curves for Curing at 150 ?C and 165 ?C                              
(MSL3+245 and  No Preconditioning) ............................................................................164 
6.15 Mechanical Properties vs. Temperature for Samples with and without                      
MSL3+245 Preconditioning ............................................................................................165 
6.16 Mechanical Properties vs. Temperature for Samples with the                                      
Different Preconditioning ................................................................................................166 
6.17 Average Shear Strength vs. Cure Temperature (The Percentage Indicates the                
Portion of the Failures Occurring at the Underfill to Die Passivation Interface) ............168 
6.18 Average Shear Strength vs. Preconditioning (The Percentage Indicates the Portion          
of the Failures Occurring at the Underfill to Die Passivation Interface) .........................168 
6.19 CSAM Images of Samples Cured at 150 ?C After MSL3+245 Preconditioning ............171 
6.20 Weibull Failure Plots for Thermal Cycling of the Flip Chip Test Assemblies................172 
6.21 Cross-Sectioned Solder Joints in the Samples Cured at 150 ?C, (a) 7500 Cycles,            
No Preconditioning; (b) 7300 cycles, MSL3+245 Preconditioning ................................173 
 
xiv 
6.22 Cross-Sectioned Solder Joints in the Samples Cured at 165 ?C, (a) 6800 Cycles,            
No Preconditioning; (b) 6500 cycles, MSL3+245 Preconditioning ................................174 
A-1 Creep Curves for Various Aging Times (Samples Aged at 80 ?C,                                    
Tested at 80, 100 ?C) .......................................................................................................189 
A-2 Creep Curves for Various Aging Times (Samples Aged at 80 ?C,                                     
Tested at 125 ?C) .............................................................................................................190 
A-3 Creep Curves for Various Aging Times (Samples Aged at 125 ?C,                                   
Tested at 80, 100 ?C) .......................................................................................................191 
A-4 Creep Curves for Various Aging Times (Samples Aged at 125 ?C,                                 
Tested at 125 ?C) .............................................................................................................192 
A-5 Creep Curves for Various Aging Times (Samples Aged at 150 ?C,                                
Tested at 80, 100 ?C) .......................................................................................................193 
A-6 Creep Curves for Various Aging Times (Samples Aged at 150 ?C,                                 
Tested at 150 ?C) .............................................................................................................194 
 
 
 
1 
CHAPTER 1  
INTRODUCTION 
 
 
Electronic packaging technology is the science of establishing interconnections between 
various levels of electronic devices, components, modules, and system.  It dictates the cost, 
performance and reliability of almost all future commercial and military electronics equipment.  
The most compact and high density electronic packaging is flip chip technology.  Most flip chip 
assemblies require underfill to improve their reliability to acceptable levels.  Otherwise, the 
small solder joints are subjected to high shear strains due to the thermo-mechanical mismatch 
between die and substrate.  Continuous improvement of packaging and related technologies has 
provided the impetus for the development of new and improved consumer electronic products. 
1.1 Electronic Packaging Technology 
Electronic packaging refers to the placement and connection of many electronic and 
electromechanical components in an enclosure that protects the system from the environment and 
provides easy access for routine maintenance.  The four major functions of an electronic package 
include signal distribution, power distribution, heat dissipation, and protection of the components 
and interconnections. 
Generally the packaging system can be divided into several interconnect levels.  At the 
first level, the integrated circuit (IC) chip and a substrate or chip carried are connected by one of 
three methods: wirebonding, tape-automated bonding (TAB), or flip chip technology.  At the 
 
2 
second level, the substrate or chip carried is connected to a printed wiring board (PWB).  This 
attachment can be achieved by using plated through hole (PTH) technology or surface mount 
technology (SMT).  At the third level, the PWB is connected to a motherboard.  Figure 1.1 
illustrates a typical configuration for electronic packaging technology. 
1.2 Flip Chip Technology 
The goals of electronic packaging engineers are to lower costs, increase packaging 
density, and improve performance with better circuit reliability.  Flip chip technology was 
introduced by IBM for mainframe computer applications in the early 1960s.  Since then, millions 
of flip chips have been processed by IBM on ceramic substrates, and they claim a reliability test 
record of 60,000 thermal cycles [1].  Presently, the automotive, computer, and cell phone 
industries all rely on flip chip technology for their success.  A typical flip chip on laminate 
assembly is shown in Figure 1.2.  Flip chip is also gaining popularity in ball grid array (BGA) 
and other chip carrier technologies, replacing wirebonding. 
In flip chip assemblies, the semiconductor chip faces down onto a substrate.  Small solder 
joints are used to both electrically and mechanically connect the silicon chip to the substrate 
using a high temperature reflow process.  Flip chip technology provides the ultimate in size and 
weight saving, since no extra area is needed to make contacts of components to the substrate.  
This is extremely important for electronics manufacturers due to increasing demands for 
miniaturized products and assemblies.  In addition, the relatively short electrical connection 
paths provide faster signal transmissions.  Finally, it is possible to have more input/output (I/O) 
connections for a given chip size.  All of these improvements yield superior performance over 
other interconnection methods. 
 
 
3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.1 - Typical Electronic Packaging Configuration 
 
 
 
Figure 1.2 - Schematic of a Flip Chip Assembly 
Solder Joint 
Passivation 
Copper Pad 
Solder Mask Silicon Chip 
Printed Circuit Board 
 
4 
In flip chip technology, there is only one level of connection between the chip and the 
circuit board. Flip chips therefore have an advantage over wirebonding because all connections 
are formed simultaneously, whereas with wirebonding, the connections are made one at a time.  
However, in practice the cost of die bumping can be high. Thus, in low volumes, wirebonding 
can still be more cost effective. 
1.3 Solder Bump Connections 
As discussed above, the silicon die in flip chip technology are connected to the substrate 
by small solder joints.  Eutectic or near eutectic tin/lead (Sn-Pb) solder has been widely used in 
the electronics industry due to its outstanding solderability and reliability.  Due to harmful 
effects on the environmental and health concerns, recent legislation has been enacted to require 
the removal of lead from electronics.  Several new lead free solders have been developed as 
alternatives to Sn-Pb solder, such as Sn-Ag-Cu (SAC) alloys [2].  Flip chip solder joints melt 
completely during the reflow process, but the surface tension in the molten solder supports the 
chip so that the extent of the joint collapse is controlled by the wettable area of the pads.  A 
solder joint based flip chip interconnection is also referred to as a controlled collapse chip 
connection (C4).  Solder bumps in flip chip assemblies serve as the structural links, electrical 
connections, and heat dissipation paths between the chip and the substrate.  Thus, failure of any 
of the solder joints will typically result in failure of the entire product. 
Among the failure modes present in flip chip assemblies, the major concern is typically 
the thermal-mechanical fatigue life of the solder joints.  Table 1.1 shows the material properties 
of the constituents generally used in flip chip packages.  During thermal cycling, large shear 
strains are developed in the solder joints due to the large coefficient of thermal expansion (CTE) 
mismatch between the silicon die and the substrate, as illustrated in Figure 1.3.  Consequently,  
 
5 
 
 
 
 
 
 
Materials E (GPa) CTE (ppm/ oC) Application 
Silicon 131 2.3 Chip or Substrate 
Silicon Dioxide 70 0.5 Underfill Fillers 
Epoxy 8-12 25-30 Underfill Polymer 
Solder 10 15-20 Interconnects 
Copper 128 17 Interconnects 
Alumina 255 4-6 Ceramic Substrate 
FR-4  PCB 22 15-20 Organic Substrate 
 
Table 1.1 - Properties of Materials Used in Flip Chip Packaging 
 
 
6 
fatigue cracks often initiate at the edges of the joints and then propagate through the interior, 
resulting in bump failure.  The likelihood of solder bump thermal fatigue failure is related to the 
chosen solder material, substrate and chip metallization, and the development of intermetallic 
compounds [3]. 
An analytical estimate of the solder joint shear strain (?) can be found by using the 
distance to neutral point approximation (DNP): 
]..[)( PNDh Tscpcb ??=? ???                                             (1.1) 
where ?pcb and ?sc are the coefficients of thermal expansion of the PCB and silicon chip, 
respectively, h is the height of the solder ball joints, ?T is the temperature change, and D.N.P is 
the distance to the neutral point.  The solder joint fatigue life can be estimated by applying 
failure criteria such as the Coffin-Manson Equation.  For example, for SnPb eutectic solder joints 
the expression is: 
96.1)(29.1 ??= ?
fN                                                               (1.2) 
where Nf is the estimated number of thermal cycles at which the solder joint will fail and ??  is 
the shear strain change during one cycle.  From these equations, it can be clearly seen that the 
solder joint fatigue life can be increased by using a smaller die, increasing the height of the 
solder ball joints, reducing the temperature change, and minimizing the CTE mismatch between 
the die and the substrate. 
For most flip chip configurations of interest, the thermal fatigue life is unacceptable and 
early joint failure occurs.  Thus, it is necessary to add an underfill encapsulant between the chip 
and substrate to assist the solder joints in maintaining the mechanical integrity of the assembly. 
 
 
7 
 
 
(a)   At Room Temperature 
 
 
(b)   Heating 
 
 
 
(c)   Cooling 
 
Figure 1.3 - Solder Joint Fatigue During Thermal Cycling 
 
 
 
Solder Joints Cu Pad 
FR4 
Die 
FR4 
Die 
DNP 
h 
Cu Pad 
FR4 
Die Solder Joints 
 
8 
1.4 Underfill Technology 
Underfill is required by most flip chips to avoid rapid solder joint fatigue failures.  Since 
its first use by IBM in the 1970s, underfill systems have been widely adopted by industry 
following the movement from ceramic substrates to organic substrates, which are the ultimate 
goal for flip chip technology [4].  Flip chips with organic substrates are often referred to as 
second generation flip chip technology. 
Underfill encapsulants are either thermosetting or thermoplastic polymers, both of which 
are widely used in industry.  Figure 1.4 shows the volume distribution for use of thermoplastic 
polymers in the United States in 2001, and the electronic packaging market was the largest [5]. 
To solve the CTE mismatch problem, an underfill material is used to fill the gap between 
the integrated circuit die and the substrate in a flip chip package to improve the solder joint 
fatigue life [6, 7].  Underfill not only connects the chip and the substrate but also provides an 
additional thermal path from the chip to the substrate.  The introduction of underfill gives the 
solder interconnections more mechanical robustness, and a significant increase in solder fatigue 
resistance results [8].  Moreover, underfill promotes evenly distributed and reduced solder joint 
strains during temperature changes, thus improving solder joint fatigue life, often by factor of 10 
or more [8].  The underfill encapsulant also protects the chip from moisture, radiation, and other 
hostile operating environments such as mechanical shock and vibration. 
The mechanical properties of underfill materials have a great influence on the reliability 
of flip chip packages.  For example, Figure 1.5 illustrates finite element prediction of the solder 
joint strains in a flip chip assembly subjected to a temperature change from -40 to 125 ?C.  The 
strain levels are much smaller when using an underfill with low CTE and high elastic modulus. 
 
9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.4 - Major Markets for Thermoplastic Resins 
 
 
 
 
 
 
 
 
 
Transportation 
5% 
Electrical/ Electronic 
3% 
Exports 
12% 
Building & Construction 
17% 
Adhesive/Coating/links 
2% 
All others 
14% 
Industry/Machinery 
1% 
Consumer & Institutional 
14% 
Furniture & furnishings 
4% 
Packaging 
28% 
 
10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.5 - Solder Joint Strain Prediction for Different Underfill Properties 
 
T = -40 to 125 oC 
 
11 
1.5 Underfill Flow Process 
A schematic of a flip chip assembly with underfill material is shown in Figure 1.6.  
Liquid underfills are thermally cured to form a heavily crosslinked molecular chain of solid state 
material.  The flow characteristics of uncured underfill materials are critical to their application 
performance.  These characteristics depend on its viscosity and dispense temperature, as well as 
the substrate material, chip passivation layer, solder bump pattern, and degree of curing.  There 
are three major processing procedures used in flip chip on board assembly and three 
corresponding underfill categories: capillary underfill, no-flow underfill, and wafer-level 
underfill. 
1.5.1 Capillary Underfill 
Capillary underfills are the most widely used in flip chip packaging.  Such materials will 
flow into the small gap between the chip and substrate via capillary action as shown in Figure 
1.7.  The encapsulant is dispensed along one side of the die after bump reflow and flows 
underneath the die and fills the gap between the die and chip carrier.  The underfill epoxy is then 
cured by heating the assembly and holding it at an elevated temperature.  This process is time 
consuming and a relatively expensive part of the manufacturing process.  However, it is crucial 
to reliability improvement. 
The filling dynamic process requires the underfill to be in a liquid state during the flow 
stage.  This phenomenon is well understood within the realm of surface chemistry and fluid 
surface chemistry, and surface tension is the driving force that produces the capillary flow.  The 
capillary underfill flow behavior can be modeled as a quasi-steady, laminar, incompressible, two 
 
12 
 
 
 
 
 
Figure 1.6 - Schematic of a Flip Chip Assembly with Underfill Material 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.7 - Underfill Capillary Flow Process [9] 
 
Solder Joint 
Passivation 
Underfill 
Copper Pad 
Solder Mask Silicon Chip 
Printed Circuit Board 
Underfill 
 
13 
dimensional flow through a pair of parallel plates using the  Washburn model [10-12]: 
)(122 tLhxp ???=?? ?                                                       (1.3) 
where p is the pressure in the liquid at the position x, ? is the absolute viscosity, h is the gap 
height, and L is the flow distance (see Figure 1.8).  The driving force for the flow is the pressure 
difference ( ? p) between the underfill and the air, which is a function of surface tension (? ), gap 
height (h), and contact angle (? ): 
hp
?? cos2=?                                                              (1.4) 
By solving equations (1.3) and (1.4), the time for the underfill material to fill the gap can be 
estimated by [10, 12, 13]: 
?
?
??
?
h
L
h
Lt 22 3
cos
3 ==   (cos? 1? )                            (1.5) 
From the expression in equation (1.5), it is clearly evident that the fill time is proportional to the 
viscosity and square of the distance traveled, and inversely proportional to the surface tension of 
the materials and standoff gap height.  Normally, the underfill, board, and components are all 
preheated to an elevated temperature to decrease the underfill viscosity, and this improves the 
wetting and flowability.  Although earlier capillary underfills experienced ?snail paced? flow 
rates due to higher viscosity resins and poor filler morphology, new underfill materials flow 
rapidly and ?snap? cure in minutes, significantly improving manufacturing throughput.  The 
general performance of underfill flow and curing times are summarized in Table 1.2 [14]. 
 
 
 
 
 
14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.8 - Underfill Capillary Flow Process Parameters 
 
 
Substrate 
? 
h 
Flip Chip 
L
 
15 
1.5.2 No-Flow Underfill 
Further improvements to the traditional capillary underfill process include the use of no-
flow underfill, which eliminates the time consuming flow process.  A fluxing controlled volume 
of underfill is dispensed directly onto bond sites before chip placement, as shown in Figure 1.9.  
The chip is then placed onto the bonding sites, compressing the liquid underfill and causing it to 
flow outward to the edges of the chip until the solder bumps contact the substrate pads.  
Compressing the underfill, producing a symmetrical outward flow pattern, helps to displace air 
and may be an attractive alternative process. 
By adding a flux agent to the underfill material, concerns about flux and underfill 
compatibility can be eliminated.  Also, this process does not require a subsequent reflow, 
dispense and cure process.  It therefore provides a significant reduction in process steps and time, 
improving both productivity and cost competitiveness.  Some considerations specific to the no-
flow underfill process are listed below: 
? Smaller bump size reduces voids 
? Larger pitch reduces voids 
? Substrate temperature is critical for the underfill material to reduce voids 
? Low deposition height increases voids and causes starvation 
? High viscosity allows compression flow to dominate and is preferred 
? Lower  viscosity allows gravity to flow that increase voids 
1.5.3 Wafer Level Underfill  
Wafer applied underfill is a revolutionary approach whereby underfill is applied to a 
bumped die at the wafer level.  Such underfill materials should be reworkable and retain their 
characteristics after assembly and any post processing steps.  Wafer level underfills can reduce  
 
16 
 
 
 
Year Flow Rate @ 80 oC Cure Time 
Pre-1995 <1 cm/min 3-6 hrs @ 150 oC 
1995 2 cm/min 30 min @ 150 oC 
1996 2.5 cm/min 15min @ 150 oC 
1997 3 cm/min 5-6 min @ 165 oC 
1998 3 to 3.5 cm/min 4-5 min @ 165 oC 
 
Table 1.2 - Historical Underfill General Performance 
 
 
 
 
 
 
 
 
 
      Dispense the Underfill         Place Chip         Reflow Solder & Cure Underfill 
Figure 1.9 - No-Flow Underfill Process [9] 
 
Substrate 
Underfill 
Placement Head 
Chip 
 
17 
processing time and cost because there is no need for individual underfill dispensing (Figure 
1.10). 
Generally a specially designed B-stageable underfill is coated onto a bumped wafer.  
After the coated wafer is diced into individual die, a single chip will be selected and placed onto 
bonding pads and the solder interconnections and underfill bonding are formed during the reflow 
process.  This approach can provide an efficient surface mount technology (SMT) process for 
flip chips by eliminating the steps of underfilling and curing each die.  However, there are some 
challenging issues associated with wafer level processes.  For example, specialized underfill 
materials must be developed that are stable at room temperature.  They must also be able to re-
liquefy during the reflow process, and they must form reliable interconnections after reflow. 
1.6 Underfill Materials 
After curing, the underfill materials used in flip chip assemblies are typically two phase 
composites consisting of an epoxy matrix filled with SiO2 (fused silica) particles.  For various 
applications, other small but necessary amounts of additives are also included in the epoxy 
formulations including fluxing agents, toughening agents, and adhesion promoters. 
Epoxy, which is the term used for compounds containing oxirane groups, is the most 
common matrix for underfill materials due to its desirable characteristics of good adhesion, 
corrosion resistance,  and physical and electrical properties.  However, the CTE of epoxy alone is 
too high to meet the requirements in most flip chip applications (>80 ppm/?C), so silica fillers 
are added to reduce the CTE and increase the effective elastic modulus of the underfill material. 
Underfill materials are then applied to fill the gap between the chip and the substrate, and 
also to bond with the solder joints.  They also provide environmental protection for the solder  
 
 
18 
 
 
 
Underfill Applied Wafer and Dicing 
 
 
 
Single Die Flip Chip before Reflow 
 
 
 
Single Die Flip Chip after Reflow 
 
Figure 1.10 - Wafer Level Underfill Process 
 
 
Die 
Die 
 
19 
joints and improves electronic package reliability, as the stress/stain level in solder joints is 
redistributed among the underfill, chip, substrate and solder joints.  Better underfill materials 
with desired values of CTE and elastic modulus are a key factor in the development of next 
generation low-cost, high-reliability flip chip technologies.  The desirable characteristics and 
advantages of an underfill materials are listed in Table 1.3 [15]. 
Some other critical properties of uncured and cured capillary flow underfills are 
viscosity, glass transition temperature (Tg), adhesion strength, and adhesion retention. Low 
viscosity (fast flow) increases manufacturing throughput.  The viscosity is affected by both filler 
content and particle size: the higher the filler content, the higher the viscosity, and the slower the 
flow rate; while a smaller filler size speeds up the flow rate.  Higher temperatures can produce 
higher kinetic energy, thus particles will diffuse more rapidly at elevated temperature with higher 
viscosity [16]. 
Good interfacial adhesion is required for high wettability of the underfill material with 
both the silicon die passivation layer and the substrate surface (soldermask).  Also, good 
adhesion retention requires that the underfill is not susceptible to environmental exposures such 
as constant temperature and humidity conditions, or thermal cycling. 
Low CTE underfills are able to reduce the thermal expansion mismatches between the 
underfill and the chip, solder bumps, and PCB.  This generally leads to better solder joint 
reliability.  A high glass transition temperature (Tg) is generally desirable because the underfill 
material becomes soft, adversely affecting its mechanical properties (stiffness and strength) when 
the temperature is close to or above the Tg.  A high elastic modulus helps counteract 
deformations due to CTE mismatches. 
 
 
20 
 
 
 
 
Characteristics Advantages 
High elastic E Low stress and stain 
High UTS High level for the cracks 
Low CTE Lower CTE mismatch between chip and substrate 
Low viscosity Good flowability 
Fine silica filler To low the CTE and fill the small gap 
Fast cure Reduce the time and cost 
Short fill time Quick fill time and low cost 
 
 
Table 1.3 - The General Desirable Characteristics and Advantages of an Underfill Material 
 
 
21 
The fundamental chemical differences between thermosetting and thermoplastic 
polymers are related the molecular bonding connections.  Thermosets are crosslinked and have 
primary covalent bonding connections between molecular chains, while thermoplastics have only 
relatively weak secondary bonding connections between chains.  Therefore, thermoplastics can 
be re-melted or re-molded, where thermosets cannot. Thermosetting epoxies are used in 
applications where high thermal and dimensional stability are required.  The mechanical 
properties of underfills, such as its elastic modulus (E), ultimate tensile strength (UTS), and 
CTE, are all strongly linked to temperature.  The glass transition temperature Tg is particularly 
important since the material characteristics undergo drastic changes around this temperature.  
The changes in relaxation modulus behavior with temperature are illustrated in Figure 1.11 for 
several different polymers [5]. 
The reliability of flip-chip technology using current underfill materials is generally lower 
than that of conventional wire-bond connection packaging materials such as epoxy molding 
compounds.  The main reason for this relatively poor performance is the high coefficient of 
thermal expansion values and moisture absorption ratios of cured underfill materials.  This 
results because underfill materials contain a smaller amount of silica filler than standard epoxy 
molding compounds to support good flowability during the underfilling process.  This problem is 
likely a major contributor to the relatively poor reliability of flip chip IC assemblies [17]. 
When using underfill, delaminations at the underfill/die or underfill/substrate interfaces 
in flip chip assemblies become the primary failure modes.  Such delaminations occur when the 
interfacial stresses are higher than the interfacial adhesion strength of the underfill polymer.  
Resistance to the initiation and growth of delaminations is therefore another critical issue for flip 
chip packages.  If interfacial cracks develop and propagate to neighboring solder bumps, the 
 
22 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.11 - Relaxation Modulus for A: Crystalline Polystyrene; B: Lightly Cross Linked 
Polystyrene; C: Amorphous Polystyrene [5] 
 
 
Temperature (oF) 
Re
lax
ati
on
 M
od
ulu
s E
, (1
0p
si)
 
Temperature (oC) 
Re
lax
ati
on
 M
od
ulu
s E
, (M
Pa
) 
 
23 
previously described stress relief on the solder joints will be lost and the onset of solder joint 
fatigue cracking will be hastened. 
1.7 Thermal Aging Process 
Mechanical properties of a material can evolve as a function of time, temperature, and 
stress level.  Of particular interest here is that the mechanical properties of an underfill can vary 
with time even when no stress is applied due to molecular structure changes over time.  Two 
phenomena must be taken into account when considering these behaviors: physical aging and 
chemical aging. 
It is well known that amorphous materials are not in thermodynamic equilibrium at 
temperatures below their glass transition temperature [18, 19].  Along with the evolution of state 
variables of volume or enthalpy, etc., there are some observable macroscopic property changes 
such as in the viscoelastic response and yield strength.  Such phenomena are referred to as 
physical aging.  The concept of free volume has been proposed to partially explain these 
behaviors [13-15].  In a closely packed system, the mobility of particles (M) depends on the free 
volume (Vf).  When material is cooled from above Tg to below Tg, the free volume and mobility 
decrease simultaneously.  However, if the free volume is greater than it would be in the 
equilibrium state, then it will continue to decrease slowly with time, and this is accompanied 
with a decrease in mobility.  Therefore, the mechanical properties of the material also change 
during the aging process. 
Meanwhile, chemical aging takes place when materials are exposed to elevated 
temperatures, the presence of humidity, and other environmental factors.  This leads to 
permanent changes in the material structure as a result of breaking or forming covalent chemical 
bonds in the polymer molecular chains.  Therefore, chemical aging is an irreversible process, 
 
24 
while physical aging is a reversible process [20].  In actual applications, chemical aging probably 
plays a decisive role in influencing the final properties of materials exposed to elevated 
temperature. 
Struik [19, 21] investigated the effect of physical aging on many polymeric and non-
polymeric materials, and found that momentary creep curves exhibit a universal shape, 
independent of chemical structure, thermal history, or test temperature.  He also listed some 
basic aspects of the physical aging process in polymers: 
? Aging affects properties primarily via changes in the relaxation times. 
? Aging is thermo-reversible, and does not affect secondary relaxations. 
? The aging range runs from above Tg to below Tg. 
? In the aging range, aging time is the most relevant material parameter. 
? In the aging range, the shift rate is close to unity for all polymers. 
? In the aging range, the small strain behavior of all polymers is almost identical. 
? Aging is a general phenomenon, and persists for very long periods of time. 
? Aging disappears at low temperature 
Due to the aging process, the mechanical properties of a polymer may change over time.  
However, analytical predictions of polymer strength and stiffness properties during irregular 
thermal or mechanical loadings are as yet extremely difficult.  They can, however, be tested 
experimentally.  For example, a study of one commercial polymer (D, L-lactide-co-glycolide) 
[22] revealed that tensile strength and shear strength exhibited a controlled decrease with aging 
time, as shown in Figure 1.12.  After nine weeks of isothermal aging, the specimens were no 
longer strong enough to be tested mechanically. 
 
