THERMO-MECHANICAL RELIABILITY MODELS FOR LIFE PREDICTION OF
AREA ARRAY ELECTRONICS IN EXTREME ENVIRONMENTS
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
__________________________________________
Naveen Chandra Singh
Certificate of Approval:
____________________________ __________________________
Jeffrey C. Suhling Pradeep Lall, Chair
Quina Distinguished Professor Associate Professor
Mechanical Engineering Mechanical Engineering
___________________________ __________________________
Roy W. Knight Stephen L. McFarland
Assistant Professor Dean
Mechanical Engineering Graduate School
ii
THERMO-MECHANICAL RELIABILITY MODELS FOR LIFE PREDICTION OF
AREA ARRAY ELECTRONICS IN EXTREME ENVIRONMENTS
Naveen Chandra Singh
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirement for the
Degree of
Master of Science
Auburn, Alabama
May 11, 2006
iii
THERMO-MECHANICAL RELIABILITY MODELS FOR LIFE PREDICTION OF
AREA ARRAY ELECTRONICS IN EXTREME ENVIRONMENTS
Naveen Chandra Singh
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon the request of individuals or institutions at their expense. The author reserves all
publication rights.
___________________________
Signature of Author
___________________________
Date of Graduation
iv
VITA
Naveen Chandra Singh, son of Dr. R. S. Singh and Smt. Pratima Singh, was born
on October 05, 1975, in Varanasi, Uttar Pradesh, India. He graduated in 1997 with a
Bachelor of Engineering degree in Aeronautical Engineering from Punjab Engineering
College, Chandigarh, India. After his baccalaureate he joined Punjab Tractors Ltd. (PTL)
as a Management Trainee in July, 1997. He worked at PTL?s R&D Divison on various
research projects in the capacity of Research and Development Engineer for more than 5
years. In the pursuit of enhancing his academic qualification he joined the M.S. Program
at Auburn University in the Department of Mechanical Engineering in Spring, 2003.
Ever since he enrolled for the M.S. program at Auburn University, he has worked under
the guidance of Professor Pradeep Lall, in the Department of Mechanical Engineering
and the Center for Advanced Vehicle Electronics (CAVE), as a Graduate Research
Assistant in the area of harsh environment electronic packaging reliability.
v
THESIS ABSTRACT
THERMO-MECHANICAL RELIABILITY MODELS FOR LIFE PREDICTION OF
AREA ARRAY ELECTRONICS IN EXTREME ENVIRONMENTS
Naveen Chandra Singh
Master of Science, May 11, 2006
(B.E. Aeronautical Engineering, Punjab Engineering College, India, 1997)
251 Typed Pages
Directed by Dr. Pradeep Lall
The increasing functionality in modern microelectronics requires more
complexity in less space and more reliability at lower cost. Demands on miniaturization
have lead to the evolution of several types of area array packages like PBGA, Flex-BGA,
Flip Chip CSPs etc. Area array packages have been increasingly targeted for use in harsh
environments such as automotive, military and space application but the thermo-
mechanical reliability of these packages in such environments is a concern for the
electronic industry. Several approaches are available today for reliability prediction
including non-linear finite element models and first-order closed form models. The first-
order models as the name suggests offer limited accuracy.
vi
In this thesis, a unique hybrid approach to reliability prediction, in order to
achieve accuracy beyond the closed-form first-order approximations, has been presented.
The perturbation approach presented in this paper enables higher-accuracy model
prediction by perturbing known accelerated-test data-sets using models, using factors
which quantify the sensitivity of reliability to various design, material, architecture and
environmental parameters. The models are based on a combination of statistics and
failure mechanics. In addition, parameter interaction effects, which are often ignored in
closed form modeling, have been incorporated in the proposed hybrid approach. The
statistics models are based on accelerated test data in harsh environments, while failure
mechanics models are based on damage mechanics and material constitutive behavior.
The framework formulated from the models is intended as an aid for
understanding the sensitivity of the component reliability to geometry, package
architecture, material properties and board attributes in different thermal environments.
The intent is to develop a decision-support system for doing trade-offs between
geometry, materials and quantitatively evaluating the impact on the reliability.
Convergence between the statistical model sensitivities and failure mechanics based
sensitivities has been demonstrated. Predictions of the sensitivities have been validated
against the experimental test data.
vii
ACKNOWLEDGEMENTS
The author acknowledges and extends gratitude for financial support received
from the NSF Center for Advanced Vehicle Electronics (CAVE). Many thanks are due
to the author?s advisor Prof. Pradeep Lall, and other committee members for their
invaluable guidance and help during the course of this study.
Deepest gratitude are also due to the author?s father, Dr. R. S. Singh and family
members for being constant source of inspiration and motivation, fianc?e, Romika Singh,
friends, Maninderjit Singh, Kshitij Mankad, Candida Stevez, Manjot Singh, Ramandeep
Ramana, Sachin Jambovane, Nokibul Islam and all other colleagues and friends whose
names are not mentioned, for their priceless love and support.
viii
Style manual or journal used Guide to Preparation and Submission of Theses and
Dissertations
Computer software used Microsoft Office 2003, Minitab 13.1, Ansys 7.0,
WinSmith Weibull 3.0, Matlab 7.0.1
ix
TABLE OF CONTENTS
LIST OF FIGURES???????????????????????..........
xiii
LIST OF TABLES??????????????????????????
xviii
Chapter 1 Introduction????????????????????????. 1
1.1 Area Array Packaging: Key to the Miniaturization of Electronics???. 1
1.2 Thermo-mechanical Reliability: A Concern for Area Array Packaging?. 2
1.3 Factors Affecting Packaging Design and Selection?????????
8
Chapter 2 Literature Review..?????????????????????. 11
2.1 Experimental Techniques??????????????????? 11
2.2 Statistical Analysis?????????????????????.. 12
2.3 Failure Mechanics Based Analytical Modeling??????????.. 14
2.4 Finite Element Based Numerical Techniques???????................. 16
2.5 Constitutive Behavior and Relationships of Solder Material?.................. 18
2.6 Solder Joint Fatigue Failure Models and Damage Relationships???? 19
2.2 Objective and Scope of Thesis????????????????? 21
2.3 Thesis Layout???????????????????????..
21
Chapter 3 Failure Mechanics Based Models for BGA Packages???????? 23
3.1 Overview?????????????????????????. 23
3.2 Modeling Methodology???????????????????.. 24
3.2.1 Maximum Shear Strain Calculation???????????.. 24
3.2.2 Hysteresis Loop Determination????????????? 27
3.2.3 Inelastic Energy Density Calculation??????????? 29
3.2.4 Life Prediction from Damage Relationship????????..
29
Chapter 4 Statistics Based Closed Form Models for BGA Packages??????.. 34
4.1 Overview?????????????????????????. 34
4.2 The Perturbation Approach??????????????????. 35
4.3 Model Library???????????????????????. 38
4.4 Linear Models???????????????????????. 38
4.4.1 Linear Model-1???????????????????. 39
4.4.1.1 Model Diagnostics?????????????.. 42
4.4.2 Linear Model-2???????????????................. 45
4.4.2.1 Model Diagnostics?????????????.. 46
4.4.3 Linear Model-3???????????????????. 49
4.4.3.1 Model Diagnostics?????????????.. 49
4.5 Non-Linear Models?????????????????????. 52
x
4.5.1 Non-Linear Model-1?????????????????. 53
4.5.1.1 Model Diagnostics?????????????.. 54
4.5.2 Non-Linear Model-2?????????????????. 58
4.5.2.1 Model Diagnostics?????????????.. 58
4.6 Model Prediction Correlation with Experimental Data???????..
61
Chapter 5 Model Validation and Design Guidelines for BGA Packages????? 64
5.1 Model Validation?????????????????????? 64
5.1.1 Packaging Density?????????????????? 65
5.1.2 Ball Count?????????????????????. 66
5.1.3 Ball Diameter???????????????????? 69
5.1.4 Board Thickness??????????????????? 69
5.1.5 Encapsulant Mold Compound Filler Content???????... 71
5.1.6 Pad Configuration??????????????????. 74
5.1.7 Board Finish????????????????????.. 77
5.1.8 Temperature Cycle Condition?????????????... 79
5.2 Convergence of Statistics and Failure Mechanics Models with Actual
Experimental Test Data???????????????????.. 81
5.3 Design Guidelines?????????????????????..
84
Chapter 6 Statistics and Failure Mechanics Based Models for Flip Chip????... 86
6.1 Overview?????????????????????????. 87
6.2 Statistics Based Modeling??????????????????... 87
6.2.1 Model Diagnostics?????????????????? 91
6.3 Failure Mechanics Based Modeling??????????????... 96
6.3.1 Shear Stress and Strains???????????????? 96
6.3.2 Hysteresis Loop Computation?????????????... 98
6.3.3 Life Prediction from Damage Relationship????????.. 100
6.4 Model Validation?????????????????????? 102
6.4.1 Die Size??????????????????????. 102
6.4.2 Ball Count?????????????????????. 103
6.4.3 Underfill Characteristic????????????????. 105
6.4.4 Solder Joint Diameter????????????????... 107
6.4.5 Pad Configuration??????????????????. 110
6.4.6 Temperature Cycle Magnitude?????????????. 112
112
6.5 Convergence of Statistics and Failure Mechanics Models with Actual
Experimental Test Data???????????????????..
Chapter 7 FEM Analysis of a Flip-Chip Package?????????????.. 117
7.1 Overview????????????????????????? 117
7.2 Model Description?????????????????????.. 118
7.2.1 Model Variables??????????????????? 119
7.2.1.1 Geometry?????????????????. 119
7.2.1.2 Material?????????????????? 119
7.2.2 Elements Used???????????????????... 122
7.2.3 Mesh and Boundary Conditions????????????? 122
xi
7.2.4 PCB Material Layers?????????????????. 125
7.2.5 Material Properties?????????????????? 129
7.2.5.1 Linear Material Properties??????????.. 129
7.2.5.2 Non-Linear Solder Material Properties?????... 129
7.2.6 Inelastic Strain Energy Density?????????????. 131
7.3 Material Characterization of Underfill Materials?????????? 133
7.3.1 UF-1?.??????????????????????.. 133
7.3.2 UF-2?.??????????????????????.. 135
7.3.3 UF-3???????????????????????... 135
7.3.4 UF-4???.????????????????????.. 138
7.3.5 Effect of Measured Properties on the Simulation Results???. 142
7.4 Solder Joint Integrity in Accelerated Thermal Cycling???????... 142
7.4.1 0-70?C??????????????????????? 144
7.4.1.1 Effect of Solder Joint Material Composition???... 149
7.4.1.2 Effect of Underfill Composition????????.. 149
7.4.1.3 Effect of Bump Gap Height??????????. 152
7.4.1.4 Effect of Bump Size????????????? 152
7.4.1.5 Summary?????????????????.. 156
7.4.2 0-90?C??????????????????????? 156
7.4.2.1 Effect of Solder Joint Material Composition???... 159
7.4.2.2 Effect of Underfill Composition????????.. 159
7.4.2.3 Effect of Bump Gap Height??????????. 164
7.4.2.4 Effect of Bump Size????????????? 164
7.4.2.5 Summary?????????????????.. 164
7.4.3 Effect of Tg (glass transition temperature) of the Underfill
Material??????????????????????.. 167
7.4.4 Field Profiles????????????????????.. 169
7.4.4.1 Profile-1?????????????????... 169
7.4.4.2 Profile-2?????????????????... 172
7.4.4.3 Profile-3?????????????????... 172
7.4.4.4 Relative Damage Index???????????... 176
7.5 Life Prediction and Field Life Correlation with ATC Life??????. 180
7.5.1 Theory??????????????????????? 180
7.5.2 Energy Partitioning Methodology????????????. 181
7.5.2.1 Hysteresis Loop??????????????... 188
7.5.3 Fatigue Life Prediction Models?????????????. 192
7.5.3.1 Eutectic (SnPbAg) Solder??????????? 192
7.5.3.2 Lead-free (SnAgCu) Solder??????????. 194
7.5.4 Field Profile Based Fatigue Life Prediction????????.. 196
7.5.4.1 Profile-1?????????????????... 196
7.5.4.2 Profile-2?????????????????... 196
7.5.4.3 Profile-3?????????????????... 196
7.6 Copper Trace Integrity???????????????????? 201
7.6.1 Model Description??????????????????. 201
7.6.2 Von-Mises Stress Comparison for Different Underfill Materials. 201
7.7 Summary and Recommendations???????????????? 207
xii
7.7.1 Development of PCB and Drive Level Tests???????? 207
7.7.2 Recommendations for the PCB Level Accelerated Test???... 209
7.7.3 Recommendations for the Drive Level Stress Test ?????..
210
Chapter 8 Summary and Conclusions??????????????????..
211
Bibliography????????????????????????????..
215
APPENDIX A List of Symbols????????????????????...
230
xiii
LIST OF FIGURES
1.1 Various components of a flip-chip package with the corresponding
approximate coefficients of thermal expansion (CTE) values
3
1.2 Solder joint fatigue failure due to thermal cycling 7
3.1 Schematic of the failure mechanics based modeling methodology 25
3.2 Calculation of area under the curve using trapezoidal method 30
3.3 Effect of temperature condition on thermal reliability of 23mm PBGA
package
33
4.1 Schematic of the perturbation approach for thermal reliability assessment 36
4.2 Residual plots for the Linear Model-1 44
4.3 Residual plots for the Linear Model-2 48
4.4 Residual plots for the Linear Model-3 51
4.5 Residual plots for the Non-Linear Model-1 57
4.6 Residual plots for the Non-Linear Model-2 60
4.7 Plot of experimental vs predicted 1% cycles to failure for the Linear Model-
3
62
4.8 Plot of experimental vs predicted 1% cycles to failure for the Non-Linear
Model-2
63
5.1 Effect of die-to-package ratio on thermal fatigue reliability of BGA
subjected to ?40 to 125 ?C Thermal Cycle
67
5.2 Effect of ball count on thermal fatigue reliability of BGA subjected to ?40
to 125 ?C Thermal Cycle
68
5.3 Effect of ball diameter on thermal fatigue reliability of BGA subjected to ?
40 to 125 ?C Thermal Cycle
70
5.4 Experimental data plot for BGAs (A to H) with die-to-package ratios
between 0.53 and 0.81, subjected to ?40 to 125 ?C Thermal Cycle and PCB
thickness 0.85 and 1.60mm
72
5.5 Model prediction plot for BGAs (A to H) with die-to-package ratios
between 0.53 and 0.81, subjected to ?40 to 125 ?C Thermal Cycle and PCB
thickness 0.85 and 1.60mm
73
xiv
5.6 Effect of mold compound filler content on thermal fatigue reliability of
16mm BGA with die-to-body ratio 0.53, subjected to ?40 to 125 ?C
Thermal Cycle
75
5.7 Effect of mold compound filler content on thermal fatigue reliability of
16mm BGA with die-to-body ratio 0.72, subjected to ?40 to 125 ?C
Thermal Cycle
75
5.8 Effect of the change in mask definition from SMD to NSMD on 15mm, 160
I/O BGA thermal reliability
78
5.9 Effect of PCB pad finish on 12mm, 132 I/O BGA thermal reliability
subjected to ?40 to 125 ?C Thermal Cycle
80
5.10 Effect of temperature cycle condition on 12mm, 132 I/O BGA thermal
reliability
82
5.11 Effect of solder ball diameter on thermal reliability of 8mm and 12mm
BGA packages under thermal cycle ?40?C to 125?C
83
6.1 Residual plots for the diagnostics of the statistical model 94
6.2 Actual vs predicted characteristic life 95
6.3 Effect of die size on thermal fatigue reliability of encapsulated flip-chip
with Sn37Pb solder joints
104
6.4 Effect of ball count on thermal fatigue reliability of encapsulated flip-chip
with leaded and lead-free solder joints
106
6.5 Effect of underfill on thermal fatigue reliability of flip-chip devices with
99.3Sn0.7Cu solder joints
108
6.6 Effect of underfill on thermal fatigue reliability of flip-chip with
95.5Sn4.0Ag0.5Cu solder joints
108
6.7 Effect of bump diameter on thermal fatigue reliability of encapsulated flip-
chip with lead-free (96.5Sn3.5Ag) solder joints and die size of 5.1 mm
subjected to ? 40?C to 125?C thermal cycle
111
6.8 Effect of pad configuration on thermal fatigue reliability of encapsulated
flip-chip with die size of 12.6 mm subjected to 0?C to 100?C thermal cycle
113
6.9 Effect of ATC temperature cycle magnitude on thermal fatigue reliability of
underfilled flip-chip devices
114
6.10 Correlation between Accelerated Test, Statistical Model, and Failure
Mechanics Model
116
7.1 Eight noded hexahedral isoparametric element 123
7.2 Fully meshed model with coordinate axes 124
7.3 Solder bump mesh for the three different gap heights 126
7.4 Schematic of the boundary conditions applied on the model for the
simulation
126
xv
7.5 Schematic of the material layers modeled for the simulation 127
7.6 Uniaxial test specimen and the assembly equipment used for the sample
preparation and cure
134
7.7 Stress-strain plot from the uniaxial tensile test for UF-1 underfill material 134
7.8 Strain distribution in UF-1 underfill with low gap height bump 136
7.9 Stress-strain plot from the uniaxial tensile test for the UF-2 underfill 137
7.10 Stress strain plot from uniaxial tensile test of UF-3 underfill material 139
7.11 Strain distribution contour plot in UF-3 underfill material with high gap
height bump configuration
140
7.12 Stress strain plot from uniaxial tensile test of UF-4 underfill material 141
7.13 Strain distribution contour plot in UF-4 underfill material with low gap
height bump configuration
141
7.14 0-70?C accelerated thermal cycle profile 145
7.15 Contour plot of nodal values of ISED in the solder bump for test case 1 147
7.16 Contour plot of the nodal values of the ISED accumulated in the solder
bump for test case 12
147
7.17 Contour plot of the nodal values of the Von-Mises stress in the solder bump
for test case 12
148
7.18 Normalized ISED for UF-1 underfill material with low and high gap height
4 mils solder bumps
150
7.19 Normalized ISED for UF-2 underfill material with mid (3 mils) and high (4
mils) gap height 4 mils solder bumps
150
7.20 Normalized ISED for UF-4 (4 mils) and UF-3 (3 mils) underfill material
with high and mid gap height solder bumps respectively
151
7.21 Normalized ISED for high gap height 4 mils eutectic solder bump with
different underfill materials
153
7.22 Normalized ISED for mid gap height 3 mils lead-free solder bumps with
different underfill materials
153
7.23 Normalized ISED for high gap height 4 mils lead-free solder bumps with
different underfill materials
154
7.24 Normalized ISED for 4 mils eutectic solder bumps with UF-4 underfill
material and different gap heights
154
7.25 Normalized ISED for 4 mils lead-free solder bumps with UF-1 underfill
material and different gap heights
155
7.26 Normalized ISED for mid gap height eutectic solder bumps with UF-3
underfill with different bump diameter
157
xvi
7.27 0-90?C accelerated thermal cycle profile 158
7.28 Normalized ISED for UF-1 underfill material with low and high gap height
4 mils solder bumps
161
7.29 Normalized ISED for UF-2 underfill material with mid (3 mils) and high (4
mils) gap height 4 mils solder bumps
161
7.30 Normalized ISED for UF-4 (4 mils) and UF-3 (3 mils) underfill material
with high and mid gap height solder bumps respectively
162
7.31 Normalized ISED for high gap height 4 mils eutectic solder bump with
different underfill materials
162
7.32 Normalized ISED for mid gap height 3 mils lead-free solder bumps with
different underfill materials
163
7.33 Normalized ISED for high gap height 4 mils lead-free solder bumps with
different underfill materials
163
7.34 Normalized ISED for 4 mils eutectic solder bumps with UF-4 underfill
material and different gap heights
165
7.35 Normalized ISED for 4 mils lead-free solder bumps with UF-1 underfill
material and different gap heights
165
7.36 Normalized ISED for mid gap height eutectic solder bumps with UF-3
underfill with different bump diameter
166
7.37 Temperature profile of the averaged thermal duty cycle 1 171
7.38 Temperature profile of the averaged thermal duty cycle 2 173
7.39 Temperature profile of the averaged thermal duty cycle 3 173
7.40 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-2 capillary flow
encapsulant
178
7.41 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-3 re-flow
encapsulant
178
7.42 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-4 re-flow
encapsulant with Tg assumed to be above 87?C
181
7.43 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-4 re-flow
encapsulant with Tg assumed to be in the range of 70-75?C
181
7.44 Energy partitioning methodology flowchart 182
7.45 Temperature dependent linear elastic modulus of the eutectic solder
material
185
xvii
7.46 Temperature dependent stress-strain data for modeling multilinear isotropic
hardening of the 62Sn36Pb2Ag solder material
186
7.47 Temperature dependent linear elastic modulus of the lead-free solder
material
186
7.48 Temperature dependent stress-strain data for modeling multilinear isotropic
hardening of the lead-free solder material
187
7.49a Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-2 capillary
flow encapsulant subjected to field profile 1
189
7.49b Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-2 capillary
flow encapsulant subjected to field profile 2
189
7.49c Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-2 capillary
flow encapsulant subjected to field profile 3
190
7.50a Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-4 reflow
encapsulant subjected to field profile 1
190
7.50b Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-4 reflow
encapsulant subjected to field profile 2
191
7.50c Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-4 reflow
encapsulant subjected to field profile 3
191
7.51 Close-up view of the flip-chip model with the copper trace, without
underfill fillet
202
7.52 Close-up view of the flip-chip model with the copper trace with underfill
fillet
202
7.53 Von Mises stress contour plot of the copper trace without underfill fillet 203
7.54 Stress distribution contour plot for UF-2 (capillary flow) and UF-3 (re-
flow) underfill
205
7.55 Stress distribution contour plot for UF-4 (re-flow) and UF-1 (capillary)
underfill
205
xviii
LIST OF TABLES
3.1 Constants for the damage relationship 33
4.1 Model Parameters and Analysis of Variance for Multi-variable Regression
Linear Model-1
41
4.2 Pearson correlation coefficient matrix for the predictor variables of the
Linear Model-1
43
4.3 Model Parameters and Analysis of Variance for Multi-variable Regression
Linear Model-2
47
4.4 Model Parameters and Analysis of Variance for Multi-variable Regression
Linear Model-3
50
4.5 Model Parameters and Analysis of Variance for Multivariate Regression
Non-Linear Model-1
55
4.6 Pearson correlation coefficient matrix for the predictor variables of the Non-
Linear Model-1
56
4.7 Model Parameters and Analysis of Variance for Multivariate Regression
Non-Linear Model-2
59
5.1 Sensitivity of the package reliability to packaging ratio and comparison of
model predictions with actual failure data
67
5.2 Sensitivity of the package reliability to the ball count and comparison of
model predictions with actual failure data
68
5.3 Sensitivity of the package reliability to the ball diameter and comparison of
model predictions with actual failure data
70
5.4 Sensitivity of the package reliability to the PCB thickness and comparison of
X-factor based on model predictions and actual failure data
73
5.5 Sensitivity of the package reliability to the EMC filler content and
comparison of X-factor based on model predictions and actual failure data
76
5.6 Sensitivity of the package reliability to the pad configuration and comparison
of X-factor based on model predictions and actual failure data
78
5.7 Sensitivity of the package reliability to the board finish type and comparison
of model predictions with actual failure data
80
xix
5.8 Sensitivity of the package reliability to thermal cycling temperature range
and comparison of X-factor based on model predictions and actual failure
data
82
6.1 Scope of Accelerated Test Database 88
6.2 Multi Variate Regression Models of BGA Thermal Fatigue Data 93
6.3 Analysis of Variance for Data-Set 93
6.4 Constants for the damage relationship 101
6.5 Sensitivity factor for the die size and model prediction comparison with the
actual failure data
104
6.6 Sensitivity factor for the ball count and model prediction comparison with
the actual failure data
106
6.7 Sensitivity factor for underfill characteristic and model prediction
comparison with the actual failure data
109
6.8 Sensitivity factor for the ball diameter and model prediction comparison with
the actual failure data
111
6.9 Sensitivity factor for pad type and model prediction comparison with the
actual failure data
113
6.10 Sensitivity factor for ATC temperature range and model prediction
comparison with the actual failure data
114
7.1 Dimensions of fixed parameters used for the finite element model 120
7.2 Material variations and the dimensions of the variable geometric parameters 121
7.3 Material properties and thickness of the PCB layers 128
7.4 Linear isotropic material properties with vendor data for the underfill
materials
130
7.5 Values of the constants of Anand?s viscoplastic model 132
7.6 Simulation results for 0-70?C thermal cycle with vendor and measured data 143
7.7 Simulation results for 0-70?C accelerated thermal cycle 146
7.8 Simulation results for 0-90?C accelerated thermal cycle 160
7.9 Simulation results for the analysis of the effect of Tg on solder joint
reliability
168
7.10 Material model data used for simulation 168
7.11 Simulation results for field profile 1 171
7.12 Simulation results for the field profile 2 174
7.13 Simulation results for the field profile 3 175
7.14 Simulations results for evaluation of relative damage index of the three field
profiles provided by the vendor
177
xx
7.15 Constants used for the time dependent creep model of the solder 185
7.16 Constants for the damage relationship 195
7.17 Failure data for profile 3 provided by the vendor 195
7.18 Predicted life for all 18 test cases for field profile 1 198
7.19 Predicted life for all 18 test cases for field profile 2 199
7.20 Predicted life for all 18 test cases for field profile 3 200
7.21 Maximum Von Mises stress from the model with fillet and without fillet 203
7.22 Simulation results for two different ATCs 206
1
CHAPTER 1
INTRODUCTION
The role of packaging [Tummala, et al. 1997] in electronic device is, signal and
power distribution, heat dissipation and protection from the environment, loads and
stresses. Electronic packaging may be understood as the embodiment of the electronic
devices and establishment of electrical interconnection among the devices for some
useful application. The advances in the semiconductor fabrication being driven into the
nanometer range [Isaac, 2005], has mounted the pressure on the IC (Integrated Circuit)
packaging technologies. The sophisticated packaging design solutions once considered
cutting edge or deemed too costly have moved into the mainstream to meet the needs of
the commercial products.
1.1 Area Array Packaging: Key to the Miniaturization of Electronics
The extreme miniaturization in the electronic devices has lead to the evolution of
area array packaging technology. Due to the increase in the device density of the IC
chips, the number of input-output interconnections (I/Os) for the same sized chip have
grown up to an extent that the perimeter of the packaged chip is not sufficient to
accommodate all the I/Os, thus driving the packaging technology towards the area array
interconnection [Lau 1996, 1997] in order to accommodate the ever increasing I/Os.
2
Area array packaging with surface mount technology [Harper, 2004] has emerged
as the solution for the problem posed by the extreme miniaturization in electronics for the
high density IC packaging. The IC packaging technology [Suhling, 2003] in the past has
evolved from the inline and peripheral array packages such as single inline package
(SIP), dual inline package (DIP), plastic leaded chip carrier (PLCC), quad flat package
(QFP) or leadless ceramic chip carrier (LCCC) to an area array packaging such as ball
grid array (BGA), flip-chip, chip scale packages (CSP) and multi-chip modules (MCM).
The mounting technology [Suhling, 2003] for the IC packages has evolved from the
earlier plated through hole (PTH) to the current state-of-art surface mount technology
(SMT).
1.2 Thermo-mechanical Reliability: A Concern for Area Array Packaging
The operation of any electronic device generates heat and with the increasing
device density of the IC chips the amount of heat flux generated by the IC chips has gone
to a level of 100-200 W/cm
2
[Nimkar, et al. 2005]. Due to this, whenever a device is
switched on, the electronic components heat-up and than cool down after the device is
switched off. This leads to a thermal cycling of the device and since the different
packaging components have different coefficients of thermal expansion (CTE), as shown
in the Figure 1.1, there is a differential in expansion of various components. This thermal
expansion differential causes stresses in the various components and the continuous
thermal cycling of the device due to on-off switching during it?s usage life finally leads to
the fatigue failure of the device. The fatigue failure of the device can occur in various
different modes [Viswanadham and Singh, 1998].
