THERMAL PERFORMANCE OF BALL GRID ARRAYS 
AND THIN INTERFACE MATERIALS 
 
Except where reference is made to the work of others, the work described in this 
dissertation is my own or was done in collaboration with my advisory committee. This 
dissertation does not include proprietary or classified information. 
 
 
_________________________________ 
Yasser Ahmed Elkady 
 
 
Certificate of Approval: 
 
 
 
 
____________________________   ___________________________ 
Jeffrey C. Suhling, Co-Chair   Roy W. Knight, Co-Chair 
Quina Distinguished Professor   Assistant Professor 
Mechanical Engineering    Mechanical Engineering 
 
 
 
 
____________________________   ___________________________ 
R. Wayne Johnson    Richard C. Jaeger 
Ginn Professor    Distinguished University Professor 
Electrical and Computer Engineering  Electrical and Computer Engineering 
 
 
 
 
____________________________ 
Stephen L. McFarland 
Acting Dean 
Graduate School 
THERMAL PERFORMANCE OF BALL GRID ARRAYS 
AND THIN INTERFACE MATERIALS 
 
 
Yasser Ahmed Elkady 
 
 
 
 
A Dissertation 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Doctor of Philosophy 
 
 
Auburn, Alabama 
August 8, 2005 
 iii
VITA 
 
 Yasser Ahmed Elkady was born on December 25, 1968, in Cairo, Egypt. He 
joined the faculty of engineering at Ain Shams University, Cairo, Egypt in 1986. He 
graduated in 1991 with a B.Sc. in Mechanical Engineering. Following graduation, he 
filled the position of Senior Integrated Manufacturing Engineer for a major international 
CAD/CAM/CAE solution provider in Cairo, Egypt. In 2000, he joined the Department of 
Mechanical Engineering at Auburn University, to pursue the degree of Doctor of 
Philosophy in Mechanical Engineering. 
 iv
DISSERTATION ABSTRACT 
THERMAL PERFORMANCE OF BALL GRID ARRAYS 
AND THIN INTERFACE MATERIALS  
 
Yasser Ahmed Elkady 
Doctor of Philosophy, August 8, 2005 
(B.Sc. Mechanical Engineering, Ain Shams University, 1991) 
176 Typed Pages 
Directed by Dr. Roy W. Knight and Dr. Jeffery C. Suhling  
 
Current electronic packages exhibit very high and ever increasing power 
densities. That trend mandates the need for enhanced thermal performance. This study 
introduces a state of the art apparatus to measure thermal resistance of electronic 
packages. The apparatus was designed to minimize human interaction and to maximize 
measurement accuracy through the use of a computer automated data acquisition and 
control system.  
The developed apparatus was used to measure thermal performance of Ball Grid 
Array packages. The impacts of different package configurations and board and assembly 
parameters on thermal performance were investigated. The parameters under 
investigation were die size, use of thermal balls, number of perimeter balls, use of 
underfill, and PCB heat spreader and thermal via design. By comparing the thermal 
 v
performances of different packages, it was observed that utilization of larger die, 
use of thermal balls, use of underfill and rich copper PCB thermal vias can reduce 
thermal resistance by up to 60%. The number of perimeter balls did not have a notable 
impact on thermal performance due to their remote location from the die surface. 
Numerical thermal simulations of all test parameters combination were developed and 
were found to be in good agreement with the experimental measurements.  
The impact of thermal cycling on thermal performance was also investigated 
experimentally. Packages expected to be least reliable (with large die and no underfill), 
showed initial increase of thermal resistance after 750 thermal cycles. Further increases 
in thermal resistance were observed with continuous thermal cycling until solder joint 
failure occurred at 1250 cycles, preventing additional measurements. The correlation 
between thermal cycling and thermal resistance was then analyzed using a numerical 
structural simulation model that predicted crack initiation in the solder joints.  
 A second apparatus based on the ASTM 5470D standard was developed to 
measure thermal resistance of thin components and interface materials used in electronic 
packaging. Thermal contact resistance versus applied force at the aluminum metering 
block surfaces was evaluated by testing 2 copper samples of different thicknesses. The 
established correlation can be used to correct future thermal resistance measurements. A 
new RTD Assembly was proposed to overcome current bare RTD fragility problems. The 
new proposed temperature probe dimensions and material were selected based on a 
numerical optimization study using a design variable sweep technique.  
 
 vi
ACKNOWLEDGEMENTS 
 
I would like express my gratitude and gratefulness to my mother, Hoda El-Sayed, 
wife, Samah Ahmed, son, Ahmed Elkady, sister, Dina Elkady, and father, Ahmed 
Elkady, for their, love, encouragement, support, understanding and patience. 
I would like to thank my advisory committee. Special thanks go to Dr. J. C. 
Suhling and Dr. R. W. Knight for their support and guidance. 
 
 
 vii
Style manual or journal used: IEEE
Computer software used: Microsoft Office 2003, Adobe Photoshop, Microstation,  
Solid Edge, COSMOS, ANSYS, MathCad, Visual Basic, LabView, and Sigma Plot. 
 
 viii
TABLE OF CONTENTS 
 
LIST OF FIGURES ...........................................................................................................xi 
LIST OF TABLES ...........................................................................................................xiv 
1. INTRODUCTION.........................................................................................................1 
1.1. History of Electronic Packaging.............................................................................1 
1.2. Ball Grid Array Construction.................................................................................2 
1.3. Impact of Temperature on Electronic Packages.....................................................4 
1.4. Heat Removal Modes.............................................................................................7 
1.5. Definition of Thermal Resistance...........................................................................8 
1.6. Experimental Measurement of Thermal Resistance...............................................9 
1.7. Correlation between Thermal Performance and Package Reliability...................11 
1.8. Experimental Thermal Resistance Measurements of Constitutive 
Components..........................................................................................................12 
1.9. Scope of Study??..............................................................................................13 
2. LITERATURE REVIEW............................................................................................15 
2.1. Thermal Performance of BGA Packages..............................................................15 
2.2. Numerical Simulation of BGA Reliability...........................................................19 
2.3. Thermal Resistance Measurements of Thin Components....................................20 
3. EXPERIMENTAL MEASUREMENT OF PARAMETERS IMPACTING 
THERMAL PERFORMANCE IN BALL GRID ARRAY PACKAGES...................23 
3.1. Study Parameters..................................................................................................23 
3.2. Test Packages and Test Board..............................................................................26
 ix
3.3.  Test Matrix...........................................................................................................29 
3.4. Testing Thermal Aspects......................................................................................29 
3.5. Testing Electronic Aspects...................................................................................31 
3.6. Testing Fixture and Cooling Circuit.....................................................................32 
3.7. Data Acquisition and Control...............................................................................33 
3.8. Diode Characterization and Calibration...............................................................35 
3.9. Testing Procedure.................................................................................................35 
3.10. Experimental Results.........................................................................................38 
3.10.1. Use of Underfill.........................................................................................41 
3.10.1.1. Packages with Thermal Balls.........................................................41 
3.10.1.2. Packages without Thermal Balls....................................................41 
3.10.2. Use of Thermal Balls.................................................................................43 
3.10.3. Die Size......................................................................................................43 
3.10.3.1. Packages with Thermal Balls.........................................................44 
3.10.3.2. Packages without Thermal Balls....................................................44 
3.10.4. Number of perimeter balls.........................................................................44 
3.10.5. Thermal Via Geometry..............................................................................45 
3.10.6. Thermal Cycling........................................................................................46 
3.11. Comparison of Study Parameters......................................................................50 
4. THERMAL SIMULATIONS OF THE BGA PACKAGES........................................53 
4.1. Models Construction.............................................................................................53 
4.2. Calculation of Thermal Resistance.......................................................................57 
4.2.1. Impact of Using Thermal Balls..................................................................59 
4.2.2. Impact of Number of Perimeter Balls........................................................59 
4.2.3. Impact of Using Underfill Material...........................................................60 
 x
4.2.4. Impact of Die Size.....................................................................................60 
4.2.5. Impact of Thermal Via Geometry..............................................................62 
4.3. Transient Thermal FEA Simulation......................................................................65 
5. STRUCTURAL SIMULATIONS OF THE BGA PACKAGES.................................67 
5.1. Model Objectives..................................................................................................67 
5.2. Models Construction.............................................................................................68 
5.3. Mesh Generation...................................................................................................71 
5.4. Material Models and Thermal Loads....................................................................74 
5.5. Evaluation of Number of Cycles to Crack Initiation............................................76 
5.6. Impact of Critical Solder Joints Crack Initiation on Thermal Resistance............81 
6. EXPERIMENTAL THERMAL RESISTANCE MEASUREMENTS OF THIN 
ELECTRONIC PACKAGING MATERIALS............................................................85 
6.1. Motivation and Objective.....................................................................................85 
6.2. Apparatus Theory of Operation............................................................................86 
6.3. Apparatus Construction........................................................................................87 
6.4. Metering Blocks Calibration.................................................................................93 
6.5. Evaluation of Sample Contact Resistance............................................................94 
6.6. Modification of Temperature Sensors................................................................100 
6.7. Structural Analysis of RTD Assembly...............................................................104 
7. SUMMARY AND CONCLUSION..........................................................................108 
BIBLIOGRAPHY............................................................................................................114 
APPENDIX A..................................................................................................................118 
APPENDIX B..................................................................................................................120 
APPENDIX C..................................................................................................................142 
APPENDIX D..................................................................................................................145
 xi
LIST OF FIGURES 
Figure 1.1: Types of Electronic Packages............................................................................3 
Figure 1.2: Types of Ball Grid Array Packages...................................................................5 
Figure 1.3: Approximate Thermal Resistor Network of a PBGA Package.......................10 
Figure 3.1: Cross Sections of BGA Packages with Thermal Balls....................................25 
Figure 3.2: Cross Sections of BGA Packages without Thermal Balls...............................25 
Figure 3.3: Schematic Representation of BGA Dimensional Parameters.........................27 
Figure 3.4: Schematic representation of thermal test chips...............................................28 
Figure 3.5: Test Board.......................................................................................................28 
Figure 3.6: Thermal Via Connection with Ground Plane..................................................30 
Figure 3.7: Cross?sectional schematic of the test fixture..................................................34 
Figure 3.8: Test Fixture......................................................................................................34 
Figure 3.9: Test Setup........................................................................................................36 
Figure 3.10: Data Acquisition and Control Software........................................................36 
Figure 3.11: Data Acquisition and Control System...........................................................37 
Figure 3.12: Diode Calibration Data..................................................................................39 
Figure 3.13: Sample of Temperature Measurements.........................................................39 
Figure 3.14: Sample IR thermal images of test packages at steady state..........................40 
Figure 3.15: Thermal Resistance Measurements (Packages with Thermal 
Balls)..................................................................................................................................42
 xii
Figure 3.16: Thermal Resistance Measurements (Packages without Thermal 
Balls)..................................................................................................................................42 
Figure 3.17: Thermal Cycling Profile................................................................................47 
Figure 3.18: Impact of Thermal Cycling (BGA #1)..........................................................48 
Figure 3.19: Impact of Thermal Cycling (BGA #2)..........................................................49 
Figure 3.20: Impact of Study Parameters on Thermal Performance of  
BGA #1..............................................................................................................................52 
Figure 3.21: Impact of Study Parameters on Thermal Performance of  
BGA #2..............................................................................................................................52 
Figure 4.1: Wire Frame Sketch Overlaid on Package Photo.............................................55 
Figure 4.2: Section Solid Model of BGA #1, with Thermal Balls....................................55 
Figure 4.3: Automatic Mesh Generated from Solid Model (BGA #2)..............................55 
Figure 4.4: Vector Plot of Resultant Heat Flux in a Thermal Ball  
(BGA #2 / Via #2 / No Underfill)?????????????????????..61 
Figure 4.5: Example Plot of the z-Direction Heat flux in BGA #2 Package 
(Via #2 / No Underfill)......................................................................................................61 
Figure 4.6: Example Plot of the z-Direction Heat Flux in the Perimeter Balls 
(BGA #2 / Via #2 / No Underfill)......................................................................................61 
Figure 4.7: Plots of z-Direction Heat Flux at the Bottom of BT Substrate for BGA#1....63 
Figure 4.8: Example Contour Plot of the z-Direction Heat Flux at the Bottom of BT 
Substrate (BGA #2)............................................................................................................63 
Figure 4.9: Vector Plot of Heat Flux in Thermal Via #1 
(BGA#1, with Thermal Balls, No Underfill).....................................................................64 
Figure 4.10: Vector plot of Heat Flux in Thermal Via #2 
(BGA#1, with Thermal Balls, No Underfill).....................................................................64 
Figure 4.11: Temperature vs. Time Plot for BGA #1 / Via #1..........................................66 
Figure 4.12: Temperature vs. Time Plot for BGA #1 / Via #2..........................................66 
Figure 5.1: Parametrically Generated FEA Model with the Solder Ball Perimeter  
Divided into 8 Elements.....................................................................................................69 
 xiii
 
Figure 5.2: Parametrically Generated FEA Model with the Solder Ball Perimeter  
Divided into 16 Elements...................................................................................................69 
Figure 5.3: The Four Steps Needed to Generate a Subpart Mesh  
(Array of Thermal Balls)...................................................................................................71 
Figure 5.4: Six Progressive Steps for Generation of the Mesh for the Complete 
BGA Assembly?????????????..............................................................73 
Figure 5.5: Mesh at the Gaps between the Solder Ball and the Soldermask ....................73 
Figure 5.6: Thermal Cycling Load Profile.........................................................................75 
Figure 5.7: Temperature Dependent Stress Strain Curves for 63 Sn - 37 Pb Solder?.....77 
Figure 5.8: Critical Solder Balls for BGA #1 with Thermal Balls....................................79 
Figure 5.9: Critical Solder Ball for BGA#1 without Thermal Balls..................................79 
Figure 5.10: Solder Balls and Regions used for Volumetric Averaging...........................80 
Figure 5.11: Crack Initiation Prediction Values Superimposed on Thermal Resistance 
Measurements for BGA Packages with Thermal Balls.....................................................84 
Figure 5.12: Crack Initiation Prediction Values Superimposed on Thermal Resistance 
Measurements for BGA Packages without Thermal Balls................................................84 
Figure 6.1: Theory of Operation of Apparatus Used to Measure Thermal  
Resistance of Thin Components........................................................................................88 
Figure 6.2: Solid Model of Apparatus...............................................................................90 
Figure 6.3: Apparatus after Assembly...............................................................................90 
Figure 6.4: Data Acquisition and Control Diagram...........................................................92 
Figure 6.5: Data Thermal Resistance Measurements of 5 and 10 mm Copper Samples...99 
Figure 6.6: Calculated Contact Resistance as a Function of Axial Force..........................99 
Figure 6.7: Proposed Modifications for Bare RTD Elements..........................................102 
Figure 6.8: Finite Element Model Detail.........................................................................102 
Figure 6.9: Temperature Distribution in RTD and Metering Block................................105 
Figure 6.10: Third Principal Stress in RTD Assembly during Assembly........................107 
 xiv
Figure 6.11: Radial Stress in RTD Assembly during Experimental 
Measurements..................................................................................................................107 
 
 
 xv
LIST OF TABLES 
 
Table 1.1: Typical Thermal Conductivity of Common Materials Used in Electronic 
Packaging...........................................................................................................................10 
Table 3.1: Test Matrix........................................................................................................30 
Table 3.2: Number of Completed Thermal Cycles............................................................47 
Table 4.1: Mesh Sizes Including Underfill/Air Layer.......................................................56 
Table 4.2: Material Properties for Thermal FEA Models..................................................56 
Table 4.3: Comparison between Experimental Measurements and Numerical  
Simulations for Packages with Thermal Balls...................................................................58 
Table 4.4: Comparison between Experimental Measurements and Numerical  
Simulations for Packages without Thermal Balls..............................................................58 
Table 5.1: Material Properties Used in the Finite Element Structural Analyses...............75 
Table 5.2: Definitions and Values of Anand Model Parameters.......................................77 
Table 5.3: Calculated Values of the Average Viscoplastic Work  
Accumulated per Cycle (BGA #1, No Underfill)?????????..........................82 
Table 5.4: Darveaux and Lall Material Correlation Constants..........................................82 
Table 5.5: Calculated Numbers of Thermal Cycles to Crack Initiation  
(BGA #1, No Underfill).....................................................................................................82 
Table 6.1: Measurements Used to Calculate Thermal Conductivity of Metering 
Blocks................................................................................................................................95 
Table 6.2: Measurements Used to Calculate Contact Resistance (5 mm thick 
sample)...............................................................................................................................97 
Table 6.3: Measurements Used to Calculate Contact Resistance (10 mm thick 
sample)...............................................................................................................................97 
Table 6.4: Material Properties Used in Finite Element Analysis.....................................105 
 1 
CHAPTER 1 
INTRODUCTION 
 
1.1 History of Electronic Packaging 
In 1947, Bardeen, Brattain and Shockley invented the first bipolar transistor at 
Bell Labs. In 1958 Jack Kilby of Texas Instruments invented the first integrated circuit 
(IC) [1]. Subsequently, larger scales of integration were developed, producing miniature 
circuits capable of performing complex tasks. The newly developed ICs needed some sort 
of packaging. The electronic packages had to perform specific tasks, such as protecting 
the fragile electronic circuit, providing connections for input/output connections, 
providing power connections, supporting the package and removing the heat generated by 
the package. 
There are numerous designs of electronic packages depending on application, 
number of I/Os and power dissipation. The first electronic packages were of ?Through-
hole? type where the package leads were inserted into through holes in the PCB. That 
was followed by surface mounting technology where components were mounted directly 
on the substrate surface [2]. The next breakthrough was the introduction of area array 
packages like flip chip and Ball Grid Array configurations. The pin counts these packages 
offered were at least ten fold of what was possible with the DIP and SOP packages. The 
first area array package was the Ceramic Pin Grid Array [3].  
 2 
The BGA did not gain popularity until 1989 when Motorola introduced the first 
BGA with a lower cost Bismaleimide Teriazine (BT) substrate, which was called 
OMPAC (Over Molded Plastic Pad Array Carrier). Illustrations of some of older and 
recent electronic packages are shown in Figure 1.1. 
 
1.2 Ball Grid Array Construction 
The high pin count of BGA (typically in the range of > 250 connections) is one of 
the most popular packages of choice in the electronic packaging industry [1]. BGAs also 
offer additional advantages such as small foot print, self alignment, elimination of the 
need for lead inspection/straightening, and convenience of using standard processes and 
equipment for surface mounting. 
In spite of these advantages, BGAs have their share of manufacturing problems 
such as difficulty of solder joint inspection and reworking, which the industry is tackling 
by using good process control such as paste inspection and reflow profiling to ensure 
good solder joints [2]. BGAs come in different varieties depending on the construction 
materials and leads geometry. However, almost all construction variations share the 
common feature of a BGA substrate that connects the die bumps to the package 
connections [3]. 
The first distinct variation of BGA packages is the material used for the BGA 
substrate (sometimes referred to as the interposer board). BGAs with ceramic substrates 
are called CBGAs, while those with plastic substrates are called PBGAs. CBGAs are 
typically hermetically sealed to eliminate the negative influence of moisture on the 
package reliability. 
 
 
 
 
 
 
(a) 
 
 
 
 
 
(b)
 
 
Copper Pad 
 
Solder Ball 
Die 
 
 
 
 
 
Substrate 
 3
 
 
 
 
 
Molding
(c) 
Figure 1.1 - Types of electronic packages 
(a) Dual In Line Package (DIP) 
(b) TSOP (Thin Small Outline Package) 
(c) PBGA (Plastic Ball Grid Array) 
 
CBGAs also exhibit higher thermal expansion coefficient mismatch with the 
PCB, which is major factor effecting package reliability. On the other hand, PBGAs offer 
simpler manufacturing techniques, less thermal expansion coefficient mismatch with the 
PCB and lower cost [2]. Another variation of the BGA construction is TBGA (Tape 
Automated Bonding Ball Grid Array), where the substrate is made of thin flexible 
material with two copper planes for ground and signal [3]. 
The second distinct variation is the method of routing the connections from the 
die to the substrate. Die may be bonded to the substrate using die attachment adhesive, 
then gold or aluminum wires connect bond pads on the die to bond pads on the substrate. 
Alternately, the chips may be flipped upside down and connected through a set of solder 
balls to pads on the substrate; such configuration is typically called FCBGA (Flip Chip 
Ball Grid Array) [3]. 
The third distinct variation is the shape of the connection between the BGA and 
the PCB. The connection may be in the form of solder balls or solder columns [4]. The 
selection of a specific BGA construction detail and material is dictated by cost 
limitations, reliability concerns and type of application. Illustrations of different types of 
BGA packages are shown in Figure 1.2. 
 
1.3 Impact of Temperature on Electronic Packages 
The life of all materials including semiconductors is normally observed to vary 
logarithmically with the reciprocal of the absolute temperature as expressed by the 
Arrhenius equation: 
)1(
/
?=
Tb
eAL         (Eq. 1.1) 
 4
 
 
Molding
Substrate 
 
 
 
 
Solder Pad 
Die Attachment 
Die 
 
(a) Plastic ball grid array 
 
 
 
 
(b) Flip chip ball grid array
 
 
 
Heat Sink
Encapsulant
Thermal Adhesive 
 5
 
 
 
 
Stiffener 
Stiffener Tape 
Adhesive 
 
(c) Tape automated bonding ball grid array 
 
 
Figure 1.2 - Types of ball grid array packages 
 
 
 
 
where:   
lifeexpectedL =  
materialtheforconstantA =  
constantBoltzmantorelatedconstantab =  
[K]etemperaturabsoluteT =  
The solution of Arrhenius equation predicts that the life of any device is halved 
for every 20? C rise in temperature [4]. The problem of high operating temperature of 
electronic packages is continuously growing due to continuous decrease of feature size of 
circuit chips as well as the massive increase in number of circuits per chip. In fact, since 
the invention of the IC in 1958, there has been a huge increase in the number of circuits 
per chip [2]. This trend has outlined the importance of thermal management for today 
electronic packages in order to minimize the maximum operating temperature by 
maximizing the efficiency of heat transfer from the package to the ambient [1]. 
The impact of temperature goes beyond material degradation and affects 
reliability of electronic packages as well. Temperature rise generates thermal stresses in 
structures that consist of different materials with different thermal expansion coefficients. 
The impact of the mismatch of thermal expansion coefficient may be augmented by non-
uniform temperature distribution within the structure, as in the case of electronic 
packages. The level of thermal stresses within electronic packages is a key factor directly 
effecting package reliability.  
 