25 
 
 
 
 
 
 
 
 
 
a ) Percentage of Tensile Strength 
 
 
 
 
 
 
 
 
 
b ) Percentage of Shear Strength 
 
Figure 1.12 - Variation of Initial Tensile and Shear Strength for (D, L-lactide-co-glycolide) with 
Aging Time [22] 
 
26 
Also, during long term thermal aging, polymer materials become stiffer, which means the 
compliance is decreased (or modulus increased) over time compared to samples that have not 
experienced the aging process.  A great deal of work has been done on evaluation of polymer 
creep behavior with aging.  These studies have indicated that the creep compliance decreases 
with aging time and a master curve can be constructed, as in the examples shown in Figures 1.13 
and 1.14 [23, 24].  For different aging times, the material creep compliance can be determined as 
in the isochronal plots in Figure 1.15 [13].  The material becomes stiffer as the aging progresses 
and the compliance value with 100 seconds aging time is reduced to around 60% of its initial 
value.  Similarly, it is possible to incorporate momentary creep curves at different aging times 
into a single master curve by applying the shifting and superposition method described below. 
Two principles, namely time temperature superposition (TTSP) and time stress 
superposition (TSSP), have been developed in order to estimate a material's mechanical 
properties by forming a master curve based on the results of multiple experimental tests, as 
shown in Figure 1.16 [5, 24].  TTSP permits users to substitute temperature for time, and thus 
perform short tests at various temperatures to predict the modulus as a function of a wide time 
period; whereas TSSP is able to perform the equivalent substitution of stress for time.  TTSP and 
TSSP can be combined into a master curve by shifting individual curves as a function of 
temperature or stress, while the relevant shift factors can be evaluated by applying the Williams-
Landel-Ferry (WLF) equation: 
)(
)(
)(
)(
1010 02
01
0
loglog TTC TTCTTTa ?+ ??== ??                                     (1.6) 
The WLF equation was developed from empirical curve fitting and C1 and C2 vary with different 
polymers.  Ferry has proposed the use of the following ?universal? constants, where T0 is taken 
to be Tg, the glass transition temperature [25]: 
 
27 
 
 
 
Figure 1.13 - Creep Compliance Curves for Syndiotactic Polystyrene (SPS140A) [24] 
 
 
 
  Figure 1.14 - Creep Compliance Curves for DGEBA/400 Diamine Epoxy Glass with 0.05% 
Mass Fraction CTBN Rubber [23] 
 
 
Aging Time 
Aging Time 
 
28 
 
 
 
 
 
 
 
 
 
a.) Creep Curves for Different Aging Time 
 
 
 
 
 
 
 
 
 
b.) Isochronal Values of Compliance 
 
Figure 1.15 - Variation of the Creep Response of Epoxy with Aging Time [13] 
 
 
 
 
29 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1.16 - Combination of TTSP and TSSP to Form a Master Curve [5, 24] 
 
 
 
 
 
30 
C1 = 17.4, C2 = 51.6                                                                  (1.7) 
 
It is important to note that the application of the WLF equation is limited to temperatures below 
the glass transition temperature, where amorphous polymers become sufficiently rigid for use in 
electronic assemblies. 
Finite element analysis (FEA) has been widely used to simulate the reliability of flip chip 
on laminate assemblies subjected to thermal cycling (e.g. -40 to 125 ?C) because of the long time 
and high costs involved to test the numerous new underfill materials emerging every year.  
However, the validity of the FEA simulation results depends strongly on the accuracy of the 
relevant material properties used for the analysis.  Underfills exhibit a complicated viscoplastic 
mechanic response that is highly sensitive to temperature, isothermal aging and thermal cycling 
effects, among others.  However, data on underfill mechanical properties are scarce on vendor 
datasheets.  In order to accurately model the behavior of underfills and other microelectronic 
encapsulants, detailed information on time and temperature dependent mechanical properties 
must be available.  Therefore, the primary goal of this research is to provide simple but accurate 
mathematic models that can be applied to predict evolution of the mechanical properties of 
underfill materials subjected to isothermal aging. 
1.8 Research Objectives 
Although there are already many studies on the characterization of the mechanical 
properties (stress-strain and creep) of underfill materials, the understanding of the effects of 
isothermal aging on the material behaviors remains inadequate.  Challenges and fundamental 
problems still need to be addressed to support successful underfill applications and ensure a long 
working life.  Finite element analysis can be used to improve the reliability of flip chip electronic 
packaging.  However, confidence in the results generated by FEA requires systematic 
 
31 
experimental data, and appropriate models that accurately describe the deformation behavior of 
the utilized underfills. 
The objectives of this research are to investigate the fundamental mechanical behaviors 
of underfill materials under various strain rates, isothermal aging processes, curing profiles and 
humidity levels as listed below: 
? Characterize the effect of the strain rate on underfill stress-strain behavior. 
? Characterize the effect of isothermal aging on underfill stress-strain behavior. 
1) Effect of different aging temperatures. 
2) Effect of different aging times. 
3) Effect of different testing temperatures. 
? Develop mathematical models for: 
1) The effect of strain rate on elastic modulus and ultimate tensile strength. 
2) The effect of isothermal aging on elastic modulus and ultimate tensile strength. 
? Investigate changes in creep behavior occurring in underfill encapsulants exposed to 
isothermal aging at elevated temperatures: 
1) Characterize the effect of isothermal aging on creep curves. 
2) Characterize the effect of isothermal aging on secondary creep rate. 
? Develop an understanding of the effects of aging temperature, aging time, and testing 
temperature on underfill creep behavior. 
? Develop mathematical models to describe the effects of isothermal aging on the 
secondary creep rate of underfill.  Provide basic underfill mechanical property data for 
finite element analyses of flip chip on laminate assemblies. 
 
 
32 
CHAPTER 2  
SPECIMEN PREPARATION AND UNIAXIAL TESTING 
 
 
2.1 Introduction 
There are some major challenges involved in building material property databases for 
underfills using representative uniaxial test samples for mechanical testing.  There are several 
possible approaches to making uniaxial specimens of underfill material, and there are no 
standards governing the specimen preparation process.  Additional problems arise due to the side 
effects of the chemical agents involved, and the existing mechanical property data are widely 
scattered.  Consequently, for this research a unique and controllable process had to be developed. 
In actual flip chip manufactured assemblies, the thickness of the underfill layer is very 
thin, typically about 75-125 ?m (3-5 mils).  Thus, the underfill layer cures relatively evenly, with 
a cure profile that is dependent on the oven temperature profile, the thermal properties of the 
materials, and configuration of the assembly materials.  However, if large bulk strip samples of 
underfill are prepared for material characterization using a molding procedure, it is likely that 
they will be subjected to non-uniform curing and thus will not accurately represent the 
mechanical response of actual flip chip underfill layers [10].  If thin samples are manufactured, 
great care must be taken to achieve the correct cure profile, constant thickness, and desired 
shape, all of which are critical.  For any size specimen, a method must be developed for 
 
33 
extracting cured test samples from the mold without inflicting damage or chemically changing 
the material.  This can be challenging since underfills are, by their nature, effective adhesives. 
Qian and coworkers [26] reported mechanical measurements on small underfill test 
samples.  In their work, 0.5 mm (20-mil) thick samples were prepared in a metal mold exposed 
to the cure profile recommended by the underfill vendor (Figure 2.1).  The samples were then cut 
by a diamond saw to have four to five times the thickness of true underfill samples.  However, 
the metal mold required the use of a release agent, which chemically altered the surface of the 
underfill samples. 
In the work of Rao, et al. [27], small samples were cast in a dog bone shaped Teflon mold 
(Figure 2.2).  The samples in this study were 0.5 mm thick and the group used a Dynamic 
Mechanical Analyzer (DMA) to characterize the stress-strain curves, temperature dependent 
storage, and loss moduli of the underfills. 
A method for generating thin (0.1 mm thick) underfill test samples was developed by Shi, 
et al. [28], who performed comprehensive mechanical testing on a typical underfill material over 
a range of temperatures and strain rates.  A rather complicated molding procedure was utilized to 
fabricate the specimens.  The mold included metal top and bottom plates made of steel and 
aluminum, respectively; and a thin silicone rubber middle layer (with a thickness of 0.1 mm in its 
compressed state) with a rectangular 20 x 3 mm cutout to define the in-plane dimensions of the 
test specimens.  The sample preparation procedure involved pouring the underfill into the 
uncovered heated mold and then placing the steel cover onto the filled silicone rubber middle 
layer.  Surplus underfill was extruded under pressure through an exit trough and the completed 
mold stack was placed in a box oven for curing.  After molding, it was necessary to use fine  
 
 
34 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.1 - Samples Used by Qian and coworkers [26] 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.2 - Samples Used by Rao, et al. [27] 
 
 
w-width of narrow section 2.5 mm G-Gage length 7.5 mm 
L-length of narrow section 10 mm D-Distance between grips 25 mm  
WO-width of overall  10 mm R-Radius of fillet 15 mm 
Lo-length overall  50 mm RO-Outer radius -- 
FP4526 Thin Strip 
Solvent 
Metal Mold 
Vacuum Chamber 
Preheating and Curing 
 
0.5 mm 
1.8 mm 
16 mm 
Diamond  
Saw Cutting 
 
35 
sandpaper on the samples to remove undesired material and adjust the specimen dimensions.  
The completed samples had nominal dimensions of 20 x 3 x 0.1 mm.  However, 10 mm of the 
length of the samples were buried in the specimen grips, leaving only a 10 x 3 x 0.1 mm sample 
of underfill subjected to stress and strain.  The length to width aspect ratio of these samples was 
therefore only 3.33, while at least 10 is typically desired to yield a reasonably pure uniaxial stress 
state in the specimen (Figure 2.3). 
Kuo, et al. [29] developed a similar method to fabricate freestanding thin sheets of 
underfill material by dispensing and curing the material between Teflon coated sheets (Figure 
2.4).  They then cut samples with dimensions of 20 x 6 mm between the specimen grips (once 
again with an aspect ratio of 3.33), and performed investigations on the effects of temperature 
and strain rate on the tensile stress-strain behavior.  This process was found to be an efficient 
way to remove the solvent and residual moisture on the substrate surface. 
Building on prior work by members of the author's research group [30], a new specimen 
preparation procedure for underfill mechanical testing was developed for this study that yields 90 
? 3 mm samples of the desired thickness (i.e., 0.075 - 0.125 mm).  During the tests, the active 
area of the extracted tensile samples (the region between the specimen grips) is 60 x 3 mm, 
giving a highly desirable aspect ratio of 20.  Using these samples, a microscale tension-torsion 
testing machine was applied to evaluate the uniaxial tensile stress-strain behavior of the underfill 
materials as a function of temperature and strain rate.  The results revealed that a three parameter 
hyperbolic tangent empirical model provides accurate fits to the observed underfill nonlinear 
stress-strain behavior over a range of temperatures and strain rates. 
 
 
36 
 
 
 
 
Figure 2.3 - Mold and Samples used by Shi, et al. [28] 
  
 
 
 
Figure 2.4 - Fabrication Process and Samples used by Kuo, et al. [29] 
 
 
 
37 
2.2 Experimental Underfill Material 
Underfill material is a special colloidal dispersion epoxy with fillers consisting of silicon 
dioxide particles incorporated into the organic liquid.  The specimen material, supplied by Lord 
Corporation (Thermoset), is Circuit SAF ME-525 flip chip underfill encapsulant.  In this work, 
the material is referred to as UF1.  It is a fast cure semiconductor grade epoxy system that 
reduces stress and adheres well to a variety of surfaces.  Due to its low viscosity, it can flow 
rapidly under devices with stand-offs as low as 25 ?m.   
General information for this underfill is listed in Table 2.1.  The manufacturer?s 
suggested curing procedure is to cure at 150 ?C for 30 minutes.  The vendor datasheet values of 
the glass transition temperature and the coefficient of thermal expansion are shown in Table 2.2.  
This material has been observed to have good adhesion to laminate, ceramic, solder mask, and 
metal surfaces.  
The underfill material microstructure and spherical silica filler are shown in the SEM 
image in Figure 2.5, in which the settling of the silica particles due to the higher density of the 
silica filler over the epoxy matrix is clearly visible.  There is a thin layer of pure epoxy on the top 
surface, with increasing amounts of the large size silica filler accumulating towards the lower 
surface.  The average size of the filler increases with depth, and the maximum diameter of the 
silica filler is about 10 ?m.  This epoxy composite has a relatively low coefficient of thermal 
expansion (CTE) that closely matches that of the solder bumps and thus minimizes the likelihood 
of crack initiation during thermal shock and thermal cycle testing.   
A typical experimental TMA result is shown in Figure 2.6.  The glass transition 
temperature marks the boundary between the two regions, and the CTE is 18.59 x 10-6 (1/ ?C) 
and 72.61 x 10-6 (1/ ?C), respectively, when the temperature is below and above the Tg. 
 
38 
 
 
 
 
Ingredient Weight % 
Bisphenol F Type Epoxy 12% 
Other Epoxy: Multifunctional Epoxy Resins 5% 
Anhydride: HHPA or Similar Hexahydrophthalic Anhydride 15% 
Filler, Fused Silica 65% 
Other Ingredients 3% 
 
Table 2.1 - Underfill Material Composition 
 
 
 
 
 
 
Underfill 
Material gT  
CTE ? (1/oC) 
(Below Tg) 
Recommended 
Cure Conditions 
UF1 137 ?C 25 x 10-6 150 ?C / 30 min 
 
 
Table 2.2 - Underfill Material Characteristics and Cure Procedure 
 
39 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.5 - Microstructure of the Underfill Material with Silica Filler 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.6 - Thermo-Expansion TMA Test Results for the Underfill Material 
 
 
-40 -20 0 20 40 60 80 100 120 140 160 180
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
C TE : 72.61 u m/m C
195.61 C
160.82 C
C T E : 18.59 u m /m C 70.97 C
7.71 C
135.52 CDi
sp
la
ce
m
en
t (
m
m
)
TM A
Tem perature (?C)
 
40 
According to the manufacturer, the combination of a moderate Tg and modulus, along 
with excellent thermal shock performance, makes this underfill material well suited to 
demanding, high-end ceramic and automotive applications.  In contrast to the older underfill 
systems, it can be quickly cured in 30 minutes at 150 ?C without the need to implement a two-
step curing process to minimize stress.  Due to its high purity formulation, it also provides the 
ionic purity level required for high-end microelectronics applications, thus minimizing the 
chances of ion-induced corrosion in these devices. 
In summary, the commercial underfill utilized in this work, UF1 is a silica filled epoxy 
with Tg = 135 ?C (TMA) and 145 ?C (DMA).  This underfill is widely used in high performance 
ceramic and automotive applications to lower the stress between the substrate and solder bumps. 
2.3 Specimen Preparation Procedure 
Frozen underfill syringes stored at -40 ?C were allowed to reach room temperature before 
dispensing.  A stacked assembly view of the uniaxial tension specimen mold utilized in this 
investigation is pictured in Figure 2.7.  Various parts of the assembly were clamped together by 
removable end clips (not shown).  The middle layer consisted of precision shims with a thickness 
of 125 ?m (5 mils) that defined the sample thickness.  Molds were made from steel and coated 
with a thin Teflon layer on all surfaces.  The top portion of the mold assembly was machined to 
contain 9 rectangular crossbars (90 x 3 mm) with a constant separation maintained via the 
remaining steel material at the ends of the crossbars.  The shims separating the two plates were 
located under the front and rear connecting regions of the steel sheet, not under the crossbars 
themselves.  The crossbars define the specimen shape and the final specimen dimensions are 
shown in Figure 2.8. 
 
 
41 
 
Figure 2.7 - Specimen Mold Assembly 
 
 
 
 
 
 
 
 
 
Dimension Typical Values (mm) 
Length 90 
Width 3 
Thickness 0.125 
 
Figure 2.8 - Underfill Uniaxial Specimens and Final Dimensions 
 
 
42 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.9 - CAM/ALOT System 3700 and Underfill Material Dispensing 
 
 
 
43 
A CAM/ALOT System 3700 machine was used to dispense the underfill material to the 
mold (Figure 2.9).  The mold assembly was first heated to 80 ?C in a box oven for about 10 
minutes to remove all moisture. It was then preheated to 105 ?C using a heat source located 
underneath the work station in the CAM/ALOT 3700, after which underfill encapsulant was 
dispensed along one side of each steel crossbar via a production line programmable dispensing 
system.  Fiducial markings were included on the top of the steel sheet to aid in the 
programmability and repeatability of the dispensing procedure.  Once dispensed, the underfill 
encapsulant quickly ran under the 5 mil thick gap under each crossbar via capillary flow.  This 
procedure consistently produced constant thickness underfill regions, which were sandwiched 
between the Teflon coated top and bottom mold plates. 
The uncured mold assemblies were then cured in a reflow oven at 150 ?C for 30 min 
(Figure 2.10), using the vendor recommended underfill cure profile.  The temperature profile 
during the underfill curing process is shown in Figure 2.11.  After curing, the material was 
removed from the oven and cooled down to room temperature.  Due to the Teflon coatings, the 
uniform thickness cured rectangular samples were easily separated from the mold.  A razor blade 
and fine silica paper were used to trim any unevenness from the ends of the samples.  Using the 
method described here produced samples with a controllable, constant thickness that were easily 
removed from the mold assembly without the need for chemical releasing agents.  Therefore, no 
changes in the underfill mechanical behavior were induced by molding process.  The lengths of 
the final trimmed samples were in the range of 70-90 mm, providing a specimen length to width 
aspect ratio of more than 20.  An added benefit of this method was that the test samples were 
cured using the same production equipment and processing conditions used in industry.  A 
comparison of the various specimen preparation methods is shown in Table 2.3.  
 
44 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.10 - Underfill Material Curing Oven 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.11 - Temperature Profile During the Underfill Material Curing Process 
 
 
 
Table 2.3 - Comparison of the Specimen Preparation Methods 
 Release Agent Length/Width Ratio Diamond Saw Cutting After Molding Finishing 
Qian [26] Yes 8 Yes No 
Rao [27] No 3 Yes SiC paper 
Shi [28] Yes 3.3 No SiC paper 
Kuo [29] No 3.3 Yes SiC paper 
Islam [30] No 20 No SiC paper 
Time (m)
0 10 20 30 40 50 60 70
Te
mp
era
tur
e (
o C
)
20
40
60
80
100
120
140
160
180
200
y = 9.3738x + 8.0146
 
45 
The steps involved in the new uniaxial specimen process for underfill materials proposed 
here are summarized below: 
? Thaw the underfill material 
? Mold dehydration at 80 ?C for about 10 minutes. 
? Pre-heat mold ambient temperature to 105 ?C  
? Align dispense process by fiducial markings 
? Determine the height of the needle above the surface (z axis) 
? Dispense underfill and post-heating ? curing process 
? Specimen release 
2.4 Mechanical Testing System 
In this study, the MT-200 microscale tension/torsion thermo-mechanical test system from 
Wisdom Technology, Inc. shown in Figure 2.13, along with its associated environmental 
chambers, was utilized to test the samples.  According to the manufacturer?s specification, the 
computer controlled actuators of the system provide an axial displacement resolution of 0.1 
micron and a rotation resolution of 0.001?.  A universal 6-axis load cell is utilized to enable users 
to simultaneously monitor three forces and three moments during sample mounting and testing, 
and then collect the data for further analysis.  Testing can be performed in tension, shear, torsion, 
bending, and combinations of these loadings on small specimens such as those used in this 
research.  In addition, cyclic (fatigue) testing can be performed at frequencies of up to 5 Hz.  Hot 
and cold environmental chambers employ a resistance heater and liquid nitrogen diffuser to 
allow samples to be tested over temperature ranges of -185 to 25 ?C and 25 to 300 ?C, 
respectively.  This system was used to fully characterize the underfill material.  Uniaxial stress-
strain tests were conducted with strain rates of ?&  = 0.001, 0.0001, 0.00001 sec-1. 
 