3
Figure 1.1 Various components of a flip-chip package with the corresponding
approximate coefficients of thermal expansion (CTE) values.
Solder Joint (24.0ppm/?C)
Passivation
Printed Circuit Board (16.0ppm/?C)
Copper Pad (16.0ppm/?C)
Solder Mask
Silicon Chip (2.0ppm/?C)
Underfill (35-70ppm/?C)
4
One of the common failure modes in electronic packages is the ?Pop Corn Failure?
which occurs during the re-flow due to the moisture content in the mold compound of the
package. Ilyas and Roberts [1993] analyzed the sensitivity of the moisture in electronic
package, on the package failures and attributed failure to 3 different types of cracking
depending upon the moisture content, chip size, and other package dimensions. Ilyas and
Roberts [1993] investigated the moisture sensitivity in several surface mount packages
that included SOJ, PLCC, TQFP, and PQFP packages. Yip, et al. [1996] studied the
moisture induced failures in case of Ball Grid Array packages, PBGA and TBGA
packages were used in the study. It was established that 16 hours baking at 115?C
essentially removes most of the moisture from the package, hence reducing possibility of
the interfacial delamination and pop-corn cracking of the package. Lee, et al. [1996]
analyzed and proposed a new lead frame design for improved reliability of the packages
by encountering the pop corn cracking. Guzman, et al. [1996] in their study on the
package cracks during the assembly process addressed various issues that lead to package
cracking at the assembly stage, such as flashing of the excess plastic molding compound,
lead forming operations and package singulation. Measures for eliminating the assembly
induced package cracks for plastic SOIC packages were proposed.
Silicon die cracking is another failure mode that takes place due to the thermal
stresses developed in the chip. The stresses might develop during the assembly stage or
during the thermal cycling of the component due to the CTE mismatch within the
package. Efforts as early as 1970?s [Dale and Oldfield 1977] have been made to analyze
the stresses developed in the plastically encapsulated devices during the assembly and
use. Lau [1993] has addressed the stresses generated during the packaging processes
5
such as wafer preparation, oxidation, diffusion, metallization, die and wire bonding,
encapsulation, re-flow and curing. Edwards, et al. [1987] evaluated shear stresses during
thermal cycling and thermal shock tests in the plastic packages and found that the shear
stresses are heavily concentrated at the corners and edges of the silicon die. Okikawa, et
al. [1987] analyzed plastic molded LSI packages subjected to thermal cycling and found
that thermal stresses cause passivation film cracks in the package. Jaegar et al. [1993,
1997] and Gee, et al. [1995] designed a test chip and piezoresistive sensor for detecting
thin film cracking and measurement of stresses in the electronic packages. Suhling, et al.
[1999] measured flip chip die stresses using piezoresistive test die, and Zou, et al. [1999]
analyzed the die surface stress variation during thermal cycling and thermal aging
raliability tests.
Thermal stresses developed due to the CTE differential during assembly or
thermal cycling can also lead to interfacial delamination, which may result in package
failure. Moore, et al. [1991, 1992] used C-SAM (C-Mode Scanning Acoustic
Microscope) for detecting delamination in the plastic packages by polarity analysis of
reflected acoustic pulses and analyzed the impact of delamination on the stress induced
failures on surface mounted ICs. Doorselaer and Zeeuw [1990] developed relation
between delamination and temperature-cycling induced failures in plastic packaged
devices. Van Gestel, et al. [1992] compared the effect of delamination on plastic
packaged devices subjected to temperature cycling test and highly accelerated stress test.
Zou, et al. [1998] analyzed the effect of delamination on the die surface stresses and
conducted the stress measurements delaminated and non-delaminated plastic packages.
6
With the shrinking interconnect size, the solder joint becomes the weakest link in
the overall package reliability. It has been established from various studies and failure
analyses [Harmon 1974, Engelmaier 1984, Katlowitz 1986, Hwang 1988, Solomon 1989,
Tien, et al. 1989, Lau 1991, Lall, et al. 1997, 2003, 2005, Suhling, et al. 2004] that the
interconnect failure due to the thermal cycling, as shown in Figure 1.2 is the most critical
mode of failure in various leaded and SMT packages such as BGA and flip-chip. Solder
joint failure has remained a serious concern and area of extensive research in electronic
packaging reliability. Vishwanadham, et al. [1993] and Emerick, et al. [1993] looked at
the solder joint reliability aspects of TSOP (Thin Small Outline Package) and proposed
method for enhancement of solder joint reliability by using encapsulation. Solder alloy
of various compositions have been conventionally used as the interconnect material in
electronic packages, eutectic solder (Sn63 Pb37) being the most popular choice, but the
RoHS (Restriction of Hazardous Substances) legislation [Iscoff, 2005] and the stringent
norms of EPA (Environmental Protection Agency), has made it inevitable for the
electronic industry to look for Pb-free solder alloys. Multitude of research studies [Lau,
et al. 2004, Wiese, et al. 2001, Zahn 2002, 2003, Kim et al. 2003, Schubert et al. 2002]
have been performed and are still underway to determine the most suitable Pb-free
replacement, although no particular replacement has been so far identified for all the
applications, but the SAC alloy (SnAgCu) has emerged out as the most popular choice.
7
Figure 1.2 Solder joint fatigue failure due to thermal cycling
L
h
At Stress Free Temperature (T)
At Temperature T
2
(T
2
T)
Silicon
PCB
8
1.3 Factors Affecting Packaging Design and Selection
Today, the OEMs have several options for making selections among the COTS
(commercial of the shelf) IC devices, for their product. But it is of utmost importance for
the manufacturer to understand the reliability of the selected devices for the given
application, because the failure of any one of the selected device would result in the
failure of the whole product. In case, reliability was the only factor for consideration
then one could have selected most robust components designed with very high reliability,
but that?s not the case. In a real situation factors like production yield, cost, size and
weight also play a vital role, keeping these factors in mind the manufacturer has to be
very wise and precise in his judgment for the design and selection of appropriate
components.
1. Exposure to the Environment: The ever increasing use of electronics in
various applications and technological areas has simplified and helped the development
in those areas, but it has certainly complicated the design and development of electronic
packaging, since the same device in different products calls for a different packaging
technology as the environment to which the device is subjected, varies with the
application. A product to be used for automotive [Adams et al. 1998, Evans et al. 1997,
Jung et al. 1998, Mawer et al. 1999] or space application is subjected to much harsher
vibration, shock and thermal environment as compared to the product such as a
workstation [Ray, et al. 1997], microwave [Bedinger, 2000], cellular application
[Sillanpaa et al. 2004] power electronics [Liu,et al. 2001] application thus requiring more
robust packaging as compared to the devices to be used in the office environment
desktops.
9
2. Size: Size of the product is another governing factor that drives the packaging
technology to be used for the electronic devices. Most of the electronic products have
witnessed a drastic decrease in their size, which is visible if one compares the size of the
mobile phones today with those of five or ten years back. The space or size constraint
also depends on the product for example the desktop computer can have much larger
space for housing all the electronic devices and circuits as compared to the laptops,
therefore the similar devices to be used for the laptops need to have much smaller
packaging.
3. Cost: One of the most important factors driving most of the technological
developments in any industry is the cost reduction. Due to the ever increasing
competition in the market the seller has no option but to go for the cost reduction of the
products in order to have an edge over the other competitors. The time has gone when
the high factor of safeties were used, now the performance of the products can be more
precisely determined thus leading to much lower safety margins and cost savings.
Various technological developments in the materials and process engineering have been
accomplished in the area of electronic packaging in order to reduce the cost of the final
product.
4. Product Life: The product life is one of the critical factors governing the type
of packaging technology to be used for the electronic devices for any particular product.
Using the components having life higher than the life for which the product is designed
unnecessarily adds to the cost of the product, on the other hand the life of components
cannot be less than the designed life of the product, otherwise the product will fail earlier
10
than it?s designed life. Thus the packaging technology that optimizes the life of the
components with that of the product life has to be developed.
There are multiple ways in which one can analyze these factors for making
appropriate selection of the components that will have optimum life. One way is to
conduct accelerated experimental testing and correlate it with the field conditions. This is
a very tedious and time consuming process, thus adding to the cost of the product and
delaying the arrival of the product in the market. The other option is FEA based
computational simulation, which is much faster, but it requires highly specialized and
skilled user otherwise it is just a weapon in the hands of an incompetent user. Another
viable option is to take help of closed form analytical models based on mechanics of
failure or statistics for analyzing the effect of various parameters. This option provides a
tool which is very quick and easy to use and does not require high skill.
11
CHAPTER 2
LITERATURE REVIEW
Solder joint failure due to thermo-mechanical fatigue is the most critical factor in
the reliability of the area array packages [Giulio 1997, Harper 2004]. This makes the
solder joint reliability analysis one of the most important and focused issue as far as the
reliability and life of the electronic packages is concerned. Multitude of published
literature addressing solder joint reliability and life prediction is available. Various
methodologies used in these literatures for the solder joint fatigue life prediction of area
array packages include, experimental techniques (accelerated thermal cycling tests),
closed form models based on the theory of failure mechanics, finite element analysis
(FEA) and statistics based regression models.
2.1 Experimental Techniques
Several experimental tests, such as accelerated thermal cycling, thermal shock,
HAST (highly accelerated stress test) and vibration test, have been used by the
researchers in the past to analyze the solder joint fatigue life for qualifying the
components for different applications. Darveaux, et al. [2000] conducted several board
level thermal cycle reliability tests, the packages used included Flex-BGA, TABGA
(Tape Array Ball Grid Array), PBGA and ?BGA. Various package and board variables
were included in the test matrix, and it was found that fatigue life increased by up to 6X
12
as dies size was reduced, and for a given die size, fatigue life was up to 2X longer for
larger packages, and solder joint fatigue life was 20% longer for 0.9mm thick test boards
compared to 1.6mm thick boards. 1.6X acceleration factor between -40?C to 125?C and
0?C to 100?C was also reported.
Mercado, et al. [2000] conducted test on flip chip PBGA package for FSRAM
(Fast Static RAM) application in order to analyze the effect of pad size and substrate
thickness on the solder joint reliability. It was reported that C5 solder joints with larger
solder pad and thicker substrates demonstrated higher reliability. Hung, et al. [2000]
investigated the effect of chip size, surface finish, Au plating thickness, epoxy thickness,
polyimide thickness and underfilling on the interconnect thermal cyclic fatigue life by
conducting experimental test on Flex-BGA packages. Chip size, polyimide thickness and
underfilling were found to have significant impacts on the joint fatigue life, epoxy
thickness was found to have little effect on the joint fatigue life.
Mitchell, et al. [2004], conducted thermal cycling tests for the BLR (board level
reliability) analysis of multiple stacked die chip scale package configurations, three
different CSP test vehicles, 8x11mm, 13x13mm and 15x15mm, with twelve different
package configurations of the 1-to-5 die stacks were evaluated. No consistent trend of
BLR performance relative to die stack configuration was found.
2.2 Statistical Analysis
Researchers have used different statistical methods for the analysis of the
experimental test failure data, the most common being regression analysis and Weibull
distribution. Clech, et al. [1994] presented statistical analysis of thermo-mechanical wear
13
out failure data from 26 accelerated tests and tested the goodness-of-fit using two and
three parameter Weibull and log-normal distributions. It was concluded that the three
parameter Weibull treatment provides more accurate reliability projections and failure-
free time prediction, potentially qualifying component assemblies that would be rated
marginal or unacceptable based on conservative two parameter Weibull or log-normal
analysis.
Muncy, et al. [2003, 2004] conducted thermal reliability test including air-to-air
thermal cycling (AATC) and liquid-to-liquid thermal shock (LLTS) on various
configurations of flip-chip on board (FCOB) packages. The failure data was then
analyzed using multiple linear regression and ANOVA (analysis of variance) to
determine the parameters that had influence on the reliability performance of the
components in accelerated life testing, the input parameters investigated included,
substrate metallization, substrate mask opening area versus the UBM area of the flip chip
bump, die size, perimeter or area array flip chip interconnect pattern, underfill material,
location of the die on the test board, frequency of cycling, number of I/O, and percent
area voiding. A model based on regression analysis was developed in order to quantify
the effect of process and design decisions on the reliability of a flip chip on board
assembly. ANOVA and linear regression was performed by Perkins, et al. [2004] to
develop a polynomial equation between the fatigue life and the design parameters. A full
factorial design of FEA simulations performed for five design parameters and fatigue life
calculated from the simulations using Coffin-Manson equation was utilized for the
analysis.
14
2.3 Failure Mechanics Based Analytical Modeling
Some researchers have used theory of mechanics to model the electronic packages
in order to analyze the thermo-mechanical reliability of the packages. This approach
provides a very quick and easy to use solution for the thermo-mechanical reliability
problems in electronic packages. Hall [1984], used the bi-metal thermostat analysis
[Timoshenko, 1925] to calculate forces, moments, displacements of a LCCCs (leadless
ceramic chip carrier) soldered to PWB (printed wire boards). The physical measurements
of the strains using the strain gages was also done in order to verify the calculations from
the theory. Hall, proposed a formulation of an axial symmetry model and reported that
the expansion mismatch between the LCCC and the PWB was absorbed mostly by the
solder shear at high temperature, and mostly by ?bi-metallic? bending at low
temperatures. The behavior was interpreted in terms of the mechanical properties of
solder.
Bi-metal thermostat theory [Timoshenko, 1925] has been extended to the tri-
material assembly [Suhir, 1986, 1990] for calculating thermally induced stresses in
adhesively bonded and soldered assemblies in microelectronics. The formulation
presented in form of formulas is simple, visible and easy-to-use and can be used for
calculation of the magnitude and distribution of the normal stresses acting in the
assembly components, without any computerization.
The diagonal lead stiffness and the compliance of the corner-most leads along
with component half-diagonal dimension in the package diagonal direction [Kotlowitz,
1988] controls majority of the cyclic load transmitted to the corner-most interconnection.
Kotlowitz formulated structural models for calculating the diagonal transmitted force for
15
SM (surface mount) leaded components, which is a key parameter for predicting long
term SM solder attachment reliability [Kotlowitz and Engelmaier, 1986, Clech, et al.
1988, 1989].
Thermo-mechanical models [Vendevelde, et al. 1998] formulated for the leadless
solder interconnections in flip chip assemblies can be used for evaluating the solder joint
forces and stresses in both the perimeter array and area array flip chip packages. These
models are based on the equilibrium of forces and moments, compatibility of
displacements and compatibility of rotation conditions. High accuracy (error low than
5%) in the calculation of forces and moments was shown in the comparison of peripheral
array models and FEM simulations, however the transformation of the joint loads into
stresses resulted in inaccuracy (errors about 20%). Barker, et al. [2002] used the thermo-
mechanical models formulated by Vendevelde to analyze the shear force behavior in
CSP, CBGA (ceramic ball grid array), PBGA (plastic ball grid array) and connector.
Clech, et al. [1993] found that predictive tools such as the AT&T?s Figure of
Merit [Clech, et al. 1989] were too erroneous when applied to the various surface mount
assemblies, this lead to the development of a comprehensive surface mount reliability
(CSMR) model, which was based on the correlation of 28 accelerated tests in the SM
reliability database and was validated by nine accelerated test datasets. The combined
effect of local and global thermal mismatches is used in the energy based fatigue law for
the reliability prediction. The CSMR model was further extended to another Design-for-
Reliability Tool, SRS (Solder Reliability Solution) model [Clech, 1996] which was used
for the reliability predictions of LCCCs as well as area array assemblies. The validation
of SRS model has been done for variety of BGA, flip chip and CSP assemblies [Clech,
16
2000]. The SRS model has also been used for conducting parametric studies for
combinations of materials, geometry and use conditions [Clech, 1997] in case of CSP and
flip chip assemblies. The solder volume effects [Clech, 1998] on the reliability of flip
chip and CSP assemblies has been analyzed by introducing the solder volume correction
factor in the existing SRS model and the model has been validated for flip chip
assemblies, micro-BGAs and CSPs with alumina interposer.
2.4 Finite Element Based Numerical Techniques
FEA (Finite Element Analysis) has been a widely used methodology for solder
joint reliability [Darveaux 1996, Syed 2001, Zahn 2002, 2003] analysis and life
prediction of various electronic packages. Darvaeux [2000] analyzed the effect of
simulation methodology on solder joint crack growth correlation and fatigue life
prediction, ANSYS 5.6 was used for the simulation and solder joint material was
modeled with Anand?s viscoplastic constitutive model [Anand 1985, Brown, et al. 1989],
which is a standard option in ANSYS. Johnson [1999] extended Darveaux?s approach
and implemented it for the finite element simulation of BGA solder joint reliability,
Gustafsson et al., [2000] also used finite element modeling for the life prediction of BGA
packages.
Lindley, et al. [1995] and Lall, et al. [2003] conducted solder joint reliability study
on BGA and CSPs for the automotive underhood application. Yeh, et al. [1996], Popelar
[1998] and Lu, et al. [2000] did parametric analysis of flip chip reliability based on solder
joint fatigue modeling, via computer simulation. Time independent plastic behavior
[Wiese, et al. 2002] of SnPb and SnAgCu solder alloy has been modeled and it?s effect
17
on the FEM (Finite Element Method) simulations of electronic packages. The solder
joint reliability prediction of electronic packages is sensitive to the damage volume
[Vendevelde, 2003] which is used for volume averaging of plastic work in the solder
joint, analysis for 7x7 area array CSP mounted on FR4 board using a quarter symmetry
model was done in order to optimize the damage volume. Hossain, et al. [2004]
presented strain based approach using FEM, for predicting the solder joint fatigue life
with and without IMC (inter-metallic compound) layer in case of a CSP, it was found that
the IMC growth significantly affect the stress distribution and inelastic strain
accumulation in the solder joint.
A novel hybrid approach [Towashiraporn, et al. 2003 Shen, et al. 2001, and Uegai,
et al. 2002] based on damage and fracture mechanics was proposed to predict crack
trajectory and fatigue life of solder joint subjected to temperature and power cycling of
144 I/O, Sn-Pb CSP and BGA packages. Warner et al. [2004] have integrated FE stress
module within CFD to predict solder joint life in case of SMT resistor, using finite
element (ANSYS, FLO/STRESS) and finite volume (PHYSICA) codes. Lau, et al.
[2004] developed thermal fatigue life prediction equation for lead-free (Sn4.0Ag0.5Cu)
bumped WLCSP (wafer level CSP) on lead-free FR-4 PCB with ENIG (electroless
nickel-immersion gold). FEM simulation based solder joint fatigue life model
methodology for both 63Sn37Pb and 95.5Sn4Ag0.5Cu solder alloy has been presented by
[Zahn, 2002, 2003, Kim et al. 2003, Schubert et al. 2002]. The effect of underfill on
solder strains and susceptibility to delamination in SBGA (Super BGA) was studied
[Pyland, et al. 2002] and it was reported that underfill does not always enhance SBGA
18
reliability, the properties of the underfill have a significant role in the over all reliability
of the SBGA packages.
Pucha, et al. [2001] and Tunga, et al. [2003, 2004] proposed a damage metric
based mapping approach for developing accelerated thermal cycling guidelines for
electronic packages with both lead and lead-free solder, the percentage contribution of
plastic and creep deformation to total inelastic deformation in the solder joint is
considered for mapping the damage accumulation in order to develop accurate ATC
(accelerated thermal cycle) for a given field condition.
2.5 Constitutive Behavior of Solder Material
Since the strength of materials models and the FEA models both require input of
constitutive relation parameters and the material models for the various materials within
the assembly, therefore the material characterization becomes an important aspect of life
prediction process. Constitutive relations are developed by fitting the stress-strain data
into various material models. Darveaux, et al. [1992] presented extensive stress-strain
data on 62Sn36Pb2Ag, 60Sn40Pb, 96.5Sn3.5Ag, 97Pb3Sn and 95Pb5Sn solder joints,
both shear and tensile loading were employed over a wide range of temperature and strain
rate. Amagai, et al. [2002] conducted material characterization tests of Sn-Pb based and
Sn-Ag based lead-free solders (63Sn37Pb, 62Sn36Pb2Ag, Sn3.5Ag0.75Cu,
Sn2.0Ag0.5Cu), and fitted the data to the Anand?s constitutive model that unifies both
rate-dependent creep and rate independent plasticity via viscoplastic flow equation and
evolution equation.
19
Nose, et al. [2003] analyzed the effects of temperature and starin rate on the
tensile strength and inelastic constitutive relationship of Sn-Pb solders, the compositions
used include 5Sn95Pb, 10Sn90Pb, 40Sn60Pb, 60Sn40Pb and 63Sn37Pb. Wiese, et al.
[2001] investigated and reported the constitutive behavior of two lead-free solder
(Sn96.5Ag3.5, Sn95.5Ag3.8Cu0.7) and two lead containing solder alloys (Sn63Pb37,
Sn59Pb40Ag1), the experiments were conducted on both bulk specimens and flip-chip
joints.
Micro-structural and mechanical characterization of 95.5Sn4Ag0.5Cu solder balls
by nano-indentation was carried out by Erinc, et al. [2004]. Xiao, et al. [2004] analyzed
and reported the aging and creep behavior of Sn3.9Ag0.6Cu solder alloy. Pang, et al.
[2004] fitted the stress strain curves for lead free (95.5Sn3.8Ag0.7Cu) solder alloy into
modified Ramberg-Osgood model and compared the results with the Anand?s model.
Liu, et al. [2002] measured and reported the micro-scale mechanical properties of fine
feature flip-chip with lead free solders. Fan, et al. [2003] conducted mechanical
characterization of board level solder (63Sn37Pb, Sn3.5Ag, Sn4Ag0.5Cu) sphere
attachment on Cu with ENIG surface finish substrate. Three different modeling
approaches were used [Feustel, et al. 2000] for time dependent material modeling of
solder in finite element analysis (ANSYS) of flip chips: viscoplasticity (Anand?s model).
power law creep with two terms + plasticity and sinh law creep + plasticity.
2.6 Solder Joint Fatigue Failure Models and Damage Relationships
The models developed from the statistical analysis don?t use any failure
mechanics theory and predict life, without using any fatigue or damage relationship, but
20
since the statistical models are based on the experimental failure data so the failure
mechanics is inherently in-built in these life prediction models. In case of failure
mechanics based or FEA based models the model out put is either in form of a strain or
strain energy, which is subsequently used in the damage relationship in order to predict
the solder joint fatigue life. Coffin-Manson type life prediction model [Coffin 1954,
Manson, et al. 1964] based on the creep strain [Syed 1990, 1997], plastic strain
[Engelmaier 1983, Solomon 1986] or total inelastic strain [Pang, et al. 1997] accumulated
in one thermal cycle has been traditionally used by several researchers. Guven, et al.
[2003] used method based on strain energy density criterion in conjunction with the
three-dimensional thermo-mechanical finite element analysis for accurate prediction of
crack growth in electronic packages.
Lall, et al. [2003] modified Darveaux?s model for the life prediction of CSPs and
PBGA, this model is energy based and the total life in this model is divided into cycles
for initiation and cycles for propagation. Recently, many researchers [Dauksher 2003,
Lau 2003, Syed 2004] have analyzed components with lead-free solder and developed
thermal fatigue life models for lead-free solder joint reliability prediction. Syed [2004]
proposed creep strain and strain energy density based thermal fatigue life prediction
models for lead-free (SnAgCu) solder joints.
Shi, et al. [1999, 2000] analyzed the effect of temperature and frequency on the
low cycle fatigue (LCF) life of eutectic solder alloy and proposed a temperature and
frequency-dependent fatigue life prediction model using the total strain range [2000] and
energy density [1999] in the frequency-modified LCF relationship. Massiot [2004] and
21
Lee [2000] reviewed various creep fatigue failure models in solder material and proposed
their applicability for the PBGA and chip scale packages.
2.7 Objective and Scope of the Thesis
The chief motivation behind this work has been to understand and quantify the
sensitivity of component reliability to various parameters such as package architecture,
geometry, material properties and board attributes. In this research task, an effort has
been made to develop a tool that can serve government contractors, OEMs and 3
rd
party
contract manufacturers for doing trade-offs between geometry and material in order to
make educated selection of appropriate components for specified mission requirements.
In this thesis, library of closed form models based on the theory of failure
mechanics and statistical analysis of experimental test failure data has been developed
and presented. Finite element analysis (FEA) for the thermo-mechanical reliability
analysis of a flip-chip has also been performed. The sensitivity of the flip-chip reliability
on the various design and material parameters has been analyzed through the FEA
simulations and the results have been presented.
2.8 Thesis Layout
The closed form model, based on the theory of failure mechanics and material
constitutive relations, developed for the BGA packages, has been presented in Chapter 3.
Chapter 4 includes the library of statistics based closed form models and the regression
analysis methodology used for developing the life prediction models for the BGA
packages on flex substrate. The models developed in Chapter 3 and 4 have been
22
validated with the experimental test data and the design guidelines for the BGA packages
has been included in the Chapter 5.
The statistics based and the failure mechanics based closed form models
developed for the flip-chip package in the present work have been presented in the
Chapter 6, which also includes a section on the validation of the models developed with
the experimental test data. Chapter 7 provides the details of the FEM analysis done on a
flipchip package. Finally the conclusions based on the present study and the
recommended future work is presented in Chapter 8.
23
CHAPTER 3
FAILURE MECHANICS BASED MODELS FOR BGA PACKAGES
Failure mechanics based models have also been referred as mathematical or
analytical models in several published literatures. These models are based on the strength
of materials analysis for a given package configuration with known geometry and
material properties.
3.1 Overview
The package life is considered to be a function of the damage due to the inelastic
strain energy that solder joint interconnect accumulates while the device undergoes
thermal cycling. The accumulation of the inelastic strain energy initiates a crack in the
solder joint and this crack propagates with the accumulation of the inelastic strain energy
as the component keeps on undergoing thermal cycling. The component finally fails
when either the solder joint cracks completely or when the crack is sufficient enough to
prevent the flow of required current through the solder joint interconnection. The
inelastic strain energy accumulated per unit volume per cycle, also referred as inelastic
strain energy density (ISED) is given by the area enclosed within the hysteresis loop of
the solder joint. The inelastic strain energy density calculation for any given package
depends on various factors like the geometry and architecture of the package, material
24
properties, assembly stiffness, local and global thermal mismatch, hysteresis loop
approximation methodology, creep and other material constitutive relations
3.2 Modeling Methodology
The flowchart shown in the Figure 3.1 describes main steps involved in the
formulation and application of failure mechanics based models. In the first step the
maximum shear strain in the solder joint is determined which is required as a initial
guesstimate for initializing the hysteresis loop iteration. The second step involves
hysteresis loop determination for both local and global thermal mismatch using various
material constitutive relations.
Once the hysteresis loops are determined for both the cases then in the next step
inelastic strain energy is calculated from the area enclosed within the loops. Finally the
sum of the inelastic strain energy density due to both local and global thermal mismatch
is used in the damage relationship for calculating the characteristic life of the package.
3.2.1 Maximum Shear Strain Calculation
The maximum shear strain in the solder joint can be calculated by the simplified
DNP formula, but the DNP formula is based on several assumptions due to which it gives
the upper bound of the maximum shear strain value. Since maximum shear strain value
is used as the primary input for initiating the hysteresis loop iteration in order to
determine the hysteresis loop for both local and global mismatch so the accuracy of the
hysteresis loop is significantly impacted by the initial input of the maximum shear strain
value. In the case of area array package the shear forces generated due to the thermal
25
Maximum Shear Strain
Calculation from Shear Force
Distribution Relations
Hysteresis Loop Determination
from Stress-Strain and Material
Constitutive Relations
Inelastic Strain Energy
Density Calculation for Local
and Global Thermal Mismatch
Life Prediction Using the
Damage Relationship
Figure 3.1 Schematic of the failure mechanics based modeling methodology
26
mismatch during thermal cycling of the component is shared by all the solder joints so
the DNP formula which does not considers the shear force distribution among the solder
joints gives a highly unrealistic value. Vandevelde, et al. [1998] proposed an analytical
thermo-mechanical model to calculate thermally induced shear force in the solder balls of
an area array package. In the present work, Vandevelde?s [1998] approach has been used
to determine ?
max
instead of the DNP formula. Since the shear force distribution among
all the solder balls for different area array configurations is taken into account in this
methodology so it gives a better estimate of the ?
max
than the DNP formula. The shear
force experienced by the solder balls in an area array with 2n x 2n balls can be calculated
by solving set of n linear equations from (3.1) for i = 1 to n [Vandevelde, et al. 1998]
??+??=????