 
 
 6
 
1.4 Heat Removal Modes 
 Heat removal from electronic packages is usually done trough a combination of 
two distinct modes. The first mode is convection, which is defined as the heat transfer 
between a solid and a moving fluid and governed by: 
)(
fs
TThAQ ?=         (Eq. 1.2) 
where:   
h = heat transfer coefficient 
A = cross sectional area for heat flow 
s
T  = surface temperature 
f
T  = Fluid temperature 
The convection heat flow equation indicates that heat removal can be enhanced by 
either increasing the flow surface area, as in the case of using finned heat sinks, or by 
increasing the heat transfer coefficient. [5].  The later approach is more complex as it 
depends on many parameters such as type of cooling fluid, fluid velocity, surface 
orientation, surface shape and surface dimension. However, since the cooling fluid in 
most electronic packaging applications is air, the improvement of heat transfer coefficient 
by increasing the cooling fluid flow velocity may have considerable restrictions imposed 
by limitation of space, power and type of application. 
The second mode is conduction heat flow which is defined as the heat transfer 
through a solid and governed by: 
?
?
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
+=
?
?
z
T
k
zy
T
k
yx
T
k
x
q
t
T
C
zyx
?     (Eq. 1.3) 
 
 7
 
where: 
T  = Temperature 
t  = time 
?  = Density 
C  = Specific heat  
q  = Heat generation rate per unit volume 
x
k , ,  = Thermal conductivity in x,y and z directions respectively 
y
k
z
k
The continuous trend of minimizing electronic packages footprint limits the 
choice of increasing heat flow by increasing the heat flow cross section [5]. The 
alternative is to increase the overall thermal conductivity of the package by us which is 
governed by constituent materials thermal properties as well as package geometry. 
 
1.5 Definition of Thermal Resistance 
Thermal resistance is defined as a measure of the ability to resist heat flow. The 
concept of thermal resistance may be simplified by taking advantage of the analogy 
between thermal and electrical systems. Using this analogy, current is analogous to heat 
flow; voltage difference is analogous to temperature difference and thermal resistance is 
analogous to electrical resistance.  
The three dimensional resistance to heat flow may be approximated by modeling 
a network of one dimensional resistors representing the various layers inside an electronic 
package. An approximate thermal resistor network for a PBGA package is shown in 
Figure 1.3. Thermal resistance definition differs depending on mode of heat transfer. For 
 8
 
conductive resistors, the thermal resistance is defined as 
Ak
L
 while for convective 
resistors the resistance is defined as
Ah
1
, where L is the length of the heat flow path, A is 
the cross section area of the heat flow path, k is the material thermal conductivity and h is 
the convection heat transfer coefficient.  
The overall thermal resistance of the package is dependent on the thermal 
resistance of its constitutive layers. The challenge of designing thermally efficient 
electronic packages arises from the fact that there is a difference of more than three 
orders of magnitude of thermal conductivity among the materials that affect the thermal 
performance of the package [3]. Table 1.1 lists thermal conductivity of common materials 
used in electronic packaging 
 
1.6 Experimental Measurement of Thermal Resistance 
Experimental thermal resistance measurements offer an insight for how to make 
design decisions and geometrical details and material choices for electronic packages in 
order to affect their thermal performance. Thermal resistance of electronic packages can 
be measured by powering the package with a known input power and measuring the 
temperature difference between the die surface and a constant reference temperature.  
JEDEC Standards JESD51 [6], JESD51-1 [7] and, JESD51-8 [8] offer tentative 
details for thermal resistance measurements describing geometry of board, package and 
test fixture as well as environmental test requirements. For packages equipped with 
external heat sinks, the temperature difference is measured between the die surface and  
 
 9
 
 
Ambient
 
 
Molding 
Molding 
 
Die
 
Die Attachment 
 
Substrate 
 
Solder Balls 
Underfill
 
 
 
 
 
Figure 1.3 - Approxim
 
 
 
Solder m
Molding compound
Die attachment 
 
 
 
 
 
 
 
 
PCB ViasPCB Bulk
Ambient
ate thermal resistor network of a PBGA package 
Table 1.1 - Typical thermal conductivity of common 
materials used in electronic packaging 
Material Thermal Conductivity [W/(m K)] 
ask 0.25 
Solder 50 
0.8 
2 
Silicon Die 140 
PCB 0.36 
Copper 390
10
 
 11
the PCB. The cold plate is usually constructed from a high conductive material such as 
copper with embedded cooling water channels. Die surface temperature may be measured 
using integrated devices such as on-chip diodes or resistors while the board temperature 
is measured using T, J or K type thermocouples.  
Although the standards offer great detail of test setup and procedures, they do not 
offer solutions to some practical problems such as how to overcome the unevenly 
distributed contact resistance between the board and the cold plate, which can be 
attributed to flatness deviation of the cold plate surface and/or board warp. Another 
cooling method is to directly expose the back surface of the PCB to a flow of cooling 
water. That later approach, however, is limited to board designs that do not allow coolant 
to leak to the front surface of the board. 
 
1.7 Correlation between Thermal Performance and Package Reliability 
Historically, thermal performance and package reliability have been researched as 
two distinct areas despite the fact that the state of stress in an electronic package depends 
on temperature distribution within the package, which is directly related to package 
thermal performance. On the other hand, cracks induced by thermal stresses can impede 
heat flow which might cause drastic changes in the package thermal resistance. Thus, it 
would be beneficial to study the impact of structural failure (such as crack initiation and 
propagation) on thermal performance of electronics. Typically, experimental package 
reliability studies are time consuming as they involve thermal cycling of electronic 
packages for extended periods of time as well as cross sectioning and polishing of 
multiple electronic packages at different levels of thermal cycling to check for crack 
 
 12
initiation and speed of propagation. However, recent research efforts offered numerical 
simulation models that are capable of predicting crack initiation and speed of propagation 
with a high degree of accuracy.  
 
1.8 Experimental Thermal Resistance Measurements of Constitutive Components 
 Since thermal resistance of individual components and materials used in the 
construction of an electronic package have direct impact on the thermal performance of 
that package, it would be helpful to be able to accurately measure thermal resistance of 
those materials and components. The problem of measuring thermal resistance of 
electronic packaging materials such as underfill and BT substrate is that they are typically 
very thin. Intrusive temperature measurement methods where temperature sensors are 
inserted/attached to a measured sample are not possible. ASTM standard D5470-95 [9] 
offers construction outlines of an apparatus that is capable of measuring thermal 
resistance of such thin components. The apparatus generates a measured one dimensional 
heat flow that passes through the sample. Temperature at the upper and lower sample 
surfaces are calculated by extrapolating measured temperature variations in the two metal 
columns of known thermal conductivity. ASTM standard D5470-95 also specifies that 
the measurements should be conducted in a vacuum environment to minimize heat loss to 
the environment. The standard defined a few recommendations for test procedure and 
construction details: 
 1- Contacting surfaces should be within 0.4 ?m of a true plane. 
2- Apply a 3 MPa ? 0.1 MPa pressure on the sample surface to minimize contact 
resistance between the sample and the metering blocks. 
 
 13
3- Average sample temperature of 50 ?C during testing. 
1.9 Scope of Study  
In this work, the impact of key design and assembly parameters on thermal 
performance of plastic BGA packages will be identified by measuring and comparing 
thermal resistance of different BGA designs and assembly options. The study parameters 
were chosen to be die size, use of thermal balls, use of underfill, number of perimeter 
balls, and thermal via design (In this study the term thermal via is used to refer to both 
copper plated through holes and their associated copper spreader). Comparison of thermal 
resistance measurements will help to identify the optimum parameters set to minimize 
package temperature. Experimental measurements were conducted using a fully 
automated computerized test setup specifically designed to facilitate testing procedures, 
data collection and report generation. 
As a second part of this investigation thermal FEA models were developed of the 
experimentally tested packages to identify major heat flow paths inside plastic BGA 
packages. In addition structural FEA models were formulated to predict crack initiation 
in the solder joints under thermal cycling loads. By comparing experimentally measured 
changes in thermal resistance due to thermal cycling with crack initiation data form FEA 
models, correlation between number of thermal cycles and degradation in thermal 
resistance can be established as well as quantifying the importance of solder balls as an 
effective heat flow path inside plastic BGA packages. In the final part of this study a new 
test setup based on ASTM 5470-95 [9] was developed that is capable of measuring the 
through the thickness thermal conductivity of thin components used in electronic 
 
 14
packaging. This data can be used to help guide design and assembly decisions that 
influence the overall thermal performance of electronic packages. 
 15 
CHAPTER 2 
LITERATURE REVIEW 
 
2.1 Thermal Performance of BGA Packages 
An examination of a BGA cross section reveals that many layers inside a BGA 
assembly share low values of thermal conductivity such as the molding compound, BT 
substrate, PCB and air layer between substrate and PCB. The challenge of designing high 
thermal performance BGA packages may be approached by establishing relatively highly 
conductive flow paths that allow heat to escape through the low thermal conductivity 
layers. Research in BGA thermal performance have indicated that high conductive paths 
can be in the form of thermal vias in the BT substrate, perimeter and thermal solder balls, 
or underfill and thermal vias in the PCB.  
The benefit of using underfill material was reported by Edwards and Handt [10] 
who conducted a set of numerical simulations to investigate different design and 
assembly parameters on BGA thermal performance. Their study reported that up to a 
50% decrease in junction to air thermal resistance was observed when underfill was used 
with a BGA with 176 perimeter balls. This investigation also cited that perimeter balls 
were effective in reducing thermal resistance only when the die size was large enough to 
overlap perimeter balls locations. The study noted superior thermal performance of BGA 
packages when compared to QFP packages. 
 16 
An analysis of the different design parameters affecting thermal performance of 
BGA packages was performed by Zhan [11] who conducted a sensitivity analysis that 
used 86 finite element models. This study reported that die size and number of perimeter 
balls had a linear impact on junction to air thermal resistance, while there was a non-
linear impact due to changing the number of PCB copper planes and heat sink thickness.  
The importance of thermal balls was cited in a parametric study by Lall [12], who 
reported that using a matrix of 36 thermal balls decreased junction to air thermal 
resistance of a PBGA having 256 perimeter solder balls by 25% when compared to 
similar packages without thermal balls. However, this work also showed that in thermal 
cycling, the added coupling between the package and the board associated with the higher 
number of thermal balls caused a 33% drop in mean fatigue life when compared to 
packages without thermal balls as calculated using the modified Coffin-Manson law.   
The effective number of thermal balls that may have significant impact on thermal 
performance of PBGA packages was reported to be in the range of 24 to 48 thermal balls 
based on a 3 dimensional FEA parametric study conducted by Mertol [13].  
Numerical simulation of PBGA packages can be expensive in terms of 
computational time, especially if small details like BT thermal via geometry are included. 
On the other hand, thermal via details must not be overlooked due to their significant 
impact on thermal resistance. In an effort to reduce computational time, Pinjala, et al. 
[14] introduced the possibility of using a simple geometry with anisotropic properties 
instead of the multilayer isotropic detailed geometry typically used in numerical 
simulations. The simple geometry model was reported to be 98% accurate when 
compared to the detailed geometry model. This study also reported that enhancement of 
 17
thermal conductivity of via fill material would have negligible impact on junction to air 
thermal resistance.  
Further research on thermal vias was conducted by Ramakrishna and Lee [15], 
who studied the impact of thermal vias in BT substrates on thermal performance of flip 
chip BGA packages. This study reported that placing a sufficient number of thermal vias 
in the substrate within the area defined by the die foot print may help reduce package 
thermal resistance by 35 to 40%. This investigation also showed that the impact of the 
number of thermal vias on package performance diminished when the thermal 
conductivity under the die was greater than 2 W/(m?K).  
The impact of PCB construction on PCB thermal conductivity was studied by 
Azar and Graebner [16], who conducted experimental measurements using infrared 
imaging to evaluate PCB orthotropic thermal conductivity as well as possible contact 
resistance at the interfaces between different layers inside the PCB. Their experimental 
results proved that no significant contact resistance was observed at the different interface 
surfaces inside the PCB. This study also introduced approximate mathematical models to 
calculate the effective in-plane and normal thermal conductivity of the PCB as a function 
of copper and glass-fiber layers thicknesses.  
 Research in thermal resistance of electronic packages has not been limited to 
experimental and numerical simulation techniques. Guenin, et al. [17] introduced a 
nonlinear lumped analytical parametric model for a cavity down thermally enhanced 
BGA to predict junction to air thermal resistance. This model accounted for natural, 
mixed, and forced convection, as well as radiation heat transfer. Their study reported that 
in a natural convection environment, radiation plays an important role in cooling a cavity 
 18
down thermally enhanced BGA, and was responsible for 42% of the total heat transfer 
from the package to environment. 
Loh, et al. [18] introduced two analytical models that can be used to predict 
thermal resistance of a depopulated PBGA. The first proposed model used an equivalent 
area approach, while the second used an equivalent thermal conductivity approach to 
simplify package geometry to the extent that an analytical model could be derived. Their 
study used numerical simulation as a bench mark for analytical model accuracy. 
Analytical prediction of thermal resistance was reported to be within 10% of the values 
predicted by numerical simulation.  
 The literature also includes research work that investigates package deterioration 
due to exposure to thermal loads. Edwards, et al. [19] employed FEA models for PBGAs 
to investigate the impact of delamination on junction to air thermal resistance in a still air 
environment. This study reported that the highest increase of thermal resistance was due 
to delamination at the chip/die attachment interface. This study also reported that thermal 
resistance was least sensitive to delamination at the upper die surface, between the die 
and the molding compound. 
Joiner and de Oca [20] conducted experimental measurements to identify the 
impact of aging on thermal performance of thermal grease used with heat sinks. Five 
different thermal grease materials were tested for 1900 hours at 150 ?C. Their study 
reported that non-cleanable silicon based and alcohol-cleanable non silicon based thermal 
greases were the materials that did not exhibit filler separation at the end of aging test. 
 
 
 19
2.2 Numerical Simulation of BGA Reliability 
Reliability of BGA packages is a major concern for the electronic packaging 
industry, which has driven research efforts to develop effective methods that are capable 
of predicting failure initiation and propagation under cycling loads. Typically, the 
reliability problem has been approached using a combination of experimental 
measurements and numerical simulation.  
Experimental measurements are conducted by thermally cycling BGA packages 
and visually inspecting sliced packages for crack initiation and speed of propagation in 
solder joints at successive intervals of thermal cycling. Numerical simulation models are 
also normally created for the packages used in the experimental measurements, and 
loaded with thermal loads similar to those applied experimentally. Finally, failure 
prediction models are developed by correlating experimental measurements with 
numerical simulation.  
The bulk of recent BGA reliability studies have used the Anand model [21] to 
simulate creep behavior of solder joints. With this approach, the amount of plastic strain 
energy density in critical solder joints is calculated using a volume averaging technique 
to reduce dependency of solution accuracy on mesh density as suggested by Darveaux 
[22]. The strain energy density calculated values are then plugged in the correlation 
equations to calculate fatigue life.  
Two different sets of correlation coefficients have been reported: the first by 
Darveaux [23] for CBGA packages and solder mask defined pads, and the second set by 
Lall, et al. [24] for PBGA packages and non solder mask defined pads.  
 20
Syed [25] preformed similar studies based on the proposed constitutive models 
for creep developed by Wong, et al. [26]. He also introduced another set of damage 
correlation coefficients based on the Monkmann-Grant equation for creep rupture. 
Numerical simulation prediction of fatigue life based on the mentioned correlation was 
reported to be within 25% of experimental measurements.  
Other studies have followed the same approach including the work done by Zhang 
et al. [27], Zhan [28], and Yan, et al. [29]. These investigations involved both slice 
models, and one quarter or one eighth symmetry coarse global models with finer 
submodels in an effort to reduce model processing time. 
In a study by Gustafsson [30], a survey of five modeling approaches was 
conducted and numerical results were compared to experimental measurements. The five 
modeling approaches were nonlinear slice model, nonlinear global model with linear 
super elements, linear global model with nonlinear submodel, nonlinear global model 
with nonlinear submodel, and nonlinear global model. This study reported that the 
nonlinear slice model was the most conservative approach. The nonlinear global model 
with linear super elements was not recommended to be used due to large errors reported. 
The most accurate approach reported was the global nonlinear model with non linear sub 
model. 
 
2.3 Thermal Resistance Measurements of Thin Components 
 ASTM D-5470 [9] guidelines have been implemented in many studies to evaluate 
thermal resistance of thin interface materials. However, the ASTM Standards give only 
schematic representation of apparatus construction and theory of operations. Thus, there 
 21
have been significant differences in the results obtained in different studies due to the 
differences in construction details such as type of temperature sensors, size of 
temperature sensors, heater powers and the temperature sensor pitch.  
The ASTM Standard also does not specify a recommended value for the metering 
block surface roughness, despite of its impact on contact resistance between the sample 
and metering blocks which in turn influences measurements accuracy. The impact of 
contact surface conditions on contact conductance was reported by Yovanovich, et al. 
[31]. Other factors that affect measurement accuracy were reported in the study 
introduced by Gwinn, et al. [32] such as temperature sensors location uncertainty, 
distortion of temperature gradient by temperature sensors, uniformity of heat flux at 
temperature sensors, and heat losses. The device developed by Gwinn, et al. [32] was 
used to measure 3 different interface materials in free air environment. This study 
reported significant change in bare contact resistance (60% drop) between the metering 
blocks after conducting tests for thermal interface materials. The change of contact 
resistance was reported to be an indication of residue interface material on the metering 
block surfaces even though the metering blocks were frequently cleaned with acetone and 
dish detergent.  
Solbrekken, et al. [33] also developed a similar apparatus following the ASTM D-
5470 guidelines and used K-type thermocouples as temperature sensors and 50 Watt 
Kapton film heaters. This study recommended using a more accurate temperature sensor 
and more powerful heaters. Another apparatus following ASTM D-5470 standards was 
developed by Cullham, et al. [34], who used Platinum RTDs as temperature sensors and 
 22
cartridge heaters. Their apparatus also addressed the problem of in-situ measurement of 
sample thickness using laser detectors.  
 
CHAPTER 3 
EXPERIMENTAL MEASUREMENT OF PARAMETERS IMPACTING 
THERMAL PERFORMANCE IN BALL GRID ARRAY PACKAGES 
 
3.1 Study Parameters 
Underfill materials are gaining wide acceptance in harsh environment electronic 
packaging applications due to their ability to enhance solder joint reliability. Underfill 
materials should have a positive impact on thermal performance as well since they offer a 
less resistive conductive path between the package and the PCB when compared to air. 
In this work, one of the study parameters chosen was the impact of using underfill 
material on thermal performance of plastic ball grid array packages. In order to allow a 
clear comparison between using and not using underfill, some test samples were 
underfilled while identical package/board combinations were assembled without 
underfill. Since underfill materials provided by different vendors have varying chemical 
compositions that could impact thermal performance, three different commercially 
available underfill materials were examined. 
The importance of thermal balls as efficient heat paths between the package and 
the PCB was also investigated in this work. Thermal balls were removed from some of 
the test samples to quantify the impact of the thermal balls on thermal performance. 
 
23 
Cross sections of packages with and without thermal balls are shown in Figure 3.1 and 
Figure 3.2, respectively. Current trends in electronic packaging include increasing power 
levels and decreasing die size, both of which have direct impact on thermal performance. 
To quantify the impact of these trends, two different BGA packages with similar major 
dimensions and different die sizes were tested. 
For BGA packages with no thermal balls and no underfill, the only paths available 
for heat flow from the package to the PCB are the air gap between the BT and the PCB, 
and the perimeter solder balls. The efficiency of perimeter balls to conduct heat from the 
package to the PCB should be dependent on the proximity of the perimeter balls to the 
die, the number of perimeter balls, and the cross sectional area of each ball.  To quantify 
the effect of number of perimeter balls on thermal performance, thermal performance 
measurements were conducted for two different packages with different number of 
perimeter balls. To quantify the impact of PCB thermal via geometry, two different 
thermal via designs were included in the test boards.  
Internal connections in electronic packages are expected to deteriorate and/or 
fracture under thermal cycling with the effect of severing efficient heat flow paths inside 
the package. However, thermal resistance is usually and incorrectly treated as a static 
parameter. To quantify the impact of thermal cycling on thermal performance, samples in 
this work were thermally cycled between -40? C and 125? C in a 90 minute cycle. After 
initial measurements were preformed on initial samples, thermal resistance measurements 
were then repeated for all packages after every 250 cycles of exposure. 
 
 
24 
 
 
 
 
 
BGA #1 
 
 
 
Figure 3.1 - Cross sections of BGA packages with thermal balls 
BGA #2 
 
 
 
 
BGA #1  
 
 
 
 
 
Figure 3.2 - Cross sections of BGA packages without thermal balls 
BGA #2  
 
 
 
 
 
25 
3.2 Test Packages and Test Board 
Two different 17 mm plastic BGA packages were tested. The first PBGA featured 
an 8.2 x 8.2 mm square die, and the second PBGA had a 7 x 4.4 mm rectangular die. 
Schematic representations of both packages layout and major dimensions are shown in 
Figure 3.3. The thermal test chip in the first BGA was equipped with 4 quadrant heaters 
and 4 P-N diodes to be used as temperature sensing devices. However, only 3 diodes 
were operational due to wire bond limitations. The thermal test chip in the second 
package contained one heater and one P-N diode. Both packages had 16 thermal balls. 
BGA #1 had 144 perimeter balls arranged in 3 rows, while BGA #2 had 192 perimeter 
balls arranged in 4 rows. Both packages had a ball pitch of 1 mm. Schematic 
representations of the die layouts for both packages are shown in Figure 3.4. 
Up to four different packages could be mounted on one test board (2 packages of 
type 1 and 2 packages of type 2). The four mounting locations on the test board were 
arranged in a 2 by 2 square matrix. The upper two package mounting locations were 
equipped with thermal via type one, which consisted of a heat spreader with a set of 
intersecting copper traces extending to 12 plated through holes. For the lower two 
package mounting locations, a second via design (thermal via type 2) was used, which 
consisted of a solid square copper heat spreader extending to a similar set of 12 plated 
through holes. Both via designs were connected to a copper ground plane buried inside 
the PCB through analogous sets of plated through holes, and differed from each other by 
their top level heat spreader layouts. A fully populated test board and thermal via details 
are shown in Figure 3.5. A schematic of the thermal via connections to the copper ground 
plane inside the PCB is shown in Figure 3.6 
26 
 
 
BGA #2 BGA #1 
 
 
 
 
 
 
 
 
 BGA #1 BGA #2 
D [mm] 17 17 
D1 [mm] 15 15 
E [mm] 17 17 
E1 [mm] 15 15 
b [mm] 0.5 0.6 
e [mm] 1 1 
A1 [mm] 0.45 0.5 
A2 [mm] 0.8 1.15 
A3 [mm] 0.36 0.36 
Number of perimeter balls 156 192 
Number of thermal balls 16 16 
Number of Heaters 4 1 
Heater resistance [Ohm] 5.5 10.7 
No of diodes 3 1 
Die Size [mm] 8.2 x 8.2 7 x 4.4 
 
 
Figure 3.3 - Schematic representation of BGA dimensional parameters 
 
 
 
27 
 
 
Figure 3.4 - Schematic representation of thermal test chips 
BGA #2 
Pad 
Heater 
Diode 
BGA #1 
Diode 
Pad 
Quadrant Heater 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
28 
Thermal Via #2 
Thermal Via #1 
BGA #1 
BGA 
#1
BGA #2 
Figure 3.5 - Test board 
BGA #2 
3.3 Test Matrix 
The test matrix consisted of 48 PBGA packages of type one and 48 PBGA 
packages of type two, mounted on 32 test boards. The BGAs were mounted on the test 
boards and underfilled with 3 different underfill materials so that any given leg of the test 
matrix was represented by four samples. The complete test matrix is listed in Table 3.1. 
 