46 
 
 
(a) Microscale Test System (MT-200) 
 
 
 
 
(b) Chamber for Elevated Temperature Testing (+25 to +300 ?C) 
 
 
 
 
(c) Chamber for Low Temperature Testing (-185 to +25 ?C) 
 
Figure 2.12 - Testing System and Environment Chambers 
 
 
 
47 
Using the mechanical test system, tensile and creep tests were conducted.  Specimen 
alignment and careful clamping techniques were used to obtain consistent and accurate testing 
results.  Specimen alignment is a critical feature for the microtester because a small bending 
moment or torque could break thin brittle samples if they are not perfectly aligned.  By carefully 
adjusting the corresponding stages during clamping, the initial forces were adjusted to be close to 
zero.  Tensile tests were performed under displacement (stoke) control, giving the stress-stain 
relationship at a particular strain rate and testing temperature.  The creep tests were performed 
under constant force mode, giving the strain response versus time under constant applied stress 
and temperature. 
2.5 Experimental Method and Mechanical Properties 
Due to the robustness and reliability required in flip chip packaging, the mechanical 
properties of the underfill material are very important.  These were intensively investigated in 
this research and mathematical models were developed to fit the measured results.  Uniaxial 
tensile stress-strain tests and creep tests were used to characterize the mechanical properties. 
2.5.1 Tensile Stress Strain Properties 
During uniaxial stress-strain testing, forces and displacements were measured.  The axial 
stress and axial strain were calculated from the applied force and measured cross-head 
displacement as follows: 
A
F=?                                                      (2.1) 
LL
L ?? =?=                                                                  (2.2) 
 
48 
where ? is the uniaxial stress, ? is the uniaxial strain, F is the measured uniaxial force, A is the 
original cross-sectional area, ? is the measured cross-head displacement, and L is the specimen 
gage length (initial length between the grips).  For the tests in this study, stroke (displacement) 
control was utilized. 
Temperature has a major impact on material properties in polymers.  The underfill 
material demonstrates five regions of viscoelastic behavior, namely the glassy, transition, 
rubbery, rubbery flow and liquid flow regions (Figure 1.11), although the last two are not seen in 
thermoset polymers.  At sufficiently high temperatures, decreases in the material modulus lead to 
a significant change in properties. 
Extensive work has been done on the results of polymer tensile tests, and various 
equations have been proposed by different authors to describe the mechanical properties of 
different kinds of underfill epoxy, as shown in Table 2.4.  Although the variables in these models 
include factors such as testing temperature and strain rate, none consider the effect of aging, 
either in the form of aging time or aging temperature.  To address this shortcoming, in this work 
constitutive models were developed to take into account isothermal aging effects. 
2.5.2 Creep Properties 
Another fundamental method used to characterize the viscoelastic time-dependent 
behavior of a polymer is the creep test.  Creep deformation is particularly likely at elevated 
temperatures.  In electronic packaging applications, creep failure is a well accepted mechanism; 
as solder ball joints cracks occur when packages are subjected to thermal or power cycling.  In 
the creep test, a constant force is applied quasi-statically to a uniaxial tensile specimen and the 
resulting deformation of the material is observed over time.  Creep behavior is the time 
dependent strain deformation at constant uniaxial stress and creep deformation is one of the 
 
49 
 
 
 
 
 
 
Table 2.4 - Models for the Mechanical Properties of Epoxy Underfills 
Model Tested Material Testing Type Variables Reference 
010 )]1([
2 EeffE Tf ???+= ?  Dexter Hysol Tensile T Rao [4] 
2101 )(log EEE +?= ?&  Lord Tensile ?&  Islam [30] 
)(ln10 GPaCTEEE ?+= ?&  Hysol FP4526 Tensile T, ?&  Qian [26] 
E/ mC?=? &   Tensile ?&  Hertzberg [31] 
E=ln(a-bT)-ce(-d/T)+E1ln?& +E0               
T<Tg 
=ln(a-bT)-ce(-d/T)+E1ln?& +E0     
T>Tg 
Hysol FP4549 Tensile T, ?&  Kuo [29] 
 
50 
major failure modes in electronic packages.  In this study, tests are carried by different loads at 
various temperatures for different prepared specimens. 
Generally, a creep curve is composed of three stages, as shown in the typical creep curve 
in Figure 2.13.  Once a constant load is applied, the initial instantaneous strain that is formed 
produces the primary creep, which consists of elastic or time-independent plastic deformation.  
This is followed by the secondary creep, or steady-state creep, which proceeds at a nearly 
constant rate.  The secondary creep region is very important, as most of the deformation over the 
lifetime of a product takes place in this period.  This is also the dominant deformation mode for 
underfill materials.  In this stage the strain rate is retarded by strain-hardening due to the action 
of the molecular chains, which repair broken chains to strengthen the network.  Finally, during 
the third stage of tertiary creep, the breakage of covalent bonds in the materials proceeds at an 
ever increasing rate and eventually the material fails in fracture. 
There are several mathematical models capable of representing the creep behaviors of 
viscoelastic materials with good accuracy.  The Boltzmann superposition principle is widely 
accepted as a linear viscoelastic model and is based on the assumption that the total strain can be 
determined from the algebraic sum of strains, no matter how the stress is applied.  This can be 
represented in the hereditary integral form [32]: 
??
????
?=?=
tt
dddtJtdtJt ???????? )()()()()(                                      (2.3) 
This equation can be used to determine the total strain for any general loading history. 
An empirical power function with good accuracy over a wide span of time for creep 
response was proposed by Findley and Khosla [33].  This approach uses what may be described 
as a separable time-independent and time-dependent strain: 
 
 
51 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.13 - A Typical Creep Curve 
 
Secondary Creep
(Steady-State)
Time, t (sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.00
0.01
0.02
0.03
Creep Curve
Tertiary Creep
Rupture
Primary Creep
Initial Strain
(Elastic +Plastic)
/dtd   ?=?&
 
52 
nt??? ?+=
0                                                     (2.4) 
 
where t is the time, n is a constant independent of stress and is generally less than one, 0?  is the 
time-independent strain, and? ?  is the coefficient of time dependent term.  Both 0?  and ? ? are 
functions of stress.  This power law equation has been widely used for creep in several different 
polymers in tension, compression, torsion, etc.  By rearranging and taking logarithms, equation 
(2.4) yields: 
tnloglog)log( 0 +?=? ???                                             (2.5) 
In the resulting log-log plot, the value of n can be determined from the slope of the straight line 
response and ? ? is the vertical axial intercept value.  To consider the nonlinear range of stress, 
the coefficients in the creep law can be taken as stress dependent.  For example: 
tleakE qctp ???? +?+= ? )()/(                                    (2.6) 
Many mechanical models have been proposed to describe the nonlinear behavior of 
viscoelastic materials.  For example, Eyring [34] suggested a hyperbolic sine law as below: 
?
??
?= sinhD&                                                    (2.7) 
where D and ? ?  are constants. 
Garofalo's hyperbolic sine law [10, 35, 36], expands on the Eyring relation and takes into 
account that steady state creep strain rates are strongly stress and temperature dependent: 
?????? ???=? RTQn e)][sinh(C&                                           (2.8) 
where ? is the applied stress, T is the temperature, R is the universal gas constant, n is the stress 
exponent, Q is the activation energy, and ? and C are material dependent constants. 
Recently, The Anand model has been proposed as a unified model that does not require 
explicit yield conditions or loading/unloading criteria.  The equation is expressed as:  
 
53 
?
?
??
?
? ?
??
?
??
? ?
?
??
?
?= RTQm
P esA
1
sinh ???&                                     (2.9) 
where p?& is the inelastic strain rate, A is a constant, ?  is the stress multiplier, ? is the stress, R is 
the gas constant, m is the strain rate sensitivity, Q is the activation energy, and T is the absolute 
temperature.  The flow equation can be easily modified to represent the hyperbolic sine model 
for secondary creep rate as shown in equation (2.8).  
The Anand model also employs a single scalar internal variable s to represent the 
isotropic resistance to inelastic flow of the material.  The scalar variable is related to the dynamic 
process of strain hardening and dynamic recovery: 
p
*
0
*s
s1
s
s1
*s
s1hs ?
?
?
?
???
?
?
?
?
???
?
?
?????? ?
??
?
??
? ?= &&                                          (2.10) 
and 
n
RT
Q
p e
Ass ???
?
?
?
?
?
= ??
??
?
??&
?*                                                 (2.11) 
where s* represents a saturation value at a given temperature and strain rate, s?  is a coefficient 
and n is the strain rate sensitivity at the saturation condition.  The nine constants presented in the 
above equations are A, Q, m, n, a, h0, ? , s? , and s0, and the initial value of the deformation 
resistance must also be determined for the viscoplastic Anand model. 
When using ANSYS finite element software to model steady state creep, the sinh law is 
included in the Anand model for the viscoplastic elements.  A user defined model can be defined 
[10]: 
)(
21
4
3)][sinh( T
C
C eCC ?= ??&                                        (2.12) 
 
54 
where C1 to C4 correspond with A, 1/m, ?/s, and Q/k, respectively.  However, viscoplastic 
element models only apply to elasticity and steady state creep, not plasticity, because they lead to 
increasing error when the deformation is low or the strain rate is high.  In an attempt to address 
this shortcoming, a double power law model has been proposed to overcome the absence of 
plastic behavior in the Anand model [10]: 
)(
4
)(
1
6
5
3
2 T
C
CT
C
C eCeC ?? += ???&                               (2.13) 
This is made up of two power law terms that need to be separately implemented for primary and 
secondary creep models, and the units for the parameters are listed below in Table 2.5. 
Currently, most researchers use multiple variable fitting methods to determine the 
constants based on experimental data.  The Anand model has been widely used in ANSYS 
software to solve the viscoelastic and plastic-elastic material problems. 
Table 2.6 summarizes the constitutive models used for epoxy material creep curves and 
the secondary creep rate.  The variables in these models include testing temperature, strain rate 
and stress level.  However, but no aging parameters (e.g. aging time or aging temperature) have 
been taken into account in prior work. 
 
55 
 
 
Parameter C1 C2 C3 C4 C5 C6 ? T ?&  
Unit s-1 - K s-1 - K MPa K s-1 
 
Table 2.5 - Table of Constant Values for the Parameters  
 
 
 
 
Creep Curve Power Law nt??+= ??? 0  
  BteA ct +?+= ? )1(00??  
 Nutting Equation nptk?? =  
 Hyperbolic Sine )/sinh()/sinh( 00 +++= ??????? nt  
Creep Stain 
Rate Norton?s Power Law ?& =A1 RT
Q
ne??  
 Arrhenius Power Law ?& =A2 RT
Q
n e
ET
E ?)(?  
 Hyperbolic Sine Law ??? ?= sinhD&  
 Garofalo Hyperbolic Sine Law ?????? ???=? RTQn e)][sinh(C&  
 Anand Model Flow Rule ??
??
?
? ?
??
?
??
? ?
?
??
?
?= RTQm
P esA
1
sinh ???&  
 
Table 2.6 - Constitutive Models for Epoxy Creep Behavior 
 
 
56 
CHAPTER 3  
EFFECTS OF TEMPERATURE AND STRAIN RATE 
 ON THE PROPERTIES OF UNDERFILL 
 
 
3.1 Introduction 
The reliability of an electronic package is strongly dependent on the thermo-mechanical 
properties of its constituent materials.  The thermo-mechanical behavior of an underfill is highly 
sensitive to temperature and strain rate because of its morphology of filled particles and polymer 
resin [26].  The detailed characterization of underfill materials is one of the major factors 
involved in the development of a new flip carrier product and largely determines its cycle and 
cost.  One of the major challenges in flip chip package development is package cracking, 
particularly die cracking and underfill cracking [27]. 
Uniaxial tensile tests are usually performed on the underfill specimen to study its 
mechanical behavior.  Underfill is often modeled using very simple elastic material concepts.  
Zhang and Shi [37] reviewed several modulus concepts for viscoelastic materials, and pointed 
out that constant strain rate tests were better able to characterize the stress-strain behavior and 
the elastic modulus.  They also suggested that the tangent modulus, or the derivative of the 
stress-strain curve at a constant strain rate, corresponded exactly with the relaxation modulus 
from the stress relaxation test.  It has also been shown that viscoelastic models for a polymeric 
encapsulant perform much better than elastic models, which induce significant errors due to a 
 
57 
lack of information concerning the time and temperature dependant properties of the polymer.  
Generally, two types of modeling approaches are used: linear elasticity and linear viscoelasticity 
[10].  The behavior of viscoelastic materials must be expressed by a constitutive equation which 
includes time as a variable.  Viscoelastic material behavior is normally studied by three types of 
experiments: stress-strain tests under constant strain rate, creep test and stress relaxation tests 
[32]. 
Rao and coworkers [4] investigated three underfill materials, and used a dynamic 
mechanical analyzer DMA to obtain the stress-strain relationship under controlled force mode, 
the storage and loss moduli with multi-frequency vibration, and the stress relaxation behavior.  
They modeled the dependence of the elastic modulus on temperature using: 
010 )]1([
2 EeffE Tf?+=                                                 (3.1) 
The strain rate effect was not taken into consideration. 
Over the range of strain rates considered by Islam, the elastic modulus shows a linear 
dependence on the logarithmic strain rate at each temperature [38]: 
2101 )(log EEE += ?&                                                 (3.2) 
where E1 and E2 are temperature dependent material constants.  Similar results were reported by 
Shi. etc [39]. 
Qian, et al. [26, 40] studied the viscoelastic-plastic properties of the HYSOL FP4526 
underfill, and proposed a constitutive model for underfill material behavior.  In their work, which 
was well below the glass transition temperature, the elastic modulus was expressed as: 
TE )02795.0(ln)1871.0(3145.17 ?+= ?&  (GPa)                          (3.3) 
where T is the absolute temperature and 
 
58 
ijij ??? &&& 3
2=                                                        (3.4) 
is the von Mises strain rate.  Furthermore, the same group used a set of three dimensional 
constitutive equations to fit and predict the stress-strain experimental curves.  They suggested 
that this framework also shows potential for the study and design of flip chips and packages. 
Kuo and coworkers [29] suggested a way to model the dependence of the elastic modulus 
on temperature and strain rate by using separate equations above and below the glass transition 
temperature of the underfill material.  They also predicted the creep behavior at different test 
temperatures and stress levels by using a hyperbolic-sine power law equation.  Ernst and 
coworkers [41] studied changes in the viscoelastic properties during the curing process by 
applying the constitutive curing theory.  In their work, the mechanical properties, time dependent 
stiffness function, and initial strain evolution were established by means of specially designed 
DMA measurements. 
In conclusion, there have been limited prior studies on underfill that have included the 
effects of viscoelasticity on their properties and behavior. 
3.2 Objectives and Testing Program 
In this chapter, the mechanical behavior of a particular underfill (UF1) was explored 
using stress-strain tests at different temperatures and strain rates.  The uniaxial tensile specimens 
for mechanical testing were prepared using the method described previously in Section 2.3.  The 
uniform specimens produced had a gage length of 60 mm, and were 3mm wide.  The tests were 
carried out under six different testing temperatures (25, 50, 75, 100, 125, and 150 ?C) with three 
different strain rates (0.001, 0.0001, and 0.00001 sec-1).  The test matrix is shown in Table 3.1.  
Each specimen was kept in the environmental chamber with the desired stable ambient 
 
59 
temperature for 5 minutes before the load was applied, and at least five specimens were tested 
for any given set of conditions.  The testing temperatures covered the entire range from below 
the Tg to well above Tg. 
3.3 Tensile Testing Data and Empirical Model  
Figure 3.1 shows a typical stress-strain curve for the underfill UF1 at a temperature T = 
100 ?C, and a strain rate of ?&  = 1 x 10-3 sec-1.  The effective elastic modulus E is defined as the 
slope of the initial linear portion of the stress-strain curve.  Since the underfill material is 
viscoelastic, this effective modulus is rate dependent and will approach the true elastic modulus 
as the testing strain rate approaches infinity.  The ultimate tensile strength ?f  (UTS) is the stress 
level at failure (fracture).  The ultimate failure strain ?f (elongation) is the maximum strain 
realized in the stress-strain test data, at which point the specimen fractures. 
Since a minimum of five specimens were tested for any given condition, an empirical 
three-parameter hyperbolic tangent model was used to model the observed nonlinear underfill 
stress-strain data.  The general representation of the hyperbolic tangent empirical relation is  
? (?) = C1 tanh (C2?) + C3?                                           (3.5) 
where C1, C2, and C3 are material constants.  Differentiation of equation (3.4) gives an 
expression for the initial (zero strain) elastic modulus: 
E = C1C2 + C3                                                      (3.6) 
Constant C3 represents the limiting slope of the stress-strain curve at high strains. The constants 
C1, C2 and C3 can be determined by performing a nonlinear regression analysis of equation 
(3.5)to a given set of experimental data. 
 
 
 
60 
 
 
 
 
 
 
 
 
 
Table 3.1 - Table of Sample Test Temperatures and Strain Rates 
 
 
 
 
Testing Temperature Strain Rate (1/s) 
25? C 50? C 75? C 100? C 125? C 150? C 
0.001 * * * * * * 
0.0001 * * * * * * 
0.00001 * * * * * * 
 
61 
 
 
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012
St
res
s, 
? (
MP
a)
0
10
20
30
40
50
60
Strain Rate = 0.001
?
f
?
f
E
 
 
       Figure 3.1 - A Typical Temperature Dependent Underfill Stress-Strain Curve 
(T = 100 ?C, and ?&  = 1 x 10-3 sec-1) 
 
 
 
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012
St
res
s, 
? (
MP
a)
0
10
20
30
40
50
60
? (?) = C1tanh (C2?) + C3?
Model
Strain Rate = 0.001E
?f
?f
 
 
 
       Figure 3.2 - Hyperbolic Tangent Model Fit to Underfill Stress-Strain Curves 
(T = 100 ?C, and ?&  = 1 x 10-3 sec-1) 
 
 
62 
Applying this empirical approach, Figure 3.2 shows the associated hyperbolic tangent 
model fit for all of the raw stress-strain data for non-aged specimens that were tested at T = 100 
?C.  At least 5 tests were performed for each set of conditions in this work.  The observed 
variation in the data between different tests under the same condition is typical for cured 
polymeric materials.  The hyperbolic tangent model fit (red curve) provides an excellent 
representation of the data that lies in the middle of all of the experimental curves. 
Similar results were recorded for the different temperatures and strain rates considered.  
In each case, the hyperbolic tangent empirical model was used to produce a mathematical 
description of the ?average? stress-strain curve for a set of experimental curves measured under a 
fixed set of test conditions.  All of the data presented in this dissertation were processed in this 
manner.  In each case, from 6-10 experimental stress-strain curves were initially measured, and 
then fit by an ?average? stress-strain curve that mathematically represented the entire data set.  
From this point on, for clarity and simplification, only the hyperbolic tangent empirical fitting 
curves are presented. 
3.4 Experimental Results and Discussions 
3.4.1 Stress-Strain Curves  
The underfill encapsulant material exhibits significant viscoelastic behavior.  Therefore, 
its stress-strain relationship greatly depends on the testing temperature and displacement strain 
rates.  In order to compare and investigate the temperature effects on the tensile mechanical 
properties of the underfill, all of the stress-strain curves at a given strain rate were combined into 
a single graph as shown in Figure 3.3.  At each strain rate, the underfill material became soft, 
with markedly reduced strength, as the testing temperature increased. 
 
63 
The curves in Figure 3.3 were re-organized into constant temperature plots as shown in 
Figure 3.4.  At each temperature, the stress-strain curves shifted lower and to the right as the 
testing strain rate went down.  Obviously, testing temperature and strain rate have a great 
influence on important underfill mechanical properties, such as elastic modulus, ultimate tensile 
strength, and elongation. 
 
3.4.2 Elastic Modulus 
The purpose of underfill material is to reduce stress between the die and substrate, so a 
relatively low elastic modulus is preferred in order to relieve the inelastic stress sustained by the 
solder joints.  On the other hand, the material must be stiff and strong enough to maintain the 
shape and co-planarity of the package.  From Figures 3.3 and 3.4, the elastic modulus decreases 
monotonically with increasing temperature and a slower strain rate.  This variation is shown 
graphically in Figure 3.5. 
The modulus decreases linearly with temperature when the temperature is below 100 ?C, 
which is far below the published glass transition temperature (Tg = 137 ?C), and the underfill 
remains in the glassy state.  When the temperature rises from 100 ?C to 150 ?C, the elastic 
modulus drops dramatically indicating the glass transition region where rubbery behavior 
dominates.  The temperature has a strong effect on the elastic modulus during the transition 
period from glassy state to rubbery state.  The elastic modulus is very low at 150 ?C (above Tg) 
due to the weak network bonding in the rubbery state.  Note that at 125 ?C the elastic modulus 
value at a strain rate of 0.001/s is much higher than for slower strain rates, which can be 
attributed to the fact that the strain rate of 0.001 sec-1 is much faster than the intrinsic regrouping 
speed of the molecular network in the rubbery state.  The molecular chains have enough time to  
 
64 
 
 
 
 
 
 
 
 
 
 
 
 
 
(a) 
 
 
 
 
 
 
 
 
 
 
 
 
 
(b) 
 
 
 
 
 
 
 
 
 
 
 
 
 
(c) 
 
    Figure 3.3 - Stress-Strain Curves for Different Temperatures at a Constant Strain 
Rate: (a) 0.001 (1/sec), (b) 0.0001 (1/sec), (c) 0.00001 (1/sec) 
 
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
Strain Rate = 0.0001
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Strain Rate = 0.00001
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
Strain Rate = 0.001
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
 
65 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    Figure 3.4 - Comparison of Stress-Strain Curves Tested at the Same Testing  
Temperature for Different Strain Rates 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
? = 0.001
? = 0.0001
? = 0.00001
T = 75 oC
Increased
Strain Rate
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
? = 0.001
? = 0.0001
? = 0.00001
T = 100 oC
Increased
Strain Rate
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
? = 0.001
? = 0.0001
? = 0.00001
T = 125 oC
Increased
Strain Rate
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
? = 0.001
? = 0.0001
? = 0.00001
T = 150 oC
Increased
Strain Rate
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
? = 0.001
? = 0.0001
? = 0.00001
T = 25 oC
Increased
Strain Rate
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
? = 0.001
? = 0.0001
? = 0.00001
T = 50 oC
Increased
Strain Rate
 
66 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.5 - Temperature Effects on the Underfill Elastic Modulus 
 
 
 
 
 
 
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
? = 0.001
? = 0.0001
? = 0.00001
Strain Rate
 
67 
slip, break and reconnect to each other under much slower strain rates, thus producing a much 
lower values of the elastic modulus. 
The underfill material shows interesting behaviors during the transition from the glassy 
state to the rubbery state as the temperature increases through the Tg.  For slow strain rates, the 
polymer molecules can break the existing cross-linked network and form a new structure when 
outside force is applied, and the local stress/strain can be released by the new orientated chain 
segment structure.  However, if the strain rate is too high, the material has insufficient time for 
the segment to regroup and faults in the structure propagate, ultimately causing a fracture to 
occur. 
3.4.3 Ultimate Tensile Strength 
The effects of temperature on the ultimate tensile strength (UTS) of the underfill material 
are presented in Figure 3.6.  The UTS decreases linearly with temperature relatively gently from 
25 ?C to 100 ?C, but then sharply decreases in the temperature range from 100 ?C to 150 ?C.  It 
is interesting to see that the temperature has similar effects on the elastic modulus and ultimate 
tensile strength.  As it moves from the glassy to the rubbery state, the UTS decreases markedly 
because of the weaker molecular bonding forces.  The discrepancy in the curve shape at 125 ?C 
can be explained by the strain rate effect, as previously described. 
3.4.4 Elongation 
The effects of temperature and strain rate on the underfill elongation are shown in Figure 
3.7.  The specimen elongation (strain at failure) is calculated using: 
%100
0
0 ??=
L
LLe f                                              (3.7) 
 
