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This is to certify that the
thesis entitled

THERMAL PERFORMANCE OF HIGH POWER TVS DIODE
ASSEMBLIES WITH SOLDER VOIDS

presented by

Iris A. Galvez

has been accepted towards fulfillment
of the requirements for the

MS. degree in Chemical Engineering

 

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIFiCIDatoDuepss-ols

THERMAL PERFORMANCE OF HIGH POWER TVS DIODE ASSEMBLIES
WITH SOLDER VOIDS

By
Iris A. Galvez

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Chemical Engineering and Materials Science

2004

ABSTRACT

THERMAL PERFORMANCE OF HIGH POWER TVS DIODE ASSEMBLIES
WITH SOLDER VOIDS

By
Iris A. Galvez

The performance of microelectronic devices is sensitive to temperature.
When a diode assembly is electrically powered, heat is generated and the
temperature in the assembly rises. In a TVS diode assembly composed of
silicon, nickel, solder and copper, the solder controls the extent of temperature
rise since it is the material with the lowest thermal conductivity. Hence, it is
essential to know the minimum value of thermal conductivity in the solder that
delivers acceptable performance and reliability. A finite element program was
used to calculate thermal transients in a diode assembly with a fixed current of
60 A. It was found that if the thermal conductivity of the solder layer falls below
12.7 W/m-K, the assembly will not operate reliably.

Voids in the solder will reduce the effective thermal conductivity of this
layer. A model was used to relate the effective thermal conductivity of the solder
layer to the void fraction and thus evaluate the maximum void fraction that allows
reliable operation and acceptable diode performance. It was found that the solder

layer should not contain more than 33% spherical voids.

ACKNOWLEDGEMENTS

I want to express my most sincere gratitude to my advising professor, Dr.
K. Jayaraman for all of his guidance, help and understanding during the
completion of this project. I would also like to thank Dr. L. Segerlind for providing
the finite element code used for this project, and helping me with any questions I
had about the program. Also, would like to thank Dr. J. Lin for providing the
funding for this project, the diode electrical characteristics and insight on the

reliability problems and failure mechanisms of TVS diode assemblies.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................. vi
LIST OF FIGURES .............................................................................................. vii
KEY TO SYMBOLS AND ABBREVIATIONS ...................................................... xii
CHAPTER 1 .......................................................................................................... 1
INTRODUCTION ................................................................................................... 1
1.1 Problem statement ...................................................................................... 1
1.2 Thesis organization ..................................................................................... 3
CHAPTER 2 .......................................................................................................... 5
TRANSIENT VOLTAGE SUPPRESSOR (TVS) DIODES ..................................... 5
2.1 Diodes ......................................................................................................... 5
2.2 Transient Voltage Suppressor (TVS) Diodes ............................................... 8
2.3 TVS Diode Assembly Description ................................................................ 9
2.4 Thermal Cycling and Power Cycling .......................................................... 11
2.5 Temperature Rise and Solder Fatigue Lifetime ......................................... 13
CHAPTER 3 ........................................................................................................ 16
HEAT TRANSFER EQUATIONS ........................................................................ 16
3.1 Power generation and temperature in the diode assembly ........................ 16
3.3 Heat conduction equations ........................................................................ 20
3.4 Boundary Conditions ................................................................................. 21
3.5 Effect of voids on the solder layer thermal properties ................................ 22
3.4 Assumptions .............................................................................................. 28
CHAPTER 4 ........................................................................................................ 29
RESULTS ........................................................................................................... 29
4.1 Finite element program .............................................................................. 29
4.1.1 Finite element program Description .................................................... 29
4.1.2 Finite Element Program Verification .................................................... 31

4.2 Power-on simulation .................................................................................. 35
4.2.1 Simulation description ......................................................................... 35
4.2.2 Temperature transients for “on” cycles ................................................ 36
4.2.3 Temperature profiles ........................................................................... 44