3.4 Testing Thermal Aspects 
The heaters on the thermal test chips were activated by means of a DC power 
supply. This method was appropriate for direct calculation of the input power by 
measuring the supply output current and the applied voltage. A 1.5? (3.81 cm) thick glass 
fiber insulation layer covered the top BGA surface, while a stream of water at known 
constant temperature was impinged on back of the PCB board. The flowing water 
temperature was monitored using four immersed K-type thermocouples touching the back 
of the board at the centers of the packages, while the on chip diodes were used to sense 
the die surface temperatures. A cross-sectional schematic of the test apparatus is shown in 
Figure 3.7. 
Using this approach, the heat flowed only from the die surface to the back of the 
board in a path that can be approximated as one-dimensional. The package thermal 
resistance can be calculated knowing the heating power, the die surface temperature, and 
the flowing water temperature according to: 
P
TT
?
cj
jc
?
=          (Eq. 3.1) 
 
29 
 
Figure 3.6 - Thermal via connection with ground plane 
 
 
 
 
 
 
 
 
 
 
 
Table 3.1 - Test matrix 
 Packages with Thermal Balls 
No 
Underfill 
Underfill 
#1 
Underfill 
#2 
Underfill 
#3 
BGA#1/Via#1 4 4 4 4 
BGA#2/Via#1 4 4 4 4
BGA#1/Via#2 4 4 4 4 
BGA#2/Via#2 4 4 4 4
 
 Packages without Thermal Balls 
No 
Underfill 
Underfill 
#1 
Underfill 
#2 
Underfill 
#3 
BGA#1/Via#1 0 0 0 0 
BGA#2/Via#1 0 0 0 0
BGA#1/Via#2 4 4 4 4 
BGA#2/Via#2 4 4 4 4
 
 
 
30 
where: 
=
jc
? Junction to case thermal resistance [K/W] 
=
j
T Junction temperature [K] 
=
C
T Case temperature [K] 
=P Input Power [W] 
 
3.5 Testing Electronic Aspects 
Using diodes for characterization of the die surface temperature offered the 
advantage of good linear behavior as well as being non-intrusive. However, due to 
inherent semiconductor device manufacturing variability, each diode needed to be in 
individually calibrated in order to ensure the measurement accuracy. The diode current-
voltage relation is given by: 
?
?
?
?
?
?
?= 1eII
nkT
qV
sd
d
        (Eq. 3.2) 
where: 
=
d
I Diode current [A] 
=
s
I Saturation current [A] 
=q Electron charge (1.6 x 10
-19
 C) 
=
d
V Diode forward voltage [V] 
=n Non-ideality factor  1 ?
=k Boltzman constant (1.36 x 10
-23
 J/K) 
=T Temperature [K] 
31 
This expression can be reformatted as: 
d
s
d
V
I
I
lnnk
q
T
?
?
?
?
?
?
?
?
=
        (Eq. 3.3) 
The term 
?
?
?
?
?
?
?
?
s
d
I
I
nkln
q
 is known as the diode temperature coefficient and ranges from  
-1.8 to -2.0 mV/K, and is a unique value for every diode. 
An important experimental detail was the selection of the diode excitation current. 
This current can be chosen from a few  to 1 mA  depending on the device size. Low 
excitation currents can lead to erroneous temperature readings due to relatively high 
leakage currents. On the other hand, high excitation currents may cause localized heating 
of the device, again causing erroneous temperature readings. The correct selection of the 
excitation current was achieved by measuring the diode current versus voltage, plotting it 
on a semi log scale, and selecting the current region which exhibits the best linear 
relation.  
A?
 
3.6 Testing Fixture and Cooling Circuit 
The test fixture was first designed as CAD solid model including the test board, 
water fittings, and gasket; and then it was manufactured from commercial grade 
aluminum alloy. Cooling water at the back of board was maintained at a constant 
temperature using a water chiller. The water inlet hoses were equipped with ball valves. 
The ball valves were used to shock the system a few times at the beginning of each test to 
purge any trapped air pockets from the system to avoid localized hot spots under the 
32 
BGA packages. A solid model and a photographic image of the test fixture are shown in 
Figure 3.8. 
 
3.7 Data Acquisition and Control 
The huge number of temperature measurements required (about 1600 temperature 
measurements per board) and the need for repetitive measurements after every 250 
thermal cycles necessitated the development of a fully automated data acquisition and 
control system. An image of the test setup is shown in Figure 3.9. 
The data acquisition and control system consisted of: 
1. Personal computer.  
2. Current source for diode excitation. 
3. DC power supply to power the heaters. 
4. Switch with 12 channels to select tested package as well as to route the diode 
excitation current to diodes and power to the heaters. 
5. GPIB card to interconnect all previous components. 
6. Data acquisition card for collecting thermocouple readouts and diode voltage. 
A special program was written in Visual Basic and Labview to set test parameters, read 
calibration data for each board, control the test sequence, acquire data and archive the 
results. The user interface of the data acquisition and control software is shown in Figure 
3.10. A schematic of the data acquisition and control system is shown in Figure 3.11. 
 
 
 
33 
 
BGA 
PCB 
 Gasket 
 
 
 
 
 
Thermocouple 
Water Inlet 
Water Exit 
 
 
Figure 3.7 - Cross?sectional schematic of the test fixture 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.8 - Test fixture 
 
 
 
34 
3.8 Diode Characterization and Calibration 
During initial testing, the diode current versus voltage was plotted on a semi log 
scale ranging from 0 to 1 mA of excitation current. The best linear behavior was observed 
in the region of 450-550 , with a mean squared error of 0.7 ? . Hence, the diode 
excitation current was selected to be 500 ? for the remainder of the experiments. The 
diode calibration process was performed by placing the test boards in an oven and 
recording each diode voltage at different temperatures while they were being excited with 
500 . The average diode temperature coefficient was found to be about ?1.75 mV/K. 
A sample of the calibration output from one of the test boards is shown in Figure 3.12. A 
sample diode calibration report is given in Appendix A. 
A? A
A
A?
Observation of diode characteristics after thermal cycling indicated a slight 
variation in diode temperature coefficients, which can be attributed to permanent 
deformations in the BGA packages. To ensure the accuracy of the diode temperature 
measurements, the calibration procedure was repeated for each diode after every 250 
thermal cycles. The data acquisition and control program was designed to automatically 
calculate the temperature coefficient of each diode and generate a report that was read by 
the testing program at the beginning of each test. 
 
3.9 Testing Procedure 
For each package, the input power during thermal performance testing was 
gradually increased from 0.1 W to 1 W, with a step of 0.1 W. At each power step, the 
average die surface and cooling water temperatures were monitored. Steady state heat  
 
35 
 
 
 
 
 
 
 
 
 
Figure 3.9 - Test setup 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.10 - Data acquisition and control software 
 
36 
 
 
A Data Acquisition Board 
B GPIB Card
C Power Supply 
D Current Source
E Switch Box
F Test Board
GPIB Instructions 
 Power to Heaters 
Diode Excitation
 Thermocouple Readout 
 Diode Voltage Readout 
 Heater Resistance Readout 
F 
E 
D 
B 
C 
Figure 3.11 - Data acquisition and control system 
A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
37 
transfer was assumed to be present when the standard deviations of 8 successive 
temperature measurements fell below 0.05 ?C. This criterion was determined based on 
preliminary observations of the system behavior. The temperature difference between the 
die surface and the cooling water was plotted against the heater power at steady state. A 
sample of a measured temperature difference versus input power data plot is shown in 
Figure 3.13. Thermal resistance, which is the slope of the observed linear variation, was 
then evaluated using a linear regression fit. A sample thermal resistance report generated 
by the data acquisition software is given in Appendix B. 
The system also incorporated an infrared thermal camera set to capture thermal 
images of the tested package at equal intervals. The sequence of still images was then 
compiled into a digital video format showing an animation of the steady state increments 
from test start to end. Sample infrared thermal images from one of the test boards are 
shown in Figure 3.14. 
 
3.10 Experimental Results 
To evaluate the impact of the various study parameters on thermal performance, 
the average test data from similar packages were calculated and then compared. All of the 
thermal resistance measurements for packages with thermal balls and without thermal 
balls are shown in Figures 3.15 and 3.16, respectively. A complete list of all recorded 
thermal resistance test data is given in Appendix C. 
 
 
38 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.12 - Diode calibration data 
Power [W]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Te
mp
era
t
ur
e Diffe
ren
c
e
 
[K]
0
5
10
15
20
25
30
BGA  #1 / Thermal Via #1 / Underfill #3
BGA  #2 / Thermal Via #1 / Underfill #3
BGA  #2 / Thermal Via #2 / Underfill #3
BGA  #1 / Thermal Via #2 / Underfill #3
Figure 3.13 - Sample of temperature measurements 
Temperature [Deg. C]
25 30 35 40 45 50 55
D
i
ode V
o
l
t
age [
V
]
0.69
0.70
0.71
0.72
0.73
0.74
0.75
39 
 
 
 
BGA #2 / Via #2 
BGA #1 / Via #1 
 
 
 
 
 
 
 
 
 
 
BGA #1 / Via #2 
BGA #2 / Via #1 
 
Figure 3.14 0 - Sample IR thermal images of test packages at steady state 
 
 
 
 
 
40 
3.10.1 Use of Underfill 
Underfilled packages consistently showed less thermal resistance than those with 
no underfill. All three underfill materials performed equally. For example, the thermal 
resistances of underfilled BGA #1 packages with thermal balls which were mounted on 
thermal via #1 were found to be 18.64 K/W, 18.74 K/W, and 18.7 K/W, when underfilled 
with underfill #1, underfill #2, and underfill #3, respectively.  
 
3.10.1.1 Packages with Thermal Balls 
The thermal resistance of BGA #1 mounted on thermal via #1 was reduced from 
23.9 K/W to 18.7 K/W (22% reduction) by using underfill. Similarly, BGA #1 packages 
mounted on via #2 exhibited a reduction in thermal resistance from 22.7 K/W to 17.9 
K/W (21% reduction) by using underfill. For BGA #2 mounted on via #1, use of underfill 
reduced the thermal resistance from 27.9 K/W to 25.5 K/W (9% reduction), while for 
BGA #2 packages mounted on via #2, the thermal resistance was reduced from 25.7 K/W 
to 23.7 K/W (8% reduction). 
 
3.10.1.2 Packages without Thermal Balls 
The thermal resistance of BGA #1 mounted on thermal via #2 was reduced from 
36.3 K/W to 20.1 K/W (45% reduction) by using underfill. For BGA #2 mounted on via 
#2, use of underfill reduced the thermal resistance from 47.6 K/W to 30 K/W (37%  
 
41 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.15 - Thermal resistance measurements
      (packages with thermal balls) 
No Underfill Underfill #1 Underfill #2 Underfill #3
Thermal Re
sis
t
anc
e 
[K/
W
]
0
10
20
30
40
50
BGA#1 / Via #2 / without Thermal Balls
BGA#2 / Via #2 / without Thermal Balls
Figure 3.16 - Thermal resistance measurements 
    (packages without thermal balls) 
No underfill Underfill #1 Underfill #2 Underfill #3
Th
er
m
a
l Resistance [K/W]
0
5
10
15
20
25
30
35
40
BGA #1 / Via #1
BGA #1 / Via #2
BGA #2 / Via #1
BGA #2 / Via #2
42 
reduction). These observations indicated that underfill material can be considered an heat 
conduit (even with its low thermal conductivity of about 0.35 W/(m?K)), because of its 
large cross sectional area. For example, the underfill cross sectional area was 289 mm
2
, 
while the sum of all of the perimeter and thermal solder ball cross section areas was only 
17.8 mm
2
. 
 
3.10.2 Use of Thermal Balls 
Investigation of the impact of thermal ball removal was conducted only for the 
more effective thermal via #2. For BGA #1, removal of the thermal balls increased the 
thermal resistance from 22.7 K/W to 36.3 K/W (60% increase) for packages without 
underfill, and from 17.9 K/W to 20.1 K/W (12% increase) for packages with underfill. 
For BGA #2, removal of the thermal balls increased the thermal resistance from 25.7 
K/W to 47.6 K/W (85% increase) for packages without underfill, and from 23.7 K/W to 
30.0 K/W (27% increase) for packages with underfill. 
 
3.10.3 Die Size 
The thermal resistances for BGA #1 were found to be consistently lower than the 
analogous configurations for BGA #2 for all test parameter combinations. These 
differences in thermal performance can be attributed to the large die surface area of BGA 
(67.24 mm
2
), which was more than double the die surface area of BGA #2 (30.8 mm
2
). 
 
43 
3.10.3.1 Packages with Thermal Balls 
The thermal resistance of BGA #1 without underfill when mounted on thermal via 
#1 was 23.9 K/W. For similar BGA #2 packages, the value was 27.9 K/W (17% 
increase). For packages mounted on thermal via #2 and without underfill, the thermal 
resistances were 22.7 K/W  for BGA #1 and 25.7 K/W for BGA #2 (13% increase). 
The thermal resistance of BGA #1 with underfill when mounted on thermal via #1 
was 18.7 K/W. For similar BGA #2 packages, the value was 25.5 K/W (37% increase). 
For packages mounted on thermal via #2 and with underfill, the thermal resistances were 
17.9 K/W for BGA #1 and 23.7 K/W for BGA #2 (32% increase). 
3.10.3.2 Packages without Thermal Balls 
The thermal resistance of BGA #1 without underfill when mounted on thermal via 
#2 was 36.3 K/W. For similar BGA #2 packages, the value was 47.6 K/W (31% 
increase). For packages mounted on thermal via #2 and with underfill, the thermal 
resistances were 20.1 K/W for BGA #1 and 30.0 K/W for BGA #2 (50% increase). 
 
3.10.4 Number of perimeter balls 
BGA #2 had 48 more perimeter balls than BGA #1. The extra balls increased the 
area of heat transfer among perimeter balls by 33%. However, BGA #2 consistently 
showed a higher thermal resistance than BGA #1 in all measured configurations. This 
was an indication that little heat flows through perimeter balls, a fact mainly due to their 
relatively large distance from the die surface where heat was generated. 
 
44 
3.10.5 Thermal Via Geometry 
For packages with thermal balls, BGA #2 packages with no underfill mounted on 
thermal via #1 showed a 9% higher thermal resistance than similar packages mounted on 
thermal via #2 (27.9 K/W and 25.7 K/W, respectively). Similarly BGA #2 packages with 
underfill when mounted on via #1 showed a 8% higher thermal resistance than similar 
packages mounted on thermal via #2 (25.5 K/W and 23.7 K/W, respectively). 
For packages with thermal balls, BGA #1 packages with no underfill mounted on 
thermal via #1 showed a 5% higher thermal resistance than similar packages mounted on 
thermal via #2 (23.9 K/W and 22.7 K/W, respectively). Similarly BGA #1 packages with 
underfill when mounted on via #1 showed a 4% higher thermal resistance than similar 
packages mounted on thermal via #2 (18.7 K/W and 17.9 K/W, respectively). 
The data clearly indicated that all packages mounted on thermal via #2 performed 
better than their counterparts that were mounted on thermal via #1. Since both via 
configurations featured exactly the same plated through hole connections to the ground 
planes inside the PCB, the difference in thermal performance can be directly attributed to 
the geometries of the copper heat spreaders used under the thermal balls. For thermal via 
#1 (cross-hatched copper heat spreader), the copper area was only 1.6 mm
2
. For thermal 
via #2 (solid copper heat spreader), the copper area was 17.6 mm
2
 (over 10 times higher) 
 
 
 
45 
3.10.6 Thermal Cycling 
After initial measurements, the test boards were subjected to thermal cycling from 
-40 to 125 ?C. By repeating the thermal resistance measurements every 250 cycles, the 
increases in thermal resistance associated with material degradation and/or fracture could 
be evaluated. The temperature profile of the 90 minute thermal cycle is shown in Figure 
3.17. 
Details of the number of thermal cycles completed for all packages are shown in 
Table 3.2. The measured variations in thermal resistance are plotted versus the number of 
thermal cycles in Figures 3.18 and 3.19 for BGA #1 and BGA #2, respectively. The first 
500 thermal cycles revealed no noticeable change in thermal performance for all BGA 
Packages. Major changes initiated at 750 cycles for BGA #1 for the case of no underfill 
and thermal balls. An accelerated increase in the thermal resistance then occurred until 
1250 thermal cycles. The thermal resistance increased from 23.9 K/W at 0 cycles to 30.5 
K/W at 1250 cycles (28% increase) for BGA #1/Via #1. Similarly, for BGA #1/Via #2, 
the thermal resistance increased from 22.7 K/W at 0 cycles to 26.4 K/W at 1250 cycles 
(16% increase). After 1250 cycles, the connection to most diodes and heaters were lost 
due to perimeter ball solder joint failures. These early failures were not unexpected due to 
the lack of underfill as well as the large die size in BGA #1. After 750 cycles, BGA #1 
with no underfill and no thermal balls showed a continuous increase of thermal resistance 
from 36.3 K/W at 0 cycles to 43.1 K/W at 1500 cycles (19% increase). 
BGA #2 with no underfill illustrated small increase in thermal resistance after 
2000 cycles. This trend is expected to continue until failure at a higher number of thermal  
 
46 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Packages with Thermal Balls 
 No Underfill Underfill #1 Underfill #2 Underfill #3 
BGA#1/Via#1 2500 2500 2500 1500 
BGA#2/Via#1 2500 2500 2500 1500 
BGA#1/Via#2 2500 2500 2500 1500 
BGA#2/Via#2 2500 2500 2500 1500 
Table 3.2 - Number of completed thermal cycles 
Time [Min.]
0 10203040506070809
Tem
per
at
u
r
e
 [
C
]
-60
-40
-20
0
20
40
60
80
100
120
140
Figure 3.17 - Thermal cycling profile 
0
 Packages without Thermal Balls 
 No Underfill Underfill #1 Underfill #2 Underfill #3 
BGA#1/Via#2 1500 1500 1500 1500 
BGA#2/Via#2 1500 1500 1500 1500
 
 
47 
BGA #1 / Via #1 / With thermal balls
Thermal Cycles
0 500 1000 1500 2000 2500 3000
The
rmal 
Resis
t
anc
e [ 
K/
W
 ]
0
5
10
15
20
25
30
35
No Underfill
Underfill #1
Underfill #2
Underfill #3
 
 
 
 
 
 
 BGA #1 / Via #2 / With thermal balls
Thermal Cycles
0 500 1000 1500 2000 2500 3000
The
rmal Resis
t
anc
e 
[ K/
W
 
]
0
5
10
15
20
25
30
No Underfill
Underfill #1
Underfill #2
Underfill #3
 
 
 
 
 
 
BGA #1 / Via #2 / Without thermal balls
Thermal Cycles
0 200 400 600 800 1000 1200 1400 1600
T
herm
a
l 
Resistance [ K/W 
]
0
10
20
30
40
50
No Underfill
Underfill #1
Underfill #2
Underfill #3
 
 
 
 
 
 
Figure 3.18 - Impact of thermal cycling (BGA #1) 
 
48 
BGA #2 / Via #1 / With thermal balls
Thermal Cycles
0 500 1000 1500 2000 2500 3000
Th
ermal 
Resis
t
anc
e [ K/W
 ]
0
5
10
15
20
25
30
35
No Underfill
Underfill #1
Underfill #2
Underfill #3
 
 
 
 
 
 
BGA #2 / Via #2 / With thermal balls
Thermal Cycles
0 500 1000 1500 2000 2500 3000
Th
ermal 
Resis
t
anc
e [ K/W
 ]
0
5
10
15
20
25
30
No Underfill
Underfill #1
Underfill #2
Underfill #3
 
 
 
 
 
 
BGA #2 / Via #2 / Without thermal balls
Thermal Cycles
0 200 400 600 800 1000 1200 1400 1600
Th
ermal 
Resis
t
anc
e [ K/W
 ]
0
10
20
30
40
50
60
No Underfill
Underfill #1
Underfill #2
Underfill #3
 
 
 
 
 
 
Figure 3.19 - Impact of thermal cycling (BGA #2) 
 
49 
cycles. In the underfilled BGA #2 packages, no signs of deterioration in the thermal 
resistance were observed up to 2500 cycles. This underscores the ability of underfill to 
increase reliability of BGA packages. 
 
3.11 Comparison of Study Parameters 
By comparing the experimental results of the study, it was possible to identify the 
best configurations that minimize thermal resistance. Plots of the influences of various 
study parameters on the thermal resistance of BGA #1 and BGA #2 are shown in Figures 
3.20 and 3.21, respectively. The best thermal performance was achieved using BGA #1 
(larger die), using underfill, having thermal balls, and mounting the package on thermal 
via #2. This configuration reduced thermal resistance by 64% relative to the worst 
parameter combination, which was BGA #2 (small die), no underfill, no thermal balls, 
and mounting the package on thermal via #1. 
Another important observation was the comparison of the impact of using 
underfill versus the impact of using thermal balls. From the BGA #1 results, it can be 
concluded that underfill was more important than the addition of thermal balls. Adding 
underfill reduced thermal resistance by 16.42 K/W, while adding thermal balls reduced 
thermal resistance by 13.56 K/W. However, the opposite was true for BGA #2, where 
adding underfill reduced thermal resistance by 17.69 K/W, while adding thermal balls 
reduced thermal resistance by 21.95 K/W. This apparent contradiction can be attributed 
to the different die sizes in the packages.  
 
50 
The ratio of the effective die area of BGA #1 to that of BGA #2 was about 2.1 to 
1. This significant difference in size allowed BGA #1 to spread heat flow over a larger 
projected area that could take better advantage of the underlying underfill encapsulant 
layer. On the other hand, the smaller die in BGA #2 concentrated heat flow on a smaller 
area that could not take as much advantage of the underfill layer, and was thus more 
influenced by the thermal balls.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
51 
T
h
e
r
mal
 Re
si
st
an
ce
 [
K
/
W
]
16
18
20
22
24
26
28
30
32
34
36
38
Figure 3.20 Impact of study parameters on thermal 
                   performance of BGA #1 
Ther
m
a
l
 R
e
s
i
s
t
anc
e
 [
K
/
W
]
20
25
30
35
40
45
50
Figure 3.21 - Impact of study parameters on thermal  
                     performance of BGA #2 
Underfill / With Thermal Balls / Via #2
Underfill / With Thermal Balls / Via #1 
Underfill / No Thermal Balls / Via #1
No Underfill / With Thermal Balls / Via #2 
No Underfill / With Thermal Balls / Via #1 
No Underfill / No Thermal Balls / Via #2
No Underfill / With Thermal Balls / Via #2 
Underfill / No Thermal Balls / Via #2 
Underfill / With Thermal Balls / Via #2 
Underfill / With Thermal Balls / Via #1 
No Underfill / With Thermal Balls / Via #1 
No Underfill / No Thermal Balls / Via #2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
52 
 53
CHAPTER 4 
THERMAL SIMULATIONS OF THE BGA PACKAGES 
 
4.1 Model Construction 
To further investigate the effects of the various packaging configurations on the 
heat conduction inside the BGA packages, 16 finite element models were developed that 
covered every combination in the experimental study discussed in the previous chapter. A 
heads up digitizing technique was used to capture package dimensions and details from 
cross-sectional photographs of the BGA assemblies. Using this method, a 2-D wire frame 
sketch was drawn against a backdrop of every package cross-section. Figure 4.1 shows 
the details of an example wire frame sketch superimposed on a package cross-sectional 
photograph. 
The 2-D sketches were then used to create detailed solid models of the BGA 
assemblies. For example, Figure 4.2 shows a sectioned solid model of one of the 
packages. Such assembly files were produced for all of the tested BGA configurations. 
This approach allowed for accurate capturing of geometrical details like thermal via 
geometry and connectivity with copper ground planes buried inside the PCB. 
Symmetry was utilized to reduce the sizes of the FEA models. Only 1/8
th
 of each 
BGA #1 configuration was modeled, taking advantage of the square dimensions of 
 
 54
the die and BGA component. For BGA #2, the die had a rectangular shape and 1/4 
models were developed.  
The assembly files were imported into a commercial FEA package (Cosmos), 
where they were automatically meshed with 4 node tetrahedral heat conduction elements. 
Since all parts were modeled as solids, the FEA package was capable of automatically 
detecting contact surfaces and adjusting mesh nodes and mesh continuity accordingly. 
One of the meshed models is shown in Figure 4.3. Different mesh densities were applied 
to different parts within the assembly files to accommodate for the large variations of the 
major dimensions in different regions. The number of nodes and elements in the various 
finite element models are listed in Table 4.1.  
Heat generation boundary conditions were applied to simulate heat generation of 
1 Watt at the top surface of the die. The effect of the cooling water at the back surface of 
the PCB was modeled by applying a constant temperature of 20 ?C at that surface. The 
top surface of the BGA and PCB were modeled as perfectly insulated. Material properties 
were obtained from vendor data sheets and the literature, and are listed in Table 4.2. For 
models with no underfill, the underfill layer mesh was not removed. Instead, the value of 
the thermal conductivity was changed from that of underfill material to that of air. Thus, 
the effects of heat conduction in the air layer between the BT substrate and the PCB were 
included in the BGA configurations without underfill.  
 