 
68 
 
 
 
 
 
 
 
 
 
Figure 3.6 - Temperature Effects on the Underfill Ultimate Tensile Strength 
 
 
 
 
 
 
 
 
 
 
Figure 3.7 - Strain Rate Effects on the Underfill Elongation 
 
 
 
Temperature, T (oC )
0 25 50 75 100 125 150 175
Elo
ng
ati
n (
%)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
? = 0.001
? = 0.0001
? = 0.00001
Strain Rate
Temperature, T (oC )
0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
20
40
60 ? = 0.001
? = 0.0001
? = 0.00001
Strain Rate
 
69 
where Lf is the final specimen gauge length at fracture, and L0 is the original specimen length.  
The underfill elongation has a nonlinear relationship with temperature as shown in Figure 3.7.  
The elongation remains relatively constant or increases slightly below 75 ?C for all strain rates.  
The underfill then becomes much softer as the temperature increases from 75 ?C to 150 ?C 
during the state phase transition, thus exhibiting greater extension ability.  The strain rate also 
exhibits its strongest effect in this region, as at lower strain rates the material has enough time for 
the molecule-chain to slip and reform to achieve a longer extension before fracture. 
The underfill material tested showed its largest elongation at 125 ?C (close to the Tg), 
because at this point it is still strong enough for the cross-linked network structure to elongate 
without early fracture.  This may explain the shorter extension of the specimen at 150 ?C due to 
its much lower ultimate tensile strength in the rubbery state.  Once the testing temperature 
exceeds the glass transition temperature, the strain rate has a weaker effect on the elongation 
because the material extends to its fullest extent in the rubbery state.  Therefore, the curves for 
all three of the different strain rates shown in Figure 3.7 merge together at 150 ?C. 
3.5 Effects of Temperature and Strain Rate on Tensile Properties 
The experimental values for the mechanical properties of the underfill material are 
summarized in Table 3.2.  From the results, the properties are strongly strain rate dependent.  
Some authors [26, 30] have pointed out that the mechanical properties are linear with the 
logarithmic strain rate: 
??? &log10 c+=                                                                (3.8) 
Figure 3.8 illustrates the linear dependence of the elastic modulus on the logarithmic 
strain rate.  The corresponding fitting constants are listed in Table 3.3.  Only a weak strain rate 
effect was observed for the elastic modulus lower temperatures, but a significant effect was 
 
70 
observed at higher temperature levels near the Tg.  The slope of the curve at 150 ?C is smaller 
because the elastic modulus values are much smaller in the rubbery state.  Similarly, the ultimate 
tensile strength shows a linear relationship to the logarithmic strain rate as shown in Figure 3.9.  
In both cases, the linear fits are poorest at T = 125 ?C, which is very near the Tg. 
Hertzberg [31] suggested a power law relation for material strength with strain rate: 
mCUTS ?&=                                                                    (3.9) 
where m is the strain-rate sensitivity factor, or strain hardening exponent.  An analogous relation 
can also be used for the elastic modulus.  Table 3.4 contains the fitting constants for power law 
models used to fit the elastic modulus and UTS data in Figure 3.8 and 3.9.  From the calculated 
R2 values, it is clear that the power law also gives a good fit for all of the experiment data. 
3.6 Simultaneous Modeling of the Effects of Strain Rate and Temperature 
A number of researchers have provided constitutive models with both temperature and 
strain rate variables.  For example, Qian [40] proposed the unified relation in equation (3.3) that 
included these two factors as independent variables, but the testing temperature range was far 
below the Tg.  Although mechanical properties were easily fitted by this simple equation, it 
cannot be used for test temperatures that are near to or above Tg. 
Pang, et al. [42] suggested empirical models for solder properties that took into account 
both factors: 
)()log()(),( 43210 kTkkTkkTE ++++= ?? &&                         (3.10) 
where k0-k4 are fitting constants, and 
[ ] )(10 32)(),( CTCUTS TCCT ++= ??? &&                                          (3.11) 
 
 
 
 
 
 
 
 
 
Strain Rate = 0.001 Strain Rate = 0.0001 Strain Rate = 0.00001 Testing 
Temperature 
(?C) 
E  
(GPa) 
UTS 
(MPa) 
e E 
(GPa) 
UTS 
(MPa) 
e E 
(GPa) 
UTS 
(MPa) 
e 
25 11.96 48.19 0.0045 11.43 46.84 0.0045 11.04 44.26 0.0046 
50 11.17 43.03 0.0044 10.24 42.15 0.0048 9.92 41.02 0.0052 
75 10.11 40.42 0.0045 9.03 38.56 0.0054 8.16 36.59 0.0056 
100 8.32 35.77 0.0059 7.44 34.04 0.0089 6.51 33.26 0.0148 
125 5.10 22.65 0.0170 2.14 15.08 0.0210 1.73 13.51 0.0230 
150 0.73 10.35 0.0190 0.66 9.27 0.0189 0.53 7.31 0.0180 
 
Table 3.2 - Mechanical Properties of Underfill Material at Different Strain Rates 
 
 
 
 
 
 
 
71
 
 
72 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.8 - Linear Dependence of the Elastic Modulus on the Logarithmic Strain Rate 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.9 - Linear Dependence of the UTS on the Logarithmic Strain Rate 
 
 
 
Strain Rate (1/s)
10-5 10-4 10-3 10-2
UT
S 
(M
Pa
)
0
20
40
60
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Strain Rate (1/s)
10-5 10-4 10-3 10-2
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
 
 
73 
 
 
 
 
 
 
Elastic Modulus Strength Temperature 
(?C) E (GPa) R2 UTS (MPa) R2 
25 ?C 13.3 + 0.46log( ?& ) 0.992 54.3+1.96log( ?& ) 0.968 
50 ?C 12.94 + 0.63log( ?& ) 0.926 46.19+1.0log( ?& ) 0.995 
75 ?C 13.0 + 0.97 log( ?& ) 0.996 46.18+1.92log( ?& ) 0.999 
100 ?C 11.0 + 0.91 log( ?& ) 0.999 39.38+1.26log( ?& ) 0.954 
125 ?C 9.73 + 168 log( ?& ) 0.839 35.36+4.57log( ?& ) 0.874 
150 ?C 1.04 + 0.1 log( ?& ) 0.971 15.1+1.52 log( ?& ) 0.972 
 
Table 3.3 - Logarithmic Model Fitting Constants 
 
 
 
 
 
 
 
Elastic Modulus Strength Temperature 
(?C) E (GPa) R2 UTS (MPa) R2 
25 ?C 13.80( ?& )0.0175 0.994 54.95( ?& )0.0185 0.964 
50 ?C 13.71( ?& )0.0258 0.993 47.86( ?& )0.0100 0.994 
75 ?C 13.27( ?& )0.0465 0.999 46.99( ?& )0.0216 0.999 
100 ?C 12.07( ?& )0.0533 0.997 39.81( ?& )0.0158 0.958 
125 ?C 23.12( ?& )0.235 0.901 46.77( ?& )0.112 0.905 
150 ?C 1.21( ?& )0.0695 0.957 17.78( ?& )0.075 0.975 
 
 
Table 3.4 - Power Law Model Fitting Constants 
 
 
 
 
74 
where C1-C3 are fitting constants.  Both of these models consider the effects of temperature and 
strain rate in a coupled manner.  For underfill materials, however, the elastic modulus and 
ultimate tensile strength cannot be easily determined considering only a linear temperature 
dependence.  Therefore, two modified empirical models are proposed for use with underfill 
materials:  
)log()( 542321 ?&KTKTKTKKE ++++=                              (3.12) 
)(2
321
54)( CTCTCTCCUTS +++= ?&                                          (3.13) 
 
where K1 through K5 and C1 through C5 are fitting constants.  Figures 3.10-3.11 illustrate the 
regression fits of equation 3.12 and 3.13 to the elastic modulus and UTS data collected in the 
present study.  Very good representatives were obtained.  The fitting parameters are listed in 
Table 3.5. 
 
 
75 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.10 - Strain Rate and Temperature Effects on the Elastic Modulus 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.11 - Strain Rate and Temperature Effects on the UTS 
 
 
 
 
76 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
* Note That E is in GPa, UTS in MPa, T in K, and ?&  in sec-1 
 
 
Table 3.5 - Fitting Constants for Empirical Models in Equations 3.12 and 3.13. 
 
 
 
K1 K2 K3 K4 K5 
-310 0.31 -0.00054 0.00065 0.11 
1C  2C  3C  4C  5C  
-316.5 2.32 -0.0036 0.00028 0.07 
 
 
77 
CHAPTER 4  
EFFECTS OF AGING ON STRESS-STRAIN BEHAVIOR AND MECHANICAL 
PROPERTIES 
 
 
4.1 Introduction 
Microelectronic encapsulants exhibit evolving properties that change significantly with 
environmental exposures such as isothermal aging and thermal cycling.  Such aging effects are 
exacerbated by the higher temperatures typical of thermal cycling qualification tests for harsh 
environment electronic packaging.  The underfill material is normally based on epoxy resin, 
which displays the intermediate range of properties between an elastic solid and a viscous liquid 
depending on the temperature and the chosen time scale.  The phenomenon of viscoelasticity is 
most obvious for amorphous polymers at temperatures near their Tg.  In many applications, such 
as in automobile components, the normal operating range is from -40 to 125 ?C.  Aging effects 
are particularly important for components used in harsh environments such as ground and 
aerospace vehicles, where safety issues become paramount due to the need to ensure long term 
reliability. 
Shi, et al. [28] and Kuo, et al. [29] have studied the effects of strain and temperature on 
the mechanical properties of typical epoxy underfills.  In both investigations, the tests were 
conducted immediately following sample preparation, and did not consider possible aging 
effects. 
 
 
78 
There is significant literature available on the effects of isothermal aging on the 
mechanical behavior of polymers.  Research in this area has been summarized in detail in the 
work of Struik [19, 21].  The main body of these studies covers glass-forming materials 
(polymers, inorganic glasses, etc.) that are briefly annealed at a temperature above their Tg and 
then rapidly cooled (quenched) to a temperature significantly below the Tg.  After quenching, the 
material remains in a non-equilibrium thermodynamic state, from which its physical properties 
(mechanical, thermodynamic, etc.) shift slowly towards equilibrium.  This process is often called 
physical aging, and the effects on the small strain (linear viscoelasticity) creep response of 
polymers have been extensively documented.  Physical aging processes are thermo-reversible at 
high temperature. 
In general, polymers subjected to thermal aging after quenching become stiffer and more 
brittle.  Additionally their creep rate or compliance gradually decreases as the aging progresses.  
Recent studies on physical aging effects in epoxy without fillers have been performed by  Lee 
and McKenna [23] and Miyano, et al. [43].  
Most studies examining the physical aging of polymers involve brief exposures of test 
samples to temperatures above the Tg, with the observed aging then occurring at temperatures 
significantly below the Tg.  The minimal exposures above the Tg are solely for the purpose of 
annealing or de-aging the samples.  In many harsh environment applications of electronic 
packaging, the assemblies are subjected to temperatures at or above the Tg for extended periods, 
but there have been few studies on the effects of aging at such high temperatures on the 
mechanical behavior of polymers.  Those that have been performed, on polystyrene [24] and 
PEEK [44] have noted new and unexpected types of behaviors after cooling.  In addition, 
 
 
79 
elevated temperature aging leads to detrimental effects on the adhesion and interfacial failure 
properties of underfills, as well as to the drop test reliability of assemblies containing underfills. 
4.2 Objectives and Testing Program 
In this work, the changes occurring in the stress-strain behavior of flip chip underfill 
encapsulants were characterized for isothermal aging at four different temperatures: far below, 
below, near, and above its Tg.  Samples were prepared and isothermally aged for up to 10 months 
at 80, 100, 125, and 150 ?C as shown in Table 4.1.  For this study, a group of non-aged samples 
were prepared, along with twenty groups of aged specimens consisting of combinations of five 
different aging times (10, 30, 100, 200 and 300 days) and four different aging temperatures (80, 
100, 125 and 150 ?C).  Stress-strain tests were then performed on both the non-aged and aged 
samples at six different temperatures, from room temperature up to 150 ?C (25, 50, 75, 100, 125, 
and 150 ?C).  For all tests, a 60 mm gage length was utilized between the specimen grips, and a 
strain rate of ?&  = .001 sec-1 was applied during the load application.  The material properties 
were extracted from the measured stress-strain cruves and the effects of aging were determined 
and modeled. 
4.3 Experimental Results and Discussion 
4.3.1 Changes in Microstructure and Cure Properties 
The material microstructure is often a the fundamental factor determining mechanical 
properties.  The first step was therefore to look for any changes in the material microstructure 
after the isothermal aging exposure.  Figure 4.1 shows SEM images of the material 
microstructure for a sample with no aging and for a sample that was aged at 150 ?C for 300 days  
 
 
 
80 
 
 
 
 
 
 
 
 
Table 4.1 - Test Matrix for Tensile Test Sample Aging Exposures 
 
 
Aging 
Temperature. 0 Day 10 Days 30 Days 100 Days 200 Days 300 Days 
80 ?C * * * * * 
100 ?C * * * * * 
125 ?C * * * * * 
150 ?C 
* 
* * * * * 
 
 
81 
(the highest curing temperature and the longest curing time).  These images reveal that the effect 
of aging on the microstructure is not profound for this underfill material, with very little 
difference visible between the two samples.  The same non-uniform structure is clearly present in 
each specimen, with the larger silica particles settling to the bottom and a thin layer of pure 
epoxy on the top surface. 
Epoxy is a thermosetting resin and is subject to cure kinetics, so that both temperature 
and time influence the completion of the thermosetting resin cure.  The material decomposition 
temperature for the underfill in this study was determined to be 330 ?C using thermogravimetric 
analysis (TGA).  Differential scanning calorimetry (DSC) tests were then performed from 0 ?C 
to 250 ?C at a rate of 10 ?C/m on samples with various amounts of aging.  Example heat flow 
plots are shown in Figure 4.2 for samples aged at 80 ?C for 10 days (light aging) and at 150 ?C 
for 300 days (heavy aging).  From the plots, the glass transition temperature was 133.9 ?C for the 
lightly aged specimen and 136.1 ?C for the heavily aged specimen.  Thus the Tg has increased 
over 2 ?C due to the additional aging.  In addition, the residual cure energy of the first sample 
was 1.436 J/g, which was almost double the value of 0.785 J/g for the more heavily aged sample.  
Clearly, aging has a noticeable effect on the glass transition behavior (temperature dependent 
mechanical properties) and degree of curing for the underfill material. 
4.3.2 Stress-Strain Data for Non-Aged Samples 
Figure 4.3 illustrates typical stress-strain curves for non-aged tested underfill samples at 
temperatures from T = -175 ?C to T = +150 ?C.  The effective elastic modulus E is defined as the 
slope of the initial linear portion of the stress-strain curves.  The plot of elastic modulus vs. 
temperature (with each data point representing the average of 5 to 10 tests) is shown in Figure 
 
 
 
82 
 
 
 
 
 
 
 
 
 
(a) Non-Aged Specimen 
 
 
 
 
 
 
 
 
 (b) Specimen Aged at 150 ?C for 300 Days 
 
 
Figure 4.1 - Aging Effects on Underfill Microstructure 
 
 
 
83 
 
 
 
 
 
 
 
 
 
(a) Aged at 80 ?C for 10 Days 
 
 
 
 
 
 
 
 
 
(b) Aged at 150 ?C for 300 Days 
 
Figure 4.2 - Aging Effects on Underfill Thermal Properties 
 
 
 
 
84 
4.4.  The glass transition region for T > +100 ?C is clearly evident in the plot, while the vendor 
datasheet value is 137 ?C. 
At this point, the effects of isothermal aging on the stress-strain curves from 25 ?C (room 
temperature) up to 150 ?C (the curing temperature of the underfill) will be explored by using the 
test matrix in Table 4.1.  Figure 4.5 shows the average stress-strain curves (empirical model fits) 
for non-aged samples tested at T = 25, 50, 75, 100, 125, and 150 ?C.  As discussed previously, 
each of these curves are a fit of equation (3.5) to the 5-10 experimental stress-strain curves 
recorded for a given set of conditions. These curves for non-aged samples will provide the 
baselines for evaluating the changes occurring due to aging. 
4.3.3 Stress-Strain Data for Aged Samples  
The effects of elevated temperature isothermal aging at 80, 100, 125 and 150 ?C on the 
underfill stress-strain curves and mechanical properties were explored in this study.  These 
particular aging temperatures were chosen since they conform to temperatures below the Tg (80 
and 100 ?C), near the Tg (125 ?C), and above the Tg (150 ?C) of the underfill material. 
For each set of aging conditions in Table 4.1, at least 60 samples were subjected to tensile 
testing.  On removal from the oven, these samples were allow to cool to room temperature (T = 
25 ?C) over a period of 24 hours.  This cooling period was kept short to avoid introducing 
additional physical aging effects as described by Struik [21].  After cooling, ten specimens were 
tested at each of six different temperatures (T = 25, 50, 75, 100, 125 and 150 ?C).  The raw data 
from each set of aging conditions and testing temperature were fit with the hyperbolic tangent 
empirical model to generate an average stress-strain curve representation for each set of aging 
and temperature conditions.  For example, the average temperature dependent stress-strain 
curves for 10, 30, 100, 200, 300 days of aging at 100 ?C are shown in Figure 4.6. 
 
 
85 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.3 - Typical Temperature Dependent Underfill Stress-Strain Curves (No Aging) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.4 - Underfill Effective Elastic Modulus vs. Temperature 
 
Strain, ?
0.000 0.005 0.010 0.015 0.020
St
res
s  
?  
(M
Pa
)
0
10
20
30
40
50
60
70
80
90
T = 150 C
T = 125 C
T = 100 C
T = 75 C
T = 50 C
T = 25 C
T =    0 C
T = -175 C
T = -150 C
T = -125 C
T = -100 C
T = -75 C
T = -50 C
T = -25 C
0
5
10
15
20
25
-200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175
Temperature, T (?C)
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
 
 
86 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.5 - Average Stress-Strain Curves (No Aging) 
 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Non Aged Samples
 
 
87 
4.3.4 Aging Time Effects and Comparisons 
The effects of isothermal aging are not immediately visible from a casual comparison of 
the curves in Figures 4.5 for the non-aged specimens with the curves in Figures 4.6 for the aged 
specimens.  Consequently, direct comparisons of the curves at each temperature for aged and 
non-aged samples are given in Figure 4.7.  The results in Figures 4.6 and 4.7 are for samples 
aged at 100 ?C.  Analogous measurements have been made for samples aged at the three other 
temperatures.  Results for aging at 80 ?C are shown in Figures 4.8 and 4.9.  Results for aging at 
100 ?C are shown in Figure 4.10 and 4.11.  Finally, results for aging at 150 ?C are shown in 
Figures 4.12 and 4.13. 
The effects of aging can be easily determined from the plots in Figures 4.7, 4.9, 4.11, and 
4.13.  The increase in modulus (initial slope) and ultimate tensile strength (failure stress) with 
aging are easily visualized in these figures.  To investigate in more detail, the curves in Figure 
4.7 for aging at 100 ?C will be discussed.  Although the initial linear behavior of the average 
stress-strain curves appears to be only slightly affected at each temperature, the ultimate tensile 
strength undergoes some notable changes with aging time.  This effect is especially noticeable at 
T = 100 ?C and T = 125 ?C.  The material properties have been extracted from the average 
stress-strain curves.  Plots of the variation of the effective modulus E and UTS with temperature 
for various aging times are shown in Figure 4.14.  The variation with temperature has been 
modeled as linearly decreasing up to 100 ?C, and as a polynomial for higher temperatures.  In 
general, the changes (increases) in E and UTS with aging were typically in the range of 10-50% 
of the non-aged values.  For example, with 300 days aging, the effective modulus at 125 ?C 
increased by 31%, from 5.1 GPa to 6.7 GPa, and the ultimate tensile strength at 125 ?C increased 
45%, from 22.65 MPa to 32.95 MPa. 
 