??
==
)i(F])P()q(F)[()i)(P)(T)((
i
1k
n
kq
cb
(3.1)
where
F(i) is shear force due to thermal mismatch in the i
th
solder joint from the center
[Vandevelde, et al. 1998]
bbccbbcc
2
b
s
c
IE
1
IE
1
IEIE
2
h
h
2
h
? ++
+
?
?
?
?
?
?
++
= (3.1.1)
ss
3
s
ss
s
cb
b
cc
c
I12E
h
GA
h
bPG6
h
bPG6
h
? ++
???
+
???
= (3.1.2)
The shear strain is then calculated for the ball with maximum value of shear force F(i)
using Equation (3.2) [Vandevelde, et al. 1998]
ss
maxs
max
AE
(i)F)?(12
?
?
?+?
= (3.2)
27
Shear force distribution and maximum shear strain calculation procedure has been
implemented in MATLAB
TM
.
3.2.2 Hysteresis Loop Determination
The thermal cycle for hysteresis loop determination is divided into 4 sections:
1. Ramp up from low temperature to high temperature
2. Dwell at high temperature
3. Ramp down from high temperature to low temperature
4. Dwell at low temperature
The solder joint response during the temperature ramps is approximated by time
independent plastic deformation relation (3.3) [Knecht and Fox, 1991].
2
P
B
AB
?
?
??
?
?
?
?
?
?
?
?
=? (3.3)
where
subscript A denotes the condition before ramp, B denotes condition after ramp and
?
p
is plasticity parameter obtained from linear curve fitting of data in [Knecht, et
al. 1991]:
C)T(300.2350588.5(psi)?
P
???= (3.3.1)
The constitutive relation (3.4.1) given by Hall [1991] has been used for stress
relaxation during the dwell period. The creep relation (3.4.2) given by Wong [1988] has
been used for time and temperature dependent creep during the dwell period.
max
?
?
?
? =+ (3.41)
28
m
creep
A(T)?? =
?
(3.42)
where
s
s
A
hK
?
?
=
(3.41.)
K is the effective assembly stiffness calculated from the formulation given by Hall
[1984] for both global and local thermal mismatch
creep
?
?
is strain rate or the time derivative of creep strain
A(T) is temperature dependent factor derived from the data by Wong [1988] and
is given by:
T(K)
5412
3
13
e
(T)E
1
107.298A(T)
?
?= (3.4.2.1)
E(T) is the temperature dependent Young?s modulus of the eutectic tin-lead
solder.
The first iteration is started with initial value of shear strain, ?
A
= ?
max
/2 and zero
shear stress. The iteration is continued each time starting with the shear strain equal to
the mean of residual strain, ?
F
, and ?
A
, of the previous iteration. The loop is stabilized
and closed when the point residual strain overlaps the initial strain, which means that the
value of ?
F
lies in the vicinity of ?
A
. The loop closure is defined by the parameter %e,
given by Equation (3.5), and the loop is considered to be closed and stabilized when %e
is equal to or less than 1%.
100
??
??
%e
AD
FA
?
?
?
= (3.5)
29
The calculations based on the equations discussed above have been incorporated
in a program in MATLAB
TM
.
3.2.3 Inelastic Strain Energy Density Calculation
The hysteresis loop is determined for both the global and local thermal mismatch
separately using the procedure discussed in section 3.2.2. Once the stabilized loops are
determined than the area enclosed within the loops which represents the amount of
inelastic strain energy density accumulated by the solder joint during one complete
thermal cycle is determined using the trapezoidal rule. According to the trapezoidal rule
the area under any curve given by a function f(x), as shown in the Figure 3.2, can be
approximated as the summation of the ?n? trapezoids used to divide the area, [Suli, et al.
2003]
?
?
=
++?+?
n
1i
b
a
ih))f(a1)h)(i(f(a
2
h
dxf(x) (3.6)
The total inelastic strain energy per unit volume per cycle (?W) is given by the
sum of the inelastic strain energy density per cycle due to global thermal mismatch
(?W
G
) and due to local thermal mismatch (?W
L
) [Clech, 1996].
?W = ?W
G
+ ?W
L
(3.7)
3.2.4 Life Prediction from Damage Relationship
The damage relationship relates the characteristic life of the component in terms
of number of thermal cycles with the total inelastic strain energy density per cycle. This
damage relationship is valid only if the failure mode of the package is solder joint
30
Figure 3.2 Calculation of area under the curve using trapezoidal method
31
cracking due to thermal cycling fatigue. The damage relationship is established from the
experimental ATC failure data. This relationship depends on the solder composition and
the package architecture. So, one has to be very careful while using the damage
relationship while predicting failure cycles for any particular component. In the current
work the damage relationships proposed by Lall, et al. [2004] and Darveaux [2000] have
been used to calculate the characteristic life (?
joint
) for life prediction of the component.
The characteristic life of the component is given by Equation (3.8).
da/dN
a
N?
0joint
+=
(3.8)
where
?a? is the joint diameter at the interface
2
10
K
W)(KN ?=
is the number of cycles for crack initiation
4
3
K
W)(K
dN
da
?= is the crack propagation rate
The value of the constants K
1
, K
2
, K
3
and K
4
used for calculation of characteristic life
cycles are given in Table 3.1.
In order to verify the model prediction one percent failure cycles predicted from
the failure mechanics based closed form model for 23mm PBGA package under two
different thermal cycling conditions has been plotted in Figure 3.3 against the
experimental values. The two thermal cycling conditions used for the model validation
are:
1. -50?C to 150?C with 15mins ramp and 30mins dwell
2. -40?C to 125?C with 15mins ramp and 30mins dwell
32
The model over predicts life for the -50?C to 150?C thermal cycle and under
predicts for the -25?C to 125?C thermal cycle. But the trend and the 1% failure life of the
package predicted by the model is consistent and lies in close proximity of the
experimental values, thus validating the model predictions.
33
Table 3.1 Constants for the damage relationship
K
1
(cycles/psi
K
2
)
K
2
K
3
(in/cycle/psi
K
4
)
K
4
Lall et al. [2004] 28769 -1.53 6x10
-7
0.7684
Darveaux [2000] 48300 -1.64 3.8x10
-7
1.04
0
500
1000
1500
2000
2500
3000
3500
4000
200 165
Delta T?C
1%
f
a
i
l
u
r
e
cy
cl
e
s
Experiment
Model
Figure 3.3 Effect of temperature condition on thermal reliability of 23mm PBGA
package
34
CHAPTER 4
STATISTICS BASED CLOSED FORM MODELS FOR BGA PACKAGES
Multi-variable regression and analysis of variance are very powerful and useful
statistical techniques for an engineer to analyze and quantify the effect of multiple
independent variables on a dependent variable. This technique has been used to establish
a mathematical relationship to correlate the independent variable like characteristic life or
cycles to 1% failure for an electronic package with the various dependent variables which
affect the life of the package. The results have been analyzed and correlated with
underlying failure mechanics in order to develop meaningful closed form statistical
models for application to area array package reliability. The results have been correlated
with the actual experimental failure data in order to gain confidence for application of
these models.
4.1 Overview
This section presents a methodology based on statistics of multi-variable
regression for assessing and predicting the reliability of area array packages under harsh
environments. One of the biggest advantage of this methodology is that it allows one to
incorporate the effect of several non-conventional predictor or dependent variables such
as board finish, pad configuration (SMD, NSMD) etc on the thermal reliability of the
package..
35
4.2 The Perturbation Approach
A unique perturbation approach based on the statistical models developed from
multivariate regression techniques has been developed and presented in the current work.
The flowchart in Figure 4.1 demonstrates a broad layout of the various steps involved in
the development and application of this perturbation approach.
The first step in the development of this approach has been the accumulation of
the actual experimental failure database of various configurations of area array packages
under accelerated thermal cycling tests. The harsh environment accelerated test database
on various configurations of packages generated in-house by the researchers at the Center
of Advanced Vehicle Electronics (CAVE) and the test data published by other
researchers in various literatures has been accumulated. The accumulated data is then
arranged in the excel spreadsheet in the form of several datasets. Number of cycles for
1% failure of the component has been used as the reliability criterion, as it is a standard
thumb rule commonly followed in the automobile and aerospace industry for assessment
and comparison of thermal reliability of the electronic components. Several conventional
and non-conventional predictor variables which are known to have impact on the
component reliability have been also included in the datasets. These parameters include
Body Size, Die Size, Die to Package Ratio, Solder Ball Size (ball diameter and height),
Solder Volume, Ball Pitch, Ball Count, Array Configuration (partial or full array), Under-
fill EMC Filler Content, Conformal Coat, Pad Size, Pad Configuration (SMD/NSMD),
Solder Mask Diameter, Solder Mask Thickness, PCB Thickness, Board Finish (HASL,
36
Harsh Environment
Reliability Database
Statistical Analysis and
Multivariate
Regression Models
Interaction Effects & Trade-offs
(Package design parameters,
thermal conditions subjected,
package reliability)
OUTPUT DESIGN PARAMETERS:
Package size, Die size, Solder Ball Composition, Ball
Pitch, Ball Count, Pad Size and Configuration, Board
Thickness and Finish, Substrate Thickness and
Material etc.
Figure 4.1 Schematic of the perturbation approach for thermal reliability assessment
37
OSP, Au), PCB material, Substrate material and Temperature Cycle Conditions such as
ramp rate, dwell time and temperature extremities.
In the next step statistical analysis of the complete datasets has been carried out
using MINITAB
TM
(statistical analysis software). Multi-variable regression and analysis
of variance techniques were employed to analyze and quantify the relative influence of
the predictor variables on the thermal reliability of the package. The output of the multi-
variable regression and analysis of variance is used to develop a mathematical equation
which correlates the sensitivities of the predictor variables with the 1% failure cycles
(N
1%f
) for a given package. The significance of the sensitivities of the predictor variables
has also been analyzed in order to retain only the significant variables in the final
equation. The multi-collinearity among the predictor variables in the reliability data has
been analyzed using the Pearson correlation coefficient matrix of the predictor variables.
The residuals have also been analyzed and verified for heteroscedasticity in the data, the
residual vs fit plot has been used for the heteroscedasticity. The normal distribution of
the residuals, which is one of the basic assumptions for the regression analysis, has also
been ensured.
Once the mathematical equation correlating the 1% failure cycles with the various
dependent parameters of the package is established and validated with the actual failure
data with significant level of confidence than it can be used for perturbing a select few or
all parameters against existing datasets for evaluation of various design options. This
allows one to analyze the interaction effects among the various package design
parameters. One can also use these models to do trade-offs with confidence within the
frame of given datasets in order to achieve a specified level of thermo-mechanical
38
reliability for any package under a given harsh environment condition. Thus this
methodology helps the user in making a final decision on the various package design
parameters such as package size, die size, solder ball composition, ball pitch, ball count,
pad size and configuration, board thickness and finish, substrate thickness and material
etc.
4.3 Model Library
Several statistical models have been developed to predict the thermal reliability of
BGAs (Flex-BGA and PBGA). The model library includes linear and non-linear models.
The number of cycles to 1% failure for different configurations of area array packages
has been used to predict and compare the thermo-mechanical reliability of the various
configurations of the packages subjected to harsh environment conditions.
4.4 Linear Models
Multi-variable regression analysis has been done on the collected experimental
failure database to generate a linear relationship between the cycles to 1% failure and the
predictor variables. In this case it has been assumed that life of the package is linearly
related to the various design parameters. The mathematical relation developed for linear
statistical model is represented in the form of Equation (4.1)
(VarN)a(Var2)a(Var1)aaN
n2101%f
KK++= (4.1)
where,
?N
1%f
?
is the cycles to one percent failure or the life of any given package, also
called dependent or the response variable
39
?Var1?, ?Var2?? ?VarN? are the design parameters which influence the package
life, these are also called independent or predictor variables
?a
0
? is a constant and ?a
1
?, ?a
2
?,?. ?a
n
? are the coefficients of the design parameters
and are called generalized degree of freedom in the problem definition
4.4.1 Linear Model-1
This is the basic form of a linear statistical model in which maximum number of
predictor variables (parameters) had been included in the model to analyze the effect of
each variable on the reliability of the package. The statistical model in form of a
mathematical equation is given by Equation (4.2)
?
?
?
?
?
?
?
?
+
+++
+++
+++
+++=
t
T
a
(??TashID)(BoardFiniaID)(Substratea
)(MaskDefIDa)(EMCFillIDaMM)(PCBPadDiaa
(PCBthkMM)a(PitchMM)a)(BallDiaMMa
)(BallCountaRatio)(DietoBodya(BodyMM)aaN
13
121110
987
654
32101%f
(4.2)
The parameters in the Equation (4.2) ending with MM indicate that the parameter
has dimension of length and is measured in millimeters. The parameters ending with ID
are dimensionless parameters. The various predictors used in this model were BodyMM
(package body size), DietoBodyRatio (ratio of die size to body size), BallCount (number
of I/Os), BallDiaMM (solder ball diameter), PitchMM (solder ball pitch), PCBthkMM
(PCB thickness), PCBPadDiaMM (PCB pad diameter), EMCFillID (EMC filler content),
MaskDefID (pad configuration), SubstrateID (substrate type), BoardFinishID, ?T
40
(thermal cycling temperature range in ?C) and
t
T
?
?
(ramp rate in ?C/min). The
dimensionless variables such as EMCFillID, MaskDefID, SubstrateID and
BoardFinishID were used as dummy variables and each dummy variable was assigned a
numerical value.
MaskDefID toggles the mask definition between SMD and NSMD. A value of 0
corresponds to SMD and value of 1 corresponds to NSMD. EMCFillID toggles the
encapsulant mold compound filler content between low and high. A value of 0
corresponds to low filler content and value of 1 corresponds to high filler content.
SubstrateID toggles the substrate material between polyimide, 2 layer tape laminate and 3
layer tape laminate. A value 0 corresponds to polyimide, value of 1 corresponds to 2
layer tape and value 2 corresponds to 3 layer tape laminate. BoardFinishID toggles the
board finish between Ni-Au, HASL and OSP. A value of 0 corresponds to Ni-Au, value
of 1 corresponds to HASL and the value of 2 corresponds to OSP finish. The coefficient
of each of the variable or the design parameter in the Equation (4.2) of this model defines
the sensitivity of that parameter on the thermal reliability of the package. A negative
value of the coefficient indicates a decrease in the number of cycles to 1% failure with
increase in value of the variable. The numerical values of these coefficients or the
generalized degrees of freedom for this model are listed in the ?Coefficient? column of
the Table 4.1.
41
Table 4.1 Model Parameters and Analysis of Variance for Multi-variable Regression
Linear Model-1
Predictor Coefficient SE Coeff t-stat p-value
Constant 3459.0 1663 2.08 0.045
BodyMM 520.2 110.2 4.72 0.000
DietoBodyRatio -3657.1 466.9 -7.83 0.000
BallCount -12.3 4.591 -2.69 0.011
BallDiaMM 7181.0 4853 1.48 0.148
PitchMM -8629.0 3338 -2.59 0.014
PCBthkMM -461.6 192.6 -2.40 0.022
PCBPadDiaMM 3086.0 4795 0.64 0.524
EMCFillID 263.9 189.5 1.39 0.173
MaskDefID 792.9 577.6 1.37 0.179
SubstrateID 14.6 116.1 0.13 0.900
BoardFinishID -230.2 188.1 -1.22 0.230
?T -14.3 5.049 -2.84 0.008
RampRate -4.1 10.51 -0.39 0.700
Analysis of Variance
Source DF SS MS f p-value
Regression 13 72832259 5602481 36.33 0.000
Residual Error 34 5243035 154207
Total 47 78075293
S = 392.7 R-Sq = 93.3% R-Sq(adj) = 90.7%
42
4.4.1.1 Model Diagnostics
The model parameters for the Linear Model-1 are listed in the Table 4.1. Analysis
of the model parameters shows that the model has good R-Sq and R-Sq(adj) value which
indicates that more than 90% of variation in the reliability data is explained by the
regression model. High p-values of the predictor variables including, BallDiaMM =
14.8%, PCBPadDiaMM = 52.4%, EMCFillID = 17.3%, MasfDefID = 17.9%,
SubstrateID = 90.0%, BoardFinishID = 23.0% and RampRate = 70.0% indicate that these
variables are statistically insignificant. But from the failure mechanics theory it is known
that these variables have significant effect on the package reliability. Since this statistical
insignificance may be attributed to the multi-collinearity among the predictor variables in
the reliability data, so the correlation coefficient matrix of the predictor variables as
shown in the Table 4-2 was calculated to check the correlation coefficients for any multi-
collinearity. It was found that BallDiaMM is highly correlated to PitchMM and has a
correlation coefficient of 0.945 where as PCBPadDiaMM is highly correlated to
PitchMM (0.78) and MaskDefID (-0.75).
Since the linear regression is based on the assumption of normal random
distribution of the residuals, so it is extremely important to look at the distribution of the
residuals in order to make sure that the basic assumption is not violated. It is also
important to check if there is any heteroscedasticity in the data which means that the
standard deviation in the distribution of the dependent variable varies with the value of
the independent variable. The residual plots as shown in the Figure 4.2 are of great help
in order to check whether the model complies with all these assumptions. The normal
plot of the residuals shows the residuals plotted against the normal score, in case the
43
Table 4.2 Pearson correlation coefficient matrix for the predictor variables of the Linear
Model-1
BodyMM DietoBod BallCoun BallDiaM PitchMM PCBthkMM PCBPadDi EMCFill
DietoBod -0.352
BallCoun 0.924 -0.229
BallDiaM 0.568 -0.307 0.381
PitchMM 0.708 -0.368 0.496 0.945
PCBthkMM 0.221 -0.173 0.101 0.285 0.296
PCBPadDi 0.580 -0.419 0.303 0.640 0.783 0.391
EMCFill -0.018 -0.049 -0.164 0.098 0.097 0.365 0.171
MasfDefI -0.342 0.333 -0.201 -0.218 -0.346 -0.280 -0.748 -0.107
Substrat 0.063 -0.001 0.233 -0.107 -0.103 0.175 -0.148 -0.184
BoardFin -0.063 -0.058 -0.108 0.045 0.036 0.009 0.002 0.100
DeltaT -0.518 0.441 -0.364 -0.205 -0.314 -0.179 -0.394 -0.125
RampRate -0.199 0.227 -0.176 -0.040 -0.079 0.091 -0.006 0.017
MasfDefI Substrat BoardFin DeltaT
Substrat -0.030
BoardFin 0.063 -0.420
DeltaT 0.234 -0.104 0.073
RampRate 0.109 -0.080 -0.010 0.358
44
8006004002000-200-400-600
10
5
0
Residual
F
r
equenc
y
Histogram of Residuals
50403020100
1000
0
-1000
Observ ation Number
R
e
s
i
dual
I Chart of Residuals
6
3
6
5
6
6
1
Mean=1.82E-13
UCL=809.6
LCL=-809.6
70006000500040003000200010000
1000
500
0
-500
Fit
R
e
s
i
dual
Re si d u a l s vs. Fi ts
210-1-2
1000
500
0
-500
Normal Plot of Residuals
Normal Score
R
e
s
i
dual
Residual Plot
Figure 4.2 Residual plots for the Linear Model-1
45
residual distribution is perfectly normal than the locus of the points on the normal plot
would be a straight line at an angle of 45?. The histogram of the residuals should be
symmetrical bell shaped if the residual distribution is normal. The I-chart of residuals is
used to verify that the residuals for all the predicted values of the model are within the
control limits of 3 sigma. The residual-vs-fit plot is used to check if the failure data holds
the assumption of homoscedasticity (constant variance). In case there is any
heteroscedasticity than the residuals either fan out or follow some pattern as we go from
the lower fits to the higher fitted values. Analyzing the residual plots of the Linear
Moidel-1 it can be concluded that the distribution of the residuals is very close to normal
distribution and there is no heteroscedasticity in the data, also all the residuals are within
the control limits of 3 sigma (?809.6).
4.4.2 Linear Model-2
Multi-collinearity was observed in the Linear Model-1, the predictors BallDiaMM
and PCBPadDiaMM were highly collinear with the predictor variable PitchMM. Linear
regression was done in the Linear Model-2 using the same failure data as in the previous
model but in order to remove the multi-collinearity, the variables BallDiaMM and
PCBPadDiaMM were neglected from the analysis. The mathematical correlation
between the number of cycles to 1% failure and the predictor variables for this model is
given by Equation (4.3)
46
?
?
?
?
?
?
?
?
++
+++
+++
+++=
t
T
a(??Ta
shID)(BoardFiniaID)(Substratea)(MaskDefIDa
)(EMCFillIDa(PCBthkMM)a(PitchMM)a
)(BallCountaRatio)(DietoBodya(BodyMM)aaN
1110
987
654
32101%f
(4.3)
The numerical values of the generalized degrees of freedom for this model are
listed in the ?Coefficient? column of the Table 4.3.
4.4.2.1 Model Diagnostics
The model parameters for the Linear Model-2 are listed in the Table 4.3 and the
residual plots are shown in Figure 4.3. In this model we notice that the R-Sq values
remain almost the same so this model also explains more than 90% of the variation in the
reliability data. Moreover the p-values for the constant, BallCount, PitchMM,
MaskDefID, BoardFinishID and ?T have improved significantly. But the variables
SubstrateID and RampRate still remain statistically insignificant having very high p-
values of 95.2% and 87.3%. Analyzing the histograms and the normal plot of the
residuals for the Linear Model-2 it can be concluded that the distribution of the residuals
is somewhat away from the normal distribution and the I-chart shows the residual for at
least one data point to be outside the control limit of 3 sigma (?740.2). Looking at the
distribution of data points in the residual-vs-fit plot it can be concluded that there is no
heteroscedasticity in the data.. Another linear regression after eliminating the predictors
SubstrateID and RampRate was done to see the effect on the model.
47
Table 4.3 Model Parameters and Analysis of Variance for Multi-variable Regression
Linear Model-2
Predictor Coefficient SE Coeff t-stat p-value
Constant 4617.0 1111.0 4.16 0.000
BodyMM 506.2 94.55 5.35 0.000
DietoBodyRatio -3674.1 468.1 -7.85 0.000
BallCount -12.6 3.78 -3.34 0.002
PitchMM -4149.0 1008.0 -4.12 0.000
PCBthkMM -399.1 187.3 -2.13 0.040
EMCFillID 250.2 186.5 1.34 0.188
MaskDefID 573.8 278.4 2.06 0.047
SubstrateID -6.9 115.5 -0.06 0.952
BoardFinishID -256.6 187.7 -1.37 0.180
?T -15.0 5.01 -2.99 0.005
RampRate -1.5 9.32 -0.16 0.873
Analysis of Variance
Source DF SS MS f p-value
Regression 11 72493777 6590343 42.51 0.000
Residual Error 36 5581517 155042
Total 47 78075293
S = 393.8 R-Sq = 92.9% R-Sq(adj) = 90.7%
48
8006004002000-200-400-600
10
5
0
Residual
F
r
equ
en
c
y
Histogram of Residuals
50403020100
1000
0
-1000
Observation Number
R
e
s
i
du
al
I Chart of Residuals
6
6
5
5
6
5
5
6
1
Mean=-1.1E-12
UCL=740.2
LCL=-740.2
70006000500040003000200010000
1000
500
0
-500
Fit
R
e
s
i
du
al
Residuals vs. Fits
210-1-2
1000
500
0
-500
Normal Plot of Residuals
Normal Score
Re
s
i
dua
l
Residual Plot
Figure 4.3 Residual plots for the Linear Model-2
49
4.4.3 Linear Model-3
Regression analysis of the Linear Model-2 indicated that the predictor variables
SubstrateID and RampRate were highly statistically insignificant. Linear regression was
done once again with same dataset for the formulation of Linear Model-3, but the
statistically insignificant predictors were dropped out of the analysis. The mathematical
correlation between the number of cycles to 1% failure and the predictor variables for this
model is given by Equation (4.4)
(??TashID)(BoardFinia)(MaskDefIDa
)(EMCFillIDa(PCBthkMM)a(PitchMM)a
)(BallCountaRatio)(DietoBodya(BodyMM)aaN
987
654
32101%f
+++
+++
+++=
(4.4)
The numerical values of the constant and other coefficients for this model are
listed in the ?Coefficient? column of the Table 4.4.
4.4.3.1 Model Diagnostics
The model parameters for the Linear Model-3 are listed in the Table 4.4 and the
residual plots are shown in Figure 4.4. The R-Sq and R-Sq(adj) value have increased
which means that this model explains more than 91% of the variation in the data.
Looking at the residual-frequency plot, it can be observed that the residuals have better
normal distribution in this case as compared to the previous linear models. The I-chart
shows that residual for only one data point is outside the control limit of 3 sigma
(?735.6). Looking at the random distribution of data points in the residual-vs-fit plot it
can be concluded that there is no heteroscedasticity in the data. Analyzing the regression
50
Table 4.4 Model Parameters and Analysis of Variance for Multi-variable Regression
Linear Model-3
Predictor Coefficient SE Coeff t-stat p-value
Constant 4616.0 941.6 4.90 0.000
BodyMM 508.65 77.49 6.56 0.000
DietoBodyRatio -3680.7 454.0 -8.11 0.000
BallCount -12.7 3.0 -4.23 0.000
PitchMM -4163.7 952.9 -4.37 0.000
PCBthkMM -407.9 165.8 -2.46 0.019
EMCFillID 252.0 180.6 1.40 0.171
MaskDefID 573.2 267.5 2.14 0.039
BoardFinishID -250.4 165.6 -1.51 0.139
?T -15.1 4.42 -3.42 0.002
Analysis of Variance
Source
DF SS MS f p-value
Regression
9 72489404 8054378 54.79 0.000
Residual Error 38 5585890 146997
Total 47 78075293
S = 383.4 R-Sq = 92.8% R-Sq(adj) = 91.2%
51
8006004002000-200-400-600-800
10
5
0
Residual
F
r
equ
en
c
y
Histogram of Residuals
50403020100
1000
0
-1000
Observation Number
Re
s
i
du
al
I Chart of Residuals
6
6
5
5
6
5
5
6
1
Mean=-7.9E-13
UCL=735.6
LCL= -735.6
70006000500040003000200010000
1000
500
0
-500
Fit
R
e
s
i
du
al
Residuals vs. Fits
210-1-2
1000
500
0
-500
Normal Plot of Residuals
Normal Score
R
e
s
i
dual
Residual Plot
Figure 4.4 Residual plots for the Linear Model-3
52
results of the model and comparing with the previous model it is also observed that the R-
Sq(adj) value has increased which shows that this model better explains the variation in
the reliability data as compared to the previous two linear models. There is also
improvement in the p-values of the predictor variables BallCount, PCBthkMM,
EMCFillID, MaskDefID, BoardFinishID and ?T as compared to the previous models.
The p-values for EMCFillID(17.1%) and BoardFinishID(13.9%) are still greater than the
significance level of 5%, which means they are statistically insignificant, but still these
predictor variables have been retained in the model as it is known from the mechanics of
failure that they have significant effect on the package reliability. Also these p-values are
not too high as in case of the other variables that were dropped from the previous model.