4.3 Power cycle testing .................................................................................... 52
4.3.1 Simulation description ......................................................................... 52
4.3.2 Temperature transients for on-off cycles ............................................. 53

4.4 Solder voids and thermal diffusivity ........................................................... 61

iv

4.5 Summary of Results .................................................................................. 66

CHAPTER 5 ........................................................................................................ 73
CONCLUSION .................................................................................................... 74

5.1 Conclusion ................................................................................................. 74

5.2 Future Research ........................................................................................ 74
APPENDIXA ....................................................................................................... 73
FINITE ELEMENT PROGRAM SAMPLE INPUT AND OUTPUT FILES ............. 73
APPENDIX B ....................................................................................................... 77
TEMPERATURE TRANSIENTS FOR “POWER-ON” TESTS. TsmK=75°C AND
TSINK=125°C ........................................................................................................ 77
APPENDIX C ...................................................................................................... 88
TEMPERATURE PROFILES FOR “POWER-ON” TESTS. TsmK=75°C AND
TSINK=125°C ........................................................................................................ 88
APPENDIX D .................................................................................................... 100
TEMPERATURE TRANSIENTS FOR POWER ON-OFF CYCLES. TsmK=75°C
AND TsmK=125°C .............................................................................................. 100
BIBLIOGRAPHY ............................................................................................... 114

LIST OF TABLES

Table 1: Thermal properties of materials in diode assembly ............................... 21

Table 2: Steady-state temperature rise in the solder for different values of
thermal diffusivity at different heat sink temperatures ......................................... 66

Table 3: Critical values of thermal diffusivity and the corresponding solder void
concentrations ..................................................................................................... 68

Table 4: Time needed to reach steady state for different values of thermal
diffusivity at different heat sink temperatures ...................................................... 68

Table 5: Temperature gradient in the solder layer for different values of thermal
diffusivity at different heat sink temperatures ...................................................... 69

Table 6: Number of cycles needed to achieve steady state for different values of
thermal diffusivity at different heat sink temperatures ......................................... 69

Table 7: Oscillation amplitude for different values of thermal diffusivity at different
heat sink temperatures ........................................................................................ 70

Table 8: Temperature drift for different values of thermal diffusivity at different
heat sink temperatures ........................................................................................ 72

vi

LIST OF FIGURES

Figure 1: Equalization of the Fermi level at equilibrium (V=O) ............................... 6
Figure 2: Reduction in barrier height due to forward bias ...................................... 6
Figure 3: Increase in barrier height due to reverse bias ........................................ 7
Figure 4: Typical current vs. voltage characteristic for a diode. ............................ 8
Figure 5: Voltage transient clamped by TVS diode ............................................... 8
Figure 6: Cross-section of diode assembly ......................................................... 10
Figure 7: Pb/Sn/Ag Ternary Phase Diagram [7] .................................................. 11
Figure 8: Number of Cycles as a Function of Solder Temperature Rise [12] ...... 15
Figure 9: Current vs. voltage diode characteristic curve ..................................... 17
Figure 10: Power vs. forward current for diode assembly ................................... 18

Figure 11: Power per unit volume vs. temperature for diode assembly at fixed

current l=6OA ...................................................................................................... 19
Figure 12: Solid and void layout in the Parallel model ......................................... 23
Figure 13: Solid and void layout in the Serial Model ........................................... 23
Figure 14: Effective thermal conductivity of Xerogel film[13]. .............................. 25
Figure 15: Solder effective thermal conductivity vs. solder void content ............. 26
Figure 16: Solder density as a function of void content ....................................... 27

Figure 17: Percent error of the numerical solution for different values of time step
............................................................................................................................ 33

Figure 18: Analytical and numerical solution of equation 3 at steady state, using
only the silicon slab ............................................................................................. 34