 
88 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    Figure 4.6 - Stress-Strain Curves for Specimens Aged at 100 ?C 
for 10, 30 100, 200 and 300 Days 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Samples Aged at
T = 100 oC for 100 Days
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Samples Aged at
T = 100 oC for 200 Days
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Samples Aged at 
T = 100 oC for 10 Days
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Samples Aged at 
T = 100 oC for 30 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
Samples Aged at
T = 100 oC for 300 Days
 
 
89 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    Figure 4.7 - Stress-Strain Curves for Specimens Aged at 100 ?C 
(T = 25, 50, 75, 100, 125 and 150 ?C) 
 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 0 3Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 25 oC
Aging at 100 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 50 oC
Aging at 100 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 75 oC
Aging at 100 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 100 oC
Aging at 100 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 125 oCAging at 100 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 150 oCAging at 100 C
Increased
Aging
 
 
90 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    Figure 4.8 - Stress-Strain Curves for Specimens Aged at 80 ?C 
for 10, 30 100, 200 and 300 Days 
 
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
80 oC Aging 10 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
80 oC Aging 30 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
80 oC Aging 100 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
80 oC Aging 200 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
80 oC Aging 300 Days
 
 
91 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.9 - Stress-Strain Curves for Specimens Aged at 80 ?C 
(T = 25, 50, 75, 100, 125 and 150 ?C) 
 
 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 25 oC
Aging at 80 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 50 oC
Aging at 80 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 75 oC
Aging at 80 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 100 oC
Aging at 80 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 125 oCAging at 80 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 150 oCAging at 80 C
Increased
Aging
 
 
92 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  Figure 4.10 - Stress-Strain Curves for Specimens Aged at 125 ?C 
for 10, 30 100, 200 and 300 Days 
 
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
125 oC Aging 10 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
125 oC Aging 30 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
125 oC Aging 100 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
125 oC Aging 200 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
125 oC Aging 300 Days
 
 
93 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  Figure 4.11 - Stress-Strain Curves for Specimens Aged at 125 ?C 
(T = 25, 50, 75, 100, 125 and 150 ?C) 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 25 oC
Aging at 125 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 50 oC
Aging at 125 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 75 oC
Aging at 125 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 100 oC
Aging at 125 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 125 oCAging at 125 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 150 oCAging at 125 C
Increased
Aging
 
 
94 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  Figure 4.12 - Stress-Strain Curves for Specimens Aged at 150 ?C 
for 10, 30 100, 200 and 300 Days 
 
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
150 oC Aging 10 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
150 oC Aging 30 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
150 oC Aging 100 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
150 oC Aging 200 Days
Strain, ?
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
St
res
s, 
? (
MP
a)
0
20
40
60
80
25 ?C
50 ?C
75 ?C
100 ?C
150 ?C
125 ?C
150 oC Aging 300 Days
 
 
95 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  Figure 4.13 - Stress-Strain Curves for Specimens Aged at 150 ?C 
(T = 25, 50, 75, 100, 125 and 150 ?C) 
 
 
 
 
 
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 25 oC
Aging at 150 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 50 oC
Aging at 150 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 75 oC
Aging at 150 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 100 oC
Aging at 150 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 125 oCAging at 150 C
Increased
Aging
Strain, ?
0.000 0.005 0.010 0.015 0.020 0.025 0.030
St
res
s, 
? (
MP
a)
0
20
40
60
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
T = 150 oCAging at 150 C
Increased
Aging
 
 
96 
Similar data were obtained for all combinations of aging temperature and test 
temperature.  These trends are illustrated in the plots of effective modulus E and ultimate tensile 
strength (UTS) versus temperature in Figures 4.14 to 4.17 for the four different aging 
temperatures.  In general, the changes (increases) were typically in the range of 10-30% for E 
and 10-50% for UTS relative to the non-aged values.  However, these were only slight variations 
in the shape of the stress-strain curves due to the aging effect.  Detailed values for the 
mechanical properties of the underfill material with different aging temperatures/times and 
testing temperatures are provided in Tables 4.2 to 4.5. 
4.3.5 Aging Temperature Effects and Comparisons 
The underfill material samples were aged at four different isothermal aging temperatures.  
By regrouping the data in Figure 4.14-4.17, it was possible to examine the effect of different 
aging temperatures on the elastic modulus and ultimate tensile strength.  Figures 4.18-4.22 
illustrate the variation of the mechanical properties with temperature for different aging 
temperatures.  In these figures, all plots on each graph have the same aging time.  The largest 
relative changes occur in Figure 4.22 (300 days aging). 
4.3.6 Property Evolution with Aging Time 
In order to examine the mechanical property evolution with aging time more closely, the 
data were plotted again with aging time on the horizontal axis.  For example, Figure 4.23 shows 
the variation of the UTS data with aging time for specimens aged at 100 ?C.  In this plot, each 
curve represents a different testing temperature.  These variations can be modeled well using a 
four parameter empirical models with linear and exponential terms: 
(4.1) 
 
( )agtCag eCtCCUTS 31210 ??++=
 
 
97 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.14 - Effective Elastic Modulus and UTS vs. Temperature for Aging at 80 ?C 
 
 
 
 
 
 
 
 
 
Figure 4.15 - Effective Elastic Modulus and UTS vs. Temperature for Aging at 100 ?C 
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 80 C
Increased 
Aging
Temperature, T (oC )
0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
10
20
30
40
50
60
70
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 80 C
Increased 
Aging
Temperature, T (oC )
0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
10
20
30
40
50
60
70
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 100 C
Increased 
Aging
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 100 C
Increased 
Aging
 
 
98 
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 125 C
Increased 
Aging
Temperature, T (oC )
0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
10
20
30
40
50
60
70
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 125 C
Increased 
Aging
Temperature, T (oC )
0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
10
20
30
40
50
60
70
80
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 150 C
Increased 
Aging
 
 
 
 
 
 
 
 
 
Figure 4.16 - Effective Elastic Modulus and UTS vs. Temperature for Aging at 125 ?C 
 
 
 
 
 
 
 
 
 
Figure 4.17 - Effective Elastic Modulus and UTS vs. Temperature for Aging at 150 ?C 
 
 
 
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aged for 0 Days
Aged for 10 Days
Aged for 30 Days
Aged for 100 Days
Aged for 200 Days
Aged for 300 Days
Aging at 150 C
Increased 
Aging
 
 
 
 
 
 
 
No Aging 80 ?C, 10 days 80 ?C, 30 days 80 ?C, 100 days 80 ?C, 200 days 80 ?C, 300 days Test 
Temp. 
(?C) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
25  11.96 48.19 11.99 49.30 12.05 49.91 12.08 50.87 12.70 53.45 12.98 54.44 
50 11.17 43.03 11.2 44.49 11.24 46.03 11.32 47.18 11.48 49.47 11.84 51.78 
75 10.11 40.42 10.25 41.39 10.44 42.02 10.59 42.71 10.71 45.44 10.98 46.70 
100 8.32 35.77 8.44 36.58 8.51 37.62 8.84 38.69 9.26 40.72 9.53 42.35 
125 5.10 22.65 5.13 22.73 5.20 24.47 5.30 27.2 5.40 27.60 5.46 30.22 
150 0.73 10.35 0.73 10.65 0.74 10.88 0.74 11.84 0.77 12.87 0.798 13.15 
  
 
Table 4.2 - Elastic Modulus and Ultimate Strength vs. Temperature for Samples Aged at 80 ?C 
 
 
 
 
No Aging 100 ?C, 10 days 100 ?C, 30 days 100 ?C, 100 days 100 ?C, 200 days 100 ?C, 300 days Test 
Temp. 
(?C) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
25 11.96 48.19 12.07 50.97 12.27 51.05 12.48 53.2 12.86 55.69 13.09 56.37 
50 11.17 43.03 11.33 45.89 11.48 46.59 11.58 48.42 11.79 51.46 12.08 52.30 
75 10.11 40.42 10.26 43.20 10.47 43.34 10.66 44.21 11.37 48.70 11.53 49.78 
100 8.32 35.77 8.73 36.99 9.19 39.19 9.32 41.65 10.31 44.96 10.52 45.81 
125 5.10 22.65 5.14 24.85 5.47 27.44 5.70 32.21 6.45 32.86 6.70 32.95 
150 0.73 10.35 0.73 11.35 0.76 11.94 0.79 12.2 0.81 13.50 0.83 13.63 
 
 
Table 4.3 - Elastic Modulus and Ultimate Strength vs. Temperature for Samples Aged at 100 ?C 
 
 
 
 
 
 
99
 
 
 
 
 
 
 
No Aging 125 ?C, 10 days 125 ?C, 30 days 125 ?C, 100 days 125 ?C, 200 days 125 ?C, 300 days Test 
Temp. 
(?C) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
25 11.96 48.19 12.14 50.76 12.34 52.54 12.48 54.20 13.10 55.97 13.46 56.82 
50 11.17 43.03 11.35 45.66 11.55 48.19 12.10 49.56 12.10 51.64 12.23 52.46 
75 10.11 40.42 10.44 41.94 10.69 43.57 10.82 44.89 11.20 49.50 11.30 50.74 
100 8.32 35.77 8.87 37.45 9.44 39.62 9.80 41.30 10.48 45.85 10.68 46.80 
125 5.10 22.65 5.25 24.75 5.71 28.28 6.10 31.50 6.55 33.04 6.62 34.40 
150 0.73 10.35 0.74 11.52 0.78 13.46 0.91 13.65 0.94 13.79 0.98 14.28 
 
Table 4.4 - Elastic Modulus and Ultimate Strength vs. Temperature for Samples Aged at 125 ?C 
 
 
 
 
No Aging 150 ?C, 10 days 150 ?C, 30 days 150 ?C, 100 days 150 ?C, 200 days 150 ?C, 300 days Test 
Temp. 
(?C) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
E  
(GPa) 
UTS 
(MPa) 
25 11.96 48.19 12.26 52.98 12.42 53.29 12.62 55.23 13.30 57.30 13.64 57.65 
50 11.17 43.03 11.73 46.86 12.00 47.99 12.17 50.32 12.20 53.31 12.5 53.85 
75 10.11 40.42 10.87 42.91 10.92 44.94 11.05 45.41 11.18 50.69 11.68 51.30 
100 8.32 35.77 9.19 39.25 9.56 40.89 10.20 42.60 10.53 46.93 10.97 47.44 
125 5.10 22.65 6.03 29.25 6.12 31.02 6.49 33.48 6.99 35.65 7.16 36.10 
150 0.73 10.35 0.80 12.78 0.81 13.50 1.19 13.68 1.21 14.20 1.24 14.58 
 
Table 4.5 - Elastic Modulus and Ultimate Strength vs. Temperature for Samples Aged at 150 ?C 
 
 
10
0
 
 
 
101 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.18 - Aging Temperature Effects on Elastic Modulus and UTS (Aged for 10 Days) 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.19 - Aging Temperature Effects on Elastic Modulus and UTS (Aged for 30 Days) 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.20 - Aging Temperature Effects on Elastic Modulus and UTS (Aged for 100 Days) 
 
 
Temperature, T (oC )
0 20 40 60 80 100 120 140 160
UT
S 
(M
Pa
)
0
20
40
60
80
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 10 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 30 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 20 40 60 80 100 120 140 160
UT
S 
(M
Pa
)
0
20
40
60
80
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 30 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 100 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 20 40 60 80 100 120 140 160
UT
S 
(M
Pa
)
0
20
40
60
80
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 100 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 10 Days
Increased  
Aging Temperature
 
 
 
102 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.21 - Aging Temperature Effects on Elastic Modulus and UTS (Aged for 200 Days) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.22 - Aging Temperature Effects on Elastic Modulus and UTS (Aged for 300 Days) 
 
 
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 200 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 20 40 60 80 100 120 140 160
UT
S 
(M
Pa
)
0
20
40
60
80
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 200 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 300 Days
Increased  
Aging Temperature
Temperature, T (oC )
0 20 40 60 80 100 120 140 160
UT
S 
(M
Pa
)
0
20
40
60
80
No Aging
80 oC Aging
100 oC Aging
125 oC Aging
150 oC Aging
Aged 300 Days
Increased  
Aging Temperature
 
 
 
103 
where tag is the aging time.  In this expression, constant C0 is the initial strength for the non-aged 
specimen, C1 is the constant rate of change for long term isothermal aging, and C2 and C3 are 
parameters that control the shape of the nonlinear transition region for short aging times.  The 
role of the various empirical model constants are illustrated in Figure 4.24.  In practice, the 
constants were found by using a nonlinear regression analysis to fit equation 4.1 to the data for a 
given set of aging and testing temperatures.  The evolution of the elastic modulus with aging 
time can be modeled using a similar empirical expression with different fitting constants: 
(4.2) 
The evolutions of the modulus and UTS with aging time are shown in Figures 4.25-4.28 
for the four different aging temperatures.  In all cases, the data for the different testing 
temperature have been fit using the empirical models in equations (4.1) and (4.3).  All of the 
fitting curves are nonlinear for short aging times.  After approximately 100 days of aging, the 
variations become quite linear.  This suggests that the properties can be estimated for longer 
aging times over 300 days with a linear extrapolation. 
4.4 Combined Models for the Effects of Aging Temperature, Aging Time, and Testing 
Temperature 
As the data in this chapter clearly show, the mechanical properties of underfill are a 
function of the aging temperature, aging temperature, and testing temperature.  As stated earlier, 
prior studies have addressed the effects of the testing temperature, but few have considered aging 
effects, let alone proposed models to describe these behaviors.  In this section, the goal was to 
provide a single empirical expression to describe the evolution of a particular mechanical 
property with aging.  In particular, it was desired to cast the material properties as functions of  
( )agtKag eKtKKE 31210 ??++=
 
 
 
104 
 
 
 
 
 
 
 
 
 
 
Figure 4.23 - Strength Evolution with Aging Time 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.24 - Empirical Fit to Material Property Evolution Data 
Aging Time (Days)
0 50 100 150 200 250 300
UT
S 
(M
Pa
)
0
20
40
60
Aged at 100 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
UT
S 
(M
Pa
)
0
20
40
60
Aged at 100 oC
T =125 ?C
Slope = C1
Intercept = C0
Transition Region
C2 & C3
( )tC210 3e1CtCCUTS ??++=
UT
S 
(M
Pa
)
 
 
 
105 
 
 
 
Figure 4.25 - Effective Elastic Modulus and UTS vs. Aging Time for Aging at 80 ?C 
 
 
 
Figure 4.26 - Effective Elastic Modulus and UTS vs. Aging Time for Aging at 100 ?C 
Aging Time (Days)
0 50 100 150 200 250 300
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aging at 80 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
UT
S 
(M
Pa
)
0
20
40
60
Aging 80 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aging at 100 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
UT
S 
(M
Pa
)
0
20
40
60
Aging at 100 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
 
 
 
106 
 
 
 
 
 
 
 
 
 
Figure 4.27 - Effective Elastic Modulus and UTS vs. Aging Time for Aging at 125 ?C 
 
 
 
 
 
 
 
 
 
 
Figure 4.28 - Effective Elastic Modulus and UTS vs. Aging Time for Aging at 150 ?C 
Aging Time (Days)
0 50 100 150 200 250 300
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aging at 125 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
UT
S 
(M
Pa
)
0
20
40
60
Aging at 125 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
Aging at 150 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
Aging Time (Days)
0 50 100 150 200 250 300
UT
S 
(M
Pa
)
0
20
40
60
Aging at 150 oC
25 ?C
50 ?C
75 ?C
100 ?C
125 ?C
150 ?C
 
 
 
107 
the three independent variables: 
),,( TtTEE agag=  
),,( TtTUTSUTS agag=                                                    (4.3) 
where agT is the aging temperature, tag is the aging time, and T is the testing temperature. 
The best way to simplify the modeling problem is to separate the independent variables.  
The variables aging temperature and aging time are related to micro-structural changes that occur 
in the material during the isothermal aging process, while the testing temperature is set 
independently after the aging has occurred.  It is therefore reasonable to consider the aging 
temperature and aging time effects first, followed by the testing temperature effects. 
Many studies have examined thermal phenomena in materials, and an Arrhenius 
relationship is often used for the temperature dependence.  To explore the effects of aging 
temperature and aging time, the experimental data must be plotted for readings taken at the same 
testing temperature.  For example, Figure 4.29 illustrates the elastic modulus dependence for 
attesting temperature of 100 ?C and various aging conditions prior to testing.  These same data 
are plotted with a 3D viewpoint in Figure 4.30, with aging temperature and aging time on the 
two in-plane coordinate axes.  In an effort to produce a unified model, the empirical model in 
equation (4.2) can be generalized to include the aging temperature.  In this work, it is proposed to 
add an Arrhenius term for the aging temperature in the form: 
3)(
210
CRT
Q
ag
agetCCCE
?
++=                                                 (4.7) 
where C0 C1 C2 and C3 are functions of the testing temperature (T), and Q is an activation energy 
for aging, which is a constant regardless of the testing temperature. 
 
 
 
 
108 
Figure 4.29-4.30 illustrate the fit of equation (4.7) to the experimental data points for a 
testing temperature of 100 ?C.  In Figure 4.31, the surface predicted by the model for other aging 
conditions is illustrated.  The same approach can also be applied to the other testing 
temperatures.  In each case, the regression analysis yields a set of values for C0, C1, C2, C3 and 
Q.  Comparing these parameters for all six of the testing temperatures revealed that the values for 
C3 and Q were almost the same for each condition.  Consequently, equation 4.7 was simplified 
by substituting the average values for C3 and Q: 
45.0
15970
210 )(
agRTteCCCE
?
++=                                                 (4.8) 
where E is in GPa, tag is in days, and Tag is in ?C.  Equation (4.8) was then simultaneously fit to 
all of the elastic modulus data (all testing temperature) yielding the corrections shown in Figure 
4.32.  The calculated parameters are summarized in Table 4.6 and plotted curves temperature in 
Figure 4.33. 
The results in Figure 4.32 illustrate that the model in equation (4.8) is able to accurately 
represent the evolution of the elastic modulus with aging.  However, the plots in Figure 4.33 
show that parameters C0, C1, and C2 have a strong dependence on temperature.  These 
dependences can be expressed using the following expression: 
 
1.13043.00 +?= TC  TeC 044.01 0003.0=  TeC 028.02 21.0=                   T ?100 ?C                (4.9) 
6.2517.00 +?= TC  21.00023.01 ?= TC   9.8058.02 +?= TC            T ?100 ?C              (4.10) 
 
Substituting these expressions into equation (4.8) yields a complicated but unified model for the 
evolution of the elastic modulus with aging: 
 
 
 
109 
 
 
 
 
 
 
Figure 4.29 - Elastic Modulus vs. Aging Effects for Testing at T = 100 ?C 
 
 
 
 
 
 
Figure 4.30 - 3D Visualization of Elastic Modulus vs. Aging Effects for Testing at T = 100 ?C 
 
 
 
 
 
 
 
Figure 4.31 - Empirical Model Fit for Elastic Modulus vs. Aging Effects for Testing at  
T = 100 ?C 
 
Aging Time (Days)
0 50 100 150 200 250 300 350
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Aged at 150 oC
Aged at 125 oC
Aged at 100 oC
Aged at 80 oC
Test T = 100 oC
0
2
4
6
8
10
12
14
16
18
0
50
100
150
200
250
300
350
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Ti
me 
(Da
ys)Ag
ing T
em p
eratu
re ( oC)
Test T = 100 oC
0
2
4
6
8
10
12
14
16
18
0
100
200
300
400
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Ti
me 
(Da
ys)Agin
g Tem
perat
ure ( oC)
Test T = 100 oC
 
 
 
110 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
Figure 4.32 - Model Fitting for E vs. Aging Effects at All Test Temperatures 
0
2
4
6
8
10
12
14
16
18
0
50
100
150
200
250
300
350
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Tim
e (D
ays)Aging Te
mpera
ture ( o
C)
Test T = 25 oC
0
2
4
6
8
10
12
14
16
18
0
50
100
150
200
250
300
350
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Tim
e (D
ays)Aging Te
mper
ature 
( oC)
Test T = 50 oC
0
2
4
6
8
10
12
14
16
18
0
50
100
150
200
250
300
350
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Tim
e (D
ays)Aging
 Tem
peratu
re ( oC
)
Test T = 75 oC
0
2
4
6
8
10
12
14
16
18
0
100
200
300
400
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Tim
e (D
ays)Aging Te
mpera
ture ( o
C)
Test T = 100 oC
0
2
4
6
8
10
12
14
16
18
0
100
200
300
400
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Tim
e (D
ays)Aging Te
mper
ature 
( oC)
Test T = 125 oC
0
2
4
6
8
10
12
14
16
18
0
100
200
300
400
75
100
125
150
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
Agin
g Tim
e (D
ays)Aging T
empe
rature
 ( oC)
Test T = 150 oC
 
 
 
111 
 
 
 
Table 4.6 - Parameter Values for the Elastic Modulus Empirical Model 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.33 - Elastic Modulus Empirical Model Parameters vs. Testing Temperature 
Testing Temperature 25 oC 50 oC 75 oC 100 oC 125 oC 150 oC 
C0 11.91 11.10 9.990 8.24 4.75 0.320 
C1 0.0008 0.004 0.009 0.023 0.088 0.140 
C2 0.372 0.986 2.017 3.037 1.951 0.157 
Testing Temperature (oC)
0 25 50 75 100 125 150
C 1
-0.05
0.00
0.05
0.10
0.15
0.20
Testing Temperature (oC)
0 20 40 60 80 100 120 140 160
C 0
0
2
4
6
8
10
12
14
Testing Temperature (oC)
0 25 50 75 100 125 150 175
C 2
0
2
4
6
8
 
 
 
112 
0.45RT
15970
ag
0.028T0.044T )ag
?
++?= eteeTE 21.00003.0(043.01.13                    T ?100 ?C          (4.11) 
0.45RT
15970
ag ))((
ag
?
+?+?+?= etTTTE )9.858.0(21.00023.017.06.25         T ?100 ?C          (4.12) 
where E is in GPa, T and Tag are in ?C, and tag is in days. 
A similar empirical model can be proposed to model the evolution of the UTS with 
aging: 
3'
'
210 )''('
CRT
Q
agteCCCUTS
?
++=                                                 (4.13) 
In this case, it was found '1C  ? 0 for all testing temperatures.  Average values of '3C  and 'Q  were 
again found, and this calculation yielded: 
38.0
24580
20 )'('
agRTteCCUTS
?
+=                                                 (4.14) 
where UTS is in MPa, T and Tag are in ?C, and tag is in days,.   The regression fits of equation 
4.14 to the experimental data are shown in Figure 4.34.  The parameters '0C and '2C  were found 
to be dependent on the testing temperature (see Table 4.7 and Figure 4.35).  The dependencies 
were well fit using: 
8.5116.00 +?=? TC                TeC 035.02 4.31800 +=?                                 T ?100 ?C             (4.15) 
5.865.00 +?=? TC                      83377.532 +?=? TC                                   T ?100 ?C            (4.16) 
Substituing these expressions into equation (4.14) yields a complicated but unified model for the 
evolution the UTS with aging: 
0.38RT
24580
ag
0.035T )) ag
?
++?= eteTUTS 4.31800((16.08.51                            T ?100 ?C            (4.17) 
 
 
 
113 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.34 - Model Fitting for UTS vs. Aging Effects at All Testing Temperatures 
0
10
20
30
40
50
60
0
100
200
300
400
75
100
125
150
UT
S 
(M
Pa
)
Agin
g Tim
e (D
ays)Agi
ng Te
mpera
ture ( o
C)
Test T = 25 oC
0
10
20
30
40
50
60
0
100
200
300
400
75
100
125
150
UT
S 
(M
Pa
)
Agin
g Tim
e (D
ays)Agi
ng Te
mpera
ture ( o
C)
Test T = 50 oC
0
10
20
30
40
50
60
0
100
200
300
400
75
100
125
150
UT
S 
(M
Pa
)
Agin
g Tim
e (D
ays)Agi
ng Te
mpera
ture ( o
C)
Test T = 75 oC
0
10
20
30
40
50
60
0
100
200
300
400
75
100
125
150
UT
S 
(M
Pa
)
Agin
g Tim
e (D
ays)Agi
ng Te
mpera
ture ( o
C)
Test T = 100 oC
0
10
20
30
40
50
60
0
100
200
300
400
75
100
125
150
UT
S 
(M
Pa
)
Agin
g Tim
e (D
ays)Agi
ng Te
mpera
ture ( o
C)
Test T = 125 oC
0
10
20
30
40
50
60
0
100
200
300
400
75
100
125
150
UT
S 
(M
Pa
)
Agin
g Tim
e (D
ays)Agi
ng Te
mpera
ture ( o
C)
Test T = 150 oC
 
 
 
114 
 
 
 
 
Table 4.7 - Parameter Values for the UTS empirical Model 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.35 - Ultimate Tensile Strength Empirical Model Parameters vs. Testing Temperature 
 
 
 
 
Testing Temperature 25 oC 50 oC 75 oC 100 oC 125 oC 150 oC 
C0 48.19 43.03 40.42 35.77 22.65 10.35 
C1 1.5e-017 2.21e-017 3.8e-017 7.8e-017 9.2e-017 1.1e-016 
C2 1868.8 2010.8 2255.9 2921.7 1703.1 234.53 
Testing Temperature (oC)
0 20 40 60 80 100 120 140 160
C 0
0
10
20
30
40
50
60
Testing Temperature (oC)
0 25 50 75 100 125 150 175
C 2
0
1000
2000
3000
4000
5000
 
 
 
115 
0.38RT
24580
)) ag
?
?+?= etTTUTS agag7.538337((5.05.86                                   T ?100 ?C             (4.18) 
where UTS is in MPa, T and Tag are in ?C, and tag is in days. 
4.5 Summary and conclusions 
In this chapter, the effect of isothermal aging on the stress-strain behavior of underfill 
was investigated.  The underfill material microstructure was found to remain unchanged during 
the aging process.  However, DSC measurements showed that the residual cure energy decreased 
during the isothermal aging process, even after the samples were cured at 150 ?C for 30 minutes, 
as per the manufacturer's suggestion. 
The results obtained revealed a clear enhancement of the underfill mechanical properties 
as a function of the aging temperature and aging time.  Both the underfill effective elastic 
modulus (initial slope) and ultimate tensile strength (highest stress before failure) increased 
monotonically with the amount of isothermal aging or aging temperature, regardless of whether 
the aging temperature was below, at, or above the Tg of the material.  With 300 days isothermal 
aging, the elastic modulus increased by up to 31% and the ultimate tensile strength increased by 
up to 45%.  For the underfill evaluated, softening behavior was observed above a temperature of 
100 ?C, although the documented Tg is about 137 ?C. 
An empirical model with linear and exponential terms and four constant parameters was 
proposed to describe the evolution of the mechanical properties of underfill with aging time.  
Furthermore, two complicated empirical models were constructed to estimate the elastic modulus 
and UTS of the underfill as functions of aging temperature, aging time, and testing temperature.  
The models provided reasonably good estimates to the experimental data. 
  