4.5 Non-Linear Models
Multi-variable regression analysis on the collected experimental failure database
was also done to generate non-linear relationship between the cycles to 1% failure and
the predictor variables. In the preceding section only linear relationships were explored
in order to get the best fit model. Since it is not necessary for the sensitivities of the all
the dependent variables to be linearly related to the package life, so it becomes extremely
important to analyze the sensitivities from the non-linear standpoint. In this case multiple
variable linear regression was done using the logarithm of the dependent and independent
variables that were used in the formulation of linear models, which means that the
predictor variable for the non-linear models can be given by Log(Independent Variable)
Thus, the final mathematical relation developed for non-linear statistical model can be
represented in the form of Equation (4.5)
53
n
b
(VarN)
2
b
(Var2)
1
b
A(Var1)N
1%f
KK= (4.5)
where,
?N
1%f
?
is the cycles to one percent failure or the life of any given package, same as
in case of the linear models
Var1?, ?Var2?? ?VarN? are the design parameters which influence the package
life, these are also called independent variables
?A? is a constant and ?b
1
?, ?b
2
?,?. ?b
n
? are the indices of the design parameters
4.5.1 Non-Linear Model-1
Maximum number of predictor variables (parameters) were included in this model
to analyze the effect of each variable on the reliability of the package. The statistical
model in form of a mathematical equation is given by Equation (4.6)
13
b
t
T
12
b
(??T
11
b
shID)(BoardFini
10
b
ID)(Substrate
9
b
)(MaskDefID
8
b
)(EMCFillID
7
b
MM)(PCBPadDia
6
b
(PCBthkMM)
5
b
(PitchMM)
4
b
)(BallDiaMM
3
b
)(BallCount
2
b
Ratio)(DietoBody
1
b
A(BodyMM)N
1%f
?
?
?
?
?
?
?
?
=
(4.6)
The index of each of the predictor variable or the design parameter in the
Equation (4.6) of this model defines the sensitivity of that parameter on the thermal
reliability of the package. A negative value of the index indicates a decrease in the
number of cycles to 1% failure with increase in value of the variable. The numerical
values of the generalized degrees of freedom or the indices are listed in the ?Coefficient?
column of the Table 4.5.
54
4.5.1.1 Model Diagnostics
The model parameters for the Non-Linear Model-1 are listed in the Table 4.5.
Though the model has good R-Sq and R-Sq(adj) values but several predictor variables
have very high p-values such as BodyMM=30.6%, BallDiaMM=38.9%,
PitchMM=79.8%, PCBPadDiaMM=88.8%, EMCFillID=76.5% and RampRate=96.4%,
which is beyond the acceptable limit of 5.0%. This means that all these variables are
statistically insignificant, but from the failure mechanics it is well known that these
variables have significant impact on the package reliability. Multi-collinearity among the
predictor variables might be one of the reason for such high p-values of these variables.
In order to check the collinearity among the various variables the Pearson correlation
coefficient matrix was calculated as shown in the Table 4.6. Analyzing the coefficient
matrix it is observed that BodyMM is highly correlated to BallCount similarly PitchMM
and PCBPadDiaMM are highly correlated to BallDiaMM. The histogram and normal
plot of the residuals for this model in the Figure 4.5 show that the residuals have fairly
normal distribution. It is evident from the I-chart of the residuals that residuals
corresponding to all the observations are within the control limit of 3 sigma (?0.211).
Since the data points in the residual-vs-fit plot are randomly scattered so there is no
heteroscedasticity in the data.
55
Table 4.5 Model Parameters and Analysis of Variance for Multivariate Regression Non-
Linear Model-1
Predictor Coefficient SE t-stat p-
LogA 4.442 1.198 3.71 0.001
LogBodyMM -1.182 1.138 -1.04 0.306
LogDietoBodyRatio -1.854 0.197 -9.42 0.000
LogBallCount 0.944 0.517 1.83 0.076
LogBallDiaMM 1.220 1.399 0.87 0.389
LogPitchMM 0.436 1.689 0.26 0.798
LogPCBthkMM -0.514 0.132 -3.89 0.000
LogPCBPadDiaMM -0.112 0.785 -0.14 0.888
LogEMCFillID -0.009 0.030 -0.30 0.765
LogMaskDefID 0.205 0.048 4.28 0.000
LogSubstrateID 0.225 0.117 1.92 0.063
LogBoardFinishID -0.085 0.049 -1.75 0.089
Log?T -1.120 0.548 -2.04 0.049
LogRampRate -0.007 0.161 -0.05 0.964
Analysis of Variance
Source DF SS MS f p-value
Regression 13 3.23068 0.24851 25.24 0.000
Residual Error 34 0.33478 0.00985
Total 47 3.56545
S = 0.09923 R-Sq = 90.6% R-Sq(adj) = 87.0%
56
Table 4.6 Pearson correlation coefficient matrix for the predictor variables of the Non-
Linear Model-1
LnBodyMM LnDietoB LnBallCo LnBallDi LnPitchM LnPCBthk LnPCBPad LnSubstr
LnDietoB -0.271
LnBallCo 0.914 -0.025
LnBallDi 0.649 -0.298 0.380
LnPitchM 0.748 -0.345 0.477 0.968
LnPCBthk 0.203 -0.196 0.082 0.259 0.267
LnPCBPad 0.580 -0.428 0.293 0.692 0.790 0.382
LnSubstr 0.076 0.017 0.220 -0.100 -0.097 0.188 -0.160
LnEMCFil -0.037 -0.066 -0.170 0.090 0.087 0.359 0.172 -0.184
LnMasfDe -0.295 0.349 -0.165 -0.193 -0.290 -0.280 -0.683 -0.030
LnBoardF -0.038 -0.034 -0.070 0.053 0.049 0.004 0.022 -0.420
LnDeltaT -0.414 0.487 -0.268 -0.185 -0.269 -0.180 -0.380 -0.104
LnRampRa -0.346 0.446 -0.240 -0.132 -0.200 -0.057 -0.226 -0.112
LnEMCFil LnMasfDe LnBoardF LnDeltaT
LnMasfDe -0.107
LnBoardF 0.100 0.063
LnDeltaT -0.125 0.234 0.073
LnRampRa -0.067 0.209 0.039 0.831
57
-0.16-0.12-0.08-0.040.000.040.080.120.160.20
0
5
10
Residual
F
r
eq
ue
nc
y
Histogram of Residuals
0 1020304050
-0.2
-0.1
0.0
0.1
0.2
Observation Number
Re
s
i
du
al
I Chart of Residuals
5
6
6
3
Mean=9.81E-1
UCL=0.2110
LCL=-0.2110
2.5 3.0 3.5 4.0
-0.2
-0.1
0.0
0.1
0.2
Fit
Re
s
i
du
al
Residuals vs. Fits
-2 -1 0 1 2
-0.2
-0.1
0.0
0.1
0.2
Normal Plot of Residuals
Normal Score
R
e
s
i
dual
Residual Plot
Figure 4.5 Residual plots for the Non-Linear Model-1
58
4.5.2 Non-Linear Model-2
It was observed that some predictor variables in the Non-Linear Model-1 were
highly correlated, so regression analysis for the formulation of another non-linear model
was done after dropping the variables with multicollinearity (BodyMM, PitchMM and
PCBPadDiaMM) and the variables with very high p-values (SubstrateID and RampRate).
The statistical model in form of a mathematical equation is given by Equation (4.7)
8
b
(??T
7
b
shID)(BoardFini
6
b
)(MaskDefID
5
b
)(EMCFillID
4
b
(PCBthkMM)
3
b
)(BallDiaMM
2
b
)(BallCount
1
b
yRatio)A(DietoBodN
1%f
=
(4.7)
The numerical values of each generalized degree of freedom or the index is listed
in the ?Coefficient? column of the Table 4.7.
4.5.2.1 Model Diagnostics
The p-values for this model listed in the Table 4.7 are approximately zero for all
the predictor variables, thus indicating the very high level of statistical significance of
these variables. The value of R-Sq(adj) also shows improvement which means that this
model fits the failure data better than the Non-Linear Model-2.
The histogram and normal plot of the residuals for this model in the Figure 4.6
show that the residuals have close to normal distribution. It is evident from the I-chart of
the residuals that residuals corresponding to all the observations are within the control
limit of 3 sigma (?0.2175). Since the data points in the residual-vs-fit plot are randomly
scattered so the assumption of homoscedasticity (constant variance) for the regression
also hold true.
59
Table 4.7 Model Parameters and Analysis of Variance for Multivariate Regression Non-
Linear Model-2
Predictor Coefficient SE t-stat p-value
LogA 3.807 0.751 5.07 0.000
LogDietoBodyRatio -1.739 0.153 -11.35 0.000
LogBallCount 0.416 0.083 4.99 0.000
LogBallDiaMM 0.949 0.278 3.41 0.002
LogPCBthkMM -0.532 0.111 -4.82 0.000
LogEMCFillID 0.191 0.043 4.41 0.000
LogMaskDefID 0.258 0.063 4.10 0.000
LogBoardFinishID -0.078 0.040 -1.93 0.061
Log?T -0.945 0.279 -3.39 0.002
Analysis of Variance
Source DF SS MS f p
Regression 8 3.21641 0.40205 44.92 0.000
Residual 39 0.34904 0.00895
Total 47 3.56545
S = 0.0946 R-Sq = 90.20% R-Sq(adj) = 88.20%
60
-0.20-0.16-0.12-0.08-0.040.000.040.080.120.160.20
0
5
10
Residual
Fr
e
q
u
e
n
c
y
Histogram of Residuals
0 1020304050
-0.2
-0.1
0.0
0.1
0.2
Observ ation Number
R
e
s
i
dual
I Chart of Residuals
5
6
6
3
Mean=3.33E-16
UCL=0.2175
LCL=-0.2175
2.5 3.0 3.5 4.0
-0.2
-0.1
0.0
0.1
0.2
Fit
R
e
s
i
du
al
Residuals vs. Fits
-2 -1 0 1 2
-0.2
-0.1
0.0
0.1
0.2
Normal Plot of Residuals
Normal Score
R
e
s
i
d
ual
Figure 4.6 Residual plots for the Non-Linear Model-2
61
4.6 Model Prediction Correlation with Experimental Data
Cycles to one-percent failure values predicted by the statistical model was plotted
against the actual values from the experimental database to assess the goodness of fit of
the model. The best fit linear model and the non-linear model were used for the
comparison of the accuracy of the prediction of these models. Figure 4.7 shows the plot
for the Linear Model-3 and the Figure 4.8 shows the plot for the Non-Linear Model-2.
The straight line at 45? in these figures represents the locus of the points for which
the predicted values match exactly to the experimental values. So the closer the data
points are scattered to this line the better are the model predictions. On comparing both
the plots it can be seen that the non-linear model gives closer and better predictions.
Thus the Non-Linear Model-2 is more accurate, so this model has been selected for
further validation and analyzing the sensitivity of the various design parameters on the
BGA packages.
62
0
500
1000
1500
2000
2500
3000
3500
0 1000 2000 3000 4000
Actual 1% failure cycles
P
r
ed
i
c
t
e
d
1%
f
a
i
l
u
r
e
cycl
es
Line for Predicted
cycles=Actual cycles
Figure 4.7 Plot of experimental vs predicted 1% cycles to failure for the Linear Model-3
63
0
500
1000
1500
2000
2500
3000
3500
0 1000 2000 3000 4000
Actual 1% failure cycles
P
r
ed
i
c
t
e
d
1
%
f
a
ilu
r
e
c
ycles
Line for Predicted
cycles = Actual
cycles
Figure 4.8 Plot of experimental vs predicted 1% cycles to failure for the Non-Linear
Model-2
64
CHAPTER 5
MODEL VALIDATION AND DESIGN GUIDELINES FOR BGA PACKAGES
Model predictions have been correlated with the experimental data to develop
confidence on the accuracy of the model. In this section the sensitivity factors developed
for various design parameters from the statistics based models and the failure mechanics
based closed form models have been validated against the sensitivity factors from the
actual accelerated test failure data for different configurations of fine pitch ball grid array
packages subjected to harsh environments. The effect of various design parameters on
the reliability of the package has been analyzed and quantified, to develop guidelines for
use in the designing and selection of the package architecture and board attributes for
application in various harsh environments such as space application or automobile under
the hood application.
5.1 Model Validation
The effect of the various design parameters on the thermal reliability of the
package has been used for the model validation and for comparing the model predictions
with the actual experimental failure test data. Statistics and failure mechanics based
sensitivity factors quantifying the effect of design, material, architecture, and
environment parameters on thermal fatigue reliability, have been used to compute life.
Convergence between statistical model sensitivities and failure mechanics based
65
sensitivities has been demonstrated. Predictions of sensitivities have been validated
against experimental test data. Non-Linear Model-2 presented in Chapter-4 (Section
4.5.2) has been used for perturbation of the failure data for validation of the predicted
values.
5.1.1 Packaging Density
Packaging density of an electronic package is defined as the ratio of the die size to
the package body size. It is also called die to body ratio. The reliability of a ball-grid
array package generally decreases with the increase in the die-to-package ratio. This
effect has been demonstrated in both rigid-substrate and flex-substrate packages. The
hybrid model has been used to evaluate sensitivity to die-to-body. Packages with
compliant elastomeric substrates (e.g. ?BGA) may not exhibit this effect. Experimental
data on thermal-fatigue reliability effect of die/body ratio on the solder joint thermal
fatigue life of different sizes of BGA packages in thermal cycle of ?40?C to 125?C with
15mins ramps and 15mins dwells has been correlated with the model predictions for 8
mm, 12 mm, 15 mm, 16 mm, 17 mm and 27 mm BGA packages with different die sizes.
The cycles for 1% failure from the experimental data and the statistical model has been
plotted against the die to body ratio of the various packages. Four layer FR-4 test boards
of 0.85 mm and 1.6 mm thickness with OSP finish and SMD pads were used for the air to
air thermal cycling test. The experimental data has been plotted along with the predicted
values from the statistical model. The predicted values from the hybrid model follow the
experimental values quite accurately and show the same trend as seen in the Figure 5.1.
The sensitivity of the package reliability to the packaging ratio has been given in the
66
Table 5.1. The number of cycles to 1% failure for the different packages predicted by the
model has also been listed along with the actual failure data.
5.1.2 Ball Count
The effect of ball count, also referred to as number of I/Os in published literature
has been investigated. Experimental data indicates that thermal reliability of the BGAs
increases with the increase in the ball count of the package. The experimental data used
for the correlation includes 7.5 mm, 8 mm, 12 mm, 15 mm and 16 mm BGA packages.
Figure 5.2 indicates a close agreement between the experimental data and the statistical
model predictions. The general trend of increase in thermal reliability with the increase
in the ball count can be seen from the plot, which is in agreement with the failure
mechanics theory. Increase in the number of solder balls distributes stresses developed
due to the thermal deformation over a larger number of solder joints reducing the stress
level in the individual ball. The sensitivity of the package reliability to the ball count has
been given in the Table 5.2. The number of cycles to 1% failure for the different
packages predicted by the model has also been listed along with the actual failure data.
67
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.
34
0.
63
0.
72
0.
75
0.
79
0.
80
0.
81
Die to Body ratio
1%
f
a
i
l
u
r
e
cycl
es
Experiment
Model
Figure 5.1 Effect of die-to-package ratio on thermal fatigue reliability of BGA subjected
to ?40 to 125 ?C Thermal Cycle
Table 5.1 Sensitivity of the package reliability to packaging ratio and comparison of
predictions from non-linear model-2 with actual failure data.
Die-to-
Body
Ratio
Ball
Count
Ball Dia
(mm)
Experiment Model Sensitivity Factor
for Die-to-Body
Ratio
0.34 40 0.45 1855 1607
0.63 208 0.45 1215 1101
0.72 280 0.45 1124 1027
0.75 132 0.45 1016 946
0.79 144 0.45 911 855
0.80 208 0.45 491 360
0.81 96 0.30 360 337
-1.74
68
0
200
400
600
800
1000
1200
1400
1600
1800
96 132 160 208 280
Ball Count
1%
f
a
i
l
u
r
e
cy
c
l
e
s
Experiment
Model
Figure 5.2 Effect of ball count on thermal fatigue reliability of BGA subjected to ?40 to
125 ?C Thermal Cycle
Table 5.2 Sensitivity of the package reliability to the ball count and comparison of
predictions from non-linear model-2 with actual failure data.
Ball
Count
Die-to-Body
Ratio
Experiment Model Sensitivity Factor
for Ball Count
96 0.81 360 337
132 0.79 667 687
160 0.49 805 947
208 0.63 1215 1101
280 0.72 1534 1433
0.416
69
5.1.3 Ball Diameter
The solder joint ball diameter has a pronounced effect on the thermal reliability of
the BGA packages. Experimental thermal reliability data has been compared with the
statistical model predictions. BGA packages evaluated include solder ball diameter of
0.30 mm, 0.45 mm and 0.50 mm. The plot in the Figure 5.3 shows correlation of 1%
failure cycles for BGA with variable ball diameter. Experimental data indicates that the
increase in the ball diameter leads to overall better thermal reliability of the package.
This trend is in compliance with the theory of failure mechanics as the increase in the
solder ball diameter increases the crack area resulting in higher thermal fatigue life.
The sensitivity of the package reliability to the ball diameter has been given in the Table
5.3. The number of cycles to 1% failure for the different packages predicted by the
model has also been listed along with the actual failure data.
5.1.4 Board Thickness
The printed circuit board thickness also affects the thermo-mechanical reliability
of the package. The decrease in reliability of a ball-grid array package with the increase
in the PCB thickness is evident from the plots in Figure 5.4 and Figure 5.5. This effect is
consistent from failure mechanics point of view as the increased PCB thickness leads to
higher assembly stiffness, which results in higher stresses in the interconnect. This effect
has been demonstrated in both rigid-substrate and flex-substrate packages. Packages with
compliant elastomeric substrates (e.g. ?BGA) do not exhibit this effect. Sensitivity factor
has been computed from the multivariate regression model for PCB thickness in the
70
0
200
400
600
800
1000
1200
1400
1600
0.30 0.45 0.50
Ball Dia (mm)
1%
f
a
i
l
u
r
e c
y
c
l
e
s
Experiment
Model
Figure 5.3 Effect of ball diameter on thermal fatigue reliability of BGA subjected to ?40
to 125 ?C Thermal Cycle
Table 5.3 Sensitivity of the package reliability to the ball diameter and comparison of
predictions from non-linear model-2 with actual failure data.
Ball Diameter
(mm)
Experiment Model Sensitivity Factor
for Ball Diameter
0.30 778 723
0.45 1238 1201
0.50 1408 1386
0.9485
71
range of 0.85 mm to 1.6 mm for BGA packages including 8 mm, 12 mm, 15 mm and 16
mm BGAs.
The sensitivity of the package reliability to the PCB thickness has been given in
the Table 5.4. The table also shows the X-factor which is the ratio of the 1% failure
cycles of a component on 1.6 mm thick PCB to that on 0.85 mm thick PCB. This
basically means that it is a factor by which the life of component reduces when it is
mounted on 1.60 mm thick board instead of 0.85 mm thick board.
5.1.5 Encapsulant Mold Compound Filler Content
In case of PBGAs and some other packages, to protect the silicon die from the
external environment it is encapsulated in a mold compound which is usually epoxy
based material. The CTE of the epoxy is much higher than the silicon, which causes very
high thermal mismatch during the thermal cycling of the component. This might cause
stresses to develop on the surface of the die. In order to reduce this thermal mismatch,
usually a filler material with very low CTE such as silica is added to the epoxy. The
thermal reliability of the BGA package decreases with the increase in the mold
compound filler content. The BGA with lower amount of the mold compound filler have
better thermal fatigue reliability. This trend is visible in the plots for two different 16mm
BGA packages with die-to-body ratio of 0.53 in Figure 5.6 and with die-to-body ratio of
0.72 in Figure 5.7. The value of 1 indicates high filler content and the value of 10
indicates low filler content. Both the components show a decrease in the 1% failure
cycles and the model predictions are in close vicinity of the experimental values which
implies the correct prediction of the sensitivity of the component?s thermal reliability to
72
EXPERIMENT
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.4 0.8 1.2 1.6 2
PCB thickne ss (mm)
1%
f
a
i
l
u
r
e
cy
cl
e
s
A
C
D
E
F
G
H
Figure 5.4 Experimental data plot for BGAs (A to H) with die-to-package ratios between
0.53 and 0.81, subjected to ?40 to 125 ?C Thermal Cycle and PCB thickness 0.85 and
1.60mm
73
MODEL
0
200
400
600
800
1000
1200
1400
1600
1800
0.4 0.8 1.2 1.6 2
PCB thickne ss (mm)
1%
f
a
i
l
u
r
e
cy
cl
e
s
A
C
D
E
F
G
H
Figure 5.5 Model prediction plot for BGAs (A to H) with die-to-package ratios between
0.53 and 0.81, subjected to ?40 to 125 ?C Thermal Cycle and PCB thickness 0.85 and
1.60mm
Table 5.4 Sensitivity of the package reliability to the PCB thickness and comparison of
X-factor based on predictions from non-linear model-2 and actual failure data.
S.No. Die-to-Body
Ratio
Experiment
X-Factor
Model
X-Factor
Sensitivity Factor
for Board Thickness
A. 0.53 0.70 0.72
C. 0.54 0.39 0.50
D. 0.72 0.73 0.72
E. 0.79 0.79 0.72
F. 0.79 0.79 0.72
G. 0.80 0.77 0.72
H. 0.81 0.86 0.72
-0.5322
74
the mold compound filler content. This trend is consistent from the failure mechanics
point of view as the higher filler content mold compound will have higher elastic
modulus and a lower CTE. Higher modulus of elasticity makes the package stiffer,
therefore higher stresses are transmitted to the solder joints and lower CTE will increase
the global thermal mismatch. Both the factors contribute to the poor solder joint thermo-
mechanical reliability of the package.
The sensitivity of the package reliability to the EMC filler content has been given
in the Table 5.5. The table also shows the X-factor values from model predictions and
the experimental data. The X-factor is a factor by which the life of component reduces
when the filler content in the encapsulant is increased from low to high. The X-factors
from the model predictions are quite close to that calculated from the experimental data,
thus validating the model sensitivity.
5.1.6 Pad Configuration
Two different solder pad configurations usually used in the electronic packages
are solder mask defined (SMD) and non-solder mask defined (NSMD). Solder joint
reliability in thermal fatigue increases with change in pad configuration from SMD to
NSMD. This trend is visible from the 1% failure plot for 15mm, 160 I/O BGA as shown
in Figure 5.8. The value of 1 indicates SMD pad configuration and the value 10 indicates
NSMD pad configuration in the plot. This effect is true for both rigid-substrate and flex-
substrate ball grid array packages. Packages with compliant elastomeric substrates (e.g.
?BGA) do not exhibit this effect. This trend may vary depending on the mode of failure.
The package may show opposite trend in case the failure is due to the tearing out of the
75
0
200
400
600
800
1000
1200
1400
1600
1800
High (1) Low (10)
EMC Filler Content
1%
f
a
i
l
u
r
e
cy
cl
e
s
Experiment
Model
Figure 5.6 Effect of mold compound filler content on thermal fatigue reliability of 16mm
BGA with die-to-body ratio 0.53, subjected to ?40 to 125 ?C Thermal Cycle
0
500
1000
1500
2000
2500
3000
High (1) Low (10)
EMC Filler Content
1%
f
a
i
l
u
r
e
cy
cl
e
s
Experiment
Model
Figure 5.7 Effect of mold compound filler content on thermal fatigue reliability of 16mm
BGA with die-to-body ratio 0.72, subjected to ?40 to 125 ?C Thermal Cycle
76
Table 5.5 Sensitivity of the package reliability to the EMC filler content and comparison
of X-factor based on predictions from non-linear model-2 and actual failure data.
Die-to-Body
Ratio
Experiment
X-Factor
Model Sensitivity Factor
for EMC Fill
0.72 0.69 0.64
0.53 0.69 0.64
0.191
77
laminate under bending as shown by Mawer et. al.[1996]. In that case the solder mask on
top of the SMD pad helps to anchor the pad to the laminate core which leads to better
thermal fatigue reliability.
The sensitivity of the package reliability to the pad configuration has been given
in the Table 5-6. The table also shows the X-factor values from model predictions and
the experimental data for 15 mm FlexBGA package with 160 I/Os. The X-factor is a
factor by which the life of component reduces when the pad configuration is changed
from NSMD to SMD. The X-factors from the model predictions are quite close to that
calculated from the experimental data, which validates the model sensitivity.
5.1.7 Board Finish
The most commonly used board finishes for PCBs are hot air solder level
(HASL), organic surface protection (OSP) and electroless immersion gold (ENIG or
Ni/Au). Experimental data from previous studies indicates that HASL and OSP are
significantly more reliable than ENIG for ball grid array packages. This effect has been
demonstrated in both rigid-substrate and flex-substrate packages. Packages with
compliant elastomeric substrates (e.g. ?BGA) may also exhibit this effect. Hung, et. al.
[2000] investigated the effect of surface finish on the solder joint reliability of 12mm
BGA with polyimide substrate, die-up, wire bonded and over-molded configuration.
Thermal cycle of ?40?C to 125?C with 15mins ramps and 15mins dwells was used for the
test. FR-4 test boards of thickness 0.8mm were used in the test. As seen in Figure 5.9,
out of the three surface finishes, the OSP finish boards exhibit maximum thermal
78
0
200
400
600
800
1000
1200
1400
1600
1800
SMD (1) NSMD (10)
Pad Configuration
1
%
f
a
ilu
r
e
c
y
c
le
s
Experiment
Model
Figure 5.8 Effect of the change in mask definition from SMD to NSMD on 15mm, 160
I/O BGA thermal reliability.
Table 5.6 Sensitivity of the package reliability to the pad configuration and comparison
of X-factor based on predictions from non-linear model-2 and actual failure data.
Device Experiment
X-Factor
Model
X-Factor
Sensitivity Factor for Mask
Definition
15mm, 160 I/O
FlexBGA
0.59x 0.57x 0.2576
79
reliability. In the plot the value 1 for the board finish corresponds to OSP finish, 10
corresponds to HASL and 100 corresponds to Ni-Au finish. This effect of board finish
on the thermal fatigue reliability is attributed to the different inter-metallic system
formation for different board finishes. The different inter-metallic systems induce
different failure modes thus having impact on the thermal fatigue reliability of the
component. Figure 5.9 demonstrates a close agreement between the experiment and the
predicted values from the statistical model.
The sensitivity of the package reliability to the board finish type has been given in
the Table 5.7. The number of cycles to 1% failure for the 12 mm BGA with 132 I/Os
predicted by the model for all the three board finishes has also been listed along with the
actual failure data. The model predictions follow the same trend as the experimental
data.
5.1.8 Temperature Cycle Condition
Temperature cycle condition affects BGA package reliability immensely. The
sensitivity of the package thermal reliability to the thermal cycling temperature range has
been quantified using the multivariate regression analysis in the statistical model. ?T is
the thermal cycling temperature magnitude. The cycles for 1% failure for 12mm, 132 I/O
BGA with Die/Body ratio of 0.54 predicted by the statistical model has been plotted with
the experimental data in the Figure 5.10. Two different temperature cycle conditions
used for the comparison are:
1. 40?C to 125?C with 15mins of dwell, 15mins ramp
2. 0?C to 100?C with 30mins of dwell, 30mins of ramp.
80
0
200
400
600
800
1000
1200
1400
1600
1800
2000
OSP (1) HASL (10) Ni-Au (100)
Board Finish
1
%
f
a
i
l
u
r
e
cy
cl
e
s
Experiment
Model
Figure 5.9 Effect of PCB pad finish on 12mm, 132 I/O BGA thermal reliability subjected
to ?40 to 125 ?C Thermal Cycle
Table 5.7 Sensitivity of the package reliability to the board finish type and comparison of
predictions from non-linear model-2 with actual failure data.
Board Finish Experiment Model Sensitivity Factor
for Board Finish
OSP (1) 1743 1668
HASL (10) 1597 1403
Ni-Au (100) 673 828
-0.07794
81
The sensitivity of the package reliability to the thermal cycling temperature range
has been given in the Table 5.8. The table also shows the X-factor values from model
predictions and the experimental data for 12 mm FlexBGA package with 132 I/Os. The
experimental data validates the thermal sensitivity of the package predicted by the model.