Figure 4.1 - Wire frame sketch overlaid on package photo 
 
 
 
 
 
 
 
 
 
Figure 4.2 - Section solid model of BGA #1, with thermal balls 
 
 
Figure 4.3 - Automatic mesh generated from a solid model (BGA #2) 
 
 
 
 
 
 
 
 
 55
Table 4.1 - Mesh sizes including underfill/air layer  
 Number of Nodes Number of Elements 
BGA #1 / Via #1 102958 588790 
BGA #1 / Via #2 79717 448677 
BGA #2 / Via #1 137343 785677 
BGA #2 / Via #2 154575 887189 
 
 
 
Table 4.2 - Material properties for thermal FEA models 
 
 
Material 
Thermal 
Conductivity 
[W/(m?K)] 
Specific 
Heat 
[J/(kg?K)] 
Density 
[kg/m
3
] 
 
Soldermask 0.25 920.9 1910
Solder (Sn-Pb) 50 167 9630 
Mold Compound 0.8 920.9 1910 
Die Attachment 
Adhesive 
2 920.9 1910 
Silicon Die 140 703 2330 
BT Substrate 1 920.9 1900 
Underfill #1 0.38 920.9 1520 
PCB 0.36 1369 1666 
Copper 390 390 8900
 
 
 
 
 
 56
 57
4.2 Calculation of Thermal Resistance 
The difference between the average temperature of the upper die device surface 
and the temperature of the back surface of the PCB (held constant at 20 ?C) was 
calculated for each model. Since the input power (heat generation) was chosen to be 1 
Watt, the calculated temperature difference was equal to the package thermal resistance.  
The calculated thermal resistance values were then compared to those measured 
experimentally. Comparisons between numerical and experimental results from packages 
with thermal balls and without thermal balls are shown in Tables 4.3 and 4.4, 
respectively. The percent differences were reasonable, ranging from 0 to 12%. Plots of 
the numerical temperature predictions for each BGA geometry are presented in Appendix 
D. 
The steady state simulations were used to calculate the amount of heat flowing 
through the various parts of the BGA assemblies. The three primary heat flow paths from 
the package to the board include the thermal balls, perimeter balls, and underfill/air layer. 
The average resultant heat fluxes were calculated for each of these paths at the plane 
defining the bottom of the BT substrate. Figure 4.4 shows an example vector plot of the 
resultant heat flux in one of the thermal balls. It can be seen that the heat flow tends to 
parallel the spherical surface of the solder. The heat flux vector at the top and bottom of 
the solder balls was found to be essentially normal to the BT substrate (z-direction), 
although there was a small in-plane component that will be neglected in further 
discussions. 
 
 
 
 
Thermal Resistance (K/W) 
Packaging Configuration
Experimental Simulation 
 
% 
Difference 
BGA#1/Via#1 
No Underfill 
23.94 26.14 -9.2 
BGA#2/Via#1 
No Underfill 
27.90 26.89 3.6 
BGA#1/Via#2 
No Underfill 
22.71 24.52 -8 
BGA#2/Via#2 
No Underfill 
25.67 23.73 7.6 
BGA#1/Via#1 
Underfill #1 
18.64 20.18 -8.3 
BGA#2/Via#1 
Underfill #1 
26.04 24.05 7.6 
BGA#1/Via#2 
Underfill #1 
18.08 18.51 -2.4 
BGA#2/Via#2 
Underfill #1 
24.01 21.27 11.4 
Table 4.3 - Comparison between experimental measurements and 
                   numerical simulations for packages with thermal balls 
 
 
 
 
 
 
 
 
 
 
 
 
Table 4.4 - Comparison between experimental measurements and 
                   numerical simulations for packages without thermal balls 
 
Thermal Resistance 
(K/W) Packaging Configuration 
Experimental Simulation 
 
% 
Difference 
BGA#1/Via#2 
No Underfill 
36.26 36.27 0 
BGA#2/Via#2 
No Underfill 
47.62 48.18 1.1 
BGA#1/Via#2 
Underfill #1 
19.84 21.92 -10.5 
BGA#2/Via#2 
Underfill #1 
29.93 33.6 -12.2 
 
 
 58
 59
 
4.2.1 Impact of Using Thermal Balls. 
The numerical simulation results illustrated the importance of using thermal balls. 
For BGA #1 mounted on thermal via #2, it was seen that 0.14 Watts flowed normal to the 
thermal balls with the use of underfill, and 0.21 Watts flowed normal to the thermal balls 
without using underfill. This means that at least 20% of the heat flowed through the 
thermal balls, in spite of their small net cross sectional area, which was less than 0.5% of 
the total projected area of the bottom face of the package. In fact, the highest value of 
heat flux (12 x 10
5
 W/m
2
) was located in the thermal balls.  
Another important observation was that the effective cross-sectional areas of the 
thermal balls were highly governed by the cross-sectional areas of the matching copper 
pads. A typical plot of z-direction flux in one of the BGA configurations is shown in 
Figure 4.5. The highest values of flux in the solder balls were found to occur in a set of 
virtual cylinders axially concentric with the connecting copper pads on the PCB.  
 
4.2.2 Impact of Number of Perimeter Balls. 
Although the number of perimeter balls was ten times larger than the number of 
thermal balls in BGA #1, and 12 times larger in BGA #2, the perimeter balls were found 
to make relatively little contribution to the heat flow. This was mainly due to their remote 
location from the die when compared to the thermal balls. For BGA #2, mounted on 
thermal via #2, the contribution of the perimeter balls was only 0.02 Watts for the case 
with no thermal balls and no underfill. In addition, the heat flux distribution was observed 
to be non-uniform over the perimeter balls. The highest value of heat flux (42 x 10
3
 
 60
W/m
2
) was observed at the perimeter ball closest to the die edge. The lowest value of 
heat flux (42 x 10
2
 W/m
2
) was observed at the perimeter ball furthest from die edge. An 
example plot of the z-direction heat flux distribution in the perimeter balls is shown in 
Figure 4.6. 
 
4.2.3 Impact of Using Underfill Material. 
The surface temperature dropped from 44.5 ?C to 18.5 ?C when using underfill 
with BGA #1 mounted on thermal via #2, which was in close agreement with the 
analogous experimental measurements. Significant variation in the z-direction heat flux 
magnitude was found at the BT/underfill interface. Fluctuation patterns changed 
according to the use of underfill and/or thermal balls. However, all package 
configurations shared one important feature, which was a strong reduction in the heat flux 
outside the die shadow. For example, in the case of BGA #1 with underfill and without 
thermal balls, the z-direction heat flux in the area underneath the die varied between 
7,000 W/m
2
 and 12,000 W/m
2
, while in the area outside of the die shadow, the values 
declined to around 500 W/m
2
. Plots of the z-direction heat flux at the package center line 
on the bottom surface of the BT laminate for different BGA #1 configurations are shown 
in Figure 4.7. 
 
4.2.4 Impact of Die Size 
The numerical simulation results also verified that die size was a major factor 
effecting the thermal performance and heat flux distribution within the BGA packages. 
Figure 4.4 - Vector plot of resultant heat flux in a thermal ball 
                    (BGA #2 / Via #2 / No underfill) 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.6 - Example plot of the z-direction heat flux in the perimeter balls
                     (BGA #2 / Via #2 / No underfill) 
Figure 4.5 - Example plot of the z-direction heat flux in BGA #2 package 
                    (Via #2 / No underfill) 
 
 
 
 
 
 
 
 
 
 
 61
 62
Similar to the experimental measurements, the BGA #2 packages with smaller die were 
found to exhibit poorer thermal performance when compared to the analogous BGA #1 
packages. The BGA #2 packages were equipped with a copper thermal via on the BT side 
that should have enhanced performance. However, the die area effect was found to be a 
much more decisive factor in the ranking of relative thermal performances.  
The smaller die area in BGA #2 had a strong impact on the maximum z-direction 
heat flux values at the bottom of the BT laminate. For example, the maximum value was 
12,000 W/m
2
 for BGA #1 with via #2, and 80,000W/m
2
 for BGA #2 with via #2. An 
example contour plot of the heat flux on the bottom surface of the BGA #2 BT substrate 
is shown in Figure 4.8. This plot indicates that the highest z-axis heat flux values exiting 
the bottom surface of the BT laminate were contained within the areas defined by the die 
perimeter and PCB thermal via.  
 
4.2.5 Impact of Thermal Via Geometry 
Comparing the resultant heat flux patterns for analogous BGA #1 configurations 
with thermal via #1 and thermal via #2 revealed that the maximum heat flux in thermal 
via #1 (7 x 10
5
 W/m
2
) was almost 3 times as much as the maximum heat flux in thermal 
via #2 (2.5 x 10
5
 W/m
2
). This was due to the increased copper area in the heat spreader in 
thermal via #2. Example vector plots of the heat flux in thermal via #1 and thermal via #2 
are shown in Figures 4.9 and 4.10, respectively for the case of BGA #1 with thermal balls 
and without underfill. These results all support the experimental observations that 
packages mounted on thermal via #2 had better thermal performance relative to similar 
packages mounted on thermal via #1. 
 
BGA #1 / Thermal Via #2
Distance From Package Center [mm]
02468
Z- D
i
rect
ion 
Heat Flux 
[
W
/m
2
]
0
2000
4000
6000
8000
10000
12000
14000
With Underfill / With Thermal Balls
Without Underfill / With Thermal Balls
With Underfill / Without Thermal Balls
Without Underfill / Without Thermal Balls
 
 
 
Thermal balls locations 
 
Thermal Via 
plated through 
 
Die perimeter 
 
 
 
 
Figure 4.7 - Plots of z-direction heat flux at the bottom of BT substrate for BGA#1
 
Die Perimeter 
Foot Print 
Thermal Balls 
Location 
Thermal Via 
Foot Print 
 
Figure 4.8 - Example contour plot of the z-direction heat flux at the bottom of 
                    BT substrate (BGA #2) 
 
 
 63
 
 
 
 
 
 
 
 
 
 
Figure 4.9 - Vector plot of heat flux in thermal via #1 
                    (BGA#1, with thermal balls, no underfill) 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.10 - Vector plot of heat flux in thermal via #2 
                      (BGA#1, with thermal balls, no underfill)   
 
 64
 65
4.3 Transient Thermal FEA Simulation 
Transient numerical simulation models were developed to investigate the times needed 
for the various package configurations to reach steady state. For the time dependent 
models, the same materials and boundary conditions as the steady state models were 
used. The temperature distributions were output at equal intervals of one second. At 
every solution sub-step, the average temperature of die surface was calculated. Using this 
data, temperature versus time plots were created as shown in Figures 4.11 and 4.12 for 
BGA #1 and Via #1, and BGA #1 and Via #2, respectively. BGA packages with the 
smallest thermal resistances reached steady state conditions faster than those with higher 
thermal resistances. For example, BGA #1 mounted on via #2 was predicted to reach 
steady state after 60 seconds for the case without underfill and without thermal balls. For 
the case with thermal balls and with underfill, the time to steady state was reduced to 40 
seconds. 
 
 
 
 
 
 
 
 
 
 
 
 
Time [Sec.]
0 10203040506
Temperature [
D
eg. 
C]
20
30
40
50
60
Underfill #1 / With Thermal Balls
No Underfill / With Thermal Balls
Underfill #1 / No Thermal Balls
No Underfill / No Thermal Balls
0
 
 
 
 
 
 
 
 
 
Figure 4.11 - Temperature vs. time plots for BGA #1 and Via #1 
 
 
Time [Sec.]
0 1020304050
Tem
perat
ure [
D
eg
. C]
20
30
40
50
60
Underfill #1 / With Thermal Balls
No Underfill / With Thermal Balls
Underfill #1 / No Thermal Balls
No Underfill / No Thermal Balls
60
 
 
 
 
Figure 4.12 - Temperature vs. time plots for BGA #1 and Via #2 
 66
67 
CHAPTER 5 
STRUCTURAL SIMULATIONS OF THE BGA PACKAGES 
 
5.1 Model Objectives  
Temperature variations within electronic packages coupled with mismatches of 
the thermal expansion coefficients of the constituent materials induce thermal stresses 
that can cause cracks and or fractures. The most common failure mode during thermal 
cycling of BGA packages is fatigue cracking of the solder joints. Typically, the cracks 
initiate at the top and/or bottom interfaces of the solder joints. Further exposure to 
thermal cycling causes growth of the initial crack until there is a total fracture across the 
solder joint.  
Reliability and thermal analyses are usually conducted as two distinct research 
studies. However, since the previously presented experimental and numerical thermal 
studies have indicated the importance of the solder joints as effective heat paths within 
BGA packages, it is important to understand the impact of crack growth in solder joints 
on thermal performance. The experimental measurements in this study have 
demonstrated that the thermal resistance of a BGA package will increase with the 
continued exposure to thermal cycling. The objective of the structural simulation part of 
this research is to predict the number of thermal cycles needed to cause cracking of the 
 
68 
solder joints. Using these results, it will be possible to establish a correlation between 
observed deterioration of thermal performance and the occurrence of solder joint crack 
initiation and propagation. 
 
5.2 Model Construction 
Although meshed models were already available from the thermal simulations 
presented in the previous chapter, there are concerns regarding the accuracy of tetrahedral 
elements in structural finite element simulations. Manual generation of brick element 
meshes for BGA packages can be a tedious task, and is especially burdensome if mesh or 
dimensional modifications are needed. Such modifications would typically necessitate a 
restart of the model generation from the beginning. However, by investing a little more 
time, it was possible in this work to develop a parametric modeling program capable of 
generating a one quarter symmetry FEA model of any plastic BGA package (with certain 
limitations) given its internal dimensions and the required mesh density. 
Using the developed parametric modeling approach, mesh generation time was 
lowered to less than one hour instead of days or weeks. The program also offered the 
advantage of allowing experimentation with different mesh densities with minimal time 
and effort. For example, two parametrically generated models with the same dimensions 
and different mesh densities are shown in Figures 5.1 and 5.2. The program for 
parametric generation was written using the ANSYS parametric development language 
(APDL). The internal dimensions of the BGAs were extracted from a set of 2-D sketches  
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.1 - Param
                    solder ball perim
 
 
 
 
 
 
 
 
 
 
 
 
etrically generated FEA model with the  
eter divided into 8 elements 
Figure 5.2 - Parametrically generated FEA model with the 
                   solder ball perimeter divided into 16 elements 
69 
70 
using the method described in the previous chapter. Using these dimensions and a set of 
prescribed mesh densities, the APDL algorithm successfully generated a set of meshes 
for structural analysis of BGA #1.  
 The developed parametric modeling program had several limitations. These 
limitations were: 
1. No underfill layer can be present. 
2. The die perimeter can not extend beyond the inner row of perimeter solders balls. 
3. The die must be square. 
4. The die width must be a multiple of the solder ball pitch 
5. The two symmetry planes of the package must not pass through the solder balls  
The algorithm implemented in the parametric model generation involved dividing the 
BGA assembly into 6 subparts. Every subpart is generated and saved to a separate mesh 
file using the model dimensions and mesh densities defined in a single mesh description 
input file. The six model subparts are: 
1. Array of thermal balls. 
2. Extent of thermal vias. 
3. Extent of die perimeter. 
4. Connection from die perimeter to array of perimeter balls. 
5. Array of perimeter balls. 
6. Extent of package and PCB perimeter. 
Since every subpart model is created using parameters from the same master file, mesh 
continuity between the different subparts was automatically preserved. After the 
generation of the subpart models, a new empty file is created into which all of the subpart 
71 
models were read in and merged. Finally, the material models, symmetry boundary 
conditions, and thermal loads are then applied to complete the finite element input file. 
 
5.3 Mesh Generation  
The mesh generation techniques for the different subpart models were identical. 
The first step was to create a 3-D wire frame sketch using a set of points, lines and arcs 
that define the major dimensions of the subpart. The wire frame sketch lines and arcs 
were then assigned the mesh densities values defined in the master mesh description 
input file. The sketch elements were merged to form a set of 2-D areas that were auto 
meshed with 2-D elements. These meshed areas were then used to generate a set of 
meshed volumes through as series of extrusions and revolutions. Finally, mirror and 
symmetry commands were applied and the subpart file was saved. As an example, details 
of the 4 steps needed to create one of the subpart files are shown in Figure 5.3. The 6 
steps needed to assemble the various subpart meshes into a mesh for the complete 
assembly are shown in Figure 5.4. 
Since the thermal balls had a shorter standoff than the perimeter balls due to the 
thickness of the copper heat spreader, the thermal ball shape was considerably different 
than the perimeter ball shape. This necessitated a different meshing approach to avoid 
highly distorted elements. To model the no bonding behavior present between the solder 
balls and the PCB and BT laminate soldermask layers, small gaps of 0.0125 mm were 
introduced to separate the solder balls from the soldermask layers. Figure 5.5 shows 
details of the gaps between the solder ball and the soldermask layers. 
 
 
 
 
 
 
 
Step 1: Read dimensions from master file 
           and create a 3-D wire frame sketch 
Step 2: Read mesh densities from master 
             file, and create meshed areas 
 
 
 
 
 
 
 
 
 
 
 
 
Step 3: Execute a set of extrusion and 
             rotation commands to create  
             meshed volumes 
Step 4: Apply mirror and array  
            commands to complete  
            subpart mesh 
 
 
Figure 5.3 - The four steps needed to generate a subpart 
mesh (Array of thermal balls) 
 
 
72 
 
 
 
 
 
1
2 3
 
 
 
 
5 64
 
Figure 5.4 - Six progressive steps for generation of the mesh for the complete 
                    BGA assembly 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.5 - Mesh at the gaps between the solder ball and 
                    the soldermask 
 
73 
74 
Two parametric models were generated for BGA #1 and no underfill for the cases 
of with and without thermal balls. The model with thermal balls consisted of 177,369 
nodes and 159,572 elements. The model without thermal balls consisted of 174,029 
nodes and 156,500 elements. A second more simple version of the parametric generation 
program was also developed, which was capable of generating more general BGA 
constructions (i.e. with no thermal vias and identical thermal and perimeter balls). 
 
5.4 Material Models and Thermal Loads 
A thermal cycling temperature load was applied to the developed finite element 
models for the BGA assemblies. As shown in Figure 5.6, two thermal cycles from -40 to 
125 ?C were simulated. As in the experimental testing, the cycles were 90 minutes in 
duration with 15 minutes ramps and 30 minutes dwells at the lower and upper extremes. 
Material property data were collected from several publications [21-23] and the CINDAS 
database [35]. The BT substrate and PCB were modeled as linear elastic orthotropic 
materials. The copper layers, silicon die, die attachment adhesive, soldermask, and 
molding compound were all modeled as linear elastic isotropic materials. Temperature 
dependent properties were utilized for the PCB, BT substrate and solder. The material 
properties used in the analysis are listed in Table 5.1.  
The solder joints were modeled using the temperature dependent Anand 
viscoplasticity model to capture the creep-plasticity behavior of the 63/37 tin/lead solder 
alloy [22-23]. The input temperature dependent stress-strain curves for solder are shown 
in Figure 5.7. The Anand viscoplasticity model consists of one flow equation and 3 
evolution equations. The flow equation is defined by: 
Figure 5.6 - Thermal cycling load profile 
Time [Sec.]
0 2000 4000 6000 8000 10000 12000
Temp
era
t
ur
e 
[ Deg. C.]
-40
-20
0
20
40
60
80
100
120
140
Table 5.1 - Material properties used in the finite element structural analyses 
 
 
 
 
 
 
 
 
 
 
 
 
Material Elastic Modulus
[MPa] 
Shear Modulus
[MPa] 
Poisson 
Ratio 
CTE 
[1/K] 
BT 
Substrate 
(XY) 
1.789 x 10
4
(Z) 
7.846 x 10
3
(XY) 
8061 
(XZ & YZ) 
2822
(XY) 
0.11 
(XZ & YZ) 
0.39 
(XY) 
12.42 x 10
-6
(Z) 
57 x 10
-6
Copper 1.29 x 10
5
 0.34 16.3 x 10
-6
Silicon Die 163 x 10
3
 0.278 2.5 x 10
-6
Die Attachment 
Adhesive 
6769  0.35 83.6 x 10
-6
Soldermask 3100  0.3 30 x 10
-6
Molding 
Compound 
23520  0.25 10 x 10
-6
PCB 
(XY) 
19303 @ -40? 
13198 @ 125? 
(Z) 
8476 @ -40? 
5836 @ 125? 
(XY) 
8709 @ -40? 
5953 @ 125? 
(XZ & YZ) 
3799 @ -40? 
2595 @ 125 
(XY) 
0.11 
(XZ & YZ) 
0.39 
(XY) 
14.5 x 10
-6
(Z) 
67.2 x 10
-6
Solder 
40426 @ -40? 
34471 @ 125? 
 0.35 24.5 x 10
-6
 
 
 
 
 
 
 
 
 
 
75 
 
          (Eq. 5.1) ()?
?
?
?
?
??
= A
p
kT
Q
s
dt
d
m exp/sinh(
1
0
??
?
 
The 3 evolution equations are defined by: 
 
          (Eq. 5.2) ()
dt
d
B
B
Bh
dt
a
?
?
?
?
?
?
?
0
0
ds
p?
?
?
?
=
 
          (Eq. 5.3) 
n
p
Q
A
d
ss
?
?
?
?
?
=
?
kTdt
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
exp^
*
 
          (Eq. 5.4) 
*
0
1
s
B =
s
?
 