 
 
 
116 
CHAPTER 5  
ISOTHEMAL AGING EFFECTS ON THE CREEP BEHAVIORS 
 
5.1 Introduction 
Materials such as solders and polymers undergo time-dependent deformation under 
mechanical stress at elevated temperatures. Various creep mechanisms may dominate at different 
temperatures, and sometimes more than one mechanism takes place simultaneously in the same 
material [45].  In reality, all deformations are time dependent but the characteristic times for 
creep deformations are orders of magnitude larger than those for either elastic or plastic 
deformations [46]. 
Creep is commonly encountered in solder joints, underfills, and printed wiring board base 
materials in electronic packaging applications.  Many electronic devices are exposed to elevated 
temperatures for long periods.  Rheological phenomena may cause structural components to 
suffer from durability shortening and about 10% of failures result from creep processes and 
stress-relaxation effects [47]. 
Creep deformation mechanisms in polymers are very different from those in metals and 
ceramics because of their unique microstructures.  Unlike most metals and ceramics with highly 
periodic crystalline structures, polymers are made of long molecules and consist of a chain of 
atoms or a three-dimensional cross-linked network bonded by covalent forces.  Consequently, 
polymer mechanical properties differ markedly from those of metals and ceramics [46].  
 
 
 
117 
Polymeric materials are generally classified into three groups: 
? Thermoplastics (crystalline and non crystalline) 
? Thermosets 
? Rubbers 
Most of the polymers used in the electronic packaging application are either thermoplastics or 
thermosets.  Thermosets have a primary three-dimensional cross-linked bonding network, while 
thermoplastics have only secondary bonding connections. 
Polymer creep behaviors are dependent not only on time, temperature and stress, but also 
on microstructure.  Polymer crystalline structures resist creep much more than amorphous 
structures, since the molecules in crystals have shorter bond distances, and consequently stronger 
intermolecular bonds.  Thermosetting materials made up of primary cross-linked molecular 
networks resist creep more readily than thermoplastic composed of secondary bonded chains of 
molecules because the cross-linked connections limit the amount of creep slippage that can take 
place. 
Creep tests are often used to characterize the viscoelastic time-dependent behavior of a 
polymer.  In a creep test, a constant force is first applied quasi-statically to a uniaxial tensile 
specimen, and then creep occurs as a slow continuous deformation of the material under stress.  
Creep behaviors are thus time dependent strain deformations at constant uniaxial stress, and 
creep deformation is one of the major failure modes in electronic packaging.  Figure 5.1 
illustrates a typical creep curve for a polymer underfill, and Figure 5.2 shows the corresponding 
creep strain rate. 
The creep curve begins with an elastic jump in strain as the load is applied.  During the 
initial period of creep deformation (primary creep), there is a steep drop in the creep strain rate.
 
 
 
118 
 
Time (sec)
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
St
rai
n, 
?
0.00
0.01
0.02
0.03
0.04
0.05
  
Figure 5.1 - Typical Creep Strain vs. Time Response 
 
 
 
Time (sec)
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Cr
ee
p S
tra
in 
Ra
te 
(se
c-1
)
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
Steady-state Strain Rate
 
Figure 5.2 - Typical Creep Strain Rate vs. Time Response 
 
 
 
 
 
119 
This is followed by a period of nearly linear response (secondary creep), where an approximately 
constant creep rate is observed.  The secondary creep rate is the slope of the creep curve in this 
relatively stable region (steady state region).  The secondary creep rate represents the material 
creep resistance factor because most deformations occur in this region.  The material continues 
to elongate until its creep deformations accumulate (tertiary creep) and failure occurs. 
It is often not economic to run lengthy creep tests at elevated temperatures, and the long 
term creep properties are sometimes predicted by substituting temperature for time, i.e., by 
estimating the long term creep behavior from short term tests at a higher temperature with the 
same stress level.  The theoretical basis for this substitution is to assume that there are no 
microstructural changes so that the time-temperature parameters can be estimated by 
extrapolating the results of short term creep tests [48, 49].  Similarly, certain relations provide 
time compression at the expense of higher temperature.  These relations, discussed earlier in 
Section 1.7, are time temperature superposition (TTSP) and time stress superposition (TSSP) 
[23, 29, and 39]. 
Research on the effects of physical aging on the creep of polymers has been summarized 
in detail in a monograph by Struik [21].  His work focused primarily on glass-forming materials 
such as polymers and inorganic glasses, which are briefly annealed at a temperature above their 
Tg, and then rapidly cooled (quenched) to a lower temperature significantly below the Tg.  After 
quenching, the material remains in a non-equilibrium thermodynamic state from which its 
physical properties (mechanical, thermodynamic, etc.) slowly evolve towards equilibrium.  This 
process is often called physical aging, and the effects on the small strain (linear viscoelastic) 
creep response of polymers have been well documented.  In general, polymers subjected to 
thermal aging after quenching become stiffer and more brittle, while their creep rate and 
 
 
 
120 
compliance gradually decrease as the aging progresses.  For example, several recent studies have 
looked at physical aging effects in epoxy without fillers (Lee and McKenna [23], and Miyano, et 
al. [43]). 
Reports in the extensive literature on physical aging of various polymers generally 
involve brief exposures to temperatures above the Tg, followed by an examination of the aging 
process at temperatures significantly below the Tg [21, 24, 43]  The minimal exposures above the 
Tg are solely for the purpose of annealing or de-aging the samples.  However, in many harsh 
environment applications of electronic packaging, the assemblies are subjected to temperatures at 
or above the Tg for extended periods.  There are few studies on the effects of aging at such 
temperatures on the mechanical behavior of underfill materials.  Those that have been 
performed, on polystyrene [24] and PEEK [44] noted unexpected types of behavior after cooling. 
Elevated temperature aging also affects the adhesion and interfacial properties of 
underfills, and has been shown to be detrimental to electronic assemblies with underfill. For 
example, Liu, et al. [50] have shown that drop reliability is severely reduced in CSP assemblies 
with underfill subjected to dry aging at 125 ?C prior to dropping. 
5.2 Objectives and Test Program 
In this study, the effects of isothermal aging on the creep behavior of a typical underfill 
(UF1) were examined for various aging temperatures, aging durations, testing temperatures, and 
stress levels. The evolution of the secondary creep rate with aging was also investigated, and an 
empirical model was developed to fit the observed variations.  Using the specimen preparation 
procedure described in Section 2.3, samples were prepared and isothermally aged for up to 10 
months at 80, 100, 125, and 150 ?C.  The samples were subjected to isothermal aging times of 1, 
 
 
 
121 
3, 10, 30, 100, 200, and 300 days, as shown in Table 5.1.  Creep test were performed on aged and 
non-aged specimens at test temperatures of 80, 100 and 125 ?C.  The applied stresses were 10, 
20, and 30 MPa for the testing temperatures of 80 and 100 ?C, and stress levels of 10, 15, and 20 
MPa were used for the 125 ?C testing temperature.  The chosen stress levels were approximately 
25%, 50% and 75% of the ultimate strength of the underfill material at each testing temperature. 
The utilized test matrix allowed for the exploration of the effects of aging temperature, 
aging time, testing temperature, and stress level on the creep behavior of the underfill material.  
Due to the long test times involved, only three specimens were tested for each set of test 
conditions (aging time, aging temperature, stress level, and test temperature). 
5.3 Experimental Results and Discussion 
During each creep test, the specimen was loaded at a strain rate 0.001 sec-1 until the 
desired stress level was reached, after which the load was held constant, and the strain vs. time 
response was recorded.  Testing was performed for a duration of up to 6000 seconds.  For each 
set of aging conditions, specimens were tested at three different temperatures (T = 80, 100 and 
125 oC) and at three different stress levels at each temperature.   Three samples were tested for 
each combination.  Therefore, for each set of aging conditions, there were 27 samples tested.  
The raw data for each testing condition were averaged to generate a creep curve to represent the 
creep behavior for each testing condition. 
Sample creep curves for non-aged specimens tested at 100 ?C are presented in Figure 5.3.  
The specimens tested at the stress level of 10 MPa did not fail during the 6000 sec duration creep 
test.  The specimens subjected to stress of 20 and 30 MPa failed without progressing to the 
tertiary range.  From the series of experimental creep curves shown in Figure 5.3, a  
 
 
 
122 
 
 
 
 
 
 
 
Aging 
Temperature 
0 
Day 
1 
Day 
3 
Days 
10 
Days 
30 
Days 
100 
Days 
200 
Days 
300 
Days 
80? C * * * * * * * 
100? C * * * * * * * 
125? C * * * * * * * 
150? C 
* 
* * * * * * * 
 
 
Table 5.1 - Matrix of Aging Exposures for Creep Tests 
 
 
 
123 
corresponding set of isochronous stress-stain curves can be extracted as shown in Figure 5.4.  
These curves give the dependence of stress on strain at particular times.  It is clear that the 
isochronous stress-strain curves are not straight lines, which shows that the epoxy material being 
studied is a nonlinear viscoelastic material, and that Boltzmann?s linear superposition principle 
cannot be applied for the load range used in this investigation. 
5.3.1 Stress Level and Test Temperature Effects and Comparison 
The creep curve recorded for specimens aged at 100 ?C  are shown in Figures 5.5-5.8 for 
aging times of 0 and 1 day (Figure 5.5), 3 and 10 days (Figure 5.6), 30 and 100 days (Figure 5.7), 
and 200 and 300 days (Figure 5.8).  For each aging duration, creep tests were performed at three 
testing temperatures: 80, 100, 125 ?C.  
The data in Figures 5.5-5.8 reveal that the specimens underwent large inelastic 
deformation with increasing stress level and testing temperature.  With lower testing temperature 
and lower stress levels, some specimens did not break during the creep tests, with their creep 
curves extending out to the full 6000 seconds.  However, some specimens failed very quickly at 
higher stress and testing temperatures, even though the load levels were lower than the ultimate 
tensile strength.  The curves show only primary and secondary creep regions, and no tertiary 
creep behavior was observed before failure occurred.  The creep curves for the non-aged 
specimens were treated here as the baseline response, to which the results for the aged specimens 
were compared.  
The observed creep behaviors were dependent on the magnitude of both the stress and the 
testing temperature.  The aging temperature and aging time also had a great impact on the epoxy 
creep behaviors, because a close examination of these results reveals that the specimens became  
 
 
 
 
124 
 
 
 
 
 
 
 
 
 
Figure 5.3 - Creep Curves for Non-Aged Specimens Tested at 100 ?C  
 
 
 
 
 
 
 
 
 
 
 
Figure 5.4 - Isochronous Stress-Strain Curves for Non-Aged Specimens Tested at 100 ?C 
 
 
Creep Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012
St
res
s, 
? (
MP
a)
0
10
20
30
40
t = 50 s
t = 100 s
t = 200 s
t = 400 s
t = 800 s
No Aging T = 100 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCNo Aging
 
 
 
125 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.5 - Creep Curves for Various Stresses (Samples Aged at 100 ?C for 0 and 1 Day, Tested 
at 80, 100, 125 ?C) 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCNo Aging
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCNo Aging
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCNo Aging
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 1 day
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 1 day
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 1 day
 
 
 
126 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Figure 5.6 - Creep Curves for Various Stresses (Samples Aged at 100 ?C for 3 and 10 Days, 
Tested at 80, 100, 125 ?C) 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 3 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 3 days
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 3 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 10 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 10 days
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 10 days
 
 
 
127 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.7 - Creep Curves for Various Stresses (Samples Aged at 100 ?C for 30 and 100 Days, 
Tested at 80, 100, 125 ?C) 
 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 30 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 30 days
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 30 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 100 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 100 days
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 100 days
 
 
 
128 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.8 - Creep Curves for Various Stresses (Samples Aged at 100 ?C for 200 and 300 Days, 
Tested at 80, 100, 125 ?C) 
 
 
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 200 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 200 days
Time, t(sec)
0 500 1000 1500 2000 2500 3000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 125 oCAged at 100 oC
for 300 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 100 oCAged at 100 oC
for 300 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 300 days
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
? = 30 MPa
? = 20 MPa
? = 10 MPa
T = 80 oCAged at 100 oC
for 200 days
 
 
 
129 
stiffer and creep was reduced with increasing aging time and aging temperature. 
5.3.2 Aging Time Effects and Comparison 
To investigate the effect of isothermal aging time on the creep behavior, the curves with 
the same stress and test temperature were extracted from Figures 5.5-5.8, and combined.  These 
results are shown in Figure 5.9 for testing at 80 and 100 ?C, and in Figure 5.10 for testing at 125 
?C.  Looking at these graphs, it is clear that for a given test time, the creep strains were much 
lower for aged samples with longer aging times.  It is also clear that the secondary creep strain 
rate decreased with longer aging times.  As discussed in the next section, this reduction in creep 
rate can be up 100X.  
Similar creep test results for the specimens aged at 80 ?C, 125 ?C and 150 ?C are shown 
in the Appendix.  All had similar trends for the effects of isothermal aging as the samples aged at 
100 ?C discussed above. 
5.4 Empirical Model for the Evolution of the Secondary Creep Rate  
For glassy polymers in ambient temperature environments, the most important 
mechanism governing their behavior is the glass to rubber relaxation mechanism.  The time scale 
for this mechanism can be protracted and the complex performance of epoxy nanocomposites 
can only be understood by combining experimental studies with effective modeling.  Therefore, 
simulation is an essential tool due to the constant demand for new materials for future 
engineering applications [51]. 
From the creep curves shown in Figures 5.5-5.10 above, the primary creep region 
exhibited a nonlinear strain vs. time relationship.  However, the secondary creep region was the 
predominant response, and the secondary creep rate for each curve was determined.  Figure 5.11  
 
 
 
130 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.9 - Creep curves for Various Aging Times (Samples Aged at 100 ?C, Tested at 80, 100 
?C) 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 10 MPa
Aged at 100 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 20 MPa
Aged at 100 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 10 MPa
Aged at 100 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 20 MPa
Aged at 100 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 30 MPa
Aged at 100 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 30 MPa
Aged at 100 oC
 
 
 
131 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.10 - Creep Curves for Various Aging Times (Samples Aged at 100 ?C, Tested at 125 ?C) 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 10 MPa
Aged at 100 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 15 MPa
Aged at 100 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 20 MPa
Aged at 100 oC
 
 
 
132 
illustrates the variations of the secondary creep rate with aging time for specimens aged 100 ?C 
prior to testing.  Each graph is for a different testing temperature (80, 100, 125 ?C) and each 
curve on a graph represents a unique value of applied stress.  The vertical axis is on a log scale, 
and the curves connecting the experimental data points in Figure 5.11 are regression fits of the 
empirical relation: 
)1(log 3210 tCeCtCC ??++=?&                                           (5.1) 
or 
)3
210 1(exp
tCeCtCC ??++=?&
                                              (5.2) 
where C0, C1, C2 and C3 are fitting constants for each set of aging conditions, testing 
temperature, and applied stress.  Constant C0 is the intercept value on the vertical axis and 
represents the initial (non-aged) creep strain rate.  Constant C1 represents the slope at which the 
secondary creep rate changes for long term aging times, and constant C2 and C3 control the 
nonlinear transition for small aging times.  Figure 5.12 combines all of the graphs in Figure5.11 
into a single three-dimensional representation of the secondary creep rate variation for aging at 
100 ?C for various test temperatures, stress levels, and aging times.  Similar results were 
obtained for the other three aging temperatures, as shown in Figure 5.13. 
Figures 5.12 and 5.13 show that the majority of the changes in the secondary creep rate 
occurs during the first 50 days of isothermal exposure, and up to a 100X reduction in the creep 
rate was observed.  These observations were true for the various aging temperatures, testing 
temperatures, and stress levels.  The rates of change (C1) for long aging times are summarized in 
Table 5.2 for all of the testing conditions.  Comparing all these values reveals that they increase 
with test temperature (up to 3X increase), and decrease with stress level (up to 4X decrease).   
 
 
 
133 
Time, t (Days)
0 50 100 150 200 250 300 350
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
?  = 30 MPa
?  = 20 MPa
?  = 10 MPa
Aged at 100 oC T = 80 oC
Time, t (Days)
0 50 100 150 200 250 300 350
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
?  = 30 MPa
?  = 20 MPa
?  = 10 MPa
Aged at 100 oC T = 100 oC
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
c. Tested at 125 ?C 
 
Figure 5.11 - Secondary Creep Rate vs. Aging Time (Samples Aged at 100 ?C) 
Time, t (Days)
0 50 100 150 200 250 300 350
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
?  = 20 MPa
?  = 15 MPa
?  = 10 MPa
Aged at 100 oC T = 125 oC
 
 
 
134 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.12 - Secondary Creep Rate vs. Aging Time (Samples Aged at 100 ?C) 
 
 
 
 
 
 
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
50
100
150
200
250
300
350
70
80
90
100
110
120130
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t 
(Day
s)
Test T
empe
rature
 ( oC)
Aged at 100 oC
?  = 10 MPa
?  = 20 MPa
?  = 30 MPa
? = 15 MPa 
 
 
 
135 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.13 - Secondary Creep Rate vs. Aging Time (Samples Aged at 80, 125 and 150 ?C) 
 
 
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
50
100
150
200
250
300
350
70
80
90
100
110120
130
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Ti
me,
 t (D
ays)Test
 Tem
perat
ure ( oC
)
?  = 10 MPa
?  = 15 MPa
?  = 20 MPa
?  = 30 MPa
Aged at 80 oC
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
50
100
150
200
250
300
350
70
80
90
100
110120
130
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Ti
me,
 t (D
ays)Tes
t Tem
perat
ure ( oC
)
?  = 10 MPa
?  = 15 MPa
?  = 20 MPa
?  = 30 MPa
Aged at 125 oC
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
50
100
150
200
250
300
350
70
80
90
100
110
120130
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Ti
me,
 t (D
ays)Test
 Tem
perat
ure ( oC
)
?  = 10 MPa
?  = 15 MPa
?  = 20 MPa
?  = 30 MPa
Aged at 150 oC
 
 
 
136 
 
 
 
 
 
 
 
 
 
 
 
  Table 5.2 - The Slope of Secondary Creep Rate vs. Aging Time for Long Term Aging 
 
 
Aging 
Temperature 
Test 
Temperature 
Slope (C1) of Variation of the Secondary 
Creep Strain Rate with Long Term Aging 
  10 (MPa) 15 (MPa) 20 (MPa) 30 (MPa) 
80 ?C -0.00054 X -0.00036 -0.00012 
100 ?C -0.00073 X -0.00043 -0.00037 
80 ?C 
125 ?C -0.00086 -0.00072 -0.00065 X 
80 ?C -0.00113 X -0.00086 -0.00037 
100 ?C -0.00146 X -0.00111 -0.00072 
100 ?C 
125 ?C -0.00161 -0.00127 -0.00089 X 
80 ?C -0.00160 X -0.00130 -0.00100 
100 ?C -0.00250 X -0.00150 -0.00140 
125 ?C 
125 ?C -0.00270 -0.00190 -0.00160 X 
80 ?C -0.00100 X -0.00030 -0.00026 
100 ?C -0.00130 X -0.00110 -0.00042 
150 ?C 
125 ?C -0.00250 -0.00120 -0.00140 X 
 
 
 
137 
This is likely because cross-links in the polymer matrix were weaker at higher temperatures near 
or above the Tg.  Also, applying a higher initial holding force caused the cross-link network to 
change dramatically, reducing the remaining extension ability available.  For test temperatures 
from 80 ?C to 125 ?C, the secondary creep rate changed by up to six orders of magnitude. 
5.5 Empirical Model for the combined Effects of Aging Temperature, Aging Time, and 
Stress Level on the Secondary Creep Secondary Rate  
In the previous section, a simple exponential relationship was proposed to describe the 
relationship of the secondary creep rate and aging time.  In real flip chip packages, however, the 
temperature and stress level are essentially random.  In addition to the aging effects, the 
secondary creep rate is a function of testing temperature, stress level, aging time, and aging 
temperature. 
The creep models summarized in Table 2.6 all focused on using stress and testing 
temperature as the independent variables, and none included the effects of aging.  In this section, 
the secondary creep rate experimental data are fitted into a single equation with multiple 
variables in an attempt to define a single empirical model that takes into account both aging 
effects and testing conditions: 
),,,( agag tTTF ?? =&                                                        (5.3) 
where T is the testing temperature, ?  is the stress level, Tag is the aging temperature, and tag is 
the aging time.  
Equation 5.3 is actually a very complicated function, with four independent variables.  To 
address this issue, the aging effects (Tag, and tag) will be considered first, followed by the testing 
conditions (?  and T).  From Figures 5.12-5.13, the semi-log plots for the secondary creep rate 
 
 
 
138 
exhibit similar trends to those seen for the elastic modulus and ultimate tensile strength in 
chapter 4, differing only in the curve bending direction.  This is probably because the material 
creeps less and less as it becomes stiffer and stronger with the aging process. 
Because they are the semi logarithmic plots, it is proposed to model the secondary creep 
rate as: 
3Cte ?
?
++= )C(CClog agRT
Q
210
ag?&                                                   (5.4) 
where Q is the activation energy associated with the creep aging process.  Following the same 
procedure described in the previous chapter, equation (5.4) was first fit to the secondary creep 
data under all aging conditions to determine single average values for Q (17800) and C3 (0.4).  
The remaining parameters (C0, C1, and C2) are taken to be functions of the appliled stress and 
testing temperature: 
4.0),(),( ?
?
++= ]eT)t,(C[CClog agRT
17800
ag210 ???? TT&                          (5.5) 
The best fits of the equation (5.5) to the creep strain rate test data are shown in Figures 
5.14, 5.15 and 5.16 for aging at 80, 100, and 125 ?C, respectively.  The calculated dependence of 
parameters C0, C1 and C2 on stress and temperature are shown in Figures 5.17 and 5.18.  Due to 
the complicated dependencies, it was not attempted to establish the function forms for C0( ?, T), 
C1( ?, T), and C2( ?, T).  However, it is clear from Figures 5.14-5.16 that equation (5.5) provides 
an accurate representation to the strain rate data. 
 