Figure 19: Temperature transients for TVS button diode assembly with one“ = 2.98
x 10'5 m2/s. T3"... = 25°C ....................................................................................... 38

vii

Figure 20: Temperature transients for TVS button diode assembly with 019“" - 1.63
X 105 m 2.]8 Tsinkz 25° C ....................................................................................... 39

Figure 21. Temperature transients for TVS button diode assembly with Geff- - 1.25
x10’5 m2/.s Tsink=25° C ....................................................................................... 40

Figure 22: Temperature transients for TVS button diode assembly with aefl= 1 0.8
x10'2.5m/s Tsink=25°C ....................................................................................... 41

Figure 23: Temperature transients for TVS button diode assembly with (Xeff: 6. 66
X 10.6 m 2.]8 Tsink= 25° C ....................................................................................... 42

Figure 24: Temperature transients for TVS button diode assembly with Gaff: 3. 51
x 10’(3 m /s. Tank: 25° C. ...................................................................................... 43

Figure2 25: Temperature profiles for TVS button diode assembly with Geff- - 2. 98 x
105 m 2.]8 Tsink= 25° C .......................................................................................... 46

Figure2 26: Temperature profiles for TVS button diode assembly with a.” = 1.63 x
105 m 2./S Tslnk= 25° C .......................................................................................... 47

Figure2 27. Temperature profiles for TVS button diode assembly with aefi- - 1 .25 x
105 m 2./S Tslnk= 25° C. ......................................................................................... 48

Figure2 28. Temperature profiles for TVS button diode assembly with (Xeff- — 1.08 x
105 m 2./S Tsink= 25° C. ......................................................................................... 49

Figure 29. Temperature profiles for TVS button diode assembly with on,“ = 6. 66 x
10’5 m2/s Tank: 25° C. ......................................................................................... 50

Figure2 30: Temperature profiles for TVS button diode assembly with aen- - 3. 51 x
105 m 2Is. Tm: 25° C .......................................................................................... 51

Figure 31: Temperature transients in an on-off cycle for a TVS button diode
assembly with a... = 2.98 x 10'5 m2/s. T3"... = 25°C. ............................................. 55

Figure 32: Temperature transients in an on-off cycle for a TVS button diode
assemny with a... = 1.63 x 10-5 m2/s. T5... = 25°C ............................................... 56

Figure 33: Temperature transients in an on-off cycle for a TVS button diode
assembly with a... = 1.08 x 10'5 mzls. T3"... = 25°C ............................................... 57

Figure 34: Temperature transients in an on-off cycle for a TVS button diode
assembly with a... = 1.01 x 10'5 m2/s. Ta... = 25°C ............................................... 58

viii

Figure 35: Temperature transients in an on-off cycle for a TVS button diode
assembly with a... = 6.66 x 10'6 m2/s. Ta... = 25°C ............................................... 59

Figure 36: Solder voids in a commercially available diode .................................. 61

Figure 37: Solder effective thermal diffusivity as a function of solder void fraction
............................................................................................................................ 64

Figure 38: Temperature rise of solder vs. effective thermal Diffusivity of Solder.67
Figure 39: Oscillation amplitude vs. effective thermal diffusivity of solder ........... 71
Figure 40: Temperature drift vs. effective thermal diffusivity of solder ............... 73

Figure 41: Temperature transients for diode with a.“ = 2.98 x 10‘5 mzls. T31...< =
75°C .................................................................................................................... 82

Figure 42: Temperature transients for diode with as“ = 1.63 x 10'5 m2/s. Tsink =
75°C .................................................................................................................... 83

Figure 43: Temperature transients for diode with ore“ = 1.31 x 10'5 m2/s. Tank =
75°C .................................................................................................................... 84

Figure 44: Temperature transients for diode with a.“ = 1.08 x 10'5 m2/s. Tsink =
75°C .................................................................................................................... 85

Figure 45: Temperature transients for diode with a.“ = 6.66 x 10‘6 m2/s. Tank =
75°C .................................................................................................................... 86