Definitions and values of the parameters in the Anand model are shown in Table 5.2. The 
advantage of using the Anand model over other available creep models in ANSYS was 
the ability to capitalize on damage relationships that were calibrated using that model in 
several recent publications [23-24]. 
 
5.5 Evaluation of Number of Cycles to Crack Initiation 
After solving the finite element models, the critical solder balls (balls with 
maximum value of the accumulated viscoplastic strain energy density per cycle) were 
located. A plot of the viscoplastic strain energy density in the perimeter and thermal 
solder balls of BGA #1 is shown in Figure 5.8. A similar plot for the BGA #1  
 
 
76 
 
STRAIN, ?
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040
STRESS, 
?
  (
M
Pa)
0
5
10
15
20
25
30
35
40
45
50
55
60
 
 
 
 
 
 
 
 
 
 
Figure 5.7 - Temperature dependent stress strain curves for 63Sn-37Pb solder 
 
 
 
Table 5.2 - Definitions and values of the Anand model parameters 
Parameter Value Definition 
S
0
 (MPa) 12.41 Initial Value of Deformation Resistance 
Q/k (1/K) 9400 Activation Energy/ Boltzmann?s Constant 
A (1/sec) 4.0E-6 Pre-Exponential Factor 
?  (dimensionless) 1.5 Multiplier of Stress 
m (dimensionless) 0.303 Strain Rate Sensitivity of Stress 
h
0
 (MPa) 1378.95 Hardening Constant 
S* (MPa) 13.79 Coefficient of Deformation Resistance Saturation Value
n (dimensionless) 0.07 Strain Rate Sensitivity of Saturation  
(Deformation Resistance) Value 
a (dimensionless) 1.3 Strain Rate Sensitivity of Hardening 
 
 
77 
configuration without thermal balls is shown in Figure 5.9. In both cases, the critical 
perimeter solder ball was located on the package diagonal, farthest from the package 
center. Similarly, the critical thermal ball in Figure 5.8 was located on the package 
diagonal, furthest from package center. 
Volumetric averaging of the viscoplastic strain energy density was preformed to 
minimize the effects of mesh density on the calculation accuracy. The accumulated 
energy density was calculated at the first and the second thermal cycles. The thermal 
balls were soldermask defined (SMD) at both the top and bottom interfaces. In this case, 
the portions of the solder used for calculating the volumetric average of the viscoplastic 
strain energy density were the parts protruding inside the solder mask (see Figure 5.10). 
The perimeter balls were soldermask defined at their top interface and non-soldermask 
defined (NSMD) at their bottom interface. In this case, the volumetric averaging was 
preformed on the protruding portion at the top interface and in a 5 mil thick layer at the 
bottom interface (see Figure 5.10). 
The accumulated plastic work per thermal cycle was calculated according to: 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
== minutes90Time
e
ee
minutes180Time
e
ee
ave
V
.V?W
V
.V?W
?W
 (Eq. 5.5) 
 
where: 
e
W = Element viscoplastic strain energy density 
e
V = Element volume 
 
 
78 
 
 
 
 
 
Critical perimeter ball 
 
 
 
 
Critical thermal ball 
 
Figure 5.8 - Critical solder balls for BGA #1 with thermal balls 
 
 
 
79 
 
 
 
 
Critical perimeter ball 
Figure 5.9 - Critical solder ball for BGA #1 without thermal balls 
 
 
 
 
 
Thermal ball
Perimeter ball 
Solder ball bulk 
Portion used for volumetric averaging of the  
viscoplastic strain energy density 
 
Figure 5.10 - Solder balls and regions used for volumetric averaging 
 
 
80 
Calculated values of the average viscoplastic work accumulated per cycle for the critical 
solder balls are listed in Table 5.3. Using material correlation data between number of 
cycles to crack initiation and plastic work developed by Darveaux, et al. [23] and Lall, et 
al. [24], the number of cycles to crack initiation of the two BGA packages was estimated 
according to: 
 
81 
?
          (Eq. 5.6) ()
KN =
2
10
K
ave
W
 
where: 
0
N = Number of cycles to crack initiation 
ave
W? = Volumetric average of viscoplastic work accumulated per thermal cycle 
1
K , = Material correlation constants given in Table 5.4. 
2
K
The calculated number of thermal cycles to crack initiation for the critical solder balls are 
listed in Table 5.5. 
 
5.6 Impact of Critical Solder Joints Crack Initiation on Thermal Resistance 
Plots of the crack initiation predictions overlaid on the thermal resistance 
measurements during thermal cycling are shown in Figures 5.11 and 5.12 for BGA #1 
without underfill and configurations with and without thermal balls, respectively. In the 
BGA with thermal balls, it was clear that the first observation of thermal resistance 
increase occurred in close proximity to the number of cycles where the finite element 
model predicted initiation of cracking in the thermal solder balls. This further confirms 
 
 
Table 5.3 - Calculated values of the average viscoplastic work  
                   accumulated per cycle (BGA #1, no underfill) 
 
 
Critical 
Perimeter Ball 
(without 
thermal balls) 
Critical 
Perimeter Ball 
(with thermal 
balls) 
Critical 
Thermal Ball 
?
?
e
ee
V
VW .
 [psi] 
@ Time= 5400 Sec. (1 Cycle)  
41.04 40.25 29.88 
?
?
e
ee
V
VW .
 [psi] 
@ Time= 10800 Sec. (2 Cycles)
55.73 54.5 47.07 
ave
W?
 [psi] 
14.69 14.25 17.19 
 
 
Table 5.4 - Darveaux and Lall material correlation constants [23,24] 
 
 
1
K  
2
K  
Darveaux 48300 -1.64
Lall 28769 -1.53
 
 
Table 5.5 - Calculated number of thermal cycles to crack initiation  
                   (BGA #1, no underfill) 
 
 
Critical Perimeter Ball 
(without thermal balls) 
Critical Perimeter Ball 
(with thermal balls) 
Critical 
Thermal Ball 
Darveaux 589 619 455 
Lall 471 494 371
 
 
 
82 
83 
the importance of thermal balls to thermal performance. For the case without thermal 
balls, the observed increases in thermal resistance were also observed to initiate in close 
proximity to the number of cycles where the finite element model predicted initiation of 
cracking in the perimeter solder balls. 
An important observation was that the FEA models predicted that cracks would 
initiate in the critical thermal ball (which is close to package center) before crack 
initiation occurred in the critical perimeter ball (which is furthest from package center) 
using both sets of material constants in the failure model. This contradicted the 
conventional wisdom that the critical perimeter balls usually crack earlier than the critical 
thermal balls. This contradiction can be attributed to the fact that thermal balls were 
mounted on a relatively thick copper heat spreader (via). That meant that the thermal 
expansion coefficient mismatch between the die and the PCB near the thermal balls was 
13.8 x 10
-6
 [1/K], while the analogous mismatch near the perimeter balls was only 12 x 
10
-6
 [1/K]. Also, due to the copper heat spreader thickness, the standoff between the 
package and the PCB was only 0.3 mm for the thermal balls, while it was 0.35 mm for 
the perimeter balls.  
 
 
 
 
 
 
 
 
BGA #1 /  Thermal Via #2 / Without Underfill / With Thermal Balls
Thermal Cycles
0 200 400 600 800 1000 1200 1400
Ther
mal Resis
t
anc
e
 [K/W]
0
5
10
15
20
25
30
Perimeter Ball (Lall)
Thermal Ball (Lall)
Thermal Ball (Darveaux)
Perimeter Ball (Darveaux)
 
Fail 
 
 
 
 
 
 
 
 
Figure 5.11 - Crack initiation prediction values superimposed on thermal 
                      resistance measurements for BGA packages with thermal balls 
 
 
BGA #1 /  Thermal Via #2 / Without Underfill / Without Thermal Balls
Thermal Cycles
0 200 400 600 800 1000 1200 1400 1600
Therma
l Res
i
stance [K/W]
0
10
20
30
40
50
Perimeter Ball (Lall)
Perimeter Ball (Darveaux)
Figure 5.12 - Crack initiation prediction values superimposed on thermal 
                      resistance measurements for BGA packages without thermal balls
84 
 85
CHAPTER 6 
EXPERIMENTAL THERMAL RESISTANCE MEASUREMENTS 
OF THIN ELECTRONIC PACKAGING MATERIALS 
 
6.1 Motivation and Objective 
Since the thermal properties of individual materials and sub assemblies used in 
manufacturing of ball grid array packages have a direct impact on the package overall 
performance, it is important to be able to accurately measure thermal resistance of such 
materials and sub assemblies. Conventional methods such as guarded hot plate method 
are not suitable to measure the thin electronic packaging materials [9, 32-34]. ASTM 
standard D5470-95 offers an alternative non-intrusive approach to measure thermal 
resistance of thin components used in electronic packaging. The suggested apparatus 
consists of two long metering blocks featuring equi-spaced holes for temperature sensors 
insertion. The first metering block (hot metering block) is heated by means of several 
electric heaters attached to one of its ends. The opposing end of the other metering block 
(cold metering block) is attached to a serpentine tube in which cooling fluid flows. The 
sample to be examined, which has a cross sectional area identical to that of the metering 
blocks, is placed in between the free ends of the two metering blocks and an axial 
 
pressure of up to 3 MPa is applied on the assembly to minimize the effect of contact 
resistance between the sample and the metering blocks. The whole assembly is placed in 
vacuum to minimize heat loss to the environment.  
 
6.2 Apparatus Theory of Operation 
Heaters attached to the base of the hot metering block generate heat that flows 
through the hot metering block, the sample, the cold metering block and ultimately the 
cooling serpentine. The heat flow generates a temperature drop across the metering 
blocks and the sample. The temperature drop across the metering blocks is sensed using 
the temperature sensors embedded inside the metering blocks. By knowing the thermal 
conductivity of the metering block material and the temperature drop across any of the 
metering blocks, the heat flowing through the system may be calculated according to: 
m
mm
m
T
QkA
L
?
=         (Eq. 6.1) 
where:  
Q  = Heat flowing through the system [W] 
m
k  = Thermal conductivity of metering blocks material [W/(m?K)] 
m
A  = Cross sectional area of metering blocks [m
2
] 
m
T?  = Temperature drop across one of the metering blocks [K] 
m
L  = Length of metering block portion corresponding to the temperature drop [m] 
The temperature drop across the thin sample is calculated by extrapolating temperature 
measurements in the cold and hot metering blocks to the sample lower and upper 
surfaces.  
 86
The thermal conductivity of the sample can then be calculated according to: 
s
s
ss
QL
k
AT
=
?
         (Eq. 6.2) 
where:  
s
k  = Thermal conductivity of sample material [W/(m?K)] 
Q  = Heat flowing through the system [W] 
s
A  = Cross sectional area of sample [m
2
] 
s
T?  = Temperature drop across sample [K] 
s
L  = Sample Thickness [m] 
A schematic of the theory of operation for the apparatus is shown in Figure 6.1. 
 
6.3 Apparatus Construction 
The apparatus was constructed from aluminum alloy 2024-T3 material. It 
included a pneumatic actuator, capable of applying up to 2358 N of axial force, attached 
to the bottom of a base plate. The metering blocks and cooling serpentine were allowed to 
slide freely on four cylindrical guides mounted on the upper surface of a base plate. The 
sliding movement was restricted to a maximum of 25 mm which defined the maximum 
sample thickness. Compressive force from the actuator was transmitted to metering 
blocks through a rubber diaphragm that also acted as vacuum seal. The value of the axial 
force was measured using a load cell sandwiched between the serpentine and a stationary 
stopper. Water and electrical feedthrough connectors were attached to base plate to allow 
routing of cooling water, power and measurements signals to the vacuum environment. 
 
 87
 
Figure 6.1 - Theory of operation of apparatus used 
to measure thermal resistance of thin components 
 
 88
 89
The power feedthrough was equipped with 8 high voltage contact points while the 
instrumentation feed though was equipped with 55 contact points. The water feedthrough 
connected cooling water lines between a water chiller and the cooling serpentine to 
maintain the temperature at the upper surface of the cold metering block constant. The 
base plate was also equipped with a vacuum port connected to a vacuum pump; the 
vacuum line was outfitted with a vacuum venting valve to quickly vent the system to 
atmospheric pressure. A shallow groove was machined and polished on the top surface of 
the base plate to provide seating for the bell jar. 
A 0.89 m high bell jar with a rubber sealing gasket attached to its bottom sat on 
the machined groove on the top surface of the base plate. The temperature sensors of 
choice were bare cylindrical 4 wire Resistance Temperature Detector, RTD, elements 1.5 
mm in diameter and 25 mm long. A total of 10 RTDs (5 RTDs in the hot metering block 
and 5 RTDs in the cold metering block) were inserted in through holes drilled in the 
metering blocks, 10 mm apart. A solid model of the apparatus and an image of the 
apparatus after assembly are shown in Figures 6.2 and 6.3, respectively. 
The RTDs were connected in series and excited with a 25 ?A supplied from a 
National Instrument data acquisition board. The same board also measured voltage drop 
across every RTD and automatically converted electrical measurements into 
corresponding temperature value. Near the bottom of the hot metering block, four 
through holes arranged in a 2 by 2 matrix housed cylindrical cartridge heaters capable of 
a maximum output of 400 watts. The heaters were wired such that upper 2 heaters heated 
the metering blocks while the lower two heaters acted as guard heaters. Two extra RTDs 
 
 
 
 
 
 
 
 
 
 
 
Figure 6.2 - Solid model of apparatus 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 6.3 - Apparatus after assembly 
 90
 91
were placed in between the upper and lower rows of heaters to balance heat flow. Two 
zero voltage cross fired heater controllers regulated heat flow to upper and lower heaters 
independently. A 4 to 20 mA signal from a second National Instrument data acquisition 
and control board controlled the power output from the heater controllers. Another 4 to 
20 mA signal controlled air pressure output from a pressure regulator that supplied air to 
the pneumatic actuator, thus controlling axial force applied on the metering blocks and 
the sample. 
The data acquisition system also collected force readings from the load cell, 
vacuum pressure from a vacuum gauge fitted to the vacuum line and inlet and exit 
cooling water temperature from two NPT threaded RTDs mounted on cooling serpentine. 
Figure 6.4 shows details of components used in data acquisition and control. 
Preliminary test runs revealed that the bare RTD elements are too fragile and can 
not be safely inserted into their designated holes in the metering blocks. They were 
especially vulnerable to fracture at the transition joint connecting the RTD element to the 
extension wires. To strengthen the transition joint, an aluminum sleeve was inserted to 
cover the joint and underfill material was dispensed to fill the tight clearance between the 
joint and the sleeve. The modification proved to be effective in eliminating transition 
joint fracture. Vacuum grade thermal grease was used to minimize contact resistance 
between the metering blocks and the RTD elements. 
 
 
Figure 6.4 - Data acquisition and control diagram 
 
 
 92
6.4 Metering Blocks Calibration 
Metering blocks thermal conductivity had to be accurately evaluated since heat 
flow and temperature gradient calculations depended on it. The metering blocks material 
had a nominal thermal conductivity of 121 [W/(m?K)]. To verify the accuracy of that 
value, the apparatus heaters were disconnected from the heater AC controllers and 
hooked to two DC power supplies. Each DC power supply powered one row of heaters. 
The upper two heaters were used to heat the metering blocks while the other two 
lower heaters functioned as guard heaters. To begin the calibration process, the vacuum 
pump was started and pressure inside the bell jar was monitored until it fell below 3 
mTorr. Then, by adjusting power output levels of the DC power supplies, a zero 
temperature difference was achieved between the two RTDs located between the upper 
and lower theaters sets. The zero temperature difference meant that all the heat generated 
in the upper heater sets would pass through the metering blocks towards the cooling 
serpentine. The values of upper heater?s current and voltage drop were measured using a 
6 digits multi-meter and the amount of heat generation was calculated according to: 
QVI=?         (Eq. 6.3) 
where:  
Q  = Heat flowing through the system [W] 
V  = Voltage drop across the heaters [V] 
I  = Current flowing through the heaters [A] 
Temperature measurements of the RTDs were recorded and fitted to a linear 
equation using least square error method. Using the best fit slope and heat flow values, 
the thermal conductivity of the metering blocks was calculated. The metering blocks  
 93
thermal conductivity was found to be 133 W/(m?K) which was higher than the 
documented value of 121 W/(m?K). Experimental measurements used for evaluating 
metering blocks thermal conductivity are listed in Table 6.1 
 
6.5 Evaluation of Sample Contact Resistance 
To evaluate the contact resistance between the sample and metering blocks, two 
25 by 25 mm copper samples of 5 mm and 10 mm thickness were tested. Copper was 
selected as the sample material because it would be a good indicator of device 
measurement accuracy due to its low thermal resistance. Since both samples were of the 
same material and varied only in thickness, thermal resistance of the 10 mm sample 
should be double that of the 5 mm sample if thermal contact resistance was negligible. 
However, since thermal resistance is usually of considerable value, it can not be 
overlooked and needs to be evaluated. 
The relation between the thermal resistances of the two samples can be written as: 
th _10mm th _ 5mm
R2R=         (Eq. 6.4) 
where: 
10
th_10mm C
10
T
RR
Q
?
+=         (Eq. 6.5) 
5
th _ 5mm C
5
T
RR
Q
?
+=         (Eq. 6.6) 
and where: 
th_10mm
R  = Thermal resistance of 10 mm sample 
th _ 5mm
R  = Thermal resistance of 5 mm sample 
 94
 
 
 
Table 6.1 - Measurements used to calculate thermal 
conductivity of metering blocks
 
Heater Voltage Drop 41.375 V 
Heater Current 0.55562 A 
Guard RTD #1 67.4 ?C 
Guard RTD #2 67.4 ?C 
Metering Block RTD #1 29.56 ?C 
Metering Block RTD #2 32.37 ?C 
Metering Block RTD #3 35.2 ?C 
Metering Block RTD #4 37.92 ?C 
Metering Block RTD #5 40.76 ?C 
Best Fit Slope 279.56 ?C/m 
Cross Sectional Area 625 x 10
-6
 m
2
 
 
 
 
 
 
 
 
 95
C
R  = Thermal contact resistance  
10
T?  = Measured temperature drop across 10 mm sample 
5
T?  = Measured temperature drop across 5 mm sample 
10
Q  = Measured heat flow through 10 mm sample 
5
Q  = Measured heat flow through 5 mm sample 
Multiplying Eq. 6.6 by 2 gives 
5
th _ 5mm C
5
T
2R 2R 2
Q
?
+=        (Eq. 6.7) 
Substituting for  with , Eq. 6.7 becomes 
th _ 5mm
2R
th_10mm
R
5
th _10mm C
5
T
R2R2
Q
?
+=        (Eq. 6.8) 
Subtracting Eq. 6.5 from Eq. 6.8 yields: 
5
C
51
TT
R2
QQ
??
=?
10
0
        (Eq. 6.9) 
By repeating measurements for the 10 mm and 5 mm samples under different 
axial loads, it was be possible to generate calibration curves that were used to account for 
contact resistance for different samples under different axial loads. The tests were 
preformed for both samples under vacuum less than 3 mTorr. The applied axial force 
varied from 890 to 3114 N with an approximate step size of 222 N. At every step the heat 
flow through the sample and temperature drop across the sample were calculated. The 
average sample temperature through the test was kept at 50 ?  0.1 ?C. 
Measurements used to calculate thermal contact resistance are listed in Tables 6.2 
and 6.3. Due to difference in calculated heat flow values between the cold and hot  
 96
 
Force [N] Q [W] 
Hot Block 
Q [W] 
Cold Block
Q [W] 
Average
T? [K]
Sample
Mean 
Sample Temperature [C]
890 27.02 27.32 27.17 4 50.02 
1134 27.11 27.4 27.26 3.73 49.97 
1357 27.1 27.52 27.31 3.64 50.04 
1579 27.29 27.5 27.4 3.53 50 
1802 27.44 27.61 27.53 3.45 50.05 
2015 27.5 27.58 27.54 3.38 50.01 
2282 27.38 27.74 27.56 3.29 50.06 
2464 27.49 27.71 27.6 3.25 50.06 
2691 27.46 27.78 27.62 3.19 50.05 
2918 27.45 27.79 27.62 3.12 50.03 
3114 27.72 27.9 27.81 3.05 50.05 
 97
 
 
Force [N] 
Q [W] 
Hot Block 
Q [W] 
Cold Block
Q [W] 
Average
T? [K]
Sample
Mean 
Sample Temperature [C]
890 26.88 27.21 27.05 4.18 50.03 
1223 27.23 27.29 27.26 3.98 50.01 
1348 27.07 27.41 27.24 3.92 50.03 
1601 27.15 27.49 27.32 3.8 50.05 
1788 27.34 27.48 27.41 3.75 50.05 
2024 27.25 27.61 27.43 3.65 50.09 
2251 27.32 27.61 27.47 3.6 50.06 
2460 27.23 27.58 27.41 3.56 50.02 
2673 27.23 27.55 27.39 3.53 50.04 
2918 27.26 27.62 27.44 3.49 50.07 
3132 27.13 27.66 27.4 3.44 50.07 
Table 6.3 - Measurements used to calculate contact resistance (10 mm thick sample) 
Table 6.2 - Measurements used to calculate contact resistance (5 mm thick sample) 
metering blocks values, the average of the two metering blocks was used. However the at 
any given step, the mismatch between the two metering blocks did not exceed 2%. 
Thermal resistance versus axial force data was fitted with exponential equation of the 
form: 
 98
c
bF
th
Rae=+         (Eq. 6.9) 
The correlation coefficients for the 5 mm sample were: 
0.080158=a  K/W  46.750824 ??= Eb  1/N   K/W 0.101625=c
The correlation coefficients for the 10 mm sample were: 
0.072374=a  K/W  48.731265 ??= Eb  1/N   K/W 0.121281=c
Measured 
T
Q
?
 values and the corresponding best fit curves are shown in Figure 
6.5.  Substituting with best fit equations in Eq. 6.9 
( ) ( )0.1212810.0723740.1016250.0801582
48.73126546.750824
+?+=
???? FEFE
c
eeR  K/W 
 
Rearranging: 
081969.00.0723740.160316
48.73126546.750824
+?=
???? FEFE
c
eeR  K/W (Eq. 6.10) 
By taking the limit as the axial force goes to infinity, the amount of permanent contact 
resistance was calculated. 
( ) 081969.0081969.00.0723740.160316
48.73126546.750824
F
Lim
=+?=
????
??
FEFE
c
eeR  K/W 
A plot of contact resistance versus axial force is shown in Figure 6.6. To calculate the 
thermal resistance of the 5mm sample,  was substituted with  in 
equation 6.5. 
th_10mm
R
th _ 5mm
2R
Force [N]
500 1000 1500 2000 2500 3000 3500
?
T/Q
 [K/W
]
0.10
0.11
0.12
0.13
0.14
0.15
0.16
5 mm Data
5 mm Best Fit
10 mm Data
10 mm Best Fit
 
 
 
 
 
 
 
 
Figure 6.5 - Thermal resistance measurements of 5 and 10 mm copper samples 
 
 
 
Force [N]
0 500 1000 1500 2000 2500 3000
Thermal
 Cont
act Resistance [K/
W]
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Thermal contact resistance
Permenant thermal conact resistance
 
 
 
 
 
 
 
 
 
Figure 6.6 - Calculated contact resistance as a function of axial force 
 
 99
10
th _ 5mm C
10
T
2R R
Q
?
+=        (Eq. 6.11) 
Subtracting Eq. 6.6 from Eq. 6.11 and taking the limit as the force goes to infinity yields: 
( ) ( )( )0.1016250.0801580.1212810.072374R
46.75082448.731265
F
th_5mm
Lim
+?+=
????
??
FEFE
ee  
019656.0101625.0121281.0
5_
=?=
mmth
R  K/W 
The conductivity of the copper material was calculated according to: 
()()
407
0.0196566625E
35E
AR
L
k
th_5mm
5
=
?
?
==  W/(m?K) 
The calculated conductivity of the copper material was 5.7% higher than the reference 
value of 385 W/(m?K). A heat flow of 30 W passing through a 5 mm thick sample with a 
385 W/(m?K) thermal conductivity would cause a 0.62 ?C drop across the sample. The 
same heat flow passing through a similar sample with a 407 W/(m?K) thermal 
conductivity would cause a 0.59 ?C drop across the sample. That meant that the 5.7% 
thermal conductivity measurement discrepancy was equivalent to a temperature 
measurement error of only 0.03 ?C. It would be expected that measurement accuracy 
should improve significantly for samples whose thermal resistance are higher than that of 
copper sample. 
 