5.2 Convergence of Statistics and Failure Mechanics Models with Actual
Experimental Test Data
Convergence of model predictions from statistics and failure mechanics has been
investigated. Figure 5.11 shows the effect of solder ball diameter on thermal reliability of
8mm and 12mm BGA packages under thermal cycling from ?40?C to 125?C with 15
mins ramp and 15 mins dwell. Comparison of experimental data with that of predicted
values for 1% failure cycles from both statistics and failure mechanics model shows good
agreement. All the three values for both the packages show a same trend of increased
thermal reliability with the increase in the ball diameter and lie in close vicinity of each
other, thus validating the model predictions. The correlation is especially important, if
one considers the vastly different approaches used in arriving at predicted life. The
statistics models are based on considerations of multivariate regression and analysis of
variance techniques and therefore account for mechanics of stress-strain only implicitly.
The failure mechanics approach are based on mechanics-of-materials, damage
mechanics, material constitutive behavior and do not address the statistical significance
and distribution of parameters explicitly.
82
0
500
1000
1500
2000
2500
100 165
Delta T ?C
1%
f
a
i
l
u
r
e
c
y
c
l
e
s
Experiment
Model
Figure 5.10 Effect of temperature cycle condition on 12mm, 132 I/O BGA thermal
reliability
Table 5.8 Sensitivity of the package reliability to temperature range and comparison of
X-factor based on predictions from non-linear model-2 and actual failure data.
Device Experiment
X-Factor
Model
X-Factor
Sensitivity Factor
for DeltaT
12mm, 132I/O
FlexBGA
0.27x 0.33x -0.9453
83
0
200
400
600
800
1000
1200
1400
0.30 0.45
Ball Dia (mm)
1
%
f
a
ilu
r
e
c
y
c
l
e
s
Experiment
Failure Mechanics Model
Statistical Model
Figure 5.11 Effect of solder ball diameter on thermal reliability of 8mm and 12mm BGA
packages under thermal cycle ?40?C to 125?C
84
5.3 Design Guidelines
The sensitivities from the multi-variable regression model have been used to
analyze the effect of various parameters on the solder joint reliability of the area array
packages. The sensitivities derived in Chapter-4 and validated in this chapter can be used
for doing the trade-offs and formulation of the design guidelines at the design and
selection stage of the area array packages for various applications.
? The reliability of solder inter-connect in a ball-grid area array package generally
decreases with the increase in the die-to-package ratio. This effect has been
demonstrated in both rigid-substrate and flex-substrate packages.
? Solder joint thermo-mechanical reliability of the BGA packages increases with
the increase in the ball count of the package.
? Increase in the ball diameter leads to overall better thermal reliability of the
solder joint in the area array package.
? The solder joint thermo-mechanical reliability decreases with the increase in the
PCB thickness.
? The BGA package with lower amount of mold compound filler demonstrate
better solder joint thermal fatigue reliability.
? Solder joint reliability in thermal fatigue increases with change in pad
configuration from SMD to NSMD.
? HASL and OSP pad finishes are significantly more reliable than ENIG for ball
grid area array packages, and OSP gives better thermo-mechanical reliability
than HASL.
85
? Thermo-mechanical reliability of the solder joint in an area array package is
inversely proportional to the temperature cycle magnitude through which the
package under goes thermal cycling.
86
CHAPTER 6
STATISTICS AND FAILURE MECHANICS BASED MODELS FOR FLIP CHIP
The term flip chip refers to the method of attachment of the silicon or the IC, in
which the chip is attached upside-down and attached directly to printed circuit board or
carrier substrate, typically using conductive solder bumps. Due to the large difference in
the CTE of the silicon and the interposer, solder joints experience fatigue damage during
the thermal or power cycling. This chapter presents the statistics based and failure
mechanics based models developed in the current research for the prediction of cycles to
failure. A perturbation approach to prediction of reliability of flip-chip devices in harsh
environments has been investigated. The proposed approach has been shown to achieve a
much higher accuracy compared to traditional first-order models by perturbing known
accelerated-test data-sets using models, using factors which quantify the sensitivity of
reliability to various design, material, architecture and environmental parameters. The
models are based on a combination of statistical analysis and failure mechanics. The
proposed approach has the potential of predicting both single and coupled factor effects
on reliability, which are often ignored in closed form models. Several solder joint
configurations and flip-chip architectures have been analyzed with statistical models and
failure mechanics models. The results have been compared with accelerated test data.
87
6.1 Overview
The proposed methodology presents a turn-key solution for product managers,
who are often faced with the problem of evaluating reliability trade-offs due to changes in
packaging format for existing designs because of component obsolescence, die shrink,
technology progression, underfills or other factors. Examples of common situations
include, vendor switches the underfill on a part which has been qualified, a perimeter die
is switched to an area-array die to achieve greater density, vendor thins the die from the
traditional 21 mils to 10 mils to achieve higher density.
6.2 Statistics Based Modeling
In this section, statistics-based closed-form models have been developed based on
multivariate regression and analysis of variance. The model parameters are based on
failure mechanics of flip-chip assemblies subjected to thermo-mechanical stresses. The
material properties and the geometric parameters investigated include die thickness, die
size, ball count, ball pitch, bump metallurgy, underfill types (capillary-flow, reflow
encapsulant), underfill glass transition temperature (T
g
), solder alloy composition
(SnAgCu, SnPbAg), solder joint height, bump size, and printed circuit board thickness.
An extensive flip-chip accelerated test reliability database based on the harsh
environment testing conducted by the researchers at the NSF Center for Advanced
Vehicle Electronics (CAVE) has been accumulated. This database has also been
supplemented with the various datasets published in the literature. Range of data
collected in each case is shown in Table 6.1. Each data point in the database is based on
the characteristic life of a set of flip-chip devices of a given configuration tested under
88
Table 6.1 Scope of Accelerated Test Database.
Parameter Data Range
Die Size 3 mm to 12.6 mm
Ball Count 42 to 184
Ball Pitch 0.2 mm to 0.457 mm
Ball Diameter 0.04 mm to 0.195 mm
Ball Height 0.04 mm to 0.147 mm
Solder Composition
Sn63Pb37, Sn96.5Ag3.5,
Sn99.3Cu0.7, Sn95.8Ag3.5Cu0.7
PCB Thickness 0.5 mm to 1 mm
T
High
in Accelerated Test 100?C, 125?C, 150?C
T
Low
in Accelerated Test -55?C, -40?C, 0?C
89
harsh thermal cycling or thermal shock conditions. Sensitivity of the reliability to the
geometry and material parameters have been derived based on the statistical models.
Minitab? and Matlab? have been used for the analysis. Characteristic life of the
various configurations of the flip-chip packages under different accelerated testing
conditions has been used as the response variable. Predictor variables include, different
thermal conditions, design parameters and material attributes of the package.
The database is fairly diverse in terms of materials and geometry parameters. The
flip-chip architectures contained in the database includes packages with both leaded and
lead-free solder bumps. Die sizes range from 3.0mm to 12.6mm, ball counts range from
42 to 184 I/O, ball pitch ranges from 0.2 to 0.457 mm, ball diameter ranges from 0.04 to
0.195 mm, ball height ranges from 0.04 to 0.147 mm. The various solder compositions
included in the database consist of Sn63Pb37, Sn96.5Ag3.5, Sn99.3Cu0.7, and
Sn95.8Ag3.5Cu0.7. Accelerated test high temperatures include 100?C, 125?C, and
150?C. The low temperatures in the accelerated test include -55?C, -40?C, and 0?C.
These models in their present form can be used for reliability comparison of the
flip-chip packages with different design and material attributes when subjected to
different extreme environments. The perturbation approach can be used to perturb
known accelerated test data sets. This approach provides higher accuracy than any first
order closed form model and also allows the user analyze the interaction effects of the
various parameters on the package reliability, which are often ignored in the various first
order closed form modeling methodologies and addressed only using finite element
models or experimental accelerated test data. The proposed form of the mathematical
model is shown in Equation (6.1).
90
)(
7
)(
6
)(
5
)(
4
)(
3
)(
2
)(
11%2.63
DeltaTb
PadTypeIDbBallDiaMMbIDSolderCompb
DUnderfillIbBallCountbDieSizeMMbaN
+
+++
+++=
(6.1)
The parameter N
63.2%
on the left hand side of the equation represents the
characteristic life of three-parameter Weibull distribution for the flip-chip package when
subjected to accelerated thermo-mechanical stresses. The parameters on the right hand
side of the equation are the predictor variables or the various parameters that influence
the reliability of the package. The coefficient of each of the parameter is the indictor of
the relative influence of that parameter on the characteristic life of the package. In this
case, parameters b
i
, for i = 1 to 7 represent the sensitivities of reliability to the respective
parameters. Parameter dimensions are indicated at the end of the parameter, e.g.
DieSizeMM represents the die size in mm. Qualitative parameters that significantly
influence the package reliability have been used as dummy variables in order to address
their affect on the package reliability. Parameters ending with the ID are dummy
variables. The PadTypeID varies between 0 and 1, with value 0 corresponding to solder
mask defined pad and 1 corresponding to non-solder mask defined pad. A 0 value for
underfillID represents non-underfill, while value of 1 corresponds to an underfilled flip-
chip device. The SolderCompID takes on 4 values 0, 1, 2, 3 corresponding to the four
alloys in the database including, Sn63Pb37, Sn95.8Ag3.5Cu0.7, Sn96.5Ag3.5, and
Sn99.3Cu0.7. The value of constant and coefficients in the model (Eq. 6.1) formulated
from the statistical analysis of the failure data are listed in the Table 6.2.
91
6.2.1 Model Diagnostics
The p-value of a parameter in, Table 6.2, indicates the statistical significance of
that parameter and the parameter with p-value less than 0.05 is considered to be
statistically significant and it should have significant effect on the reliability of the
package, with confidence level of more than 95.0%. All the predictor variables except
the SolderCompID are statistically significant with p-values in the neighborhood of 0.
SolderCompID has p-value of 0.062 which indicates 93.8% confidence level which is
little less than the 95.0% confidence level but it has still been included in the model as we
know from failure mechanics that the solder composition has significant effect on the
thermo-mechanical reliability of the flip-chip packages. A negative value of the index
indicates a decrease in cycles-to-1% failure with increase in value of the variable. The
model has an R
2
of 99.4% indicating that a large part of the variation in the data has been
explained by the model. A high f-value in Table 6.3 indicates statistical significance of
difference between groups.
Normality of the distribution of residuals has been verified. Residual plots of the
statistical model are shown in Figure 6.1. If we plot the residuals against the normal
score of the residuals then a perfectly normal distribution is represented by a straight line
at 45? on the normal plot of the residuals. The normal plot of residuals for this model
indicates a fairly normal distribution of the residuals as it is quite close to a straight line
at 45? (Figure 6.1). The histogram plot of residual vs frequency exhibits a nearly
symmetrical bell-shape pattern, which is consistent with a sample from a normal
distribution. The chart of individual observations reveals that the residuals for all the
observations are within the three sigma limits of (-406.9 and 406.9) which implies that all
92
the data points in the analysis are fitted within the control limits of 3 sigma. We can see
fairly random distribution of the residuals in the residual vs fits plot, which demonstrates
the linear relationship between the predictors and the response variable in the model. If
the relationship is not linear than the residuals follow some curved pattern distribution.
The plot also holds the assumption of homoskedasticity (constant variance) in the data as
the residuals do not fan out or show any pattern as we go from the lower fits to the higher
fitted values.
Characteristic Life (63.2% failure of population) values predicted by the statistical
model have been plotted against the actual values from the experimental database to
assess the goodness of fit of the model. The straight line at 45? in Figure 6.2 represents
the perfect fit of the predicted values. After comparing the various statistical models for
the fit of the predicted values with that of actual 1% failure cycles values form the
experimental data, the model with the best fit has been finally selected. The plot in the
Figure 6.2 for the model show?s that the predicted values are consistent with the
experimental values within close tolerance.
93
Table 6.2 Multi Variable Regression (MVR) Model of Flip Chip
Predictor Coeff SE Coeff t P-Value
Constant 11374 1526 7.45 0
DieSizeMM -456.18 62.32 -7.32 0
BallCount 21.994 4.413 4.98 0.001
BallDiaMM 19873 6553 3.03 0.016
PadTypeID 1781.2 261.5 6.81 0
DeltaT -72.546 6.838 -10.61 0
PitchMM 11860 2884 4.11 0.003
BallHeightMM -16102 4624 -3.48 0.008
SolderCompID 124.17 57.38 2.16 0.062
S R-Sq R-Sq(adj)
213.5 99.40% 98.80%
Table 6.3 Analysis of Variance for Data-Set.
Analysis of Variance
Source SS MS f P
Regression 59005565 7375696 161.84 0
Residual Error 364599 45575
Total 59370164
94
300240180120600-60-120-180-240
6
5
4
3
2
1
0
Residual
F
r
e
q
ue
nc
y
Histogram of Residuals
151050
500
0
-500
Observation Number
Re
si
d
u
al
I Chart of Residuals
Mean=-7.0E-12
UCL=406.9
LCL=-406.9
70006000500040003000200010000
300
200
100
0
-100
-200
Fit
Res
i
d
u
al
Residuals vs. Fits
210-1-2
300
200
100
0
-100
-200
Normal Plot of Residuals
Normal Score
Re
sid
u
a
l
Figure 6.1 Residual plots for the diagnostics of the statistical model
95
0
1000
2000
3000
4000
5000
6000
7000
0 100200300400500600700
Actual characteristic Life (cycles)
P
r
e
d
ic
te
d
C
h
a
r
a
c
te
ris
t
ic
L
i
f
e
(cy
c
l
e
s)
Figure 6.2 Actual vs predicted characteristic life
96
6.3 Failure Mechanics Based Modeling
The formulation and application of the failure mechanics based modeling
methodology in the current work is based on a combination of Timoshenko beam theory
[1925], and its application to tri-material assemblies [Suhir 1986, 1991], calculation of
time-independent plastic deformation [Knecht 1991], calculation of stress relaxation
[Wong 1991], hysteresis loop calculation [Clech 1996], life prediction [Darveaux 1992,
1995, 2000; Lall 2004]. In the first step the maximum shear strain developed in the
solder joint during thermal cycling is determined which is the required input for the
hysteresis loop determination. The second step involves hysteresis loop determination
using the various material constitutive relations for both local and global thermal
mismatch separately. Once the hysteresis loops have been determined, the total inelastic
strain energy density is determined which is given by the sum of the area enclosed within
the hysteresis loops for local and global thermal mismatch. Finally the characteristic life
for the package is calculated from the damage relationships.
6.3.1 Shear Stresses and Strains
Previous researchers have computed the maximum shear strain in the solder joint
during thermal cycling using the DNP (distance to neutral point) formula approximation,
but due to the assumptions on which the DNP formula is based, it gives the exaggerated
values of the maximum shear strain that are normally much higher than the actual values.
The simplified form of the DNP formula usually given by Equation (2) assumes that the
solder joint withstands the complete thermal expansion differential between the package
97
and the PCB in form of a shear strain given by ?
max
. Bending of the package and the PCB
is also completely ignored in the DNP formula [Clech, 1996],
T
h
L
s
D
max
?????=?
(2)
Shear stresses and strain computation is based on the Timoshenko Beam theory
for Bi-material assemblies [Timoshenko, 1925] and its application to flip-chip assemblies
[Suhir 1986, 1990]. In order to facilitate the load distribution of the thermal mismatch,
an assembly of width equal to the flip-chip pitch has been analyzed. The x-displacements
at the bottom of the flip-chip and top of the substrate are respectively given by, [Suhir,
1986]
() () ()
()
??
??
?
+??+??????=
x
0
1
11
x
0
1111
d
2
h
xdFtxxu
(3)
() () ()
()
??
??
?
???????+??=
x
0
2
22
x
0
2222
d
2
h
xdFtxxu
(4)
where, ?
i
is the axial compliance for the i
th
component, for i = 1, 2, 3 corresponding to the
flip-chip, underfill and the printed circuit board. E
i
and ?
i
are the elastic modulus and
poisson?s ratio, h
i
is the layer thickness and F
i
is the force in the i
th
component, [Suhir,
1986]
i
i
2
i
h
E
1 ??
=?
(5)
The interfacial compliance, ?
i
of the i
th
component is given by, [Suhir, 1986]
i
i
i
G3
h
=?
(6)
98
and G
i
is the shear modulus of the i
th
component, ? is the radius of curvature, ?
i
(x) is the
shear stress in the i
th
interface. The relationship between forces and radius of curvature is
calculated using the equilibrium equations for the underfill, the shear stresses can be
represented by, [Suhir, 1986]
()
klcosh
kxsinht
x
??
???
=?
(7)
where
321
2 ?+?+?=?
, and
?
?
=k
6.3.2 Hysteresis Loop Computation
In the current approach the reliability or the life of a package is considered to be a
function of the damage due to the plastic work that the solder joint interconnect
accumulates while the device undergoes thermal cycling. The accumulation of the plastic
work initiates a crack in the solder joint and this crack propagates as the component
keeps on undergoing thermal cycling. The component finally fails when either the solder
joint cracks completely or when the crack is sufficient enough to prevent the flow of
required current through the solder joint interconnection. Failure criterion for any
component during the accelerated thermal cycling tests has been defined in several
different ways by different researchers in the published literature. A 100% increase in
the electrical resistance of the component has been commonly used as the failure
criterion. The plastic work accumulated per unit volume per cycle which is also referred
as inelastic strain energy density, is given by the area enclosed within the hysteresis loop
of the solder joint undergoing the thermal cycling.
99
Loop iteration is done using the methodology by Clech [1996] until the loop
converges. The thermal cycle is divided into 4 sections: (1) Ramp-up (2) Dwell at high
temperature (3) Ramp-down (4) Dwell at low temperature. The solder joint response
during the temperature ramps is approximated by time independent plastic deformation
[Knecht and Fox,1991],
2
P
B
AB
?
?
?
?
?
?
?
?
?
?
=???
(8)
where, subscript A denotes the condition before ramp, B denotes condition after ramp
and ?
P
is plasticity parameter obtained from linear curve fitting of data in Knecht [1991]:
)C(T07.279.348)Mpa(
P
???=? (9)
The constitutive relations given by Hall [1984] and Wong [1991] have been used
for stress relaxation and the time dependent creep during the dwell period,
max
?=
?
?
+?
(10)
3
creep
)T(A ?=?
?
(11)
where,
creep
?
? is strain rate or the time derivative of creep strain, A(T) is temperature
dependent factor derived from the data by Wong [1991], and
s
s
A
hK?
=? where K is
effective assembly stiffness derived from the formulation given by Hall [1984] for the
LCCCs
100
6.3.3 Life Prediction from Damage Relationship
The damage relationship relates the characteristic life of the component in terms
of number of thermal cycles with the total inelastic strain energy density per cycle. This
damage relationship is valid only if the failure mode of the package is solder joint
cracking due to thermal cycling fatigue. The damage relationship is established from the
experimental ATC failure data. This relationship depends on the solder composition. So,
one has to be very careful while using the damage relationship while predicting failure
cycles for any particular component. In the current work the damage relationships
proposed by Lall [2004] and Darveaux [1992, 2000] have been used to calculate the
characteristic life (t
63.2%,joint
) for life prediction of the component. The characteristic life
of the component has been calculated using the damage relationship given by Equation
(12).
da/dN
a
Nt
0joint 63.2%,
+=
(12)
2
10
K
W)(KN ?=
(13)
4
K
3
W)(K
dN
da
?=
(14)
Where, ?a? is the joint diameter at the interface, N
0
is the number of cycles for
crack initiation and da/dN is the crack propagation rate. The value of the constants K
1
,
K
2
, K
3
and K
4
used for calculation of characteristic life cycles are given in Table 6.4.
The above mentioned approach has been used to correlate the experimental data
from accelerated test with failure mechanics model predictions for -40?C to 125?C, -55?C
101
Table 6.4 Constants for the damage relationship
K
1
K
2
K
3
K
4
Lall, et al.
[2004]
28769 -1.53 6x10
-7
0.7684
Darveaux
[2000]
48300 -1.64 3.8x10
-7
1.04
102
to 125?C and 0?C to 100?C. The correlation between the predicted and the experimental
values, in addition to convergence with statistical models will be discussed later in the
chapter.
6.4 Model Validation
The statistical model presented earlier in the Section 6.2 has been validated
against the experimental accelerated test failure data. The effect of the various design
parameters on the thermal reliability of the package has been presented. Statistics and
failure mechanics based sensitivity factors quantifying the effect of design, material,
architecture, and environment parameters on thermal fatigue reliability, have been used to
compute life. The predictions from the statistical model have been also compared with
the experimental data.
6.4.1 Die Size
The thermo-mechanical reliability of a flip-chip devices generally decreases with
the increase in the die size. This effect has been demonstrated in flip-chip devices
soldered to both FR4-substrate and BT-substrates. The statistical model has been used to
evaluate sensitivity to die size. Wafer-level devices with compliant elastomeric
substrates (e.g. ?BGA) may not exhibit this effect. In addition, the model predictions
focus on solder interconnect failure. If the failure mode is different, such as underfill
cracking, then the failure response will be different. The cycles for 63.2% failure from
the experimental data and the statistical model has been plotted against the die size of
various devices. The predicted values from the statistical model follow the experimental
values quite accurately and show the same trend (Figure 6.3). This trend is also
103
consistent from the failure mechanics standpoint, as the solder joints with larger die are
subjected to much higher strains due to the increased distance from the neutral point, thus
having lower reliability.
Encapsulated flip-chip packages with die sizes of 5.1mm, 6.5mm and 10mm have
been used for the comparison of the model predictions with the actual test failure data.
All the three packages had eutectic (Sn37Pb) solder joints of different ball diameter, pitch
and pad definition and were subjected to different ATC (Table 6.5). Thus, the model is
being tested for its ability to predict both single and coupled effects. Since a linear model
has been used to quantify the sensitivity, so the sensitivity factor of -456.18 means that
the characteristic life of a flip-chip decreases by 456 cycles when the die size increases
by 1 mm and all the other parameters remaining constant. The characteristic life of the
three packages plotted in the Figure 6.3 has also been listed in the Table 6.5.
6.4.2 Ball Count
The effect of ball count on thermo-mechanical reliability of the flip-chip devices
has been demonstrated in the Figure 6.4. A trend of increase in the reliability with the
increase in the ball count is visible, which is also supported by the failure mechanics
theory. With the increase in the ball count the shear stress generated in the solder joints
due to the thermal mismatch gets distributed, thus reducing the stress in the individual
joint and increasing the life of the solder joint. Since this failure mechanics is only
applicable in the case where the failure mode is solder joint cracking, so the trend might
104
0
500
1000
1500
2000
2500
3000
3500
4000
5.1 6.5 10
Die Size (mm)
C
h
ar
act
er
i
s
t
i
c L
i
f
e
(
cycl
e
s
)
Experiment
Model
Figure 6.3 Effect of die size on thermal fatigue reliability of encapsulated flip-chip with
Sn37Pb solder joints
Table 6.5 Sensitivity factor for the die size and MVR model prediction comparison with
the actual failure data
Characteristic Life
(cycles)
Die Size
(mm)
Ball
Count
Pitch
(mm)
Ball
Dia
(mm)
ATC
Experiment Model
Sensitivity
Factor
5.1 88 0.2 0.112 -25?C to
140?C
3485 3656
6.5 96 0.25 0.098 -55?C to
140?C
2764 2843
10 184 0.2 0.126 -25?C to
140?C
2407 2426
-456.18
105
be different for other failure modes such as underfill delamination or copper trace
cracking.
Three different encapsulated flip-chip packages with ball count of 88, 96 and 137
subjected to different ATC test condition (Table 6.6) have been used to validate the effect
of ball count on the thermo-mechanical reliability predicted by the model. The three
packages used for comparison had been subjected to different ATC test conditions and
include different solder joint compositions and die sizes. The characteristic life predicted
by the model lies in close proximity to the actual characteristic life from the experimental
thermal cycling test. The sensitivity factor indicates that with an increase of every single
ball in the total ball count keeping all other parameters constant the characteristic life of
the flip-chip package increases by 22 cycles.
6.4.3 Underfill Characteristic
Flip-chip devices with the underfill or encapsulation show very high thermo-
mechanical reliability as compared to the flip-chip devices without underfill. This trend
hold true for both eutectic (Sn37Pb) and lead-free flip-chip devices mounted on both BT
and FR-4 substrate. The main reason for this trend from thermo-mechanics standpoint is
that the underfill material provides a mechanical support and shares the shear stresses
generated in the solder joints due to the thermal mismatch between the chip and the
board. However this trend is reversed for the case where the failure mode is trace
cracking, because the application of underfill leads to much higher stresses on the Cu
traces and has a peeling effect. Underfill cracking and delamination are the other failure
modes commonly associated with encapsulated flip-chip devices along with solder joint
106
0
1000
2000
3000
4000
5000
6000
88 96 137
Ball Count
C
h
ar
ac
t
e
r
i
s
t
i
c
L
i
f
e
(
c
yc
le
s)
Experiment
Model
Figure 6.4 Effect of ball count on thermal fatigue reliability of encapsulated flip-chip
with leaded and lead-free solder joints.
Table 6.6 Sensitivity factor for the ball count and MVR model prediction comparison
with the actual failure data
Characteristic Life
(cycles)
Ball
Count
Die
Size
(mm)
Pitch
(mm)
Solder
Composition
ATC
Experiment Model
Sensitivity
Factor
88 5.1 0.2 Sn3.5Ag -55?C to
140?C
2383 2410
96 12.6 0.46 Sn37Pb -25?C to
140?C
2722 2697
137 12.6 0.2 Sn0.7Cu 0?C to
140?C
5322 5048
21.99
107
failure and Cu trace cracking. Figure 6.5 shows the comparison of actual and predicted
characteristic life of 12.6mm flip-chip device with and without underfill having Sn0.7Cu
solder joints, subjected to different thermal cycling conditions.. Figure 6.6 shows the
actual and predicted effect of the encapsulation on the flip-chip device with different die
sizes subjected to thermal cycling of -40?C to 125?C.
The 30x to 40x improvement in the characteristic life of underfilled flip-chip
compared to the non-underfilled flip-chip devices is partially due to the coupled effects of
die size and thermal cycling conditions and cannot be attributed to absence of underfill
alone. The correlation demonstrates that the model is robust enough to accurately predict
coupled effects. The added advantage of the perturbation approach demonstrated here is
that single effects can also be predicted for configurations which were never tested. For
example, the presence of underfill alone is predicted to increase life by 1336 cycles in the
configuration analyzed. The underfill factor shows a positive sensitivity versus thermo-
mechanical reliability, indicating increase in solder-joint reliability with presence of
underfill. The sensitivity factor derived to quantify the effect of the encapsulation on the
thermo-mechanical reliability of the flip-chip device has been listed in the Table 6.7. The
model prediction for the characteristic life of the device matches with the actual ATC test
failure data within small variation.
6.4.4 Solder Joint Diameter
The thermo-mechanical reliability of the flip-chip devices is also influenced by
the solder joint or bump diameter. Flip-chip with bigger bump size usually give higher
reliability for the device. This trend is supported by the characteristic life plot for the
108
0
1000
2000
3000
4000
5000
6000
Underfilled Non-Underfilled
Underfill Characteristic
C
h
ar
act
er
i
s
t
i
c L
i
f
e
(
cyc
l
es)
Experiment
Model
Figure 6.5 Effect of underfill on thermal fatigue reliability of flip-chip devices with
99.3Sn0.7Cu solder joints.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Underfilled Non-Underfilled
Underfill Characteristic
C
h
ar
act
e
r
i
s
t
i
c L
i
f
e
(
cycl
es)
Ex per iment
Model
Figure 6.6 Effect of underfill on thermal fatigue reliability of flip-chip with
95.5Sn4.0Ag0.5Cu solder joints.
109
Table 6.7 Sensitivity factor for underfill characteristic and MVR model prediction
comparison with the actual failure data
Characteristic Life
(cycles)
Encapsulation Die
Size
(mm)
Solder
Composition
ATC
Experiment Model
Sensitivity
Factor
Underfilled 12.6 Sn0.7Cu 0?C to
110?C
5322 5048
Non-
Underfill
12.6 Sn0.7Cu -40?C to
140?C
171 213
Underfiled 5.1 Sn4Ag0.5Cu -40?C to
140?C
4243 3958
Non-
Underfill
12.6 Sn4Ag0.5Cu -40?C to
140?C
101 41
1336
110
flip-chip device for two different ball diameters. Flip-chip with larger bumps have lower
stress concentration and longer crack propagation path in the solder interconnects, thus
adding to the thermo-mechanical reliability of the device. The encapsulated flip-chip
used for the validation had a die size of 5.1 mm with solder joint composition of
96.5Sn3.5Ag, ball count of 88, and ball diameter of 0.1 mm and 0.12 mm respectively
(Figure 6.7). The thermal cycling conditions and all other parameters are constant in both
the cases (Table 6.8), so the coupled effects are not included in the life prediction. Model
predictions show good correlation with experimental data.