 
 
 
139 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.14 - Secondary Creep Rate vs. Aging Time (Samples Aged at 80 ?C) 
 
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 80 oC  ? = 10 MPa
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 80 oC  ? = 30 MPa
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 80 oC  ? = 20 MPa
 
 
 
140 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.15 - Secondary Creep Rate vs. Aging Time (Samples Aged at 100 ?C) 
 
 
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 100 oC  ? = 10 MPa
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 100 oC  ? = 20 MPa
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 100 oC  ? = 30 MPa
 
 
 
141 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.16 - Secondary Creep Rate vs. Aging Time (Samples Aged at 125 ?C) 
 
 
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 125 oC  ? = 10 MPa
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 125 oC  ? = 15 MPa
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0
100
200
300
400 80
100
120
140
160
Cr
ee
p S
tra
in 
Ra
te 
(m
m/
se
c)
Agin
g Tim
e, t (
Day
s) Aging Te
mpera
ture (
o C)
Test T = 125 oC  ? = 20 MPa
 
 
 
142 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.17 - Calculated Parameters C0, C1 and C2 vs. Stress and Temperature 
 
 
-9.0
-8.5
-8.0
-7.5
-7.0
-6.5
-6.0
-5.5
70
80
90
100
110
120
130
5
1015
2025
30
Co
ns
tan
t C
0 
Te
stin
g T
em
per
atu
re 
(o C
)
Stess Lev
el (MPa)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
70
80
90
100
110
120
130
5
1015
2025
3035
Co
ns
tan
t C
1 
Te
stin
g T
em
per
atu
re 
(o C
)
Stess Le
vel
0
200
400
600
800
1000
1200
1400
1600
70
80
90
100
110
120
130
5
1015
2025
3035
Co
ns
tan
t C
2 
Te
stin
g T
em
per
atu
re 
(o C
)
Stess Le
vel
 
 
 
143 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.18 - Calculated Parameters C0, C1 and C2 vs. Stress Level 
 
 
Stess Level (MPa)
5 10 15 20 25 30 35
Co
ns
tan
t C
0 
-10
-9
-8
-7
-6
-5
-4
Test T = 125 oC
Test T = 100 oC
Test T = 80 oC
Stess Level (MPa)
5 10 15 20 25 30 35
Co
ns
tan
t C
1 
0
1
2
3
4
5
Test T = 125 oC
Test T = 100 oC
Test T = 80 oC
Stess Level (MPa)
5 10 15 20 25 30 35
Co
ns
tan
t C
2 
0
500
1000
1500
2000
Test T = 125 oC
Test T = 100 oC
Test T = 85 oC
 
 
 
144 
5.6 Summary and Conclusions   
In this chapter, a study was performed on the evolution of underfill creep behavior with 
isothermal aging.  The recorded isochronous stress-strain curves showed that the underfill being 
studied was a nonlinear viscoelastic material.  Thermal aging had a significant effect on the 
secondary creep rate, which decreased with both the aging temperature and the aging time.  Up 
to a 100X reduction in the creep rate was observed, and the major changes occurred during the 
first 50 days of the isothermal aging.  Also, the slope for the long term variation of the secondary 
creep rate changed by up to 3X with testing temperatures from 80 to 150 ?C, and up to 4X with 
stress level changes.  An empirical model was developed to describe the secondary creep rate as 
function of aging temperature, aging time, and stress level for a fixed testing temperature. 
 
 
 
 
 
145 
CHAPTER 6  
CURE PROFILE EFFECTS ON THE MECHANICAL BEHAVIOR AND RELIABILITY OF 
FLIP CHIP ON LAMINATE ASSEMBLIES 
 
 
 
6.1 Introduction 
There has been extensive research into the properties and behaviors of epoxy materials 
because of their many important technical applications.  Underfill manufacturers have generally 
focused on optimizing the curing conditions (cure time and temperature, moisture environment 
etc).  This research has additional significance as epoxy resin cohesion obtained by the cross-
linking reaction in the presence of hardeners is largely dependent on the curing conditions and 
the preconditioning that follows.  Variations in underfill curing procedures induce different 
material properties and stress distributions in the assembly, thus affecting the properties and 
overall reliability of the packaging. 
A standard epoxy formulation can absorb about 1-7 wt% moisture [52].  Other than that, 
a significant problem in the micro-packaging industry is the presence of moisture, which 
contributes to various failure mechanisms.  Moisture can cause corrosion, popcorn failure, poly 
degradation, and hydro-stress in the packaging.  The majority of contemporary underfill 
materials is epoxy based, and hence highly susceptible to moisture absorption as they are polar 
resins and thus readily interact with high polarity water molecules.  Soles suggested that water 
enters the epoxy network through surface nanopores (5-6 ?) [53].  The weight gain by moisture 
 
 
 
146 
absorption under a normal lab environment is show in Figure 6.1 [54].  The moisture content 
reaches saturation state after 100 hours, with a weight gain of up to 0.23%. 
Several research groups have investigated the effects of environmental exposures 
(isothermal aging with and without controlled humidity) on underfill response [29, 55-59].  
These studies have primarily focused on the evolution/degradation of interfacial failure 
properties with duration of exposure.  For example, Kuo, et al. [29] observed dramatic reductions 
in the interfacial (adhesion) strength of underfill and soldermask interfaces in lap shear 
specimens that had been exposed to a combination of humidity and temperature (60 ?C and 95% 
RH for 168 hours) (Figure 6.2).  The fracture strengths decreased by 33% in non-solder mask flip 
chips, whereas the fracture strengthen decreased by up to 50% for solder mask defined flip chips. 
The focus of interfacial failure can be shifted from the upper to the lower FR4/solder 
mask as a result of the environmental preconditioning utilized.  Kuo, et al. [29] also 
demonstrated changes in the constitutive behavior of their lap shear specimens after 
thermal/humidity aging by observing fracture surfaces for various displacement rates, 
preconditioning conditions and specimen types. 
Studies by Ferguson and Qu [55, 56], revealed that exposures to various combinations of 
humidity and temperature (e.g. 85 ?C and 85% RH for 168 hours) had only a negligible effect on 
the elastic modulus of their epoxy samples once the current conditions of the samples had been 
equilibrated by dry baking.  However, the samples' interfacial toughness was shown to drop with 
duration and severity of environmental exposure, including exposure to 85 ?C with no moisture 
(dry heat). 
 
 
 
147 
 
 
 
 
 
 
 
 
Figure 6.1 - Moisture Absorption of Underfill under Normal Lab Environment (Sample 
Thickness: 2 mm) [54] 
 
 
 
 
 
 
 
 
 
 
Figure 6.2 - Fracture Strength as a Function of Different Displacement Rate, Preconditioning 
Condition and Specimen Type [29] 
 
W
eig
ht 
ga
in 
(%
)
0           50            100          150           200
Time (hour)
W
eig
ht 
ga
in 
(%
) 0.5 
0.4 
0.3 
0.2 
0.1 
0 
Epon828 + MDA
Epon8281+2E4MZ-CN
Epon8281+LBR-2+2E4MZ-CN
Fra
ctu
re 
Str
en
gth
 (K
gf)
I           II          III        IV          V
Fra
ctu
re 
Str
en
gth
 (K
gf)
I II III II II III I
80 
 
60 
 
40 
 
20 
 
0 
I      RT 
II     25 oC/60% 
III    25 oC/95% 
IV    60 oC/60% 
V     60 oC/95% 
Non-solder mask 
Solder mask defined 
 
 
 
148 
Similar results were observed by Luo and Wong [12, 57], who found that thermal cycling 
had no effect on the inherent adhesion strength between the underfill and the passivation layer.  
The interfacial strength in special mechanical testing specimens was degraded with duration 
under thermal/humidity aging conditions of 85 ?C and 85% RH (85/85).  The adhesion strength 
became steady after 96 hrs of 85/85 aging, although the moisture absorption reached saturation 
after 20 hrs, as shown in Figures 6.3 and 6.4.  The degradation of adhesion strength was ascribed 
mainly to a decrease in the underfill modulus, which was itself linked to the liquid accumulating 
on the interface.  In another approach, Zhang and co-workers [59] measured crack opening 
displacements to characterize the changes in stress intensity and foundnterfacial cracking along 
the underfill and silicon chip passivation interface served as a function for both dry and moist 
condition aging at 85 ?C.  Finally, the author' group have measured the effects of various types of 
preconditioning (JEDEC and MSL3) and cure profiles on the stress-strain behaviors and 
mechanical properties of underfills, as well as the reliability of flip chip assemblies [58]. 
The influence of underfill aging on the performance of electronic assemblies has also 
been investigated by several groups [11, 60, 61].  Chaware, et al. [60] have shown that three 
weeks dry aging at 85 ?C had little effect on the reliability of flip chip assemblies made with 
several different underfills.  However, combined hydrothermal exposures at 85 ?C and 85% RH 
had a significant effect on all the configurations examined: both underfill fillet cracking and 
passivation interface delaminations at the underfill were accelerated during thermal cycling 
testing.  Okura, et al. [11] modeled the same configurations, and proposed that the new failure 
modes were created as a result of hydro-mechanical swelling.  Wong and co-workers [61] 
studied failures occurring in flip chip assemblies during elevated temperature aging exposures, 
 
 
 
149 
 
 
 
 
 
 
 
 
Figure 6.3 - Moisture Absorption of a 2 ? 2 ? 50 mm Long Orthogonal Bar of G25 Underfill 
during 85/85 Aging [57] 
 
 
 
Figure 6.4 - Adhesion Strength of G25 on SiN vs. Aging Time [57] 
 
 
 
150 
and compared the results at different temperature levels.  They suggested that stress corrosion 
and debonding at the under-fill-die interface was responsible for the observed exponential 
difference in the life at 85 ?C/85% RH compared to that at 120 ?C/100% RH aging.  The 
underfill material curing temperature may well prove to be the simplest and most effective 
method to improve moisture resistance and autoclave performance. 
Dimke [62] examined the effects of the underfill material?s cure temperature on adhesion 
strength, and concluded that higher cure temperatures resulted in better adhesion.  In this work, a 
2.5 x 2.5 mm die with bumps was adhered to substrates with capillary flow underfills and shear 
tests were performed.  A possible drawback in the method used for this study was that there was 
some fillet formation along the dispensing edge, so the die shear force measurements were not 
solely measuring the interfacial adhesion, but also contributions from the underfill fillet. 
The size of the shift needed to align the individual experimental data for specific testing 
temperatures was generally described by the Williams-Landel-Ferry relationship (WLF):  As 
discussed above, prior investigations have concentrated on the effects of thermal (dry) and 
isothermal aging on the failure properties of both underfills and assemblies with underfill.  
However, few studies have explored the effects of aging on the material constitutive behavior of 
underfills (e.g. stress-strain and creep behaviors). 
6.2 Objectives 
In this chapter, the effects of underfill cure temperature and JEDEC MSL preconditioning 
on underfill mechanical and strength properties, as well as flip chip assembly reliability, are 
explored.  Baseline stress-strain curves, mechanical properties, and interfacial shear strengths of 
a capillary underfill were recorded for samples cured at 150 ?C and 165 ?C (30 minutes).  In 
 
 
 
151 
addition, changes in the mechanical and strength properties resulting from MSL3 and MSL2 
preconditioning were also evaluated.  The MSL preconditioning of the underfill samples 
included the JEDEC specified humidity and temperature exposures, with three simulated reflows 
at 245 ?C or 260 ?C.   
Thermal cycling life tests from -55 to 125 ?C were also conducted on daisy chain flip 
chip assemblies incorporating the same underfill.  The test matrix for the reliability test included 
both 150 ?C and 165 ?C curing profiles, and two levels of preconditioning (none, MSL3).  
Finally, the failure mechanisms in the flip chip assemblies were studied using CSAM, x-ray and 
SEM analyses. 
6.3 Experimental Procedures 
The commercially available underfill utilized in this work was the silica filled epoxy UF1 
described in earlier chapters.  The underfill mechanical/shear test specimens and the underfilled 
flip chip assemblies were prepared with two different curing profiles consisting of a 30 minute 
isothermal exposure at either 150 ?C or 165 ?C in a box oven. 
After curing, but before testing, various groups of samples were preconditioned to several 
different JEDEC standard, MSL and humidity levels, with the case of no preconditioning serving 
as the control group.  The preconditioning exposures consisted of a timed exposure at fixed 
temperature and humidity, followed by a three solder joint reflow temperature profile.  Table 6.1 
summarizes the notations and conditions applied for the various sample preconditioning 
exposures used in the work reported here. 
For each of the two curing temperatures, groups of test specimens were subjected to no 
preconditioning, humidity, or MSL3+245 with three time exposures.  The reflow process  
 
 
 
152 
 
 
Preconditioning 
Nomenclature 
Environmental 
Exposure 
Reflow Profile 
Exposures 
None None None 
Humidity 30 ?C and 60% RH for 192 hours None 
MSL2+245 85 ?C and 60% RH for 168 hours 245 ?C Peak 3 Exposures 
MSL2+260 85 ?C and 60% RH for 168 hours 260 ?C Peak 3 Exposures 
MSL3+245 30 ?C and 60% RH for 192 hours 245 ?C Peak 3 Exposures 
MSL3+260 30 ?C and 60% RH for 192 hours 260 ?C Peak 3 Exposures 
 
Table 6.1 - Sample Preconditioning Exposures 
 
 
 
Figure 6.5 - The MSL3 + 245 Reflow Process Temperature Profile 
 
 
 
 
 
153 
temperature profile is shown in Figure 6.5.  Stress-strain tests were then performed with samples 
from the various specimen sets with several different temperature settings: -55, -25, 0, +25, +85, 
+125, and +150 ?C.  For each set of test conditions (sample curing temperature, sample 
preconditioning, and test temperature), six stress-strain tests were performed. 
 
6.4 Experimental Shear Strength Measurements 
Interfacial de-adhesion occurs on the interface between two contacting materials, and the 
interfacial strength depends on the chemical and mechanical properties of the interfaces.  Shear 
strength is characterized in terms of the interface fracture toughness, which is the maximum 
mechanical work transferred across the interface before the separation.  In electronic packaging, 
interface failures can occur at either the die or the substrate, and delaminations are a common 
failure mode. 
Adhesion is difficult to measure in general, and especially problematic on samples that 
simulate real manufacturing environments, which must take into account potential problems due 
to process contamination, flux residue, reflow temperature, and so on.  However, a good 
understanding of the fundamental process involved for materials and interfaces, in this case 
interfacial shear strength adhesion tests, can still be useful.  The measured shear strength at the 
die/underfill interface of a typical underfill flip chip is a combination of shear force and the 
energy required to break the fillet.  Consequently, shear strength is the energy required to rupture 
the chemical bonds formed in die passivation and at the underfill interface.  Chemical bonds with 
the fillets may be formed at the edge of the die during the underfilling process.  Therefore, care 
should be taken to eliminate the contribution from the fillets if possible. 
 
 
 
154 
The method utilized in this work for shear force application is illustrated in Figure 6.6.  
The height of the underfill material was about 4?s after the solder ball joints collapsed.  Force 
was applied to the side of the chip, and was transmitted to a cylindrically shaped underfill region 
adhered to both the die passivation layer and the topside of the PCB.  The solder balls were not 
attached or reflowed to the printed circuit board, but instead used to provide a fixed stand-off 
distance of approximately 125 ?m.   
To assemble these samples, a bare FR4 laminate strip without soldermask and with planar 
dimensions of 100 x 25 mm was first dehydrated for 24 hours at 125 ?C before assembly.  The 
FR4 strip was then placed on the stage (unheated) of a CAM/ALOT 3700 dispensing system.  
Ten underfill dots were dispensed, each of which had a diameter of approximately 2 mm.  A 
bumped test chip (5 x 5 mm with 88 I/O) was centered and placed on top of each underfill dot 
using an automatic pick and place machine with a placement force of 2.94 N.  The underfill dots 
in the shear force testing specimen were then cured in box oven for 30 minutes under either the 
150 ?C or 165 ?C curing profile.  Several test coupons were assembled with each curing 
temperature.  For the 165 ?C cure cycle, some samples were also exposed to each of the five 
preconditioning exposures listed in Table 1. 
The die shear tests were performed using a Dage 2400 System with a loading head speed 
of 50.8 ?m/sec and the force range of 1 N.  A microscope was used to align the die edge, which 
had to be parallel to the shear blade to ensure the applied force was uniform along the die edge.   
The assembled test coupons are shown in Figure 6.7, which shows the samples both 
before and after die attaching.  The 5 x 5mm dies were attached to the PCB by a single drop of 
underfill material.  Two primary failure modes were observed: adhesive failure at the interface  
 
 
 
155 
Shear
Force
Die
PCB
Underfill
 
 
Figure 6.6 - Schematic of the Underfill Adhesion Shear Test 
 
 
 
 
Figure 6.7 - Assembled Shear Test Coupons Before and After Die Attaching 
 
 
 
Figure 6.8 - Cured Underfill Dot After Shear Test 
 
 
 
 
 
 
 
 
 
 
 
 
156 
between die passivation and underfill or adhesive failure interface between the PCB and 
underfill.  Figure 6.8 shows the dot remaining of a typical underfill after die passivation and 
underfill interfacial failure.  The original spherical shape of the underfill dot was distorted after 
the shear test. 
6.5 Thermal Cycling Reliability Tests 
Fatigue failures occur with the initiation of a microscopic crack and at much lower stress 
due to accumulation damage when subjected to the thermal cycling process.  The crack can 
continue to propagate steadily steady until the initial crack becomes unstable under cyclic 
stresses.  Fatigue failure is one of the most commonly encountered problems in the electronic 
packaging design industry.  However, packaging reliability can be improved by better 
understanding the crack propagation mechanism. 
Thermal cycling reliability tests were performed over a range from -55 to +125 ?C in a 
single compartment environmental chamber.  The PB8 daisy chain test chips used for this 
experiment had dimensions of 5 x 5 mm and featured a single row of 88 perimeter 63Sn-37Pb 
eutectic solder bumps on an 8 mil (200 ?m) pitch.  Each test board contained 10 test chips, and 
individual daisy chains were monitored during thermal cycling..  The in-plane dimensions of the 
test boards were 135.9 x 88.9 x 1.25 mm, and they were fabricated using FR-406 laminates with 
copper traces and an electroless Nickel immersion Gold finish.  The test boards were assembled 
on the SMT Line at Auburn University. 
Prior to placement, the test chip solder balls were dipped into Kester TSF 6522 tacky, no-
clean solder flux with a 20-30 ?m shim thickness.  The dies were then aligned and placed on the 
test substrates using a high speed pick and place machine with a placement force of 2.94 N.  
 
 
 
157 
Reflow was performed in a Nitrogen atmosphere in a Heller EXL1800 reflow oven using a 
reflow profile with a peak temperature of 220 ?C.  The underfill was dispensed using a 25 gauge 
needle onto a heated substrate.  The stage temperature was 105 ?C, leading to an actual substrate 
temperature of approximately 95-100 ?C.  A corner dot dispense pattern was used, and the 
underfill was cured in a box oven for 30 minutes using either a 150 ?C or 165 ?C cure profile.  
Before reliability testing was conducted, some of the boards cured under different temperatures 
were also subjected to MSL3+245 preconditioning.  A photograph of a fully populated test board 
is shown in Figure 6.9, while a photograph of a typical die mounting site is shown in Figure 6.10. 
C-mode scanning acoustic microscopy (CSAM) and x-ray analyses were performed on 
all test boards after assembly.  These procedures were done in order to inspect for manufacturing 
defects and underfill delaminations.  The assembled parts were then subjected to thermal cycling.  
Monitoring the various daisy chain networks was performed throughout the cycling process 
using a high accuracy digital multimeter coupled with a high performance Labview controlled 
switching system.  The resistance of each daisy chain was recorded during thermal cycling, and 
opening was treated as assembly failure.   
The failure data were statistically analyzed using two parameter Weibull models.  The 
standard parameters used for these models are the Weibull Slope ? , and the Characteristic 
Life? , which is the number of cycles required to cause failure of 63.2% of the samples from a 
particular leg of the test matrix.  From these values, a particular configuration in the test matrix, 
the cumulative failures (percent) after any number of thermal cycles can be calculated.  Failure 
analyses of cycled test boards were conducted using CSAM, x-ray, and scanning electron 
microscopy (SEM) of cross-sectioned parts. 
 