6.6 Modification of Temperature Sensors. 
Although bare RTD elements proved to be a good choice from measurement 
accuracy standpoint, they were extremely fragile. RTD elements needed to be replaced 
repeatedly to the extent that RTD fracturing imposed a serious impediment to practical 
use of the apparatus. RTD elements were fractured due to deformation of their respective 
 100
 101
holes under axial force. It was clear that modifications of RTD element were needed in 
order to ensure continuous reliable performance of the apparatus. 
The modifications had to satisfy several objectives.  They were: 
1. Provide protection to RTD elements. 
2. Provide good contact between the sensor and the metering blocks 
3. Overall thermal resistance of the sensor should be as close as possible to that of 
the metering blocks to maximize measurements accuracy. 
Protection of RTD elements may be achieved by encasing them in metallic 
sheaths.  A thin underfill layer would bond the RTD to the sheath as well as to function 
as a protective cushion for the RTD due to its relatively low stiffness. A solid model 
representation of proposed modifications is shown in Figure 6.7. By machining the outer 
diameter of the sheath to a slightly oversized dimension than that of the holes in the 
metering blocks, a tight fit and better contact would be achieved between the metering 
blocks and the sensors. 
A 2-D half symmetry parametric finite element model was introduced that would 
help identify the optimum dimensions and sheath material that would satisfy the design 
requirements. The model was meshed with 18960 quad elements and 19609 nodes. Detail 
of the finite element model is shown in Figure 6.8. Material properties of RTD material 
was assumed to be that of 98% pure Alumina based on information supplied from the 
RTDs vendor. All material properties used were extracted from www.matewb.com, 
except for underfill material.  
 
 
 
 
 
 
 
 
 
Metallic sheath 
Underfill layer 
RTD element 
Figure 6.7 - Proposed modifications for bare RTD elements 
Fixed Temperature 
RTD - Sheath Assembly 
 102
Metering 
Blocks 
Sample 
Underfill 
Ceramic RTD
Heat Flux 
Sheath 
Figure 6.8 - Finite element model detail 
 103
The thermal conductivity and thermal expansion coefficient of the underfill were 
obtained from vendor data sheet; Young?s modulus data was obtained from CAVE 
(Center for Advance Vehicle Electronics at Auburn University) testing data. Material 
properties used in finite element model are shown in Table 6.4. 
An optimization analysis was preformed using the finite element model using the 
design variables sweep technique. Sheath material, sheath thickness, underfill thickness 
were used as the input variables for the optimization analysis. For every design variable a 
search range was defined. The search ranges were 0.5 to 385 W/(m?K), 0.1 to 2 mm and 
0.25 to 0.5 mm for sheath thermal conductivity, sheath thickness, and underfill thickness 
respectively. 
Using temperature distribution in RTD elements obtained from the finite element 
solution, sample thermal conductivity was calculated using the same approach used in 
experimental measurements. The objective function of the optimization analysis was set 
to minimize the difference between the calculated thermal conductivity of the sample and 
the actual value defined in the model. 
The first design optimization run using aluminum as the metering block did not 
identify a practical choice for the sheath material that would satisfy design requirements. 
Optimization results indicated that sheath material thermal conductivity would need to be 
higher than 385 W/(m?K) (the set upper search limit of the optimization algorithm). That 
was due to the fact that aluminum had a relatively high thermal conductivity and the need 
for sheath material thermal conductivity to be higher than that of the metering blocks 
material to compensate for the low thermal conductivity of the ceramic RTD and the 
underfill layer. Rerunning the optimization analysis using stainless 304 for the metering 
 104
blocks material proved to be successful. Although stainless steel metering blocks would 
require higher heat flow to maintain the average sample temperature around 50 ?C, that 
should not be a problem for the 400 watts capacity of the apparatus heaters. 
The optimization results were: 
Underfill Thickness: 0.25 mm 
Sheath Thickness: 0.52222 mm 
Sheath Conductivity: 38 W/(m?K) 
Conducting material property search in www.matweb.com for a thermal 
conductivity of 38 W/(m?K) revealed that the Toughmet alloy (77% Cu, 15% Ni, 8% Sn) 
had a thermal conductivity value of 38 W/(m?K) and good machinability. Since there 
would be a practical limit on the degree of accuracy to which the sheath thickness can be 
machined, the sheath thickness was selected to be 0.52 mm. Reviewing FEA results using 
the parameters values proposed by the optimization analysis confirmed that RTD 
elements were effectively sampling the correct temperature readings. For a sample of 5 
mm thickness and 385 W/(m?K), the FEA model predicted a measurement of 387.75 
W/(m?K) , an error of only 0.7%. Finite elements results showing temperature distribution 
in one of the RTDs is shown in Figure 6.9. 
 
6.7 Structural Analysis of RTD Assembly 
An interference fit would be the best solution to maintain good contact between 
the RTD assembly and the metering blocks. The assembly process would be conducted 
by heating the metering blocks and then inserting the oversized RTD assemblies. After 
cooling down, a compressive stress should guarantee permanent contact between the  
 
 Elastic Modulus 
GPa 
Poisson?s 
Ratio 
Thermal Conductivity 
W/(m?K) 
CTE  
1/K 
Ceramic 370E9 0.22 30 @ 20 ?C. 
26 @ 100 ?C. 
7.6 x 10
-6
Underfill 4.76@ 25 ?C. 
4.29@ 50 ?C. 
3.8@ 75 ?C. 
3.11@ 100 ?C. 
1.32@ 125 ?C. 
 
 
0.3 0.38 35 x 10
-6
Metering 
Blocks 
195 0.29 16.2 @ 0 to100 ?C 
21.5 @ 500 ?C 
17.3 x 10
-6
Table 6.4 - Material properties used in finite element analysis 
 
 
Figure 6.9 - Temperature distribution in RTD and metering block 
(Model Parts in gray color are outside the legend temperature limits)  
 105
 106
RTD assemblies and the metering block. The challenge would be to select the amount of 
interference required to enforce contact while not loading the RTD elements with high 
stress values that might cause fracture during the assembly process. 
To investigate the accepted level of interference, a structural analysis was 
conducted by changing element types from thermal to structural in the thermal FEA 
model. To simulate the interference fit between the sheath and metering blocks, a free 
stress state was modeled while maintaining metering blocks temperature at 200 ?C and 20 
?C for the RTD assemblies. The metering blocks were then loaded with a temperature of 
20 ?C. The effect of the cooling process was checked and found to be equivalent to a 10 
micron interference fit. 
The associated maximum compressive stress in the RTD element was found to be 
72 MPa. The maximum allowable compressive stress listed in www.mateb.com was 2700 
MPa, which indicated that stress levels associated with the assembly process should not 
cause fracture of the RTD elements. Third principal stress distribution in RTD assembly 
is shown in Figure 6.10. To simulate the net effect of metering blocks holes expansion 
and interference fit on the contact status while taking experimental measurements, the 
structural model was subsequently loaded with the temperature profile obtained from the 
thermal run as well as an axial load of 3 MPa. 
Simulation results indicate that RTD assembly would maintain contact with the 
metering blocks under a 148 MPa compressive stress during experimental measurements. 
Radial stress distribution during experimental measurements is shown in Figure 6.11. 
 
 
 
Figure 6.10 - Third principal stress in RTD assembly during assembly 
 
Figure 6.11 - Radial Stress in RTD assembly during experimental measurements 
 107
 108
CHAPTER 7 
SUMMARY AND CONCLUSION 
 
A new automated system for measuring thermal resistance of plastic Ball Grid 
Array packages was built. The system used P-N diodes integrated into die surface as 
temperature sensor devices. The new system included a special module for calibration of 
the temperature sensing diodes. The automated system was capable of conducting 
calibration, experimental measurement and report generation with minimal user 
interaction. The testing apparatus used a stream of water from a water chiller to maintain 
the back surface of test boards at a constant temperature. The cooling water temperature 
was continuously monitored using K type thermocouples. Thermal resistance 
measurements were conducted by heating the die surface using surface heaters integrated 
into test packages die surface and recording die surface temperature, cooling water 
temperature and heater power at steady state condition. 
Using the mentioned system, the impact of several package, board and assembly 
parameters on thermal performance was investigated. The investigated parameters were 
use of underfill, use of thermal balls, die size, number of perimeter balls and thermal via 
geometry. For every test parameters combination, 4 identical packages were tested. The 
test samples included packages underfilled with three different types of underfill. 
 
 109
Other tested packages were not underfilled to be used as basis of comparison. 
Evaluation of the effect of using thermal balls was preformed by removing all 16 thermal 
balls from some of the package and comparing their thermal performance to similar 
packages with thermal balls. The effect of die size and number of number of perimeter 
balls was quantified by testing two different packages with different die size and different 
number of perimeter balls. Two different thermal vias were fabricated into test boards 
and their impact on thermal performance was evaluated. Thermal via type #1 was 
fabricated as a set of intersecting copper traces while thermal via type two was fabricated 
as a solid square copper slab. Both designs connected thermal balls to a set of plated 
trough holes which were in turn connected to copper ground plane buried inside the PCB. 
The test matrix consisted of 32 test boards and 96 packages. 
Experimental measurements proved that using underfill can significantly reduce 
thermal resistance. A drop of thermal resistance between 8% and 45% was observed due 
to the use of underfill depending on package configuration. Removal of thermal balls 
caused an increase in thermal resistance as low as 12% and as high as 85% depending on 
package configuration. Packages with larger die size constantly exhibited better thermal 
performance. Packages fitted with the smaller die showed up to 37% higher thermal 
resistance than packages fitted with the larger die. That may be attributed to the fact that 
large dies had more than double the projected surface area of the smaller dies. 
Packages fitted with the small dies had more 48 perimeter balls than the packages 
fitted with the large dies which meant a 33% increase in the cross sectional area of 
perimeter balls. However that extra area of the relatively high conductive solder did not 
help to enhance thermal performance to match that of the packages fitted with the large 
 110
dies, which may attributed to the relatively remote distance of the perimeter balls from 
the die where heat was generated. 
The solid copper slab design proved to be better than the intersected copper traces 
design. Packages mounted on the solid copper thermal vias had up to 9% less thermal 
resistance when compared to similar packages mounted on the intersected copper traces 
thermal vias. The best thermal performance was observed in package that had the large 
dies, had underfill, had thermal balls and were mounted on the solid copper slab via. 
Thermal performance of packages with the smaller die was more sensitive to the use of 
thermal balls than the use of underfill. The converse was true for package fitted with the 
large dies. 
After performing thermal resistance measurements for all packages, they were 
placed in an oven and thermally cycled between -40 and 125 ?C to investigate the impact 
of thermal cycling on thermal resistance. The oven cycle duration was 90 minutes. 
Thermal cycles consisted of 15 minute ramps and 30 minutes dwells at the lower and 
upper temperature extremes. 
The first 500 thermal cycles revealed no noticeable change in thermal 
performance for all BGA Packages. Major changes appeared at 750 cycles for BGA #1 
with no underfill/with thermal balls as a continuous gradual increase of thermal 
resistance. At 1250 thermal cycles thermal resistance increased from for 23.9 K/W at 0 
cycles to 30.5 K/W (28% increase) for BGA #1/Via #1. Similarly, for BGA #1/Via #2 
thermal resistance increased from for 22.7 K/W at 0 cycles to 26.4 K/W (16% increase). 
After 1250 cycles most diodes and heaters have failed for that package type. This early 
failure was expected due to no use of underfill as well as the large die size of BGA #1. 
 111
After 750 cycles BGA #1 with no underfill and no thermal balls started showing a 
continuous increase of thermal resistance from for 36.3 K/W at 0 cycles to 43.1 K/W 
(19% increase). 
Thermal finite element simulation model for transient and steady state conditions 
were introduced to help understand heat flow patterns inside BGA packages. Finite 
element models were created using auto meshing of solid models of different packages. A 
total of 16 different models were created covering every study parameters combination. 
Simulation results were in agreement with experimental measurements. The difference 
between simulation results and experimental measurement varied between 0% and 12%.  
Transient numerical simulation models proved that packages with the least thermal 
resistance would be the first to reach steady state condition by up to 25 seconds. 
Correlation between solder joints cracking due to thermal cycling and degradation 
of thermal performance was investigated with the help of structural numerical simulation. 
A fully parameterized BGA finite element model was developed using Ansys parametric 
development language (APDL) which helped cut down model generation time from days 
to less than one hour. The structural model predicted the number of thermal cycles to 
crack initiation in solder balls under thermal cycling loads. The predicted number of 
thermal cycles was in the vicinity of the number of thermal cycles where an increase of 
thermal resistance was observed experimentally. 
A new apparatus for measuring thin components used in electronic packaging was 
designed, manufactured and tested. The apparatus was designed according to ASTM 
standard D5470-95 guidelines. Measurements were performed by inserting thin samples 
of 25 x 25mm cross-section between long slender metering blocks of similar cross 
section. The metering blocks were made from Aluminum 2024-T3. One of the free ends 
of the metering blocks was heated using a set of cartridge heaters while the opposite free 
end on the second metering block was cooled using a serpentine drawing water from a 
water chiller. Five bare RTDs (Resistance temperature detector) were inserted in equi-
spaced through holes in the hot metering block. The cold metering block was fitted with a 
similar number of RTDs. Axial force from a pneumatic actuator was applied on the 
metering blocks and the sample sandwiched between them to minimize contact 
resistance. The amount of axial force applied was measured using an inline load cell. 
Temperature measurements were performed in a vacuum environment of less than 3 
mTorr to minimize heat loss to the environment. The testing process was fully automated 
from a PC through a set of data acquisition and control boards. 
Thermal conductivity of the metering blocks was checked using 2 DC power 
supplies to power the cartridge heaters and was found to be 133 W/(m?K). The amount of 
power supplied from the heaters was calculated by measuring temperature distribution of 
the metering blocks using the RTDs. Temperature of the upper and lower sample surfaces 
were calculated by linear extrapolation of the metering blocks temperatures. 
By conducting measurements on 2 copper samples of 5 mm and 10 mm, the 
relation between the applied axial force and contact resistance between the sample and 
the metering blocks was established. The contact resistance was found to be of the form: 
08183.0072434.016029.0
3891367.33996004.2
+?=
???? FEFE
C
eeR  
Thermal conductivity of the copper samples was also calculated and found to be 
405.2 W/(m?K), which was 5.2% more than the reference value of 385 W/(m?K). The 
thermal conductivity measurement error was equivalent to a temperature measurement 
 112
 113
error of 0.0311. It would be expected that higher accuracy of thermal conductivity 
measurement would be achieved for samples with less thermal conductivity than copper. 
Although bare RTD elements provided accurate temperature measurement, their 
fragility was an obstacle to continual use of the apparatus. A proposed modification that 
would help protect the RTD elements was introduced. The propose modification would 
shield the RTD element with a metal sheath, bonding between the RTD element and the 
sheath would be achieved by using a thin underfill layer. A thermal numerical 
optimization simulation was preformed to select the optimum dimensions and sheath 
material that would maximize measurement accuracy. No possible solution was found for 
the aluminum metering blocks. Rerunning the analysis for a stainless steel metering 
blocks proved to be successful. The optimum dimensions were 0.25 mm for the underfill 
layer thickness and 0.52 mm for the metallic sheath thickness. The analysis was also 
solved for the thermal conductivity of the sheath material and was found to be 38 W/mK.  
A material property search was conducted to find such material. The Toughmet 
alloy (77% Cu, 15% Ni, 8% Sn) was found to have a thermal conductivity of 38 W/mK 
and good machinability. A structural analysis was also preformed to investigate the 
possibility of using interference fit between the new RTD assembly and the metering 
blocks to enhance contact between the RTD assembly and the metering blocks. 
Simulation results indicated that 10 micron interference fit between the RTD assembly 
and metering blocks should maintain good contact between the RTD assembly and the 
metering block. Simulation results also indicated the compressive stresses associated with 
the interference fit were not expected to cause fracture of the RTD elements. 
 
114 
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 118 
APPENDIX A 
 
 
Sample Diode Calibration Report 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 119 
Diode calibration for Board No. 1 
Test started on Aug 9/02 - 02:13 
Start temperature:  30 [C]  End temperature:  50 [C] 
Step:  5 [C]  Dwell:  10 [Sec.] Current:  500 [U Amp.] 
Diode coefficients: 
-1.704E-03 
.747191 
-1.699E-03 
.746975 
-1.702E-03 
.747118 
-1.755E-03 
.738808 
-1.711E-03 
.745888 
-1.709E-03 
.745753 
-1.709E-03 
.745768 
-1.739E-03 
.735667 
Test Details: 
Temp. Diode 
#1 
Diode 
#2 
Diode 
#3 
Diode 
#4 
Diode 
#5 
Diode 
#6 
Diode 
#7 
Diode 
#8 
 30.1 .747191 .746975 .747118 .738808 .745888 .745753 .745768 .735667
 35.1 .738844 .738696 .738794 .730021 .737464 .737362 .737367 .727151
 40 .730445 .730315 .730422 .721392 .729022 .728925 .728916 .71857 
 45 .721948 .721841 .721916 .712714 .720498 .720412 .720399 .709919
 50.1 .713118 .713005 .713093 .703682 .711686 .711598 .711614 .70095 
Calibration ended successfully on Aug 9 02 02:33 
 
 120 
APPENDIX B 
 
Sample Thermal Resistance Report 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 121 
Thermal BGA Test Results - Board No.  1 
Test Started on 08 27 02 - 16 53 
Sampling Points:  8 
Max Standard Deviation:  .01 
Test Packages: BGA#1_1, BGA#2_1, BGA#2_2, BGA#1_2 
 