6.4.5 Pad Configuration
Two different configurations, SMD and NSMD, are usually used for mounting the
flip-chip device on the PCB. Flip-chip devices mounted on PCB with NSMD pad
configuration have been shown to have higher thermo-mechanical reliability. The solder
mask in the SMD pad creates a sharp edge in the solder joint which leads to a stress
concentration and early failure of the joint, thus resulting in poor reliability compared to
solder interconnects with NSMD pad configuration. This is true only when the failure
mode is solder joint cracking under thermo-mechanical stresses. SMD pads provide a
better reliability in the cases where the failure mode is peeling-off of the pad or cracking
of the Cu trace, in that case the cover film over the edges of the SMD pad provides the
support to the pad and restrains the pad from peeling off. This is often the case in large
out-of-plane deformation, shock and vibration. Figure 6.8 shows the comparison of the
characteristic life of underfilled 12.6 mm x 7.46 mm flip-chip devices with different pad
configurations. The pad definition effect has been modeled with dummy variables with
111
0
500
1000
1500
2000
2500
3000
3500
4000
0.1 0.12
Solder Joint Diameter (mm)
C
h
a
r
a
c
te
r
i
s
t
i
c
L
i
fe
(c
y
c
l
e
s
)
Ex per iment
Model
Figure 6.7 Effect of bump diameter on thermal fatigue reliability of encapsulated flip-
chip with lead-free (96.5Sn3.5Ag) solder joints and die size of 5.1 mm subjected to ?
40?C to 125?C thermal cycle.
Table 6.8 Sensitivity factor for the ball diameter and MVR model prediction comparison
with the actual failure data
Characteristic Life
(cycles)
Ball
Dia
(mm)
Die
Size
(mm)
Solder
Composition
ATC
Experiment Model
Sensitivity
Factor
0.1 5.1 Sn3.5Ag -25?C to
140?C
3092 3104
0.12 5.1 Sn3.5Ag -25?C to
140?C
3456 3249
19873
112
value ?0? indicating an SMD pad and value ?1? indicating an NSMD pad. The factor has
been shown to have positive sensitivity indicating an increased in thermo-mechanical
reliability for change in pad definition from SMD to NSMD. The sensitivity factor
derived to quantify the effect of the encapsulation on the thermo-mechanical reliability of
the flip-chip device has been listed in the Table 6.9.
6.4.6 Temperature Cycle Magnitude
The thermo-mechanical life of the flip-chip devices, similar to other package
architectures, is a function of the environment or the testing condition to which it is
subjected. Magnitude of the temperature range experienced during the accelerated test is
an influential parameter. The characteristic life of the package decreases with the
increase in the temperature range of the ATC (Figure 6.9). Temperature cycle magnitude
has a negative sensitivity factor, indicated by decrease in thermo-mechanical reliability
with increase in temperature cycle magnitude. Data presented (Table 6.10) includes
coupled effects of other parameter variations such as, die size, ball diameter, ball count
and cycle time. The predicted values for characteristic life calculated based on the
statistical model match the experimental values from the ATC test very accurately.
6.5 Convergence of Statistics and Failure Mechanics Models with Actual
Experimental Test Data
Convergence of model predictions from statistics and failure mechanics has been
investigated. Figure 6.10 shows the effect of die size on thermal reliability of 5.1 mm,
6.5 mm, and 10 mm flip-chip devices under thermal cycling from 0?C to 100?C, ?40?C
113
0
1000
2000
3000
4000
5000
6000
7000
SMD NSMD
Pad Type
C
h
ar
a
c
t
e
r
i
st
i
c
L
i
f
e
(
cyc
l
e
s
)
Experiment
Model
Figure 6.8 Effect of pad configuration on thermal fatigue reliability of encapsulated flip-
chip with die size of 12.6 mm subjected to 0?C to 100?C thermal cycle.
Table 6.9 Sensitivity factor for pad type and MVR model prediction comparison with the
actual failure data
Characteristic Life
(cycles)
Pad
Type
Die
Size
(mm)
Solder
Composition
ATC
Experiment Model
Sensitivity
Factor
SMD 12.6 Sn0.7Cu 0?C to
100?C
5322 5048
NSMD 12.6 Sn37Pb 0?C to
100?C
6588 6328
1781.2
114
0
500
1000
1500
2000
2500
3000
3500
165 180
De lta T (?C)
C
h
a
r
a
c
te
r
i
s
t
i
c
L
i
fe
(c
y
c
l
e
s
)
Experiment
Model
Figure 6.9 Effect of ATC temperature cycle magnitude on thermal fatigue reliability of
underfilled flip-chip devices
Table 6.10 Sensitivity factor for ATC temperature range and MVR model prediction
comparison with the actual failure data
Characteristic Life
(cycles)
ATC Cycle
Time
(mins)
Die
Size
(mm)
Ball
Count
Ball
Diameter
(mm)
Experiment Model
Sensitivity
Factor
-25?C to
140?C
60 5.1 88 0.10 3092 3104
-55?C to
125?C
17 5.1 88 0.12 2383 2410
-72.55
115
to 125?C, and ?55?C to 125?C. Comparison of experimental data with that of predicted
values for 63.2% failure cycles from both statistics and failure mechanics model shows
good agreement. All the three values for both the devices show a same trend of increased
thermal reliability with the increase in the die size.
The correlation can be used in building confidence during trade-off studies by
arriving at consistent results in terms of reliability impact of changes in material,
configuration and geometry using different modeling approaches. The correlation is
especially important, if one considers the vastly different approaches used in arriving at
predicted life. The statistics models are based on the two-parameter Weibull distribution,
multivariate regression and analysis of variance techniques and therefore account for
mechanics of stress-strain only implicitly. The failure mechanics approach are based on
Timoshenko beam theory, damage mechanics, material constitutive behavior and do not
address the statistical significance and distribution of parameters explicitly.
116
0
500
1000
1500
2000
2500
3000
3500
4000
5.1 6.5 10
Die size (mm)
C
h
ar
act
er
i
s
t
i
c L
i
f
e
(
c
ycl
e
s
)
Ex per iment
Statistical Model
Failure Mechanics
Model
Figure 6.10 Correlation between Accelerated Test, Statistical Model, and Failure
Mechanics Model
117
CHAPTER 7
FEM ANALYSIS OF A FLIP-CHIP PACKAGE
FEM (Finite Element Method) has been widely used for the reliability assessment
and analysis of the various electronic components . Several modeling and life-prediction
methodologies have been developed for electronics subjected to thermal-cycling [Lall, et
al. 2003, Clech 1997, Syed 1995 and Zahn 2002] . Both 2-D (two dimensional) and 3-D
(three dimensional) models have been used for the analysis [Pang 1997, Syed 2001].
Usually 3-D models have been shown to give better accuracy and more realistic results as
compared to the 2-D models [Vendevelde 2003, Zahn 2003]. Depending upon the
geometric and material symmetry of the actual package different configuration of 3-D
models like full model, 1/4
th
or 1/8
th
symmetry model and diagonal slice model [Zahn
2003 and Pang 2001] can be used for the simulation. Use of 3-D diagonal slice model
configuration is preferred over the other configurations for the fully symmetric packages
due to its computational efficiency and ability to capture true boundary conditions.
7.1 Overview
In the present study 3-D diagonal slice model has been used for all of the FEA
purposes. Various other parameters such as material non-linearity, element type, shape
and size also affect the simulation accuracy. The finite element models used in the
current work have been checked for their element shapes (aspect ratio and angles) and a
118
finer mesh in the region of solder bump has been employed for better accuracy. In order
to capture the true nature of solder bump, time and temperature dependent non-linear
constitutive model has been employed for the simulation.
Exhaustive research has been done on the solder joint reliability of various
electronic packages subjected to thermal cycling. It has been established by many
researchers that the fatigue life of the solder interconnect is dependent on the amount of
inelastic strain energy density (ISED) accumulated by the solder joint during each
thermal cycle. A correlation between the solder joint reliability and the ISED output
from FEA has also been developed in the past for both leaded [Darveaux 2000] and lead-
free [Syed 2004] interconnect. The ISED calculations done from the simulations run for
different configuration and various thermal cycles have been used in the current work for
the solder joint reliability prediction using the life prediction correlations.
Both linear and non-linear material properties have been used for analyzing the
effect of various parametric variations on the reliability of the package. The parametric
variations include both design parameters (geometry and material) and the thermal
cycling parameters. The two failure modes analyzed for the relative comparison of
reliability due to the various parametric variations include solder joint failure and copper
trace cracking. Failure modes such as silicon die cracking and delamination have not
been analyzed in the present study.
7.2 Model Description
3-D diagonal slice model incorporated with time and temperature dependent non-
linear and linear material properties has been developed in ANSYS
TM
. Four different
119
geometries had been modeled in order to generate a total of 18 different configurations
for the analysis.
7.2.1 Model Variables
Several configurations have been developed for the analysis of flip-chip solder
joint integrity and Copper trace integrity. The parametric variations in the model include
both geometric and material property variables. Analyses with these variations give an
insight into the effect of various parameters on the flip chip reliability.
7.2.1.1 Geometry
The variations in the geometry considered in the FEA analysis. include three
bump heights (low, mid and high) and two bump sizes or diameters. The exact geometric
dimensions for the model construction were measured from the images of the flip-chip
bump cross-section. The dimensions of the fixed parameters are given in the Table 7.1
and the dimensions of variable parameters are listed in the Table 7.2.
7.2.1.2 Material
Both eutectic (62Sn36Pb2Ag) and lead-free (Sn3.5Ag0.75Cu) solder material
have been considered for the analysis. Also three different underfill materials have been
considered for the analysis. The material variations used in all the 18 configurations for
the simulation have been listed in the Table 7.2.
120
Table 7.1 Dimensions of fixed parameters used for the finite element model
Parameter Dimension (inch)
Pad thickness 0.0007
Slice length (Si Die) 0.096
Slice length (PCB) 0.192
Slice width 0.0056
Height (Si Die) 0.028
Height (PCB) 0.0212
121
Table 7.2 Material variations and the dimensions of the variable geometric parameters
Test
Case
Solder Underfill
Bump Height
(mils)
Bump Size
(mils)
1 62Sn36Pb2Ag UF-4 1.0 (Low) 4
2 62Sn36Pb2Ag UF-1 2.5 (High) 4
3 62Sn36Pb2Ag UF-4 2.5 (High) 4
4 62Sn36Pb2Ag UF-4 2.0 (Mid) 4
5 62Sn36Pb2Ag UF-1 1.0 (Low) 4
6 62Sn36Pb2Ag UF-3 2.0 (Mid) 4
7 62Sn36Pb2Ag UF-2 2.5 (High) 4
8 62Sn36Pb2Ag UF-2 2.0 (Mid) 3
9 62Sn36Pb2Ag UF-3 2.0 (Mid) 3
10 Sn3.5Ag0.75Cu UF-2 2.5 (High) 4
11 Sn3.5Ag0.75Cu UF-2 2.0 (Mid) 3
12 Sn3.5Ag0.75Cu UF-4 2.5 (High) 4
13 Sn3.5Ag0.75Cu UF-4 2.0 (Mid) 3
14 Sn3.5Ag0.75Cu UF-3 2.5 (High) 4
15 Sn3.5Ag0.75Cu UF-3 2.0 (Mid) 3
16 Sn3.5Ag0.75Cu UF-1 1.0 (Low) 4
17 Sn3.5Ag0.75Cu UF-1 2.0 (Mid) 4
18 Sn3.5Ag0.75Cu UF-1 2.5 (High) 4
122
7.2.2 Elements Used
The model has been map meshed using brick shaped 8 noded hexahedral
isoparameteric elements (Figure 7.1). Since the 8 noded hexahedral element provides
better results and higher accuracy as compared to the tetrahedral elements so the
hexahedral elements have been used for meshing the entire model. 2x2x2 Gaussian
quadrature integration option has been used for the solution.
VISCO107 elements have been used for the solder bump and SOLID45 elements
for the rest of the materials. VISCO107 has rate-dependent large strain plasticity
capabilities and is used to represent non-linear behavior of visco-plastic materials.
Another advantage of using VISCO107 for solder is to facilitate the constitutive
modeling of the solder material using Anand?s model. SOLID45 element also has large
strain capabilities.
7.2.3 Mesh and Boundary Conditions
The complete meshed model had 11,850 elements in all for the models with high
and medium bump height and 11,130 elements with low bump height models. Fully
meshed model with the coordinate system is shown in Figure 7.2. The bump region has
been finely meshed in order to get higher accuracy. The geometry of the elements has
been checked for the AR (aspect ratio) and the angles as the simulations run with the
model having elements with poor AR and angles can give inaccurate and misleading
results.
Three different solder joints with different bump gap heights have been modeled.
The Low gap bump with height 1.0mil, mid gap bump with height 2.0mils and high gap
123
Figure 7.1 Eight noded hexahedral isoparametric element
124
Figure 7.2 Fully meshed model with coordinate axes
125
bump with height 2.5mils have been modeled for the analysis. Both the Copper pads
have been meshed with two element layers each. As shown in Figure 7.3 the low gap
bump has been meshed with 3 element layers and the other two bump configurations
have been modeled with six layers each. Since the objective of the simulation is to
analyze solder joint failure so the solder joint has to be finely meshed.
Symmetry boundary conditions as described in the Figure 7.4 have been used for
simulating true conditions. The boundary conditions have been applied on the nodes.
The coupled boundary condition applied on the symmetry plane implies that the nodes on
that surface are constrained to remain coplanar. One node on the bottom left corner of
the model has been fully constrained in order to prevent the rigid body motion.
7.2.4 PCB Material Layers
Various material layers have been modeled with the geometric dimensions
provided by the Vendor. For simplification the underfill fillet has not been considered
for the solder joint integrity simulation but it was considered for the Copper trace
integrity simulation as the fillet has significant impact on the stresses developed in the
trace. A close view of the schematic of the different layers modeled has been shown in
Figure 7.5. The thickness and the material properties of each layer of the PCB has been
listed in the Table 7.3.
126
Figure 7.3 Solder bump mesh for the three different gap heights
Figure 7.4 Schematic of the boundary conditions applied on the model for the simulation
127
Figure 7.5 Schematic of the material layers modeled for the simulation
128
Table 7.3 Material properties and thickness of the PCB layers
Layer
Material
Thickness
(mils)
Material
Properties
?(Kpsi) 500.38
Cover film 1.0
? 18 ppm/
0
C
E(Kpsi) 105.88
Adhesive 1 0.8
? 118 ppm/
0
C
E 9717.53
Copper 0.7
? 17 ppm/
0
C
E(Kpsi) 105.88
Adhesive 2 0.7
? 118 ppm/
0
C
E(Kpsi) 500.38
Base polyimide 1.0
? 18 ppm/
0
C
E(Kpsi) 159.54
Adhesive 3 1.0
? 218 ppm/
0
C
E(Kpsi) 10007.6
Aluminum 16.0
? 10 ppm/
0
C
129
7.2.5 Material Properties
7.2.5.1 Linear Material Properties
Linear isotropic material properties have been assigned to all the elements except
the solder bump elements. The solder bump elements have been modeled with both
linear and non-linear constitutive relations. The linear isotropic material properties
assigned in the model have been listed in the Table 7.4. The non-linear constitutive
relations for the solder bump has been discussed in the next section.
7.2.5.2 Non-Linear Solder Material Properties
Solder alloy is a viscoplastic material which means that it exhibits both time
dependent creep and plasticity. Thus it is essential to use time and temperature
dependent non-linear material model for the solder bump. Widely used and established
Anand?s model which is also a standard feature in ANSYS
TM
has been used to model
both eutectic (62Sn36Pb2Ag) [Darveaux, 2000] and lead-free [Amagai et al, 2002] solder
material. In the Anand?s model both creep and plasticity have been coupled together
with the help of flow and evolutionary equations:
Flow equation
?
?
?
?
?
?
?
=
kT
Q
sA
dt
d
m
o
p
exp)/(sinh(
1
??
?
Evolutionary equation
()
dt
d
B
B
Bh
dt
ds
p
a
o
o
?
?
?
?
?
?
?
?
?
?
?
=
where, B= 1-
*
s
s
o
and
n
p
kT
Q
A
dtd
ss
?
?
?
?
?
?
?
?
?
?
?
?
= exp
^*
?
130
Table 7.4 Linear isotropic material properties with vendor data for the underfill materials
Material E(psi) Poisson's ratio CTE (per ?C)
Silicon 23641000 0.278 2.50E-06
UF-1 1232800 0.25 3.30E-05
UF-2 812211 0.25 4.50E-05
UF-3 391602 0.25 6.10E-05
UF-4 449617 0.25 6.70E-05
Lead-free Solder 5729100 0.3 2.00E-05
Eutectic Solder 4163600 0.35 2.45E-05
Copper pad 18710000 0.34 1.63E-05
Cover film 500400 0.3 1.80E-05
Adhesive 1 105900 0.35 1.18E-04
Copper 9717500 0.34 1.70E-05
Adhesive 2 105900 0.35 1.18E-04
Base polyimide 500400 0.35 1.80E-05
Adhesive 3 159500 0.35 2.18E-04
Aluminum 10008000 0.3 2.30E-05
131
The constants of the Anand?s model for the simulation have been assigned
through the standard input for VISCO107 element in ANSYS
TM
. The value of the
constants used for modeling both the eutectic [Darveaux 2000] and lead-free [Amagai, et
al. 2002] solder material have been listed in the Table 7.5.
7.2.6 Inelastic Strain Energy Density
Several researchers have established inelastic strain energy density (ISED to be
the damage proxy for solder joint thermo-mechanical reliability of electronic packages.
Damage relationships correlating the solder joint life with the ISED accumulated per
thermal cycle by the solder joint have also been developed. These relationships can be
used for the life prediction of the electronic packages with solder joint cracking as the
failure mode. The ISED can be calculated from the simulation. In ANSYS
TM
VISCO107
element has plastic work (PLWK) as a standard output, ISED has been calculated in the
present study by volume averaging PLWK over the whole solder bump volume. Some
researchers volume average PLWK over the few layers in the vicinity of the interface
instead of the whole solder volume. Plastic work accumulated in the solder joint over the
complete thermal cycle has been found to be stabilized after the first cycle. Consequently
the simulation is run for only two cycles and the ISED is calculated based on the plastic
work accumulated during the second thermal cycle. ISED for the solder joint is given by:
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
=?
?
?
=
=
elementstotal
n
n
elementstotal
n
n
n
i
V
VW
ISEDW
_
1
_
1
)(
)(
132
Table 7.5 Values of the constants of Anand?s viscoplastic model
Anand's constants for solder
Pb-free Eutectic
Sn3.5Ag0.75Cu 62Sn36Pb2Ag
Value
ANSYS
Input
Model
Parameter
Value Definition
135.72 C1 So (psi) 1800 Initial Value of
Deformation Resistance
8400 C2 Q/k (1/K) 9400 Activation Energy /
Boltzmann.s Constant
4610000 C3 A (1/sec) 4000000 pre-exponential factor
0.038 C4 ? 1.5 multiplier of stress
0.162 C5 m 0.303 stain rate sensitivity of
stress
448000 C6 ho (psi) 200000 hardening constant
150.8 C7 s^ (psi) 2000 coefficient for deformation
resistance saturation value
0.0046 C8 n 0.07 Strain rate sensitivity of
saturation (deformation
resistance) value
1.56 C9 a 1.3 strain rate sensitivity of
hardening
133
where
)(n
W? is plastic work accumulated by n
th
element during the second
thermal cycle of the simulation and it is standard output in ANSYS
TM
for VISCO107
element in form of PLWK and
n
V
volume of the n
th
element.
7.3 Material Characterization of Underfill Materials
The material characterization of the underfill materials provided by the supplier
has been performed. The stress-strain curve for five different materials has been plotted
from the uni-axial tensile testing of the samples fabricated with the in house facilities
(Figure 7.6) at Auburn University. The elastic modulus for the linear range has also been
calculated in order to verify the vendor data. The simulations for 0-70?C ATC has been
run with both the vendor data and the measured properties in order to see the impact of
difference in the material properties on the plastic work accumulated in the solder joint
during the thermal cycle.
7.3.1 UF-1
UF-1 is a capillary flow underfill material with highest value of elastic modulus
and lowest value of CTE (coefficient of thermal expansion) among all the underfill
materials tested. The stress-strain curve from the test data has been plotted in Figure 7.7.
The samples were tested at the starin rate of 0.001 sec
-1
, as the strain rates encountered
during the ATC of flip-chip fall in this range.
The maximum strains encountered by the underfill during the simulation of both
0-70?C and 0-90?C thermal cycles had been measured in order to make sure that the
elastic properties used for the simulations falls within the linear range. The point P
1
and
134
Figure 7.6 Uniaxial test specimen and the assembly equipment used for the sample
preparation and cure.
Figure 7.7 Stress-strain plot from the uniaxial tensile test for UF-1 underfill material
135
P
2
corresponds the maximum strains encountered by the UF-1 underfill during 0-70?C
and 0-90?C ATC respectively. It can be seen that the maximum strain for 0-90? is about
3000 microns and this point falls well within the linear range of the stress-strain curve.
The contour plot of the strain distribution has been shown in the Figure 7.8. This shows
that the maximum strain occurs on the top edge of the underfill just below the silicon die.
The elastic modulus of the UF-1 underfill material for the linear region measured from
the uniaxial tensile test has been found to be 9.21 GPa which is a 8.35% higher than the
value of 8.5 GPa provided by the vendor
7.3.2 UF-2
UF-2 is also a capillary flow underfill with elastic modulus lower than the UF-1
underfill and the CTE higher. The stress strain curve from the uniaxial tensile test data
has been plotted in the Figure 7.9 and the test was again carried out at the strain rate of
0.001 sec
-1
. The points P
1
and P
2
plotted on the curve indicate the maximum strain
encountered during the 0-70? and 0-90?C test cycle simulation and it is seen that the
maximum strain during the 0-90?C test cycle is about 5000 microns which is higher than
the UF-1 underfill material but still it lies well within the linear range of the material.
The elastic modulus for the linear region measured from the uniaxial tensile test is 5.22
GPa which is 6.78% lower than the value of 5.6 GPa provided by the vendor.
7.3.3 UF-3
UF-3 is a reflow type underfill material with elastic modulus lower and the CTE
higher than the capillary flow underfill materials. The stress-strain curve from the
136
Figure 7.8 Strain distribution in UF-1 underfill with low gap height bump
137
Figure 7.9 Stress-strain plot from the uniaxial tensile test for the UF-2 underfill
138
uniaxial tensile test data has been plotted in the Figure 7.10. It is visible form the plot
that the maximum strain during the 0-90?C test cycle is around 5500 microns which lies
well within the linear range of the material. The elastic modulus of the UF-3 material for
the linear region measured from the uniaxial tensile test is 3.11 GPa which is 15.18%
higher than the value of 2.7 GPa provided by the vendor. Figure 7.11 shows the strain
distribution contour plot for the UF-3 underfill material with high bump gap height
configuration.
7.3.4 UF-4
UF-4 is also a reflow type underfill material with elastic modulus lower and the
CTE higher than the UF-3 underfill material. The stress-strain curve from the uniaxial
tensile test data has been plotted in the Figure 7.12. It is visible form the plot that the
maximum strain (5500 microns) goes just beyond the linear region of the material. But
still the linear isotropic material properties have been used in the simulation for the
approximation. Figure 7.13 shows the strain distribution in the UF-4 underfill material
from 0-90?C thermal cycle simulation.
It is seen from the Figure 7.13 that the maximum strain in case of the UF-4
material lies at the solder bump and underfill interface edge as compared to the die and
underfill interface edge in case of other underfill materials. The elastic modulus of the
UF-4 material for the linear region measured from the uniaxial tensile test is 2.53 GPa
which is 18.4% lower than the value of 3.1 GPa provided by the vendor.
139
Figure 7.10 Stress strain plot from uniaxial tensile test of UF-3 underfill material
140
Figure 7.11 Strain distribution contour plot in UF-3 underfill material with high gap
height bump configuration.
141
Figure 7.12 Stress strain plot from uniaxial tensile test of UF-4 underfill material
Figure 7.13 Strain distribution contour plot in UF-4 underfill material with low gap
height bump configuration
142
7.3.6 Effect of Measured Properties on the Simulation Results
The correct input of material properties in the FEA model is vital for getting
accurate results from the simulation. The simulations for 0-70?C ATC were run with
both the material properties measured in house as well as with the material data provided
by the vendor for the 15 different configurations provided by the vendor. Difference in
the simulation results can be observed from the Table 7.6.
Since higher value of ISED for the same configuration implies lower reliability,
thus except UF-1 underfill all the other three underfill give higher reliability with the
vendor data. So the models will under predict the solder joint reliability in case of UF-1
and over predict in other cases if the vendor data is used in the simulation.
7.4 Solder Joint Integrity in Accelerated Thermal Cycling
The most serious concerns in the flip-chip reliability is the solder interconnect
fatigue failure due to thermal cyclic loading. Due to the CTE mismatch within the
various components of the flip-chip package, stresses are developed in the component
whenever thermal cycling takes place. These stresses lead to the fatigue failure of the
component when the thermal cycling is continued for long. It has been established
through various experimental studies and field failure analysis that the solder
interconnect is the most susceptible to such fatigue failures. Due to this finite element
analysis and simulation of solder joint integrity becomes extremely important. In the
current study simulation of 0-70?C and 0-90?C ATC along with three different field
profiles has been done and presented in this chapter.
143
Inelastic Strain Energy
Density Per Cycle (psi) Test
Case
Solder
Composition
Underfill
Bump
Gap
Height
Bump
Size
(mils)
Computed
with Vendor
Data
Computed
with AU
Data
1 62Sn36Pb2Ag UF-4 Low 4 33.65 37.98
2 62Sn36Pb2Ag UF-1 High 4 10.75 10.65
3 62Sn36Pb2Ag UF-4 High 4 28.42 29.01
4 62Sn36Pb2Ag UF-4 Mid 4 29.73 31.05
5 62Sn36Pb2Ag UF-1 Low 4 12.49 12.13
6 62Sn36Pb2Ag UF-3 Mid 4 25.95 26.89
7 62Sn36Pb2Ag UF-2 High 4 16.52 16.65
8 62Sn36Pb2Ag UF-3 Mid 3 16.89 17.11
9 62Sn36Pb2Ag UF-3 Mid 3 28.22 27.19
10 Sn3.5Ag0.75Cu UF-3 High 4 14.09 14.06
11 Sn3.5Ag0.75Cu UF-3 Mid 3 15.80 15.86
12 Sn3.5Ag0.75Cu UF-4 High 4 25.52 25.67
13 Sn3.5Ag0.75Cu UF-4 Mid 3 29.40 30.05
14 Sn3.5Ag0.75Cu UF-3 High 4 22.66 22.31
15 Sn3.5Ag0.75Cu UF-3 Mid 3 26.48 25.82
Table 7.6 Simulation results for 0-70?C thermal cycle with vendor and measured data
144
7.4.1 0-70?C
The thermal profile shown in the Figure 7.14 has been simulated in ANSYS
TM
for
the analysis of solder joint integrity and the comparative study in order to see the effect of
various variations on the solder joint reliability. The cycle starts at the room temperature
(25?C) has a dwell of 12 mins at the extreme temperatures of 0?C and 70?C and the ramp
time between the extreme temperatures is 3 mins, therefore the total time period for the
cycle is 30 mins. Simulations for the eighteen different configuration listed earlier in the
section 2.1.2 have been run for this profile and the simulation results are listed in Table
7.7. Inelastic strain energy density averaged over the complete solder volume has been
calculated as discussed in section 2.6. Since ISED is a true indicator of the damage
accumulated by the solder joint, which leads to the crack initiation and finally failure of
the solder joint, so it has been used as the basis for the comparison of reliability for
different configurations of the flip-chip.