 
 
158 
 
 
 
 
Figure 6.9 - Flip Chip Thermal Cycling Test Board 
 
    
(a)                                                (b) 
 
Figure 6.10 - (a) Die Site (b) Finger Design for I/O 
 
 
 
159 
6.6 Experimental Results 
6.6.1 Mechanical Testing of Underfill Material 
The average temperature dependent stress-strain curves for the specimens cured at 150 ?C 
and 165 ?C (no preconditioning) are shown in Figure 6.11.  The range of the maximum strain of 
the average curve for each temperature was found by averaging the failure strains from each of 
the six tests used in the regression fit for that temperature.  Figure 6.12 shows direct comparisons 
of the corresponding stress-strain curves at T = -55, +25, +85, +125, and + 150 ?C for these two 
curing conditions. 
In Figure 6.12, the solid lines are for the specimens cured at 165 ?C and the dashed lines 
are the specimens cured at 150 ?C.  It can be observed qualitatively that the stress-strain curves 
are shifted towards the left and upward by increasing the curing temperature under the same test 
temperature, which means that the effective modulus increases when reached via the higher 165 
?C curing temperature.  This trend can also be applied to the UTS. 
These observations are confirmed by the plots in Figure 6.13, where the E and UTS 
values are plotted as a function of testing temperature.  When the testing temperature is above 
100 ?C, there are only slight differences in the mechanical properties of underfills formed with 
the two curing temperatures.  In this case the test temperatures are close to or above the glass 
transition temperature (Tg).  From these phenomena, the glass transition region can be 
determined by rapid degradation of the mechanical properties, even though the exact Tg 
temperature cannot be determined by the tensile test.  However, for T lower than room 
temperature, the differences are significant.  At T = -55 ?C, the material property UTS is  
 
 
 
 
160 
 
 
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
St
res
s  
? (
MP
a)
0
20
40
60
80
100
Curing: 30 Minutes @ 150 oC
Preconditioning: None
T = -55 C
T = -25 C
T = 0 C
T = +85 C
T = +125 C
T = +150 C
T = +25 C
 
(a)   Curing at 150 ?C 
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
St
res
s  
? (
MP
a)
0
20
40
60
80
100
Curing: 30 Minutes @ 165 oC
Preconditioning: None
T = -55 C
T = -25 C
T = 0 C
T = +85 C
T = +125 C
T = +150 C
T = +25 C
 
(b)   Curing at 165 ?C 
Figure 6.11 - Underfill Stress-Strain Curves for Curing at 150 ?C and 165 ?C (No 
Preconditioning) 
 
 
 
 
161 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 6.12 - Comparison of Stress-Strain Curves for Curing at 150 ?C and 165 ?C (No 
Preconditioning) 
 
 
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
St
res
s  
? (
MP
a)
0
20
40
60
80
100
Curing: 30 Minutes @ 150 oC
Curing: 30 Minutes @ 165 oC
T = -55 C
T = +85 C
T = +125 C
T = +150 C
T = +25 C
 
 
 
162 
 
Temperature, T (oC )
-75 -50 -25 0 25 50 75 100 125 150 175
Ef
fec
tiv
e M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
25
Curing: 30 Minutes @ 165 oC
Curing: 30 Minutes @ 150 oC
 
(a)   Effective Modulus vs. Temperature  
 
 
 
 
 
 
 
 
 
(b)   Ultimate Tensile Strength vs. Temperature 
Figure 6.13 - Mechanical Properties Comparisons for Underfill with Two Cure Conditions (No 
Preconditioning) 
 
 
Temperature, T (oC )
-75 -50 -25 0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
20
40
60
80
100
Curing: 30 Minutes @ 165 oC
Curing: 30 Minutes @ 150 oC
 
 
 
163 
approximately 30% higher compared to underfill cured at 165 ?C, with an elastic modulus about 
25% higher.   These increases are due to the higher density of epoxy cross-linking obtained 
during the higher temperature cure procedure.  The degree of cross-linking increases with the 
extent of cure for the partially cured epoxy resin. 
Regarding the effect of moisture, the average temperature dependent stress-strain curves 
for the specimens cured at 150 ?C and 165 ?C, and then subjected to MSL3+245 preconditioning 
are shown in Figure 6.14.  The corresponding curves for the un-preconditioning case are also 
included for the purpose of comparison. 
Similarly, MSL preconditioning significantly raised the UTS at temperatures below 100 
?C, while little or no change was observed in the effective elastic modulus E at any temperature.  
Plots directly illustrating the effects of the MSL preconditioning on the E and UTS as a function 
of temperature are shown in Figure 6.15.  At T = -55 ?C, the UTS was approximately 32% higher 
after the moisture MSL3+245 per-conditioning for specimens cured at 150 ?C, whereas UTS was 
about 25% higher after the moisture per-conditioning for specimens cured at 165 ?C.  It is 
interesting to see this phenomenon because normally the moisture degrades the material 
properties but this is not the case for this type of underfill material. 
Figure 6.16 summarizes the pre-conditioning effects on mechanical properties, elastic 
modulus and ultimate tensile strength for underfill materials cured at 150 ?C.  From the bar plots, 
the elastic modulus dropped as a result of humidity pre-conditioning (30 ?C and 60% RH for 192 
hours), then increased after the reflow process (MSL3+245), although all these changes were 
small, at less than 5%.  The ultimate tensile strengths increased monotonically with humidity and 
MSL3+245 pre-conditioning, and these changes are profound, with an increase of about 30%.  
 
 
 
 
164 
 
 
 
 
 
 
 
 
(a)   Curing at 150 ?C 
 
 
 
 
 
 
 
 
 
(b)   Curing at 165 ?C 
 
  Figure 6.14 - Underfill Stress-Strain Curves for Curing at 150 ?C and 165 ?C (MSL3+245 and  
No Preconditioning) 
 
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
St
res
s  
? (
MP
a)
0
20
40
60
80
100
Curing: 30 Minutes @ 165 oC
MSL3+245
None
Preconditioning:
T = -55 C
T = -25 C
T = 0 C
T = +85 C
T = +125 C
T = +150 C
T = +25 C
Strain, ?
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
St
res
s  
? (
MP
a)
0
20
40
60
80
100
Curing: 30 Minutes @ 150 oC
MSL3+245
None
Preconditioning:T = -55 C
T = -25 C
T = 0 C
T = +85 C
T = +125 C
T = +150 C
T = +25 C
 
 
 
165 
 
 
 
 
 
 
 
 
(a)   Effective Modulus vs. Temperature  
 
 
(b)   UTS vs. Temperature  
 
  Figure 6.15 - Mechanical Properties vs. Temperature for Samples with and without MSL3+245 
Preconditioning 
Temperature, T (oC )
-75 -50 -25 0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
20
40
60
80
100
Curing: 30 Minutes @ 150 oC
MSL3+245
None
Preconditioning:
Temperature, T (oC )
-75 -50 -25 0 25 50 75 100 125 150 175
UT
S 
(M
Pa
)
0
20
40
60
80
100
MSL3+245
None
Curing: 30 Minutes @ 165 oC
Preconditioning:
Temperature, T (oC )
-75 -50 -25 0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
25
MSL3+245
None
Curing: 30 Minutes @150oC
Preconditioning:
Temperature, T (oC )
-75 -50 -25 0 25 50 75 100 125 150 175
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
25
Curing: 30 Minutes @165oC
Preconditioning:
 
 
 
166 
 
 
 
 
 
 
 
 
 
(a)   Effective Modulus vs. Pre-conditioning Procedures 
 
 
 
 
 
 
 
 
 
 
(b)   UTS vs. Pre-conditioning Procedures 
Figure 6.16 - Mechanical Properties vs. Temperature for Samples with the Different 
Preconditioning 
 
Temperature, T (oC )
Ela
sti
c M
od
ulu
s, 
E 
(G
Pa
)
0
5
10
15
20
30 Min @ 150 ?C 
30 Min @ 150 ?C & Humidity
30 Min @ 150 ?C & MSL3+245
-55            -25         0          25                          85              125       150
Temperature, T (oC )
UT
S 
(M
Pa
)
0
20
40
60
80
100
30 Min @ 150 ?C 
30 Min @ 150 ?C & Humidity
30 Min @ 150 ?C & MSL3+245
-55            -25         0          25                          85              125       150
 
 
 
167 
Based on these findings, we can conclude that the samples cured at 165 ?C exhibited 
significantly increased effective elastic modulus and ultimate tensile strength.  Moreover, MSL3 
preconditioning had only a minor effect on the effective elastic modulus, but significantly 
improved the ultimate tensile strength.  The results of the interfacial shear strength tests 
demonstrated slight variations between strength with preconditioning, but significant shifts in the 
location of the shear failures to the underfill-substrate interface for the 165 ?C cured samples. 
6.6.2 Shear Strength 
The average measured shear strengths for samples prepared with the two cure conditions 
(no preconditioning) are shown in Figure 6.17.  Interfacial adhesive failures were observed at 
both the underfill to die passivation and underfill to PCB interfaces.  The percentages of the 
samples failing at the die passivation interface are also indicated.  With the higher cure 
temperature of 165 ?C, it was observed that the shear strength dropped slightly.  However, the 
higher cure temperature also led to 45% fewer failures at the underfill to die passivation 
interface; instead, the failures tended to shift toward the underfill to PCB interface when using 
the higher cure temperature.  Therefore, one might conclude that using a higher cure temperature 
enhances the adhesion at the underfill to die passivation interface. 
The effects of MSL preconditioning on the shear strength were also studied for the cure 
temperature of 165 ?C.  Figure 6.18 illustrates the average measured shear strengths for samples 
subjected to the five different preconditioning exposures listed in Table 6.1.  Once more, the 
failure modes consisted of interfacial adhesive failures at both the underfill to die passivation and 
underfill to PCB interfaces.  Both MSL2 preconditioning exposures (MSL2+245 and 
MSL2+260) reduced the shear strength but increased the percentage of samples failing at the  
 
 
 
 
168 
 
 
 
 
 
 
 
 
 
Figure 6.17 - Average Shear Strength vs. Cure Temperature (The Percentage Indicates the 
Portion of the Failures Occurring at the Underfill to Die Passivation Interface) 
 
 
 
 
 
 
 
 
 
 
Figure 6.18 - Average Shear Strength vs. Preconditioning (The Percentage Indicates the Portion 
of the Failures Occurring at the Underfill to Die Passivation Interface) 
 
Curing Condition
Sh
ea
r S
tre
ng
th 
(M
Pa
)
0
10
20
30
40
50
60
70
80
90
100
30 min @ 150 oC 30 min @ 165 oC
50%95%
Underfill Cured for 30 Minutes @ 165 oC
Preconditioning Exposure
Sh
ea
r S
tre
ng
th 
(M
Pa
)
0
10
20
30
40
50
60
70
80
90
100
None MSL2+245 MSL2+260 MSL3+245 MSL3+260
50%
95% 55% 20% 10%
 
 
 
169 
underfill to die passivation interface.  Thus, MSL2 preconditioning was generally detrimental to 
the adhesion of the underfill.  For the two MSL3 preconditioning exposures, the strength levels 
dropped slightly.  However, the failure location then shifted to the underfill to PCB interface, 
which suggests that the adhesion to the die passivation interface actually increased. 
6.6.3 Thermal Cycling Reliability Tests  
The thermal cycling test matrix consisted of four different underfill curing and 
preconditioning configurations: 
xrhombus Curing at 150 ?C, No Preconditioning 
xrhombus Curing at 165 ?C, No Preconditioning 
xrhombus Curing at 150 ?C, MSL3+245 Preconditioning 
xrhombus Curing at 165 ?C, MSL3+245 Preconditioning 
Three test boards were assembled for each configuration, and 28-30 functional daisy 
chain dies with no delaminations were available before preconditioning and thermal cycle test.  
After preconditioning at MSL3+245 but before thermal cycling, delaminations at the underfill to 
die passivation interface were discovered in some of the samples cured at 150 ?C, while no 
delaminations were presented in the MSL preconditioned samples cured at a cure temperature of  
165 ?C.  No solder joint failures occurred in any of the test chips during assembly 
preconditioning. 
Of the 30 test chips in the set cured at 150 ?C  and with MSL+245 preconditioning, 4/30 
experienced full delaminations and 15/30 showed slight delaminations after preconditioning.  
Thus, approximately 65% of the samples in this test contained delaminations before thermal 
cycling.  These initial interfacial flaws obviously placed this testing group at a severe  
 
 
 
 
170 
disadvantage from the reliability standpoint.  Figure 6.19 depicts the CSAM images showing 
delaminations in the preconditioned samples cured at 150 ?C. 
The Weibull failure plots (electrical opens) for the four test configurations are shown in 
Figure 6.20.  The calculated Weibull slope, characteristic life (cycles to 63.2% failure) and one 
percent life (N1%, cycles to 1% failure) are tabulated in Table 6.2.  As expected, the samples 
cured at 150 ?C with MSL3+245 preconditioning performed poorly due to the initial 
delaminations present.   
The data clearly indicate that the samples assembled at a cure temperature of 165 ?C were 
significantly more reliable than those cured at a temperature of 150 ?C.  The MSL3+245 
preconditioning also appeared to increase the reliability of the samples cured at 165 ?C.  Other 
factors that contributed to enhancing sample reliability included the increase in UTS (see Figure 
6.16) with preconditioning, as well as the change in location of the interfacial shear failures 
when the samples were preconditioned (see Figure 6.18).   
6.6.4 Microstructures 
SEM photos of the cross-sectioned solder joints after thermal cycling are shown in 
Figures 6.21(a) and 19(b) for the cases of underfill curing at 150 ?C with no preconditioning and 
with MSL3+245 preconditioning, respectively.  Complete solder joint cracking is seen in the no 
preconditioning case, while extreme underfill to die interfacial cracks and complete solder joint 
cracking are observed for the MSL3+245 preconditioning sample.  
Analogous SEM photos for the 165 ?C cured samples are also shown in Figure 6.22.  
Limited solder joint cracking was observed for both cases of preconditioning, even after more 
than 6500 thermal cycles. 
 
 
 
171 
 
 
 
 
 
 
 
(a)   No Delaminations 
 
 
(b)   Slight Delaminations 
 
 
 
 
 
 
 
 
(c)   Fully Delaminated 
Figure 6.19 - CSAM Images of Samples Cured at 150 ?C After MSL3+245 Preconditioning  
 
 
 
172 
 
 
 
 
 
 
 
 
 
 
 
Figure 6.20 - Weibull Failure Plots for Thermal Cycling of the Flip Chip Test Assemblies 
 
Configuration Weibull Slope, ?  Characteristic Life, ? 
(cycles) 
%1N  (Cycles) 
150 ?C, None 5.218 3303 1368 
165 ?C, None 4.812 5007 1925 
150 ?C, MSL3+245 1.559 1391 73 
165 ?C, MSL3+245 5.286 5602 2346 
 
Table 6.2 - Calculated Weibull Parameters 
 
 
 
 
173 
 
 
 
 
 
 
 
 
 
(a) 
 
 
 
 
 
 
 
 
(b) 
 
Figure 6.21 - Cross-Sectioned Solder Joints in the Samples Cured at 150 ?C, (a) 7500 Cycles, No 
Preconditioning; (b) 7300 cycles, MSL3+245 Preconditioning 
 
 
 
174 
 
 
 
 
 
 
 
 
 
(a) 
 
 
 
 
 
 
 
 
(b) 
Figure 6.22 - Cross-Sectioned Solder Joints in the Samples Cured at 165 ?C, (a) 6800 Cycles, No 
Preconditioning; (b) 6500 cycles, MSL3+245 Preconditioning 
 
 
 
175 
6.7 Summary and Conclusions 
The results presented in this chapter clearly indicate that the advantages that accrued 
from subjecting the specimens to a higher cure temperature included improved mechanical 
properties, superior thermal cycling fatigue life, and enhanced resistance to detrimental effects 
from moisture exposure and solder reflow. 
The effects of curing profile and MSL preconditioning on the mechanical and failure 
properties of underfills, and the reliability performance of underfill flip chip assemblies were 
investigated.  The higher cure temperature of 165 ?C led to a significant increase in the values of 
the effective elastic modulus and also the ultimate tensile strength of the underfill material. 
Although MSL3 preconditioning had only a minor effect on the effective elastic modulus, 
it significantly improved the ultimate tensile strength.  The results of the interfacial shear 
strength tests also demonstrated only slight variations of strength with preconditioning, but the 
location of the shear failures was shifted significantly to the underfill-substrate interface for the 
165 ?C cured samples. 
Moreover, the MSL3+245 preconditioning exposure was found to generate delaminations 
in the samples cured at 150 ?C, but no delaminations in the samples cured at 165 ?C.  During 
thermal cycling, the reliabilities of the 150 ?C cured samples were also found to be low relative 
to the analogous 165 ?C samples.  This trend was supported by failure analysis, which utilized 
both cross-sectioning and SEM microscopy.  Overall, the use of the higher temperature cure 
cycle produced better underfill properties and improved the performance of flip chip assembly in 
all cases. 
 
 
 
 
176 
CHAPTER 7  
SUMMARY AND CONCLUSIONS 
 
 
7.1 Literature Review for the Flip Chip Technology and Underfill Materials 
The technology for electronic packaging and underfill materials was reviewed 
extensively for this dissertation based on the three currently used underfill flow processes.  
Underfill technology is often considered the major breakthrough in electronics that made 
possible flip chip technology.  A discussion of the composition of underfill material was 
included, as well as an explanation of the mechanisms governing variations in the mechanical 
properties due to different underfill materials and thermal aging effects.  Although many 
constitutive models are available to describe the underfill material tensile properties and creep 
behaviors, there are no reports of models that take into account aging parameters.  In order to 
improve the reliability of packaging applications, models that include these parameters are 
necessary for use in FEA simulations. 
7.2 Unique Specimen Preparation Procedure 
In this research, a unique specimen preparation procedure was successfully developed to 
produce uniform underfill material specimens.  Under this procedure, uniaxial tensile specimens 
with the desired thickness can be made into testing coupons with large length-width ratios.  
These specimens were made using Teflon coating plates to avoid potential problems due to 
 
 
 
177 
sample contamination with mold releasing agents, so the specimens could be made and cured 
similarly to the methods used industrially for electronic packaging.  Therefore, the results 
obtained from specimens made by this method should be easily transferrable to industrial 
applications. 
7.3 Strain Rate Effects 
Tensile test with three strain rates were investigated for underfill materials.  Both 
effective elastic modulus and ultimate tensile strength decreased monotonically with testing 
temperature and lower displacement strain rate.  The material mechanical properties were 
strongly dependent on temperature, strain rates, and Tg.  The material showed the largest 
elongation at 125 ?C, with relatively high bonding strength. 
With the newly developed constitutive models, the mechanical properties of underfill 
material were predicted for all testing conditions by applying variables of strain rate and 
temperature. 
7.4 Isothermal Aging Effects on the Underfill Tensile Properties 
Specimens were isothermally aged at four different temperatures for periods from 10 
days to 300 days, and then subjected to tensile testing.  Aging effects on the tensile properties 
were also studied for the elastic modulus and ultimate tensile strength.  After various durations of 
isothermal aging, the underfill illustrated softening behaviors at temperatures exceeding 100 ?C, 
although the documented Tg was about 137 ?C. 
The underfill mechanical properties were enhanced as a function of the aging temperature 
and aging time.  Similarly, aged specimens were subjected to creep tests.  Both the effective 
elastic modulus (initial slope) and ultimate tensile strength (highest stress before failure) 
 
 
 
178 
increased monotonically with isothermal aging or aging temperature, regardless of whether the 
aging temperature was below, at, or above the Tg of the material. 
With the isothermal aging, the underfill material mechanical properties became linear 
with aging time.  Both linear and exponential empirical models with four constant parameters 
were proposed to describe the mechanical property behaviors, and the slope of the linear portion 
for long term aging could be obtained easily.  Furthermore, constitutive models were constructed 
in order to estimate material mechanical properties as functions of aging temperature, aging time 
and testing temperature. Reasonable agreement was found between the predictions generated by 
these models and the experimentally observed data. 
7.5 Isothermal Aging Effects on the Underfill Creep Behaviors 
Underfill material creep behavior is a kinetics phenomenon associated with the aging 
process. Isochronous creep curves indicated that the epoxy is a viscoelastic material with 
medium nonlinearity, and the Boltzmann?s linear superposition principle could not be applied for 
the load range used in this study. 
The results of the creep tests revealed that the underfill epoxy behaviors were more 
sensitive to the test temperature than the loading force, although inelastic strain was exhibited 
with both increasing load and increasing temperature. 
For a given time, the creep strains were much lower for the aged samples compared to 
non-aged samples.  Thermal aging had a significant effect on the secondary creep rate, which 
decreased with both the aging temperature and the aging time.  A reduction of up to 100X in the 
creep rate was observed, and significant changes occurred during the first 50 days of the 
isothermal aging.  Also, the slope for the long term secondary creep rate increased 3X with test 
 
 
 
179 
temperatures from 80 to 150 ?C, but degradation increased up to four-fold with stress, down to 
25% to 75% of the material's original ultimate tensile strength.  More sophisticated constitutive 
models were proposed in this study to describe the long term secondary creep rate under 
different aging temperatures and time, along with various testing temperature and stress levels. 
7.6 Moisture Effects and Reliability Tests 
The effects of moisture and different curing profiles on various material mechanical 
properties and package reliability were also included in this investigation.  The higher of the two 
curing temperatures tested was found to offer a number of advantages, namely improved 
mechanical properties, superior thermal cycling fatigue life, and enhanced resistance to 
detrimental effects from moisture exposure and solder reflow. 
With higher curing temperature (165 ?C), the effective elastic modulus and ultimate 
tensile strength of the underfill material also increased significantly.  In addition, MSL3 
preconditioning had no profound effect on the effective elastic modulus, but significantly 
improved the ultimate tensile strength. 
Interfacial shear strength tests demonstrated slight variations in strength with 
preconditioning, but an interesting finding was the accompanying shift in the location of the 
shear failures for samples cured at 165 ?C. 
The MSL3+245 preconditioning exposures were discovered to result in delaminations in 
many of the samples cured at 150 ?C.  However, no delaminations were found in the samples 
cured at 165 ?C.  During thermal cycling, specimens cured at 150 ?C were found to be less 
reliable those cured at 165 ?C.  This trend was supported by failure analysis performed using 
cross-sectioning and SEM microscopy.  Overall, the higher curing cycle led to better underfill 
 
 
 
180 
properties and enhanced flip chip assembly performance in all cases.  
These mechanical property results, obtained from strain rate tests, tensile tests, and creep 
tests, could be input into the underfill mechanical properties database, and the constitutive model 
could be used in FEA simulations to evaluate the reliability of an electronic package at various 
temperature conditions. 
 
 
 
 
 
181 
 
 
 
 
 
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187 
APPENDIX 
Additional Creep Data for Specimens Aged at 80, 125, and 150 ?C 
 
 
 
 
 
 
 
188 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A-1 - Creep Curves for Various Aging Times (Samples Aged at 80 ?C, Tested at 80, 100 
?C) 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 20 MPa
Aged at 80 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 30 MPa
Aged at 80 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 20 MPa
Aged at 80 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 30 MPa
Aged at 80 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 10 MPa
Aged at 80 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 10 MPa
Aged at 80 oC
 
 
 
189 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A-2 - Creep Curves for Various Aging Times (Samples Aged at 80 ?C, Tested at 125 ?C) 
 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 10 MPa
Aged at 80 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 15 MPa
Aged at 80 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 20 MPa
Aged at 80 oC
 
 
 
190 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A-3 - Creep Curves for Various Aging Times (Samples Aged at 125 ?C, Tested at 80, 100 
?C) 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 10 MPa
Aged at 125 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 20 MPa
Aged at 125 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 30 MPa
Aged at 125 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 10 MPa
Aged at 125 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 20 MPa
Aged at 125 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 30 MPa
Aged at 125 oC
 
 
 
191 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A-4 - Creep Curves for Various Aging Times (Samples Aged at 125 ?C, Tested at 125 ?C) 
 
 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 10 MPa
Aged at 125 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 15 MPa
Aged at 125 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 20 MPa
Aged at 125 oC
 
 
 
192 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A-5 - Creep Curves for Various Aging Times (Samples Aged at 150 ?C, Tested at 80, 100 
?C) 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 10 MPa
Aged at 150 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 20 MPa
Aged at 150 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 80 oC
? = 30 MPa
Aged at 150 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 10 MPa
Aged at 150 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 20 MPa
Aged at 150 oC
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 100 oC
? = 30 MPa
Aged at 150 oC
 
 
 
193 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure A-6 - Creep Curves for Various Aging Times (Samples Aged at 150 ?C, Tested at 150 ?C) 
 
 
Time, t(sec)
0 1000 2000 3000 4000 5000 6000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 10 MPa
Aged at 150 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 15 MPa
Aged at 150 oC
Time, t(sec)
0 200 400 600 800 1000
Cr
ee
p S
tra
in,
 ?
0.000
0.005
0.010
0.015
0.020
0 day
1 day
3 days
10 days
30 days
100days
200 days
300 days
T = 125 oC
? = 20 MPa
Aged at 150 oC