BGA#1_1 Package Data: 
Underfill: #1 
Power Start:  0.1 [W] 
Power Step:  0.1 [W] 
Power End:  1 [W] 
Fractured Balls: None 
BGA#1_1 Test Started on 08 27 02 - 16 53 
BGA#1_1 Test Data 
Set 
Power 
[W] 
T1 
[?C] 
T2 
[?C] 
T3 
[?C] 
Cooling 
Temperature 
[?C] 
Actual 
Power 
[W] 
Standard 
Deviation 
[?C] 
Thermal 
Resistance 
[K/W] 
0.1 23.71 23.93 24.29 23.57 0.101 N/A N/A 
0.1 24.96 24.9 25.08 23.5 0.101 N/A N/A 
0.1 25.34 25.24 25.39 23.58 0.101 N/A N/A 
0.1 25.54 25.43 25.57 23.56 0.101 N/A N/A 
0.1 25.65 25.52 25.65 23.56 0.101 N/A N/A 
0.1 25.71 25.58 25.71 23.53 0.101 N/A N/A 
0.1 25.75 25.62 25.75 23.53 0.101 N/A N/A 
0.1 25.77 25.64 25.76 23.51 0.101 0.60 N/A 
0.1 25.79 25.66 25.76 23.55 0.101 0.26 N/A 
0.1 25.8 25.66 25.78 23.94 0.101 0.15 N/A 
0.1 25.8 25.67 25.79 23.53 0.101 0.09 N/A 
 122 
0.1 25.8 25.67 25.77 23.53 0.101 0.05 N/A 
0.1 25.81 25.68 25.77 23.54 0.101 0.03 N/A 
0.1 25.8 25.65 25.79 23.55 0.101 0.02 N/A 
0.1 25.81 25.67 25.79 23.52 0.101 0.01 22.03 
0.2 26.18 26.39 26.78 23.47 0.208 N/A N/A 
0.2 27.51 27.41 27.63 23.51 0.203 N/A N/A 
0.2 27.88 27.75 27.93 23.5 0.203 N/A N/A 
0.2 28.06 27.92 28.08 23.59 0.203 N/A N/A 
0.2 28.18 28.04 28.19 23.51 0.203 N/A N/A 
0.2 28.23 28.08 28.23 23.55 0.203 N/A N/A 
0.2 28.28 28.12 28.26 23.51 0.203 N/A N/A 
0.2 28.3 28.15 28.29 23.54 0.203 0.61 N/A 
0.2 28.31 28.15 28.32 23.54 0.203 0.26 N/A 
0.2 28.32 28.17 28.31 23.57 0.203 0.15 N/A 
0.2 28.34 28.17 28.32 23.55 0.203 0.09 N/A 
0.2 28.35 28.19 28.32 23.52 0.203 0.06 N/A 
0.2 28.35 28.18 28.32 23.49 0.203 0.04 N/A 
0.2 28.34 28.19 28.33 23.52 0.203 0.02 N/A 
0.2 28.35 28.18 28.32 23.48 0.203 0.01 N/A 
0.2 28.35 28.18 28.32 23.57 0.203 0.01 23.22 
0.3 28.69 28.87 29.29 23.53 0.305 N/A N/A 
0.3 30.04 29.93 30.17 23.48 0.305 N/A N/A 
0.3 30.45 30.31 30.51 23.49 0.306 N/A N/A 
0.3 30.66 30.5 30.69 23.49 0.306 N/A N/A 
0.3 30.77 30.61 30.79 23.55 0.306 N/A N/A 
0.3 30.86 30.68 30.83 23.52 0.306 N/A N/A 
0.3 30.9 30.7 30.88 23.5 0.306 N/A N/A 
0.3 30.92 30.74 30.9 23.56 0.306 0.65 N/A 
0.3 30.94 30.75 30.92 23.47 0.306 0.28 N/A 
0.3 30.95 30.75 30.92 23.5 0.306 0.16 N/A 
0.3 30.95 30.75 30.92 23.48 0.306 0.09 N/A 
0.3 30.94 30.75 30.92 23.49 0.306 0.05 N/A 
0.3 30.95 30.76 30.93 23.54 0.306 0.03 N/A 
0.3 30.96 30.76 30.93 23.51 0.306 0.02 N/A 
0.3 30.96 30.78 30.94 23.54 0.306 0.01 N/A 
0.3 30.95 30.77 30.94 23.56 0.306 0.01 23.96 
 123 
0.4 31.3 31.41 31.83 23.5 0.403 N/A N/A 
0.4 32.53 32.4 32.63 23.52 0.404 N/A N/A 
0.4 32.92 32.73 32.96 23.77 0.404 N/A N/A 
0.4 33.15 33.05 33.13 23.98 0.404 N/A N/A 
0.4 33.26 33.16 33.23 23.53 0.404 N/A N/A 
0.4 33.28 33.08 33.27 23.54 0.404 N/A N/A 
0.4 33.32 33.1 33.3 23.47 0.404 N/A N/A 
0.4 33.34 33.13 33.34 23.52 0.404 0.61 N/A 
0.4 33.35 33.14 33.33 23.54 0.404 0.27 N/A 
0.4 33.37 33.16 33.35 23.55 0.404 0.14 N/A 
0.4 33.38 33.16 33.35 23.5 0.404 0.06 N/A 
0.4 33.38 33.17 33.36 23.49 0.404 0.04 N/A 
0.4 33.38 33.16 33.35 23.51 0.404 0.03 N/A 
0.4 33.39 33.17 33.36 23.49 0.404 0.02 N/A 
0.4 33.39 33.17 33.36 23.48 0.404 0.01 N/A 
0.4 33.39 33.18 33.36 23.51 0.404 0.01 24.23 
0.5 33.74 33.86 34.33 23.5 0.505 N/A N/A 
0.5 35.06 34.91 35.17 23.49 0.506 N/A N/A 
0.5 35.47 35.28 35.52 23.47 0.506 N/A N/A 
0.5 35.67 35.46 35.85 23.54 0.506 N/A N/A 
0.5 35.8 35.58 35.81 23.5 0.506 N/A N/A 
0.5 35.86 35.64 35.86 23.57 0.506 N/A N/A 
0.5 35.92 35.68 35.9 23.48 0.506 N/A N/A 
0.5 35.95 35.7 35.92 23.48 0.506 0.64 N/A 
0.5 35.96 35.72 35.93 23.47 0.506 0.28 N/A 
0.5 35.97 35.73 35.95 23.48 0.506 0.15 N/A 
0.5 35.97 35.74 35.94 23.53 0.506 0.08 N/A 
0.5 35.98 35.74 35.95 23.49 0.506 0.06 N/A 
0.5 35.98 35.74 35.95 23.5 0.506 0.04 N/A 
0.5 35.98 35.74 35.96 23.5 0.506 0.02 N/A 
0.5 35.98 35.75 35.96 23.55 0.506 0.02 N/A 
0.5 35.99 35.76 35.96 23.54 0.506 0.01 N/A 
0.5 36 35.75 35.97 23.5 0.506 0.01 N/A 
0.5 36 35.76 35.97 23.5 0.506 0.01 N/A 
0.5 36 35.77 35.98 23.52 0.506 0.01 24.48 
0.6 36.37 36.46 36.96 23.52 0.610 N/A N/A 
 124 
0.6 37.68 37.47 37.76 23.5 0.601 N/A N/A 
0.6 37.99 37.75 38.02 23.48 0.602 N/A N/A 
0.6 38.17 37.93 38.17 23.55 0.602 N/A N/A 
0.6 38.27 38.02 38.25 23.53 0.602 N/A N/A 
0.6 38.34 38.08 38.31 23.5 0.602 N/A N/A 
0.6 38.37 38.11 38.36 23.49 0.602 N/A N/A 
0.6 38.39 38.14 38.38 23.5 0.602 0.57 N/A 
0.6 38.4 38.14 38.38 23.49 0.602 0.23 N/A 
0.6 38.41 38.16 38.4 23.48 0.602 0.14 N/A 
0.6 38.42 38.15 38.39 23.49 0.602 0.08 N/A 
0.6 38.42 38.15 38.39 23.49 0.602 0.05 N/A 
0.6 38.41 38.16 38.4 23.54 0.602 0.03 N/A 
0.6 38.42 38.16 38.4 23.48 0.602 0.02 N/A 
0.6 38.43 38.16 38.4 23.47 0.602 0.01 24.67 
0.7 38.79 38.86 39.38 23.47 0.709 N/A N/A 
0.7 40.14 39.94 40.28 23.52 0.710 N/A N/A 
0.7 40.56 40.32 40.63 23.52 0.711 N/A N/A 
0.7 40.79 40.52 40.81 23.49 0.711 N/A N/A 
0.7 40.91 40.64 40.92 23.52 0.711 N/A N/A 
0.7 40.99 40.71 40.99 23.51 0.711 N/A N/A 
0.7 41.03 40.74 41.02 23.47 0.711 N/A N/A 
0.7 41.06 40.78 41.03 23.52 0.712 0.66 N/A 
0.7 41.07 40.79 41.07 23.53 0.712 0.30 N/A 
0.7 41.09 40.81 41.06 23.52 0.712 0.17 N/A 
0.7 41.1 40.8 41.08 23.47 0.712 0.10 N/A 
0.7 41.1 40.8 41.08 23.55 0.712 0.06 N/A 
0.7 41.11 40.83 41.08 23.51 0.712 0.04 N/A 
0.7 41.11 40.82 41.09 23.56 0.712 0.03 N/A 
0.7 41.12 40.83 41.1 23.49 0.712 0.02 N/A 
0.7 41.12 40.82 41.1 23.52 0.712 0.01 N/A 
0.7 41.11 40.81 41.09 23.52 0.712 0.01 24.58 
0.8 41.47 41.51 42.07 23.48 0.814 N/A N/A 
0.8 42.76 42.5 42.85 23.54 0.804 N/A N/A 
0.8 43.06 42.78 43.1 23.47 0.805 N/A N/A 
0.8 43.23 42.93 43.25 23.5 0.805 N/A N/A 
0.8 43.34 43.02 43.33 23.46 0.805 N/A N/A 
 125 
0.8 43.39 43.08 43.38 23.5 0.805 N/A N/A 
0.8 43.43 43.12 43.43 23.5 0.805 N/A N/A 
0.8 43.46 43.15 43.45 23.48 0.805 0.56 N/A 
0.8 43.47 43.16 43.46 23.51 0.805 0.23 N/A 
0.8 43.48 43.16 43.58 23.55 0.805 0.14 N/A 
0.8 43.48 43.17 43.45 23.52 0.805 0.09 N/A 
0.8 43.48 43.17 43.47 23.56 0.805 0.06 N/A 
0.8 43.5 43.18 43.48 23.49 0.805 0.04 N/A 
0.8 43.51 43.19 43.49 23.5 0.805 0.03 N/A 
0.8 43.51 43.2 43.48 23.54 0.805 0.02 N/A 
0.8 43.51 43.18 43.48 23.51 0.805 0.02 N/A 
0.8 43.52 43.2 43.5 23.52 0.805 0.01 N/A 
0.8 43.52 43.19 43.49 23.5 0.805 0.01 N/A 
0.8 43.52 43.21 43.48 23.49 0.805 0.01 24.72 
0.9 43.84 43.84 44.41 23.55 0.903 N/A N/A 
0.9 45.13 44.86 45.26 23.49 0.904 N/A N/A 
0.9 45.53 45.22 45.59 23.55 0.905 N/A N/A 
0.9 45.75 45.41 45.76 23.49 0.905 N/A N/A 
0.9 45.86 45.52 45.88 23.56 0.905 N/A N/A 
0.9 45.94 45.6 45.94 23.52 0.905 N/A N/A 
0.9 45.98 45.64 45.99 23.52 0.905 N/A N/A 
0.9 46.02 45.68 46.01 23.51 0.905 0.63 N/A 
0.9 46.04 45.7 46.03 23.53 0.905 0.29 N/A 
0.9 46.04 45.7 46.03 23.51 0.905 0.17 N/A 
0.9 46.05 45.71 46.04 23.57 0.905 0.10 N/A 
0.9 46.06 45.72 46.05 23.5 0.905 0.07 N/A 
0.9 46.06 45.72 46.05 23.51 0.905 0.04 N/A 
0.9 46.07 45.72 46.05 23.51 0.905 0.03 N/A 
0.9 46.07 45.73 46.06 23.54 0.905 0.02 N/A 
0.9 46.07 45.72 46.06 23.49 0.905 0.01 N/A 
0.9 46.07 45.73 46.06 23.54 0.905 0.01 24.76 
1 46.43 46.42 47.02 23.51 1.015 N/A N/A 
1 47.78 47.5 47.94 23.58 1.016 N/A N/A 
1 48.23 47.89 48.29 23.53 1.017 N/A N/A 
1 48.41 48.01 48.39 23.53 1.005 N/A N/A 
1 48.43 48.1 48.47 23.51 1.017 N/A N/A 
 126 
1 48.58 48.16 48.51 23.48 1.005 N/A N/A 
1 48.49 48.12 48.45 23.55 1.005 N/A N/A 
1 48.47 48.1 48.46 23.56 1.005 0.61 N/A 
1 48.49 48.11 48.47 23.5 1.005 0.22 N/A 
1 48.48 48.1 48.46 23.56 1.005 0.08 N/A 
1 48.48 48.11 48.47 23.54 1.005 0.04 N/A 
1 48.47 48.1 48.46 23.57 1.005 0.03 N/A 
1 48.49 48.11 48.44 23.54 1.005 0.02 N/A 
1 48.49 48.11 48.47 23.53 1.005 0.01 24.70 
 
BGA#1_1 Thermal Resistance = 25.0891 [K/W] 
BGA#1_1 Test Ended on 08 27 02 - 17 07 
 
BGA#2_1 Package Data: 
Underfill: #1 
Power Start:  .1 [W] 
Power Step:  .1 [W] 
Power End:  1 [W] 
Fractured Balls: None 
BGA#2_1 Test Started on 08 27 02 - 17 07 
BGA#2_1 Test Data: 
 
Set 
Power 
[W] 
T1 
[?C] 
Cooling 
Temperature [?C] 
Actual 
Power [W]
Standard 
Deviation [?C] 
Thermal 
Resistance 
[K/W] 
0.1 25.78 23.46 0.098 N/A N/A 
0.1 26.87 23.46 0.103 N/A N/A 
0.1 27.19 23.5 0.103 N/A N/A 
 127 
0.1 27.31 23.42 0.103 N/A N/A 
0.1 27.38 23.44 0.103 N/A N/A 
0.1 27.42 23.44 0.103 N/A N/A 
0.1 27.45 23.47 0.103 N/A N/A 
0.1 27.47 23.45 0.103 0.57 N/A 
0.1 27.48 23.43 0.103 0.21 N/A 
0.1 27.48 23.46 0.103 0.10 N/A 
0.1 27.49 23.46 0.103 0.06 N/A 
0.1 27.5 23.46 0.103 0.04 N/A 
0.1 27.5 23.46 0.103 0.03 N/A 
0.1 27.5 23.45 0.103 0.02 N/A 
0.1 27.5 23.45 0.103 0.01 N/A 
0.1 27.5 23.5 0.103 0.01 38.80 
0.2 28.4 23.45 0.207 N/A N/A 
0.2 29.65 23.47 0.207 N/A N/A 
0.2 29.93 23.49 0.207 N/A N/A 
0.2 30.05 23.49 0.207 N/A N/A 
0.2 30.12 23.47 0.207 N/A N/A 
0.2 30.16 23.48 0.207 N/A N/A 
0.2 30.19 23.48 0.207 N/A N/A 
0.2 30.2 23.48 0.207 0.61 N/A 
0.2 30.22 23.46 0.207 0.19 N/A 
0.2 30.22 23.47 0.207 0.10 N/A 
0.2 30.22 23.44 0.207 0.06 N/A 
0.2 30.22 23.49 0.207 0.04 N/A 
0.2 30.22 23.47 0.207 0.02 N/A 
0.2 30.23 23.43 0.207 0.01 N/A 
0.2 30.23 23.45 0.207 0.01 32.80 
0.3 31.11 23.41 0.305 N/A N/A 
0.3 32.34 23.49 0.305 N/A N/A 
0.3 32.61 23.47 0.305 N/A N/A 
0.3 32.74 23.48 0.305 N/A N/A 
0.3 32.8 23.49 0.305 N/A N/A 
0.3 32.84 23.5 0.305 N/A N/A 
0.3 32.87 23.48 0.305 N/A N/A 
0.3 32.89 23.45 0.305 0.60 N/A 
 128 
0.3 32.89 23.49 0.305 0.19 N/A 
0.3 32.9 23.49 0.305 0.10 N/A 
0.3 32.91 23.48 0.305 0.06 N/A 
0.3 32.91 23.5 0.305 0.04 N/A 
0.3 32.91 23.45 0.305 0.02 N/A 
0.3 32.91 23.48 0.305 0.02 N/A 
0.3 32.91 23.48 0.305 0.01 30.93 
0.4 33.77 23.48 0.406 N/A N/A 
0.4 34.98 23.46 0.406 N/A N/A 
0.4 35.25 23.46 0.406 N/A N/A 
0.4 35.37 23.48 0.406 N/A N/A 
0.4 35.44 23.5 0.406 N/A N/A 
0.4 35.48 23.46 0.406 N/A N/A 
0.4 35.5 23.52 0.406 N/A N/A 
0.4 35.51 23.52 0.406 0.59 N/A 
0.4 35.53 23.47 0.406 0.19 N/A 
0.4 35.53 23.47 0.406 0.10 N/A 
0.4 35.53 23.48 0.406 0.06 N/A 
0.4 35.54 23.47 0.406 0.03 N/A 
0.4 35.54 23.46 0.406 0.02 N/A 
0.4 35.54 23.46 0.406 0.02 N/A 
0.4 35.54 23.47 0.406 0.01 N/A 
0.4 35.54 23.46 0.406 0.01 29.73 
0.5 36.51 23.49 0.516 N/A N/A 
0.5 37.77 23.47 0.504 N/A N/A 
0.5 37.92 23.5 0.504 N/A N/A 
0.5 38.03 23.53 0.504 N/A N/A 
0.5 38.09 23.48 0.504 N/A N/A 
0.5 38.13 23.53 0.504 N/A N/A 
0.5 38.15 23.49 0.504 N/A N/A 
0.5 38.16 23.49 0.504 0.56 N/A 
0.5 38.17 23.47 0.504 0.14 N/A 
0.5 38.18 23.48 0.504 0.09 N/A 
0.5 38.19 23.51 0.504 0.05 N/A 
0.5 38.19 23.51 0.504 0.03 N/A 
0.5 38.2 23.52 0.504 0.02 N/A 
 129 
0.5 38.2 23.5 0.504 0.02 N/A 
0.5 38.2 23.51 0.504 0.02 N/A 
0.5 38.2 23.51 0.504 0.01 N/A 
0.5 38.21 23.51 0.504 0.01 29.12 
0.6 39.18 23.5 0.614 N/A N/A 
0.6 40.44 23.48 0.601 N/A N/A 
0.6 40.59 23.52 0.602 N/A N/A 
0.6 40.69 23.5 0.601 N/A N/A 
0.6 40.74 23.53 0.602 N/A N/A 
0.6 40.78 23.53 0.602 N/A N/A 
0.6 40.8 23.49 0.602 N/A N/A 
0.6 40.82 23.51 0.602 0.55 N/A 
0.6 40.83 23.51 0.602 0.14 N/A 
0.6 40.83 23.52 0.602 0.08 N/A 
0.6 40.84 23.5 0.602 0.05 N/A 
0.6 40.84 23.48 0.602 0.04 N/A 
0.6 40.84 23.52 0.602 0.02 N/A 
0.6 40.84 23.54 0.602 0.01 N/A 
0.6 40.84 23.5 0.602 0.01 28.84 
0.7 41.77 23.54 0.707 N/A N/A 
0.7 43.09 23.51 0.707 N/A N/A 
0.7 43.39 23.51 0.707 N/A N/A 
0.7 43.52 23.53 0.707 N/A N/A 
0.7 43.59 23.52 0.707 N/A N/A 
0.7 43.64 23.54 0.707 N/A N/A 
0.7 43.67 23.51 0.707 N/A N/A 
0.7 43.69 23.52 0.707 0.65 N/A 
0.7 43.7 23.51 0.707 0.21 N/A 
0.7 43.71 23.56 0.707 0.11 N/A 
0.7 43.72 23.52 0.707 0.07 N/A 
0.7 43.72 23.5 0.707 0.05 N/A 
0.7 43.72 23.56 0.707 0.03 N/A 
0.7 43.73 23.52 0.707 0.02 N/A 
0.7 43.73 23.54 0.707 0.01 N/A 
0.7 43.73 23.51 0.707 0.01 N/A 
0.7 43.73 23.51 0.707 0.01 28.59 
 130 
0.8 44.61 23.53 0.807 N/A N/A 
0.8 45.88 23.55 0.807 N/A N/A 
0.8 46.17 23.48 0.808 N/A N/A 
0.8 46.29 23.51 0.808 N/A N/A 
0.8 46.36 23.55 0.808 N/A N/A 
0.8 46.41 23.54 0.808 N/A N/A 
0.8 46.44 23.53 0.808 N/A N/A 
0.8 46.46 23.54 0.808 0.62 N/A 
0.8 46.47 23.55 0.808 0.20 N/A 
0.8 46.48 23.52 0.808 0.11 N/A 
0.8 46.49 23.56 0.808 0.07 N/A 
0.8 46.49 23.53 0.808 0.05 N/A 
0.8 46.5 23.55 0.808 0.03 N/A 
0.8 46.5 23.53 0.808 0.02 N/A 
0.8 46.5 23.54 0.808 0.02 N/A 
0.8 46.5 23.52 0.808 0.01 N/A 
0.8 46.51 23.53 0.808 0.01 28.45 
0.9 47.29 23.55 0.905 N/A N/A 
0.9 48.43 23.54 0.906 N/A N/A 
0.9 48.68 23.55 0.906 N/A N/A 
0.9 48.8 23.53 0.906 N/A N/A 
0.9 48.86 23.56 0.906 N/A N/A 
0.9 48.9 23.53 0.906 N/A N/A 
0.9 48.93 23.54 0.906 N/A N/A 
0.9 48.94 23.56 0.906 0.56 N/A 
0.9 48.95 23.56 0.906 0.18 N/A 
0.9 48.96 23.56 0.906 0.10 N/A 
0.9 48.97 23.56 0.906 0.06 N/A 
0.9 48.98 23.54 0.906 0.04 N/A 
0.9 48.98 23.53 0.906 0.03 N/A 
0.9 48.97 23.55 0.906 0.02 N/A 
0.9 48.98 23.55 0.906 0.02 N/A 
0.9 48.98 23.55 0.906 0.01 N/A 
0.9 48.97 23.57 0.906 0.01 28.04 
1 49.97 23.55 1.019 N/A N/A 
1 51.25 23.55 1.003 N/A N/A 
 131 
1 51.37 23.56 1.003 N/A N/A 
1 51.46 23.57 1.003 N/A N/A 
1 51.53 23.55 1.003 N/A N/A 
1 51.56 23.59 1.003 N/A N/A 
1 51.59 23.58 1.003 N/A N/A 
1 51.6 23.55 1.003 0.55 N/A 
1 51.61 23.53 1.003 0.13 N/A 
1 51.62 23.55 1.003 0.09 N/A 
1 51.62 23.53 1.003 0.06 N/A 
1 51.63 23.53 1.003 0.03 N/A 
1 51.63 23.54 1.003 0.02 N/A 
1 51.64 23.58 1.003 0.02 N/A 
1 51.64 23.56 1.003 0.01 N/A 
1 51.64 23.53 1.003 0.01 N/A 
1 51.64 23.56 1.003 0.01 28.00 
 
BGA#2_1 Thermal Resistance = 26.7658 [W/K] 
BGA#2_1 Test Ended on 08 27 02 - 17 18 
 