Figure 7.15 shows the distribution of the magnitude of the ISED accumulated in
the solder joint during one complete thermal cycle for test case 1 which consist of low
gap height eutectic solder bump with UF-1 underfill. It is visible that the magnitude of
the ISED accumulated is maximum at the top left corner of the bump, which indicates
that the crack would initiate at this location and than propagate, also there is a high ISED
accumulation region at the bottom right corner of the bump which implies a possibility of
secondary crack initiation in this region before the primary crack completely propagates.
Figure 7.16 and Figure 7.17 show the contour plot of the distribution of the ISED
accumulated and the Von-Mises stress in the solder bump. The plots shown here are for
test case 12 which consist of high gap height lead-free solder bump with UF-4
145
Figure 7.14 0-70?C accelerated thermal cycle profile
146
Table 7.7 Simulation results for 0-70?C accelerated thermal cycle
Test
Case
Solder
Composition
Underfill
Bump
Gap
Height
Bump
Size
(mils)
Normalized Inelastic
Strain Energy
Density per Cycle
1 62Sn36Pb2Ag UF-4 Low 4 4.415
2 62Sn36Pb2Ag UF-1 High 4 1.208
3 62Sn36Pb2Ag UF-4 High 4 3.543
4 62Sn36Pb2Ag UF-4 Mid 4 3.716
5 62Sn36Pb2Ag UF-1 Low 4 1.423
6 62Sn36Pb2Ag UF-3 Mid 4 3.487
7 62Sn36Pb2Ag UF-2 High 4 1.964
8 62Sn36Pb2Ag UF-2 Mid 3 2.024
9 62Sn36Pb2Ag UF-3 Mid 3 3.550
10 Sn3.5Ag0.75Cu UF-2 High 4 1.795
11 Sn3.5Ag0.75Cu UF-2 Mid 3 1.890
12 Sn3.5Ag0.75Cu UF-4 High 4 3.444
13 Sn3.5Ag0.75Cu UF-4 Mid 3 3.890
14 Sn3.5Ag0.75Cu UF-3 High 4 3.047
15 Sn3.5Ag0.75Cu UF-3 Mid 3 3.483
16 Sn3.5Ag0.75Cu UF-1 Low 4 1.045
17 Sn3.5Ag0.75Cu UF-1 Mid 4 1.012
18 Sn3.5Ag0.75Cu UF-1 High 4 1.000
147
Figure 7.15 Contour plot of nodal values of ISED in the solder bump for test case 1
Figure 7.16 Contour plot of the nodal values of the ISED accumulated in the solder
bump for test case 12
148
Figure 7.17 Contour plot of the nodal values of the Von-Mises stress in the solder bump
for test case 12
149
underfill. It is visible that the distribution for both the ISED accumulated and the Von-
Mises stress remains more or less the same but in this case it can be observed that the
region for the secondary crack has shifted from the bottom right (test case-1) to the top
right. This shift in the secondary crack location may speed up the failure, as now the
primary crack does not have to travel until the other end in order to cause a failure. It is
also seen that the contour plot of ISED follows almost the stress contour.
7.4.1.1 Effect of Solder Joint Material Composition
It is visible form the Figure 7.18 that the value of ISED accumulated per cycle for
eutectic solder bump is higher as compared to the lead-free bump for the capillary flow
UF-1 underfill material for both high gap and low gap height bumps. For eutectic solder
bumps the difference in the ISED accumulated between the high and low gap height
bump is higher as compared to the lead-free solder bumps.
The eutectic solder bumps have higher value of ISED than the lead-free bumps in
case of UF-2 underfilled flip-chip also for both the mid and high gap height bumps. But
the difference in the value of ISED between mid and high gap for UF-2 is higher in the
case of lead-free bumps. For both the re-flow encapsulant materials the ISED
accumulated in the solder joint per cycle is less for the lead-free bump. UF-4 is more
sensitive to the solder joint composition as far as the solder joint reliability is concerned.
7.4.1.2 Effect of Underfill Composition
Solder joint reliability is also sensitive to the undefill material, a trend of higher
reliability with the capillary flow encapsulants as compared to the re-flow encapsulants is
150
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
62Sn36Pb2Ag Sn3.5Ag0.75Cu
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High Gap
Low Gap
Figure 7.18 Normalized ISED for UF-1 underfill material with low and high gap height
bump diameter 4 mils
1.65
1.7
1.75
1.8
1.85
1.9
1.95
2
2.05
62Sn36Pb2Ag Sn3.5Ag0.75Cu
N
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High Gap
Mid Gap
Figure 7.19 Normalized ISED for UF-2 underfill material with mid (3 mils) and high (4
mils) gap height and bump diameter 4 mils
151
3.38
3.4
3.42
3.44
3.46
3.48
3.5
3.52
3.54
3.56
62Sn36Pb2Ag Sn3.5Ag0.75Cu
N
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UF-4
UF-3
Figure 7.20 Normalized ISED for UF-4 (4 mils) and UF-3 (3 mils) underfill material
with high and mid gap height solder bumps respectively
152
visible form the Figure 7.21 to Figure 7.23. Figure 7.21 shows the comparison of ISED
for three different underfill materials with eutectic solder bumps.
The value of ISED is higher for the re-flow encapsulants in the case of lead-free
solder bumps also (Figure 7.22 and Figure 7.23). UF-4 has the highest value of ISED
accumulated per cycle in the solder joint and the UF-1 capillary flow encapsulant has the
lowest. This implies that the flip chip encapsulated with the UF-1 underfill will have
maximum solder joint reliability.
7.4.1.3 Effect of Bump Gap Height
Figure 7.24 shows the normalized ISED accumulated by the eutectic solder joint
of three different gap heights for a flip-chip with UF-4 encapsulant. Trend of increasing
ISED with decreasing gap height is observed. It is also observed that the ISED increases
more drastically when the solder bump height is reduced from mid gap height to low gap
height as compared to the change from high gap height to mid gap height. Figure 7.25
shows the normalized ISED in case of lead-free solder with capillary flow underfill.
Same trend is also observed for the lead-free solder bumps with both reflow and capillary
flow encapsulant.
7.4.1.4 Effect of Bump Size
Two different bump sizes have been used for the simulation of the 18
configurations. The solder bump with the bigger size (4 mils) have lower ISED value
and thus higher reliability. Flip-chip with eutectic bumps and UF-3 re-flow
153
0
0.5
1
1.5
2
2.5
3
3.5
4
UF-1 UF-2 UF-4
N
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IS
ED
Figure 7.21 Normalized ISED for high gap height 4 mils eutectic solder bump with
different underfill materials
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
UF-1 UF-2 UF-3 UF-4
N
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Figure 7.22 Normalized ISED for mid gap height 3 mils lead-free solder bumps with
different underfill materials
154
0
0.5
1
1.5
2
2.5
3
3.5
4
UF-1 UF-2 UF-3 UF-4
N
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Figure 7.23 Normalized ISED for high gap height 4 mils lead-free solder bumps with
different underfill materials
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
High Mid Low
N
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Figure 7.24 Normalized ISED for 4 mils eutectic solder bumps with UF-4 underfill
material and different gap heights
155
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
High Mid Low
N
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IS
ED
Figure 7.25 Normalized ISED for 4 mils lead-free solder bumps with UF-1 underfill
material and different gap heights
156
encapsulant has been used (Figure 7.26) to show the effect of the bump size on the
thermal reliability.
7.4.1.5 Summary
? Lead-free solder have lower ISED compared to eutectic tin-lead solder for all
investigated underfills. However, this does not necessarily mean that lead-free
solder will have better reliability as the damage relationships for the two different
solder materials will be different.
? Increase in gap height lowers ISED for both eutectic and lead-free solders, this
means that the flip-chip with higher gap height will have higher reliability.
? For the underfills investigated, capillary flow underfills exhibit lower ISED as
compared to the reflow encapsulant for both eutectic as well as lead-free solders.
? Increase in the bump size lowers the ISED for both eutectic and lead-free solders.
7.4.2 0-90?C
Thermal profile shown in Figure 7.27 has been simulated for the analysis of solder
joint reliability when the flip-chip is subjected to 0-90?C ATC. The cycle starts at the
room temperature (25?C) has a dwell of 12 mins at the extreme temperatures of 0?C and
90?C and the ramp time between the extreme temperatures is 3 mins, therefore the total
time period for the cycle is 30 mins.
Simulations for the eighteen different configuration have been run for this profile
and the simulation results are listed in Table 7.8. Since the UF-4 underfill material has a
Tg (glass transition temperature) in the range of 70-75?C, so the it behaves very
157
3.45
3.46
3.47
3.48
3.49
3.5
3.51
3.52
3.53
3.54
3.55
3.56
3 mils 4 mils
N
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D
Figure 7.26 Normalized ISED for mid gap height eutectic solder bumps with UF-3
underfill with different bump diameter
158
Figure 7.27 0-90?C accelerated thermal cycle profile
159
differently as compared to the other underfill materials whose Tg is above 90?C. The
normalized ISED listed in the Table 7.8 has been evaluated considering the Tg of UF-4
above 90?C so that the Tg does not affect the relative comparison of the reliability of
various configurations. The effect of Tg of the underfill material on the solder joint
reliability has been analyzed separately.
7.4.2.1 Effect of Solder Joint Material Composition
It is observed form the Figure 7.28-7.31 that the lead-free solder bumps
accumulate higher ISED per cycle as compared to the eutectic solder bumps for all the
configurations. Thus there is a reversal in the trend for the 0-90? ATC as compared to the
trend for 0-70?C. This however does not necessarily mean higher reliability for the lead-
free solder bumps, as the reliability prediction depends on the damage relationship which
is different for both the solder compositions. This means that inspite of higher ISED
value the flip-chip with lead-free bump might exhibit higher reliability.
7.4.2.2 Effect of Underfill Composition
The reliability trend for the underfill composition when the flip-chip is subjected
to 0-90?C ATC remains the same as in case of 0-70?C ATC. Figures 7.32, 7.33 and 7.34
exhibit the trend of increased value of normalized ISED from capillary to re-flow
encapsulant for various configurations of the flip-chip.
160
Table 7.8 Simulation results for 0-90?C accelerated thermal cycle
Test
Case
Solder
Composition
Underfill
Bump
Gap
Height
Bump
Size
(mils)
Normalized
Inelastic Strain
Energy Density
per Cycle
1 62Sn36Pb2Ag UF-4 Low 4 3.354
2 62Sn36Pb2Ag UF-1 High 4 0.931
3 62Sn36Pb2Ag UF-4 High 4 2.678
4 62Sn36Pb2Ag UF-4 Mid 4 2.780
5 62Sn36Pb2Ag UF-1 Low 4 1.093
6 62Sn36Pb2Ag UF-3 Mid 4 2.710
7 62Sn36Pb2Ag UF-2 High 4 1.489
8 62Sn36Pb2Ag UF-2 Mid 3 1.548
9 62Sn36Pb2Ag UF-3 Mid 3 2.732
10 Sn3.5Ag0.75Cu UF-2 High 4 1.653
11 Sn3.5Ag0.75Cu UF-2 Mid 3 1.720
12 Sn3.5Ag0.75Cu UF-4 High 4 2.834
13 Sn3.5Ag0.75Cu UF-4 Mid 3 3.204
14 Sn3.5Ag0.75Cu UF-3 High 4 2.346
15 Sn3.5Ag0.75Cu UF-3 Mid 3 2.940
16 Sn3.5Ag0.75Cu UF-1 Low 4 1.115
17 Sn3.5Ag0.75Cu UF-1 Mid 4 1.030
18 Sn3.5Ag0.75Cu UF-1 High 4 1.000
161
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
62Sn36Pb2Ag Sn3.5Ag0.75Cu
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High Gap
Low Gap
Figure 7.28 Normalized ISED for UF-1 underfill material with low and high gap height 4
mils solder bumps
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
62Sn36Pb2Ag Sn3.5Ag0.75Cu
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High Gap
Mid Gap
Figure 7.29 Normalized ISED for UF-2 underfill material with mid (3 mils) and high (4
mils) gap height 4 mils solder bumps
162
2.5
2.55
2.6
2.65
2.7
2.75
2.8
2.85
2.9
2.95
3
62Sn36Pb2Ag Sn3.5Ag0.75Cu
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UF-4
UF-3
Figure 7.30 Normalized ISED for UF-4 (4 mils) and UF-3 (3 mils) underfill material
with high and mid gap height solder bumps respectively
0
0.5
1
1.5
2
2.5
3
UF-1 UF-2 UF-4
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IS
ED
Figure 7.31 Normalized ISED for high gap height 4 mils eutectic solder bump with
different underfill materials
163
0
0.5
1
1.5
2
2.5
3
3.5
UF-1 UF-2 UF-3 UF-4
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Figure 7.32 Normalized ISED for mid gap height 3 mils lead-free solder bumps with
different underfill materials
0
0.5
1
1.5
2
2.5
3
UF-1 UF-2 UF-3 UF-4
N
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Figure 7.33 Normalized ISED for high gap height 4 mils lead-free solder bumps with
different underfill materials
164
7.4.2.3 Effect of Bump Gap Height
It is observed from the Figure 7.34 and 7.36 that the normalized ISED is much
more sensitive to bump height in case of lead-free solder bumps as compared to the
eutectic solder bumps. However, the effect of bump height on the solder joint reliability
for both eutectic and lead-free solder in the case of 0-90?C ATC remains the same as in
case of 0-70?C ATC. The ISED value decreases with the increase in the bump gap
height.
7.4.2.4 Effect of Bump Size
The 4 mil bump exhibits higher reliability than the 3 mil bump which was also
true in case of 0-70?C ATC. Also the bump with larger size will have larger crack length
so it will take longer for the crack to propagate throughout the solder joint before the
failure occurs. Thus both the effects will be coupled and will add up to the solder joint
reliability. The effect of bump size on the normalized ISED of the solder joint is shown
in the Figure 7.36.
7.4.2.5 Summary
? For 0-70?C ATC the eutectic solders had higher ISED as compared to the lead-
free solder, but in the case of 0-90?C ATC a reversal in the trend has been
observed. The lead-free solder has higher ISED as compared to the eutectic
solder.
? Decrease in gap height increases the ISED and this has greater impact on the lead-
free solders for both capillary flow and re-flow underfill materils.
? Increase in the bump size reduces the ISED.
165
0
0.5
1
1.5
2
2.5
3
3.5
4
High Mid Low
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Figure 7.34 Normalized ISED for 4 mils eutectic solder bumps with UF-4 underfill
material and different gap heights
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
High Mid Low
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IS
ED
Figure 7.35 Normalized ISED for 4 mils lead-free solder bumps with UF-1 underfill
material and different gap heights
166
2.695
2.7
2.705
2.71
2.715
2.72
2.725
2.73
2.735
3 mils 4 mils
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Figure 7.36 Normalized ISED for mid gap height eutectic solder bumps with UF-3
underfill with different bump diameter
167
7.4.3 Effect of Tg (glass transition temperature) of the Underfill Material
Material properties like CTE and elastic modulus change drastically once the
working temperature of the material rises beyond the Tg of that material. The material
properties of the underfill have a very significant impact on the solder joint reliability,
thus it is advisable to use the underfill material which has Tg above the working
temperature of the component. UF-4 has a Tg in the range of 70-75?C therefore
simulations for special test cases of the UF-4 with modified properties were run in order
to understand the effect of Tg on the solder joint reliability.
Four different material models listed in the Table 7.10 have been considered for
the analysis. The material model D represents the actual behavior of the UF-4 underfill.
Model C represents the behavior of UF-4 in case the Tg of UF-4 is above 90?C. The
results from the simulation are listed in the Table 7.9, which shows that the ISED value
for the UF-4 reduces to 0.18X if the Tg of the UF-4 material is above 90?C for the 0-
90?ATC. The simulation run for the various temperature ranges show that there is drastic
increase in the ISED once the operating temperature goes above the Tg range. The
increase of the maximum temperature from 70?C to 75?C leads to a increase in the ISED
value by 5.4X.
168
Table 7.9 Simulation results for the analysis of the effect of Tg on solder joint reliability
Temp
Cycle
Material
Model
Normalized
ISED
0-90?C A 206.63
0-90?C B 64.4
0-90?C C 51.85
0-70?C D 33.65
0-75?C D 182.02
0-80?C D 191.75
0-85?C D 257.49
0-90?C D 289.72
Table 7.10 Material model data used for simulation
A B C D
Temp
(?C)
CTE
(ppm)
E
(Gpa)
CTE
(ppm)
E (Gpa) CTE
(ppm)
E (Gpa) CTE
(ppm)
E
(Gpa)
25 67 3.1 67 3.1 67 3.1 67 3.1
50 67 3.1 67 3.1 67 3.1 67 3.1
70 67 3.1 67 3.1 67 3.1 67 3.1
75 281 3.1 100 3.1 67 3.1 281 0.74
80 281 3.1 100 3.1 67 3.1 281 0.74
90 281 3.1 100 3.1 67 3.1 281 0.74
169
7.4.4 Field Profiles
Three different field profiles acquired by the hard drive manufacturer for different
field applications were used for the simulation and the analysis of solder joint reliability.
Simulations were run with all the three field profiles. Again the ISED has been used as
the index of the damage for comparison for relative solder joint reliability comparison.
7.4.4.1 Profile 1
Profile 1 is an averaged thermal duty cycle for 4 hrs of writing and 30 minutes of
reading. The temperature profile shown in the Figure 7.37 has been simulated for the
analysis. This thermal cycle has a 4 hour dwell at the high temperature of 87?C and two
quick ramp-up of 1sec from 63?C to 87?C and 2 seconds from 87?C to 63?C and has a
slow ramp of 30 minutes from 63?C to 58?C. Since the UF-4 material has Tg in the
range of 70-75?C which is below the operating range of the field profile so for the
configurations with UF-4 underfill material test cases were run with the actual material
model i.e. Tg in the range of 70-75?C and the ideal case with Tg above the operating
range. The values in the parenthesis in the results table are for the ideal test case, in
which the Tg of the UF-4 is considered to be above the operating range of 87?C. The
simulation result for the profile-1 for all the 18 configurations has been listed in the Table
7.11.
170
Figure 7.37 Temperature profile of the averaged thermal duty cycle 1
171
Table 7.11 Simulation results for field profile 1
Test
Case
Solder
Composition
Underfill Bump
Gap
Ht.
Bump
Size
(mils)
Normalized Inelastic
Strain Energy
Density per Cycle
1
62Sn36Pb2Ag
UF-4 Low 4 434.6 (13.5)
2
62Sn36Pb2Ag
UF-1 High 4 3.89
3
62Sn36Pb2Ag
UF-4 High 4 345.28 (11.12)
4
62Sn36Pb2Ag
UF-4 Mid 4 360.98 (11.7)
5
62Sn36Pb2Ag
UF-1 Low 4 4.59
6
62Sn36Pb2Ag
UF-3 Mid 4 11.19
7
62Sn36Pb2Ag
UF-2 High 4 6.87
8
62Sn36Pb2Ag
UF-2 Mid 3 7.10
9
62Sn36Pb2Ag
UF-3 Mid 3 11.37
10
Sn3.5Ag0.75Cu
UF-2 High 4 3.47
11
Sn3.5Ag0.75Cu
UF-2 Mid 3 3.99
12
Sn3.5Ag0.75Cu
UF-4 High 4 332.39 (6.52)
13
Sn3.5Ag0.75Cu
UF-4 Mid 3 352.32 (8.22)
14
Sn3.5Ag0.75Cu
UF-3 High 4 5.90
15
Sn3.5Ag0.75Cu
UF-3 Mid 3 7.38
16
Sn3.5Ag0.75Cu
UF-1 Low 4 1.98
17
Sn3.5Ag0.75Cu
UF-1 Mid 4 1.90
18
Sn3.5Ag0.75Cu
UF-1 High 4 1.89
172
7.4.4.2 Profile 2
Profile 2 is an averaged thermal duty cycle for 10 minutes of writing, 2 minutes of
reading and 8 minutes of rest. The temperature profile shown in the Figure 7.38 has been
simulated for the analysis. This thermal cycle has a 10 minute dwell at the high
temperature of 82?C, 2 minute dwell at 58?C and 8 minute dwell at 50?C with ramp time
of 1 seconds from each dwell temperature to the next dwell temperature. The
temperature profile shown in the Figure 7.38 has been simulated for the analysis and the
simulation result for this profile is listed in Table 7.12.
7.4.4.3 Profile 3
Profile 3 is a very short time duration profile. It provides highly accelerated
testing in terms of time as the number of ATC that a component undergoes while thermal
cycling with Profile 3 is very high for a given period of time. The temperature profile
shown in Figure 7.39 has been used for the simulation purpose. There are two dwell
periods in this profile at a high temperature of 82?C and low temperature of 50?C
respectively. Ramp time of 1 second has been used for going from one dwell temperature
to the other. The result from the simulations run for all the 18 test cases has been listed in
the Table 7.13. The normalized ISED per cycle values indicated in the parenthesis are
for the ideal case of UF-4 underfill material considering that the Tg of the UF-4 is above
the maximum temperature of 82?C during the thermal cycling.
173
Figure 7.38 Temperature profile of the averaged thermal duty cycle 2
Figure 7.39 Temperature profile of the averaged thermal duty cycle 3
174
Table 7.12 Simulation results for the field profile 2
Test
Case
Solder
Composition
Underfill Bump
Gap
Height
Bump
Size
(mils)
Normalized Inelastic
Strain Energy
Density per Cycle
1
62Sn36Pb2Ag
UF-4 Low 4 358.55 (13.54)
2
62Sn36Pb2Ag
UF-1 High 4 3.97
3
62Sn36Pb2Ag
UF-4 High 4 281.46 (11.72)
4
62Sn36Pb2Ag
UF-4 Mid 4 322.17 (12.17)
5
62Sn36Pb2Ag
UF-1 Low 4 4.59
6
62Sn36Pb2Ag
UF-3 Mid 4 11.43
7
62Sn36Pb2Ag
UF-2 High 4 6.52
8
62Sn36Pb2Ag
UF-2 Mid 3 6.81
9
62Sn36Pb2Ag
UF-3 Mid 3 11.94
10
Sn3.5Ag0.75Cu
UF-2 High 4 3.17
11
Sn3.5Ag0.75Cu
UF-2 Mid 3 3.67
12
Sn3.5Ag0.75Cu
UF-4 High 4 258.96 (6.83)
13
Sn3.5Ag0.75Cu
UF-4 Mid 3 311.62 (8.51)
14
Sn3.5Ag0.75Cu
UF-3 High 4 6.17
15
Sn3.5Ag0.75Cu
UF-3 Mid 3 7.64
16
Sn3.5Ag0.75Cu
UF-1 Low 4 1.59
17
Sn3.5Ag0.75Cu
UF-1 Mid 4 1.58
18
Sn3.5Ag0.75Cu
UF-1 High 4 1.57
175
Table 7.13 Simulation results for the field profile 3
Test
Case
Solder
Composition
Underfill Bump
Gap
Height
Bump
Size
(mils)
Normalized Inelastic
Strain Energy
Density per Cycle
1 62Sn36Pb2Ag UF-4 Low 4 224 (4.71)
2 62Sn36Pb2Ag UF-1 High 4 1.23
3 62Sn36Pb2Ag UF-4 High 4 221 (4.62)
4 62Sn36Pb2Ag UF-4 Mid 4 223 (4.65)
5 62Sn36Pb2Ag UF-1 Low 4 1.40
6 62Sn36Pb2Ag UF-3 Mid 4 4.41
7 62Sn36Pb2Ag UF-2 High 4 2.30
8 62Sn36Pb2Ag UF-2 Mid 3 2.60
9 62Sn36Pb2Ag UF-3 Mid 3 5.09
10 Sn3.5Ag0.75Cu UF-2 High 4 1.12
11 Sn3.5Ag0.75Cu UF-2 Mid 3 1.36
12 Sn3.5Ag0.75Cu UF-4 High 4 204 (2.73)
13 Sn3.5Ag0.75Cu UF-4 Mid 3 222 (3.63)
14 Sn3.5Ag0.75Cu UF-3 High 4 2.63
15 Sn3.5Ag0.75Cu UF-3 Mid 3 3.45
16 Sn3.5Ag0.75Cu UF-1 Low 4 0.64
17 Sn3.5Ag0.75Cu UF-1 Mid 4 0.58
18 Sn3.5Ag0.75Cu UF-1 High 4 0.58
176
7.4.4.4 Relative Damage Index
Relative damage index gives the indication of the comparative damage inflicted
per cycle on the solder joint by the three different field profiles. The Figures 7.41 to 7.44
show the plot of the relative damage index for the three field profiles for different
configurations of the flip-chip. It is observed that for most of the configurations the
damage done by the filed profile 1 is the highest and the damage done by the profile 3 is
the lowest. The reason behind this being the difference in the dwell period among the
profiles. Profile 1 has the maximum dwell period as compared to the other two profiles.
Since the solder joint creeps during the dwell period which results in the accumulation of
the non-linear plastic work, thus the ISED accumulated by the solder joint due to the
profile 1 is maximum. This means that the profile 1 will have the highest acceleration
factor in terms of life in cycles, however this does not mean that the profile 1 will have
the highest acceleration factor in terms of the time.
The life prediction in the section 5 shows that the solder joint life in terms of time
is lowest for the profile 3. In spite of the lowest damage index value of the profile 3 it
accumulates highest damage in terms of time because the ISED accumulates itself in the
solder joint after every consequent cycle and since the cycle time for profile 3 (1 min 12
secs) is minimum as compared to the profile 1 (4 hrs 30 mins 3 secs) and profile 2
(20mins 3 secs) so the component is subjected to much higher number of cycles in case
of profile 3 as compared to the other two profiles. This results in accumulation of higher
amount of ISED in case of profile 3 for the same period of time, which means that the
components would take more number of cycles to fail when subjected to profile 3 but still
in terms of time the profile 3 will cause failures much earlier than the other 2 profiles.
177
Table 7.14 Simulations results for evaluation of relative damage index of the three field
profiles provided by the vendor
Underfill Solder
Bump
Size
Normailzed Inelastic
Strain Energy Density
(psi) Tg effect
(mils)
Profile
1
Profile
2
Profile
3
UF-2
Sn3.5Ag0.75Cu
4 2.70 2.61 1.00
UF-3 Sn3.5Ag0.75Cu 4 4.61 4.73 2.24
UF-4
Sn3.5Ag0.75Cu
4 5.13 5.23 2.32 Tg > 87?C
UF-4
Sn3.5Ag0.75Cu
4 213.36 188.13 157.31 Tg = 70-75?C
178
2.70
2.61
1.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Profile-1 Profile-2 Profile-3
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Figure 7.40 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-2 capillary flow encapsulant
4.61
4.73
2.24
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Profile-1 Profile-2 Profile-3
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Figure 7.41 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-3 re-flow encapsulant
179
5.13
5.23
2.32
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Profile-1 Profile-2 Profile-3
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I
S
ED
Figure 7.42 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-4 re-flow encapsulant with Tg
assumed to be above 87?C
213.36
188.13
157.31
0.00
50.00
100.00
150.00
200.00
250.00
Profile-1 Profile-2 Profile-3
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I
SED
Figure 7.43 Relative damage index of the three field profiles for the lead-free solder
bumps with high gap height, bump size 4 mils and UF-4 re-flow encapsulant with Tg
assumed to be in the range of 70-75?C
180
7.5. Life Prediction and Field Life Correlation with ATC Life
Life prediction is a very essential part of the product design and manufacturing for
the upfront reliability assessment in order to manufacture robust assemblies that will meet
product life requirements. Modeling and ATC tests are employed for this purpose. Finite
element modeling and analysis has been used in the current work in order to analyze the
solder joint reliability and copper trace integrity.
7.5.1 Theory
Development of life prediction modeling involves several steps as mentioned
below:
? Determination of accurate thermal cycle (ATC) in order to simulate the field
condition and same failure mechanism as encountered in the field. Energy
partitioning method has been used in the FEA for the determination of the correct
ATC.