 
BGA#2_2 Package Data: 
Underfill: #1 
Power Start:  .1 [W] 
Power Step:  .1 [W] 
Power End:  1 [W] 
Fractured Balls: None 
BGA#2_2 Test Started on 08 27 02 - 17 18 
BGA#2_2 Test Data: 
 132 
Set 
Power 
[W] 
T1 
[?C] 
Cooling 
Temperature [?C] 
Actual 
Power [W]
Standard 
Deviation [?C] 
Thermal 
Resistance 
[K/W] 
0.1 24.28 23.5 0.102 N/A N/A 
0.1 25.28 23.5 0.102 N/A N/A 
0.1 25.5 23.5 0.102 N/A N/A 
0.1 25.59 23.5 0.102 N/A N/A 
0.1 25.65 23.5 0.102 N/A N/A 
0.1 25.68 23.4 0.102 N/A N/A 
0.1 25.7 23.5 0.102 N/A N/A 
0.1 25.72 23.5 0.102 0.49 N/A 
0.1 25.72 23.5 0.102 0.15 N/A 
0.1 25.73 23.5 0.102 0.08 N/A 
0.1 25.73 23.5 0.102 0.05 N/A 
0.1 25.73 23.5 0.102 0.03 N/A 
0.1 25.73 23.4 0.102 0.02 N/A 
0.1 25.73 23.5 0.102 0.01 N/A 
0.1 25.74 23.4 0.102 0.01 23.09 
0.2 26.59 23.5 0.204 N/A N/A 
0.2 27.73 23.5 0.204 N/A N/A 
0.2 27.96 23.5 0.204 N/A N/A 
0.2 28.06 23.5 0.204 N/A N/A 
0.2 28.11 23.4 0.204 N/A N/A 
0.2 28.15 23.5 0.204 N/A N/A 
0.2 28.17 23.5 0.204 N/A N/A 
0.2 28.18 23.4 0.204 0.54 N/A 
0.2 28.19 23.4 0.204 0.16 N/A 
0.2 28.19 23.4 0.204 0.08 N/A 
0.2 28.2 23.5 0.204 0.05 N/A 
0.2 28.2 23.5 0.204 0.03 N/A 
0.2 28.2 23.5 0.204 0.02 N/A 
0.2 28.2 23.5 0.204 0.01 N/A 
0.2 28.21 23.5 0.204 0.01 23.20 
0.3 29.12 23.5 0.309 N/A N/A 
0.3 30.26 23.5 0.300 N/A N/A 
0.3 30.41 23.5 0.300 N/A N/A 
 133 
0.3 30.5 23.5 0.300 N/A N/A 
0.3 30.54 23.5 0.300 N/A N/A 
0.3 30.57 23.5 0.300 N/A N/A 
0.3 30.59 23.4 0.300 N/A N/A 
0.3 30.6 23.5 0.300 0.50 N/A 
0.3 30.61 23.4 0.300 0.12 N/A 
0.3 30.62 23.5 0.300 0.07 N/A 
0.3 30.62 23.5 0.300 0.04 N/A 
0.3 30.63 23.4 0.300 0.03 N/A 
0.3 30.63 23.5 0.300 0.02 N/A 
0.3 30.63 23.5 0.300 0.02 N/A 
0.3 30.63 23.5 0.300 0.01 N/A 
0.3 30.63 23.5 0.300 0.01 23.78 
0.4 31.54 23.5 0.405 N/A N/A 
0.4 32.74 23.5 0.405 N/A N/A 
0.4 32.99 23.5 0.405 N/A N/A 
0.4 33.09 23.5 0.405 N/A N/A 
0.4 33.14 23.5 0.405 N/A N/A 
0.4 33.18 23.5 0.405 N/A N/A 
0.4 33.2 23.5 0.405 N/A N/A 
0.4 33.21 23.5 0.405 0.57 N/A 
0.4 33.22 23.5 0.405 0.16 N/A 
0.4 33.23 23.4 0.405 0.08 N/A 
0.4 33.23 23.5 0.405 0.05 N/A 
0.4 33.24 23.5 0.405 0.03 N/A 
0.4 33.24 23.5 0.405 0.02 N/A 
0.4 33.24 23.5 0.405 0.02 N/A 
0.4 33.24 23.5 0.405 0.01 N/A 
0.4 33.25 23.5 0.405 0.01 24.08 
0.5 34.09 23.5 0.508 N/A N/A 
0.5 35.22 23.5 0.508 N/A N/A 
0.5 35.45 23.4 0.509 N/A N/A 
0.5 35.55 23.5 0.509 N/A N/A 
0.5 35.6 23.4 0.509 N/A N/A 
0.5 35.63 23.5 0.509 N/A N/A 
0.5 35.66 23.4 0.509 N/A N/A 
 134 
0.5 35.67 23.5 0.509 0.53 N/A 
0.5 35.68 23.5 0.509 0.16 N/A 
0.5 35.68 23.5 0.509 0.08 N/A 
0.5 35.69 23.5 0.509 0.05 N/A 
0.5 35.69 23.5 0.509 0.03 N/A 
0.5 35.69 23.5 0.509 0.02 N/A 
0.5 35.7 23.5 0.509 0.01 N/A 
0.5 35.7 23.5 0.509 0.01 N/A 
0.5 35.7 23.5 0.509 0.01 23.93 
0.6 36.53 23.5 0.605 N/A N/A 
0.6 37.65 23.5 0.605 N/A N/A 
0.6 37.87 24 0.605 N/A N/A 
0.6 37.97 23.5 0.605 N/A N/A 
0.6 38.02 23.5 0.605 N/A N/A 
0.6 38.05 23.5 0.605 N/A N/A 
0.6 38.07 23.5 0.605 N/A N/A 
0.6 38.08 23.5 0.605 0.53 N/A 
0.6 38.09 23.5 0.605 0.15 N/A 
0.6 38.1 23.5 0.605 0.08 N/A 
0.6 38.1 23.5 0.605 0.05 N/A 
0.6 38.1 23.5 0.605 0.03 N/A 
0.6 38.11 23.5 0.605 0.02 N/A 
0.6 38.1 23.4 0.605 0.01 N/A 
0.6 38.1 23.5 0.605 0.01 24.20 
0.7 39.01 23.4 0.710 N/A N/A 
0.7 40.22 23.5 0.710 N/A N/A 
0.7 40.47 23.5 0.710 N/A N/A 
0.7 40.58 23.5 0.710 N/A N/A 
0.7 40.63 23.5 0.710 N/A N/A 
0.7 40.67 23.5 0.710 N/A N/A 
0.7 40.7 23.5 0.710 N/A N/A 
0.7 40.71 23.5 0.710 0.57 N/A 
0.7 40.72 23.5 0.710 0.17 N/A 
0.7 40.73 23.5 0.710 0.09 N/A 
0.7 40.73 23.5 0.710 0.05 N/A 
0.7 40.73 23.5 0.710 0.04 N/A 
 135 
0.7 40.73 23.5 0.710 0.02 N/A 
0.7 40.73 23.4 0.710 0.01 N/A 
0.7 40.73 23.5 0.710 0.01 24.29 
0.8 41.59 23.5 0.816 N/A N/A 
0.8 42.72 23.5 0.816 N/A N/A 
0.8 42.95 23.5 0.816 N/A N/A 
0.8 43.05 23.4 0.816 N/A N/A 
0.8 43.11 23.5 0.809 N/A N/A 
0.8 43.03 23.5 0.795 N/A N/A 
0.8 42.9 23.5 0.795 N/A N/A 
0.8 42.88 23.5 0.795 0.50 N/A 
0.8 42.87 23.5 0.795 0.12 N/A 
0.8 42.87 23.5 0.795 0.09 N/A 
0.8 42.87 23.4 0.795 0.10 N/A 
0.8 42.87 23.5 0.795 0.09 N/A 
0.8 42.87 23.6 0.795 0.06 N/A 
0.8 42.87 23.5 0.795 0.01 N/A 
0.8 42.87 23.5 0.795 0.00 24.34 
0.9 43.76 23.5 0.906 N/A N/A 
0.9 44.97 23.5 0.899 N/A N/A 
0.9 45.22 23.5 0.907 N/A N/A 
0.9 45.32 23.5 0.907 N/A N/A 
0.9 45.38 23.4 0.907 N/A N/A 
0.9 45.41 23.5 0.899 N/A N/A 
0.9 45.44 23.5 0.907 N/A N/A 
0.9 45.45 23.5 0.900 0.57 N/A 
0.9 45.46 23.5 0.907 0.17 N/A 
0.9 45.47 23.5 0.907 0.09 N/A 
0.9 45.47 23.5 0.907 0.05 N/A 
0.9 45.47 23.5 0.900 0.03 N/A 
0.9 45.47 23.5 0.907 0.02 N/A 
0.9 45.47 23.5 0.907 0.01 N/A 
0.9 45.48 23.5 0.900 0.01 24.45 
1 46.44 23.5 1.019 N/A N/A 
1 47.61 23.5 1.003 N/A N/A 
1 47.68 23.5 1.003 N/A N/A 
 136 
1 47.75 23.5 1.003 N/A N/A 
1 47.8 23.5 1.003 N/A N/A 
1 47.83 23.5 1.003 N/A N/A 
1 47.86 23.5 1.003 N/A N/A 
1 47.87 23.5 1.003 0.48 N/A 
1 47.88 23.6 1.003 0.10 N/A 
1 47.88 23.5 1.003 0.07 N/A 
1 47.88 23.5 1.003 0.05 N/A 
1 47.88 23.6 1.003 0.03 N/A 
1 47.89 23.5 1.003 0.02 N/A 
1 47.89 23.4 1.003 0.01 24.40 
 
BGA#2_2 Thermal Resistance = 24.6336 [W/K] 
BGA#2_2 Test Ended on 08 27 02 - 17 29 
BGA#1_2 Package Data: 
Underfil1: #1 
Power Start:  .1 [W] 
Power Step:  .1 [W] 
Power End:  1 [W] 
Fractured Balls: None 
BGA#1_2 Test Started on 08 27 02 - 17 29 
BGA#1_2 Test Data: 
Set 
Power 
[W] 
T1 
[?C] 
T2 
[?C] 
T3 
[?C] 
Cooling 
Temperature 
[?C] 
Actual 
Power 
[W]r 
Standard 
Deviation 
[?C] 
Thermal 
Resistance 
[K/W] 
0.1 23.61 23.93 24.21 23.93 0.101 N/A N/A 
0.1 24.78 24.82 24.94 23.75 0.105 N/A N/A 
0.1 25.14 25.13 25.21 23.77 0.105 N/A N/A 
0.1 25.3 25.28 25.34 23.5 0.105 N/A N/A 
 137 
0.1 25.38 25.35 25.4 23.76 0.105 N/A N/A 
0.1 25.43 25.39 25.44 23.79 0.105 N/A N/A 
0.1 25.45 25.41 25.46 23.61 0.105 N/A N/A 
0.1 25.47 25.42 25.47 23.75 0.105 0.52 N/A 
0.1 25.47 25.43 25.48 23.77 0.105 0.21 N/A 
0.1 25.48 25.44 25.48 23.5 0.105 0.11 N/A 
0.1 25.47 25.41 25.44 23.79 0.101 0.06 N/A 
0.1 25.44 25.41 25.46 23.52 0.105 0.03 N/A 
0.1 25.47 25.43 25.48 23.75 0.105 0.02 N/A 
0.1 25.48 25.44 25.49 23.76 0.105 0.02 N/A 
0.1 25.48 25.44 25.48 23.77 0.105 0.02 N/A 
0.1 25.48 25.44 25.49 23.56 0.105 0.02 N/A 
0.1 25.48 25.44 25.49 23.79 0.105 0.02 N/A 
0.1 25.48 25.44 25.49 23.76 0.105 0.02 N/A 
0.1 25.48 25.44 25.49 23.77 0.105 0.01 N/A 
0.1 25.48 25.44 25.49 23.76 0.105 0.00 16.32 
0.2 25.91 26.22 26.54 23.58 0.201 N/A N/A 
0.2 27.09 27.1 27.24 23.76 0.202 N/A N/A 
0.2 27.42 27.39 27.48 23.59 0.202 N/A N/A 
0.2 27.57 27.53 27.6 23.8 0.202 N/A N/A 
0.2 27.65 27.6 27.67 23.61 0.202 N/A N/A 
0.2 27.7 27.64 27.71 23.78 0.202 N/A N/A 
0.2 27.72 27.66 27.73 23.76 0.202 N/A N/A 
0.2 27.73 27.67 27.74 23.46 0.202 0.51 N/A 
0.2 27.74 27.68 27.74 23.77 0.202 0.20 N/A 
0.2 27.74 27.69 27.75 23.51 0.202 0.10 N/A 
0.2 27.74 27.69 27.75 23.8 0.202 0.06 N/A 
0.2 27.75 27.68 27.75 23.75 0.202 0.03 N/A 
0.2 27.75 27.68 27.75 23.75 0.202 0.02 N/A 
0.2 27.74 27.68 27.75 23.73 0.202 0.01 N/A 
0.2 27.74 27.68 27.75 23.77 0.202 0.01 19.59 
0.3 28.18 28.47 28.81 23.58 0.302 N/A N/A 
0.3 29.37 29.36 29.51 23.8 0.302 N/A N/A 
0.3 29.7 29.65 29.76 23.77 0.302 N/A N/A 
0.3 29.86 29.8 29.89 23.55 0.302 N/A N/A 
0.3 29.94 29.87 29.95 23.76 0.303 N/A N/A 
 138 
0.3 29.98 29.91 29.99 23.79 0.303 N/A N/A 
0.3 30 29.92 30 23.57 0.303 N/A N/A 
0.3 30.01 29.93 30.01 23.74 0.303 0.51 N/A 
0.3 30.02 29.94 30.02 23.48 0.303 0.20 N/A 
0.3 30.03 29.94 30.02 23.74 0.303 0.10 N/A 
0.3 30.03 29.95 30.03 23.49 0.303 0.05 N/A 
0.3 30.03 29.95 30.03 23.77 0.303 0.03 N/A 
0.3 30.03 29.95 30.03 23.59 0.303 0.01 N/A 
0.3 30.03 29.95 30.03 23.77 0.303 0.01 20.62 
0.4 30.49 30.78 31.13 23.5 0.405 N/A N/A 
0.4 31.73 31.7 31.87 23.56 0.405 N/A N/A 
0.4 32.08 32.01 32.14 23.77 0.409 N/A N/A 
0.4 32.24 32.16 32.27 23.79 0.406 N/A N/A 
0.4 32.3 32.18 32.27 23.78 0.399 N/A N/A 
0.4 32.27 32.16 32.26 23.79 0.399 N/A N/A 
0.4 32.27 32.17 32.27 23.76 0.399 N/A N/A 
0.4 32.28 32.17 32.27 23.52 0.399 0.50 N/A 
0.4 32.28 32.18 32.27 23.77 0.399 0.17 N/A 
0.4 32.28 32.18 32.27 23.5 0.399 0.06 N/A 
0.4 32.28 32.18 32.27 23.48 0.399 0.01 21.99 
0.5 32.72 32.98 33.36 23.75 0.503 N/A N/A 
0.5 33.96 33.91 34.09 23.51 0.504 N/A N/A 
0.5 34.31 34.22 34.36 23.8 0.504 N/A N/A 
0.5 34.48 34.36 34.49 23.78 0.504 N/A N/A 
0.5 34.56 34.44 34.56 23.76 0.504 N/A N/A 
0.5 34.61 34.48 34.6 23.77 0.504 N/A N/A 
0.5 34.63 34.51 34.63 23.78 0.504 N/A N/A 
0.5 34.65 34.52 34.64 23.77 0.504 0.54 N/A 
0.5 34.66 34.53 34.65 23.53 0.504 0.21 N/A 
0.5 34.66 34.54 34.65 23.78 0.504 0.11 N/A 
0.5 34.67 34.54 34.65 23.55 0.504 0.06 N/A 
0.5 34.67 34.54 34.65 23.75 0.504 0.04 N/A 
0.5 34.67 34.54 34.65 23.49 0.504 0.02 N/A 
0.5 34.67 34.54 34.65 23.48 0.504 0.01 N/A 
0.5 34.67 34.54 34.66 23.48 0.504 0.01 22.10 
0.6 35.13 35.38 35.78 23.58 0.608 N/A N/A 
 139 
0.6 36.37 36.27 36.45 23.77 0.600 N/A N/A 
0.6 36.63 36.51 36.67 23.58 0.601 N/A N/A 
0.6 36.77 36.64 36.78 23.54 0.601 N/A N/A 
0.6 36.85 36.71 36.84 23.75 0.601 N/A N/A 
0.6 36.89 36.74 36.88 23.75 0.601 N/A N/A 
0.6 36.91 36.76 36.89 23.79 0.601 N/A N/A 
0.6 36.92 36.77 36.9 23.77 0.601 0.49 N/A 
0.6 36.93 36.78 36.92 23.75 0.601 0.18 N/A 
0.6 36.94 36.79 36.92 23.6 0.601 0.10 N/A 
0.6 36.94 36.79 36.92 23.78 0.601 0.05 N/A 
0.6 36.95 36.79 36.92 23.8 0.601 0.03 N/A 
0.6 36.95 36.8 36.93 23.75 0.601 0.02 N/A 
0.6 36.95 36.8 36.93 23.51 0.601 0.01 N/A 
0.6 36.95 36.8 36.93 23.49 0.601 0.01 N/A 
0.6 36.95 36.79 36.92 23.59 0.601 0.01 22.13 
0.7 37.4 37.62 38.04 23.78 0.705 N/A N/A 
0.7 38.63 38.5 38.69 23.78 0.696 N/A N/A 
0.7 38.87 38.73 38.9 23.77 0.696 N/A N/A 
0.7 39.01 38.85 39.02 23.74 0.696 N/A N/A 
0.7 39.09 38.91 39.07 23.61 0.696 N/A N/A 
0.7 39.12 38.95 39.1 23.77 0.697 N/A N/A 
0.7 39.15 38.97 39.12 23.77 0.697 N/A N/A 
0.7 39.16 38.99 39.14 23.77 0.697 0.48 N/A 
0.7 39.17 39 39.14 23.59 0.697 0.17 N/A 
0.7 39.18 39 39.15 23.8 0.697 0.10 N/A 
0.7 39.18 39.01 39.15 23.77 0.697 0.05 N/A 
0.7 39.18 39.01 39.15 23.53 0.697 0.03 N/A 
0.7 39.19 39 39.16 23.79 0.697 0.02 N/A 
0.7 39.19 39.01 39.16 23.57 0.697 0.01 N/A 
0.7 39.19 39.01 39.16 23.78 0.697 0.01 22.02 
0.8 39.63 39.82 40.25 23.5 0.804 N/A N/A 
0.8 40.88 40.77 41 23.77 0.804 N/A N/A 
0.8 41.25 41.08 41.28 23.58 0.805 N/A N/A 
0.8 41.42 41.24 41.42 23.78 0.805 N/A N/A 
0.8 41.51 41.32 41.49 23.76 0.805 N/A N/A 
0.8 41.56 41.36 41.53 23.77 0.805 N/A N/A 
 140 
0.8 41.59 41.39 41.56 23.77 0.805 N/A N/A 
0.8 41.6 41.4 41.57 23.48 0.805 0.55 N/A 
0.8 41.62 41.41 41.58 23.49 0.805 0.22 N/A 
0.8 41.62 41.42 41.59 23.51 0.805 0.12 N/A 
0.8 41.63 41.42 41.59 23.51 0.805 0.07 N/A 
0.8 41.63 41.43 41.59 23.49 0.805 0.04 N/A 
0.8 41.63 41.43 41.59 23.76 0.805 0.03 N/A 
0.8 41.63 41.43 41.6 23.53 0.805 0.02 N/A 
0.8 41.64 41.44 41.6 23.51 0.805 0.01 N/A 
0.8 41.64 41.44 41.6 23.49 0.805 0.01 22.44 
0.9 42.06 42.21 42.65 23.51 0.904 N/A N/A 
0.9 43.27 43.12 43.38 23.61 0.905 N/A N/A 
0.9 43.62 43.43 43.65 23.75 0.905 N/A N/A 
0.9 43.79 43.58 43.78 23.75 0.906 N/A N/A 
0.9 43.87 43.66 43.85 23.74 0.906 N/A N/A 
0.9 43.93 43.7 43.89 23.6 0.906 N/A N/A 
0.9 43.95 43.73 43.92 23.76 0.906 N/A N/A 
0.9 43.97 43.74 43.93 23.76 0.906 0.53 N/A 
0.9 43.98 43.75 43.94 23.75 0.906 0.22 N/A 
0.9 43.98 43.75 43.94 23.75 0.906 0.12 N/A 
0.9 43.99 43.76 43.94 23.48 0.906 0.07 N/A 
0.9 43.99 43.76 43.95 23.74 0.906 0.04 N/A 
0.9 43.99 43.76 43.95 23.6 0.906 0.02 N/A 
0.9 44 43.76 43.95 23.77 0.906 0.02 N/A 
0.9 44 43.77 43.96 23.5 0.906 0.01 N/A 
0.9 44 43.77 43.95 23.78 0.906 0.01 22.22 
1 44.45 44.59 45.07 23.78 1.011 N/A N/A 
1 45.69 45.48 45.72 23.55 1.006 N/A N/A 
1 45.97 45.79 46.06 23.75 1.013 N/A N/A 
1 46.21 45.93 46.13 23.76 1.007 N/A N/A 
1 46.2 45.94 46.15 23.77 1.007 N/A N/A 
1 46.21 45.96 46.17 23.74 1.007 N/A N/A 
1 46.22 45.96 46.17 23.74 1.001 0.49 N/A 
1 46.22 45.96 46.17 23.78 1.007 0.17 N/A 
1 46.23 45.97 46.18 23.76 1.007 0.06 N/A 
1 46.23 45.97 46.18 23.74 1.007 0.02 N/A 
 141 
1 46.24 45.98 46.18 23.78 1.007 0.02 N/A 
1 46.24 45.98 46.19 23.5 1.007 0.01 N/A 
1 46.25 45.99 46.19 23.49 1.001 0.01 N/A 
1 46.25 45.99 46.2 23.51 1.007 0.01 N/A 
1 46.25 45.99 46.2 23.76 1.007 0.01 N/A 
1 46.26 45.99 46.2 23.77 1.007 0.01 22.22 
 
BGA#1_2 Thermal Resistance = 23.0286 [W/K] 
BGA#1_2 Test Ended on 08 27 02 - 17 44 
 
 
 
 
 
 
 
 
 142 
APPENDIX C 
 
Thermal Resistance Measurements at 0 Cycles 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 143 
Packages with Thermal Balls 
 
  
Board 
#1 
Board 
#2 
Board 
#3 
Board 
#4 
Average 
Standard 
Deviation 
BGA #1/Via #1 23.47 24.75 23.48 24.08 23.94 0.61 
BGA #1/Via #2 22.82 22.91 21.54 23.60 22.72 0.86 
BGA #2/Via #1 27.41 30.24 26.50 27.53 27.92 1.62 
No Underfill 
BGA #2/Via #2 25.34 27.54 24.78 25.02 25.67 1.27 
BGA #1/Via #1 17.63 19.32 18.76 18.86 18.64 0.72 
BGA #1/Via #2 17.68 18.05 18.35 18.24 18.08 0.29 
BGA #2/Via #1 26.09 25.53 26.54 25.98 26.04 0.41 
Underfill #1 
BGA #2/Via #2 23.76 23.76 24.38 24.16 24.01 0.31 
BGA #1/Via #1 18.09 18.40 18.96 18.85 18.74 0.30 
BGA #1/Via #2 17.71 17.27 17.63 17.64 17.57 0.20 
BGA #2/Via #1 25.40 25.89 25.22 24.72 25.31 0.48 
Underfill #2  
BGA #2/Via #2 23.19 23.42 23.28 23.97 23.56 0.36 
BGA #1/Via #1 19.13 18.93 18.59 18.59 18.70 0.19 
BGA #1/Via #2 17.51 18.10 17.73 18.31 17.91 0.36 
BGA #2/Via #1 25.08 25.04 25.06 24.85 25.01 0.11 
Underfill #3  
BGA #2/Via #2 22.98 23.45 23.84 22.89 23.39 0.48 
 
 
 
 
 
 
 
 144 
Packages without Thermal Balls 
 
  
Board 
#1 
Board 
#2 
Board 
#3 
Board  
#4 
Average 
Standard 
Deviation
BGA #1/Via #2 36.37 34.62 36.65 37.40 36.26 1.18 
No 
Underfill 
BGA #2/Via #2 47.44 46.98 47.66 48.38 47.62 0.58 
BGA #1/Via #2 19.72 19.70 19.85 20.08 19.84 0.18 
Underfill 
#1 
BGA #2/Via #2 29.60 29.90 29.88 30.33 29.93 0.30 
BGA #1/Via #2 19.71 19.36 19.97 19.83 19.72 0.26 
Underfill 
#2 
BGA #2/Via #2 29.49 28.93 29.11 N/A 29.18 0.13 
BGA #1/Via #2 20.64 20.71 20.74 21.12 20.80 0.22 
Underfill 
#3 
BGA #2/Via #2 31.19 30.94 30.29 30.82 30.81 0.34 
 
 145 
APPENDIX D 
 
Numerical Simulation Temperature Distributions [?C] 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
BGA #1 / Via #1 / W
ith Underfill / With The
r
mal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 146 
 
 
 
 
 
 
 
BGA #1 / Via #1 / W
ith
out Underfill / W
ith The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 147 
 
 
 
 
 
 
BGA #1 / Via #1 / W
ith Underfill / Withou
t The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 148 
 
 
 
 
 
BGA #1 / Via #1 / Without Underf
ill / Without Thermal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 149 
 
 
 
 
 
 
BGA #1 / Via #2 / W
ith Underfill / With The
r
mal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 150 
 
 
 
 
 
 
 
BGA #1 / Via #2 / W
ith
out Underfill / W
ith The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 151 
 
 
 
 
 
 
BGA #1 / Via #2 / W
ith Underfill / Withou
t The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 152 
 
 
 
 
 
 
BGA #1 / Via #2 / Without Underf
ill / Without Thermal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 153 
 
 
 
 
 
 
BGA #2 / Via #1 / W
ith Underfill / With The
r
mal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 154 
 
 
 
 
 
 
 
BGA #2 / Via #1 / W
ith
out Underfill / W
ith The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 155 
 
 
 
 
 
 
 
BGA #2 / Via #1 / W
ith Underfill / Withou
t The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 156 
 
 
 
 
 
 
 
 
BGA #2 / Via #1 / Without Underf
ill / Without Thermal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 157 
 
 
BGA #2 / Via #2 / W
ith Underfill / With The
r
mal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 158 
 
 
 
 
 
 
 
BGA #2 / Via #2 / W
ith
out Underfill / W
ith The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 159 
 
 
 
 
 
 
 
BGA #2 / Via #2 / W
ith Underfill / Withou
t The
r
ma
l Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 160 
 
 
 
 
 
 
 
 
BGA #2 / Via #2 / Without Underf
ill / Without Thermal Balls 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 161