? Acquisition of actual test data on the components subjected to ATC with the
various failure mechanisms encountered. Actual test failure data provided by the
Vendor has been used to determine the constants and the scaling factors for the
life prediction.
? Constitutive equations and , material properties for the applicable range of stress-
strain conditions. Constitutive equations from the published literature and the
material properties measured at Auburn Univeristy has been used in the present
study.
181
? Simulations for calculating the ISED for the life prediction of the solder joints has
been done in ANSYS
TM
using a 3-D diagonal slice model as described in section
2.
? Development of the correlation between the damage parameter and life of the
package.
? Determination of correct acceleration factor correlating the field life to the ATC
life. Mapping based on the statistical analysis has been used in order to determine
the correct acceleration factors.
7.5.2 Energy Partitioning Methodology
Determination of accurate ATC and correct acceleration factor for the
experimental testing for the thermo-mechanical reliability assessment of the electronic
package is extremely important. The flow chart in the Figure 7.44 describes the
methodology used for the energy partitioning for determination of correct ATC.
Different ATCs induce different failure modes in the component, it is extremely critical
to match failure mode induced in the ATC to the failure mode encountered in the field
application for the accurate life prediction. In case the failure mode induced in the ATC
is different than the one encountered in the field application, then there is no way to
predict actual life of the component based on the ATC testing and it?s not possible to
establish a correlation between the field life and the life of the component subjected to
ATC. The damage or the strain energy accumulated in the solder joint during it?s life
which causes it to crack and finally fail can be divided into two portions, one due to the
182
Figure 7.44 Energy partitioning methodology flowchart
183
time independent plastic deformation and the second due to the time dependent creep
deformation.
The philosophy behind the application of energy partitioning methodology for
development of field life correlation and solder joint life prediction is that in order to
induce the same failure mode in the ATC as encountered in the field, the ratio of the
ISED accumulated due to both time dependent plastic and time independent creep
deformation has to remain the same. The energy partitioning methodology allows to
separate the contribution of both the factors, thus enabling the user to determine the ratio
of both the contributions towards the total ISED. Thus by matching the ratio one can
determine the correct ATC for the accelerated testing of a component.
In order to separate the effect of plastic and creep deformation, a separate creep
model and plasticity model have to be used in ANSYS
TM
instead of the Anand?s
viscoplasticity model. Anand?s model combines both the effects in form of evolution and
flow equations, preventing the user from separating the two effects.
Time Dependent Creep Model The Garofalo?s equation (7.1) has been used as a
constitutive model for the solder in the simulation for representing the time dependent
creep.
?
?
?
?
?
??
=
RT
Q
A
n
exp)][sinh(???& (7.1)
The constants in the Garofalo equation used for both the 62Sn36Pb2Ag solder and the
lead-free solder (Sn3.5Ag0.75Cu ) have been listed in the Table 7.15.
184
Time Independent Plasticity Model The time independent plasiticity of the solder joint
has been modeled in ANSYS
TM
using the linear and non-linear MISO (multilinear
isotropic hardening) option. The MISO option is preferred for the large strain cycling.
The MISO option allows user to specify up to 20 temperature-dependent stress-strain
curves. The uniaxial behavior is described by a piece-wise linear total stress-total strain
curve, starting at the origin, with positive stress and strain values. The curve has to be
continuous from the origin through 100 (max) stress-strain points. The slope of the first
segment of the curve must correspond to the elastic modulus of the material and no
segment slope should be larger. No segment can have a slope less than zero. The data
collected from the uniaxial tensile test conducted at Auburn University has been used for
modeling both the linear elastic and multilinear isotropic hardening. Figure 7.45 shows
the linear elastic modulus used for the simulation in ANSYS
TM
.
The MISO data for the eutectic solder has been input for the three different
temperatures, T1= -25?C, T2= 25?C and T3= 85?C. The plot of the stress-strain data
input in the ANSYS
TM
for the three temperatures has been shown in the Figure 7.46.
Temperature dependent non-linear elastic modulus has been used for the lead-free
solder material, Figure 7.47 shows the plot of the elastic modulus data input in the
ANSYS
TM
for the simulation. The MISO data for the lead-free solder has been input for
the five different temperatures, T1= 0?C, T2= 25?C, T3= 50?C, T4= 75?C and T5=
100?C. The plot of the stress-strain data input in the ANSYS
TM
for all the five
temperatures has been shown in the Figure 7.48.
185
Table 7.15 Constants used for the time dependent creep model of the solder
Solder Alloy A ? n Q
62Sn36Pb2Ag [Zahn 2003] 10 0.001379 2.0 5401.2
Lead-free [Wiese, et al. 2001] 277984 1.688E-4 6.41 6500.0
Figure 7.45 Temperature dependent linear elastic modulus of the eutetctic solder
material
186
Figure 7.46 Temperature dependent stress-strain data for modeling multilinear isotropic
hardening of the 62Sn36Pb2Ag solder material
Figure 7.47 Temperature dependent linear elastic modulus of the lead-free solder
material
187
Figure 7.48 Temperature dependent stress-strain data for modeling multilinear isotropic
hardening of the lead-free solder material
188
7.5.2.1 Hysteresis Loop
The shear stress-strain data from the simulation has been plotted to analyze the
hysteresis loops for solder joint with both the capillary flow and re-flow encapsulants,
when subjected to the three field profiles. The hysteresis loop shows the amount of the
non-linear plastic work accumulated by the solder joint during the thermal cycle. The
ISED accumulated by the solder joint during the thermal cycle is given by the area
enclosed within the hysteresis loop for that cycle. Hysteresis loop also shows the manner
in which the solder joint behaves when subjected to the thermal cycle. The vertical line
region in the hysteresis loop shows the stress relaxation taking place during the dwell
periods of the cycle. This is the region where the creep takes place within the solder
joint. The region of horizontal or the inclined line shows the plastic deformation
happening during the ramps.
The stress-strain data during the thermal cycling of the flip-chip has been taken
from the simulation run in ANSYS
TM
. The top left corner element with the maximum
strain has been used for the output of the stress-strain data. Hysteresis loop has been
plotted from this stress-strain data for all the three field profiles. Figure 7.49a, 7.50b and
7.50c shows the hysteresis loop plot for the capillary flow encapsulant subjected to field
profile 1, 2 and 3 respectively. Figure 7.50a, 7.50b and 7.50c show the hysteresis loop
plot in the case of re-flow encapsulant. It is visible form the hystersis loops for both the
capillary flow and the re-flow underfill materials that the plastic work or the ISED
accumulated per cycle in the solder joint is maximum for the profile 1 and minimum for
the profile 3.
189
Figure 7.49a Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-2 capillary
flow encapsulant subjected to field profile 1
Figure 7.49b Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-2 capillary
flow encapsulant subjected to field profile 2
190
Figure 7.49c Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-2 capillary
flow encapsulant subjected to field profile 3
Figure 7.50a Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-4 reflow
encapsulant subjected to field profile 1
191
Figure 7.50b Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-4 reflow
encapsulant subjected to field profile 2
Figure 7.50c Hysteresis loop for the Sn3.5Ag0.75Cu solder bump with UF-4 reflow
encapsulant subjected to field profile 3
192
7.5.3 Fatigue Life Prediction Models
Fatigue life prediction models, also known as the damage relationships have been
used to correlate the life of the solder joint to the strain energy density or the strain
(plastic, creep or total strain) accumulated during each ATC.. Several strain energy and
strain based life prediction models for the eutectic solder have been used by the
researchers in the past and published in the literature. The life prediction models
developed for the lead-free solder are very few.
7.5.3.1 Eutectic (SnPbAg) Solder
Some of the fatigue life prediction models for eutectic solder published in the
literature are listed below:
1. Engelmaier?s [1983] Model based on total shear strain range
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
cT
f
N
1
65.02
1 ?
Ductility exponent, c = -0.442 -6?10-4(Tmean) +1.72?10-2Ln(1+?)
where, Tmean is the mean temperature and ? is the cycling frequency
2. Solomon?s [1986] low cycle fatigue model based on plastic shear strain range
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
5.0
1
36.1
p
p
N
?
3. Knecht and Fox?s [1991]model based on creep shear strain range
c
c
N
??
=
9.8
193
4. Pang?s [1997] model based on Miner?s superposition rule of creep-fatigue
interaction
1
11
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
=
pc
T
NN
N
5. Morrow?s energy based fatigue model modified by Spraul, et al. [2004]
2
)(
1
C
f
WCN ?=
where, C
1
= 537.15, C
2
= -1.0722
6. Shi et al?s [2000] frequency modified model based on total strain range
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
m
t
h
f
C
N
1
)1(
?
?
where,
m = 0.731 ?(1.63?10-4)T +(1.392?10-6)T2 ?(1.15?10-8)T3
C = 2.122 ?(3.57?10-3)T +(1.329?10-5)T2 ?(2.502?10-7)T3
h = 0.919 ?(1.765?10-4)T ?(8.634?10-7)T2
? = 0.0139
7. Shi et al?s [1999] frequency modified model based on Morrow?s energy model
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
mh
f
W
C
N
1
)1(
?
?
where, m = 0.7, C = 1.69, h = 0.9
8. Darveaux?s [2000] energy based model with CAVE modified constants
da/dN
a
NN
0e
+=
where,
194
?a? is the joint diameter at the interface
2
10
K
W)(KN ?=
is the number of cycles for crack initiation
4
W)(K
dN
da
K
3
?= is the crack propagation rate
The value of the constants K
1
, K
2
, K
3
and K
4
used for calculation of characteristic life
cycles are given in Table 7.16.
7.5.3.2 Lead-free (SnAgCu) Solder
Some of the fatigue life prediction models for lead-free solder published in the
literature are listed below:
1. Shi et al?s [2000] frequency modified Coffin-Manson model based on total strain
range fitted by Pang [2004]
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
m
t
h
f
C
N
1
)1(
?
?
where, m = 0.93, C = 12.9, h = 0.95,
2. Shi et al?s [1999] frequency modified model based on Morrow?s energy model
fitted by Pang [2004]
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
m
h
f
W
C
N
1
)1(
?
where, m = 0.877, C = 1487.3, h = 0.82
3. Morrow?s energy based fatigue model fitted by Lau et al. [2004]
2
)(
1
C
f
WCN ?=
where, C
1
= 18.15, C
2
= -1.96
195
Table 7.16 Constants for the damage relationship
K
1
(cycles/psi
K
2
)
K
2
K
3
(in/cycle/psi
K
4
)
K
4
Lall, et al. [2004] 28769 -1.53 6x10
-7
0.7684
Darveaux [2000] 48300 -1.64 3.8x10
-7
1.04
196
7.5.4 Field Profile Based Fatigue Life Prediction
Solder joint fatigue life prediction for all the eighteen configurations for the three
different field profiles provided by the vendor has been done. The experimental failure
data for the Profile 3 provided by the vendor (Table 7.17) has been used for the Weibull
plot and calculation of constants and scaling factors for the fatigue life prediction for all
the three profiles. UF-4L and UF-4H is for the re-flow (UF-4) encapsulant with low and
high gap height respectively. VAR1 and VAR2 indicate UF-4 underfill material with
different size of filler material. The solder joint fatigue life prediction for the test cases
with eutectic bumps has been done using both Darveaux?s model modified with CAVE
constants as well as Morrow?s model. In case of lead-free alloy predictions using only
Morrow?s model has been presented.
7.5.4.1 Profile-1
Table 7.18 lists the predicted life from the simulation results for all the 18 test
cases subjected to profile-1.
7.5.4.2 Profile-2
The solder joint fatigue life prediction from the simulation, for the 18 test cases
when subjected to field profile 2 has been listed in Table 7.19.
7.5.4.3 Profile-3
Life prediction in the case of field profile 3 has been listed in Table 7.20.
197
Table 7.17 Failure data for profile 3 provided by the vendor
Test
Case
No. of
Failures
Total Units
in Test
Characterstic Life
(Hrs)
Characterstic Life
(Cycles)
UF-1 0 8 - -
UF-2 0 8 - -
UF-4L 6 6 790 39500
UF-4H 5 5 675 33750
VAR1 8 8 249 12450
VAR2 8 8 441 22050
198
Table 7.18 Predicted life for all 18 test cases for field profile 1
Test
Case
Scaled Fatigue Life Based
on Darveaux's Model with
CAVE Constants
Scaled Fatigue Life Based
on Morrow's Model
cycles hours cycles hours
1 2036 9163 1620 7288
2 120915 544117 254340 1144528
3 2416 10874 2073 9327
4 2337 10519 1976 8893
5 101148 455168 212992 958462
6 41001 184507 81922 368651
7 66415 298870 138221 621993
8 54934 247206 133425 600415
9 33741 151838 80533 362397
10 124250 559125
11 109929 494680
12 2273 10230
13 2160 9721
14 78006 351027
15 64103 288464
16 203231 914539
17 210716 948223
18 211694 952622
199
Table 7.19 Predicted life for all 18 test cases for field profile 2
Test
Case
Scaled Fatigue Life Based
on Darveaux's Model with
CAVE Constants
Scaled Fatigue Life Based
on Morrow's Model
cycles hours cycles hours
1 2036 11748 3916 9953
2 120915 591334 197111 1244242
3 2416 14082 4694 12902
4 2337 12725 4242 11162
5 101148 505743 168581 1064958
6 41001 200879 66960 400397
7 66415 350293 116764 730957
8 54934 287174 95725 697634
9 33741 160631 53544 382088
10 672521 224174
11 591457 197152
12 14149 4716
13 12029 4010
14 375020 125007
15 310930 103643
16 1231714 410571
17 1238548 412849
18 1245464 415155
200
Table 7.20 Predicted life for all 18 test cases for field profile 3
Test
Case
Scaled Fatigue Life Based
on Darveaux's Model with
CAVE Constants
Scaled Fatigue Life Based
on Morrow's Model
cycles hours cycles hours
1 33458 669 (790) 33266 665 (790)
2 4588994 91780 8821451 176429
3 33778 676 (675) 33716 674 (675)
4 33572 671 33426 669
5 3920391 78408 7678171 153563
6 1055782 21116 2243723 44874
7 2180067 43601 4509119 90182
8 1703533 34071 3953683 79074
9 788387 15768 1923949 38479
10 3349661 66993
11 2825215 56504
12 34945 699
13 32334 647
14 1584396 31688
15 1248814 24976
16 5471989 109440
17 5965388 119308
18 5965388 119308
201
7.6 Copper Trace Integrity
Copper trace failure mode is another critical failure mode in the flip-chip devices
and other electronic packages. Since the copper trace has negligible effect on the solder
joint reliability so the copper trace was ignored in the solder joint integrity analysis.
7.6.1 Model Description
A copper trace of 0.7mils thick and 2 mils wide has been added to the 3-D
diagonal slice model. Four models with low gap height bump and 4 mils pad have been
generated for all the four different underfill materials for the copper trace integrity
analysis. For the simplicity of the model the underfill fillet was initially not considered in
the model (Figure 7.51). Later an underfill fillet (Figure 7.52) was also added for the
accuracy of the result.
7.6.2 Von-Mises Stress Comparison for Different Underfill Materials
The Von Mises stress contour plot (Figure 7.53) in the case of the model without
underfill fillet shows the stress concentration in the copper trace in the region outside the
underfill away from the die edge. The actual copper trace failure however occurs at the
die edge just below the underfill fillet. Since the FEA without the underfill fillet was not
able to simulate the actual failure thus the model was recreated with an underfill fillet for
the better results.
Simulation with the underfill fillet showed the high stress region below the
underfill fillet, which is also the location of failure in field and experimental testing. This
generates the confidence in model. The values of maximum Von Mises stress from the
202
Figure 7.51 Close-up view of the flip-chip model with the copper trace, without underfill
fillet
Figure 7.52 Close-up view of the flip-chip model with the copper trace with underfill
fillet
203
Figure 7.53 Von Mises stress contour plot of the copper trace without underfill fillet
Table 7.21 Maximum Von Mises stress from the model with fillet and without fillet
Underfill
Material
Max Stress (Psi)
Von Mises
with fillet w/o fillet
UF-1 35821 40057
UF-2 35577 38073
UF-3 34092 34604
UF-4 34344 34945
204
simulation run without fillet is higher by approximately 10% than the values of the model
with fillet.
Figure 7.54 and 7.57 show the stress contour plots for the models with fillet for 0-
70?C ATC, it is visible form the plots that the high stress region occurs just below the
underfill fillet in all the cases. Von Mises stress has been used for the plots and the
comparison of stresses because Von Mises stress is the failure criterion for the failure of
ductile materials under fatigue
In all 16 simulations have been run for two different ATC profiles for all the four
underfill materials with eutectic as well as lead-free solder bumps. The results have been
listed in Table 7.22 The results indicate that there is hardly any difference in the value of
max. stress of the copper trace between the eutectic and the corresponding lead-free
cases, the stresses for lead-free being slightly higher than the eutectic cases.
The ultimate tensile strength of oxygen free electronic copper is in the range of
32054 to 65993 psi and the tensile yield strength is in the range of 10008 to 52940 psi.
Thus the copper trace failure is predicted for all the test cases in case of the -55 to 125?C
ATC but it may not fail when the flip-chip is subjected to 0-70?C ATC.
205
Figure 7.54 Stress distribution contour plot for UF-2 (capillary flow) and UF-3 (re-flow)
underfill
Figure 7.55 Stress distribution contour plot for UF-4 (re-flow) and UF-1 (capillary)
underfill
206
Table 7.22 Simulation results for two different ATCs
Underfill
Material
Max Stress (Psi)
Von Mises
Max Stress (Psi)
Von Mises
0-70?C -55 to 125?C
Eutectic Lead-free Eutectic Lead-free
UF-1 35821 35802 85718 85626
UF-2 35577 35575 83444 83372
UF-3 34092 34166 67691 68195
UF-4 34344 34396 65031 65594
207
7.7 Summary and Recommendations
This section gives a briefing on the methodology of using the life prediction
models and life prediction calculation for the solder joint reliability. Recommendations
on the selection of the accelerated test methodologies is also provided at the end of the
section. The solder joint life acceleration factors depend on various parameters:
? The ATC (accelerated thermal cycle) selected for the field life prediction.
? The field profile for which the life is to be predicted.
? Material, geometry and assembly parameters.
? Duty cycle in terms of average number of field cycles that the component
is subjected to during it?s application on a per day basis.
These factors have to be kept in the mind while performing any life prediction
calculations. One has to be extremely careful and wise while using the modeling and
simulation tools, as if not wisely used it may give the user a set of completely irrelevant
results which may prove fatal in the design and selection of component instead of helping
the designer.
7.7.1 Development of PCB and Drive Level Tests
Calculation of Acceleration Factors
For the simplicity of understanding the various steps involved in the solder joint
life prediction calculation for a sample test case has been demonstrated for the test case-1
with field profile-3. The acceleration factor has also been calculated for the ATC 0-90?C
based on the field profile-3.
208
Since the UF-4 material has Tg below the maximum temperature (82?C) of the
profile-3 so the weighted average of the ISED has been used to calculate the scaled ISED
and used for the life calculation. The weight factor (WF) of 2 and the scaling factor (SF)
of 10 for the profile 3 has been used in the calculation.
SISED (?W) = (WF)*(SF)*(ISED)
= 2*0.1*4.71
= 0.942 psi
Now from Darveaux?s model modified with CAVE?s constants, as mentioned in section
5.3.1
2
10
K
W)(KN ?=
= 25768 cycles
4
K
3
W)(K
dN
da
?=
= 4.73E-7
da/dN
a
NN
0e
+=
= 34226 cycles
If we assume that the flip-chip encounters 20 averaged thermal duty cycles of
profile 3 per day than the field life of the component would be 1711 days or 4 yrs and 8.3
months.
Now using the same calculations with appropriate values of the constants and
ISED for 0-70?C ATC, the characteristic life (N) comes out to be 8854 cycles. This
means that 8854 cycles of 0-70?C test cycles correspond to 4yrs 8.3 months of drive level
209
field life. Since the cycle time for 0-70?C ATC is 30 mins therefore the characteristic life
is 4427 hrs or 184 days.
Thus the acceleration factor (AF) for 0-70? PCCA level test cycle w.r.t. drive
level field profile 3 is 9.3X (AF = 1711 / 184) in terms of time. Similarly the calculations
can be done for any drive level profile and PCB level accelerated test using any of the life
prediction models for which the results are presented in section 5.4.
7.7.2 Recommendations for the PCB Level Accelerated Test
The following recommendations can be made for the accelerated test
methodologies at the PCB level to predict solder joint reliability based on the finite
element analysis.
? Before selecting the accelerated test cycle for the thermo-mechanical
testing of the component it is extremely critical to make sure that the
failure mode and the mechanism in the ATC testing remains identical as
failure mode and mechanism encountered in the field application.
? In the present study it is observed that for the UF-4 underfill material the
ISED accumulated in the solder joint increases drastically for the thermal
cycles having maximum temperature above the Tg (70-75?C).
? It is extremely important to check the maximum temperature encountered
by the solder joint in the field application and select a underfill material
which has Tg above the maximum field temperature.
? The ATC should also be selected so that the maximum temperature in the
test cycle is not above the Tg of the underfill material.
210
? 0-70?C ATC is recommended for the comprehensive accelerated testing of
the flip chip with all the underfill materials. The solder joint failure for the
0-70?C test cycle remains independent of the Tg of the underfill material
for all the capillary flow and re-flow underfills. However 0-90?C ATC
can be used for the testing of flip-chips with the capillary flow underfills.
7.7.3 Recommendations for the Drive Level Stress Test
Three drive-level test profiles (Profile 1, Profile 2, Profile 3) provided by the
vendor as shown in Figures 7.38, 7.39, 7.40, have been investigated in this study. The
hysteresis loops and energy partitioning in the profiles was investigated (Figures 7.50,
7.51). Model predictions indicate that significant plastic work per cycle can be obtained
by using a much accelerated profile 3. It is hypothesized that, a large portion of the
plastic work is accumulated during the ramps, enabling compression of time during the
accelerated test. Therefore, profile 3 is recommended over profiles 1 and 2.
In general, the high temperature for profile 3, which is presently at 82?C, should
be lower than the glass transition temperature for the underfill. In the current study the
Tg for UF-1, UF-2, and UF-3 is above 82?C, but not for the UF-4 underfill. Due to this it
is recommended that the high temperature should be reduced to 70?C as the Tg of UF-4
is in the range of 70?C-75?C. This may not be a concern, if the UF-4 material is
improved such that the glass transition temperature becomes significantly higher than
82?C.
211
CHAPTER 8
SUMMARY AND CONCLUSIONS
In this work, the decision-support models for deployment of area array devices
under various harsh thermal environments have been formulated. The devices for which
the decision-support models can be used include both flip chip and flex substrate ball grid
array packages. Separate set of models have been formulated for the BGA packages and
flip-chip packages. The sensitivities of reliability to design, material, architecture and
environment parameters have been developed and validated with the experimental data.
The model predictions for various parametric variations show the similar trends in the
effect on the reliability of the packages of various configurations. The sensitivities
developed in this paper can be used to analyze quantitatively the impact of various design
parameters on the reliability of area array packages in harsh environments.
Hybrid modeling methodology presented in this paper provides a technique to
perturb accelerated test data and evaluate trade-offs. The methodology developed in this
work provides an extremely cost effective and time effective solution for doing trade-offs
and the thermo-mechanical reliability assessment of the area array devices subjected to
extreme environments. Thus, providing a turn key approach, for making trade-offs
between geometry and materials and quantitatively evaluating the impact on reliability.
Accuracy greater than normally achieved by 1st order models has been demonstrated.
Convergence between the experimental, statistical and failure mechanics based model
212
results validates the application of these models to compare the reliability of the different
area array packages with various parametric variations.
The broad conclusions that can be drawn from the present analysis of BGA
packages are:
? The reliability of the BGA package is highly sensitive to the die-to-body ratio
(also known as package density) and the life of the package decreases with the
increase in the die-to-body ratio.
? The thermo-mechanical reliability increases with the increase in the ball count
(number of I/Os).
? Solder joint diameter also has a great influence and the reliability of the package
increases with the increase in the solder joint diameter.
? Increase in the PCB thickness decreases the package reliability.
? Higher encapsulant mold compound filler content in the package provides better
thermo-mechanical reliability.
? NSMD pad configuration imparts higher reliability to the package as compared to
the SMD pad configuration.
? Increase in the temperature range of the thermal cycle reduces the solder joint life
of the package.
The conclusions from the statistics and failure mechanics based analysis of the flip-
chip package are as follows:
? The thermo-mechanical reliability of flip-chip devices generally decreases with
the increase in the die size.
213
? Increase in the solder joint diameter increases the reliability of the package.
? The thermo-mechanical reliability of the package increases with the increase in
the number of I/Os.
? The encapsulation of a flip-chip has a huge bearing on the reliability of the
package. The encapsulated flip-chip exhibits characteristic life upto 30x to 40x
as compared with the non-encapsulated flip-chip.
? Flip-chip with NSMD pad configuration exhibits better reliability as compared to
the flip-chip with SMD pads.
? Increase in the temperature range of the thermal cycle reduces the solder joint life
of the flip-chip.
FEA model for flip-chip solder joint reliability and copper trace integrity has been
developed and presented in this work. Damage based methodology for flip-chip solder
joint reliability prediction has also been presented which has been used for the
development of appropriate accelerated thermal cycle for the experimental testing and
developing field life correlation. Solder joint reliability analysis for both leaded
(62Sn36Pb2Ag) and lead-free (95.5Sn4.0Ag0.5Cu) solder alloy has been done and
presented in this work.
The finite element analysis of the flip-chip done in the current work leads to below
mentioned conclusions:
? For 0-70?C ATC the eutectic solders had higher inelastic strain energy (ISED)
accumulation per cycle as compared to the lead-free solder, but in the case of 0-
90?C ATC a reversal in the trend has been observed. The lead-free solder has
higher ISED as compared to the eutectic solder.
214
? Decrease in gap height increases the ISED and this has greater impact on the lead-
free solders for both eutectic and lead-free solders
? Increase in the bump size reduces the ISED.
? For the underfills investigated, capillary flow underfills exhibit lower ISED as
compared to the reflow encapsulant for both eutectic as well as lead-free solders.
? The simulation shows that there is drastic increase in the ISED once the operating
temperature goes above the Tg range of the underfill material
? The simulation for the copper trace integrity test shows that the failure mode
might shift to the copper trace cracking for the -55 to 125?C ATC. This implies
that -55 to 125?C ATC should be used for the accelerated testing only if the
failure mode in field mode is copper trace cracking.
? The underfill fillet plays a significant role in reducing the Cu trace stresses and
the effect of solder alloy used for bumping is negligible.
There is still a scope of further improvement in these models and validation with
wider database of experimental results. Formulation of similar design-support models
with more extensive accelerated test failure database with the methodology presented in
this work is desired. The models presented in this paper should not be used for absolute
solder joint life prediction, rather they should be used as a tool for educated evaluation of
relative thermal reliability performance of ball grid array and flip-chip packages up-front
in the design phase or during the selection of a package for specified mission
requirements.
215
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APPENDIX A
List of Symbols
? Coefficient of thermal expansion
? Shear strain
? Interfacial complaince
? Axial complaince
? Poisson?s ratio
? Dimensional parameter
? Shear stress
A Area, mm
2
BGA Ball grid array
CTE Coefficient of thermal expansion
DF Degrees of freedom
E Modulus of elasticity, MPa
EMC Encapsulant mold compound
f (mean square of residual error) / (mean square of regression error)
F Shear force
G Shear modulus
231
h Height, mm
I Cross-sectional moment of inertia
N Number of thermal cycles
NSMD Non-solder mask defined
p-value p-value of the coefficient
P Pitch
PCB Printed circuit board
R-sq Multiple coefficient of determination
R-sq(adj) R-sq adjusted for degrees of freedom
S Standard deviation
SE Coeff Standard error of the coefficient
SMD Solder mask defined
t-stat t-statistic of the coefficient
u Displacement
?T Thermal cycling temperature differential (?C)
?W Inelastic strain energy density
Subscripts
1%f 1% failure life
63.2% Characteristic life
b PCB
c Component
s Solder ball