Figure 46: Temperature transients for diode with as“ = 2.98 x 10'5 m2/s. Tsmk =
125°C .................................................................................................................. 87

Figure 47: Temperature transients for diode with one“ = 1.63 x 10'5 mzls. Tank =
125°C .................................................................................................................. 88

Figure 48: Temperature transients for diode with one“ = 1.08 x 10'5 mzls. Tsink =
125°C .................................................................................................................. 89

Figure 49: Temperature transients for diode with one“ = 6.66 x 10'6 m2/s. Tm =
125°C .................................................................................................................. 90

Figure 50: Temperature transients for diode with a... = 4.51 x 10’6 m2/s. Tsink =
125°C .................................................................................................................. 91

Figure 51: Temperature profiles for diode with 019“ = 2.98 x 10’5 m2/s. Tsink = 75°C
............................................................................................................................ 93

ix

Figure 52: Temperature profiles for diode with one“ = 1.63 x 10'5 m2/s. Tsrnk = 75°C
............................................................................................................................ 94

Figure 53: Temperature profiles for diode with as” = 1.31 x 10'5 m2/s. Tsrnk = 75°C
............................................................................................................................ 95

Figure 54: Temperature profiles for diode with def, = 1.08 x 10'5 m2/s. T3... = 75°C
............................................................................................................................ 96

Figure 55: Temperature profiles for diode with aetr = 6.66 x 10’5 mzls. Tsrnk = 75°C
............................................................................................................................ 97

Figure 56: Temperature profiles for diode with or... 2.98 x 10'5 m2/s. Tm =
125°C .................................................................................................................. 98

Figure 57: Temperature profiles for diode with aeff 1.63 x 10'5 m2/s. Tsrnk =
125°C .................................................................................................................. 99

Figure 58: Temperature profiles for diode with a...” 1.33 x 10’5 mzls. Tsrnk =
125°C ................................................................................................................ 100

Figure 59: Temperature profiles for diode with due“ 1.08 x 10’5 m2/s. Tsrnk =
125°C ................................................................................................................ 101

Figure 60: Temperature profiles for diode with aeff 6.66 x 10*3 m2/s. Tsink =
125°C ................................................................................................................ 102

Figure 61: Temperature profiles for diode with one“ = 4.51 x 1043 m2/s. Tsmk =
125°C ................................................................................................................ 103

Figure2 62: Temperature transients in an on-off cycle for diode with one“ = 2. 98 x
105 m 2/8 Tsink- '- 75° C ....................................................................................... 105

Figure2 63: Temperature transients in an on-off cycle for diode with orefi=1.63 x
105 m 2.]8 Tsink- - 75° C ....................................................................................... 106

Fi ure 64: Temperature transients in an on-off cycle for diode as“ = 6.66 x 1045
m IS. Tsink = 75°C .............................................................................................. 108

Figure2 65: Temperature transients in an on-off cycle for diode with den = 2. 98 x
105 m 2./S Tslnk=125°c ..................................................................................... 109

Figure2 66: Temperature transients in an on-off cycle for diode with aeff=1.63 x
105 m 2./S Tsink=125°C ..................................................................................... 110

Figure 67: Temperature transients in an on-off cycle for diode with one“ = 1.08 x
10’5 m2/s. T5"... = 125°C ..................................................................................... 111

Figure 68: Temperature transients in an on-off cycle for diode with ore“ = 6.66 x
1045 m2/s. T5"... = 125°C ..................................................................................... 112

xi

KEY TO SYMBOLS AND ABBREVIATIONS

ATC Accelerated Temperature Cycling

PCT Power Cycling Test

E
Ec

EF

Energy

Conduction band energy
Fermi level energy
Valence band energy

Voltage

Forward Voltage
Reverse Voltage

Current

Fonivard Current

Power

Power per unit volume
Time

Void fraction

Contact

Heat capacity

Density

Thermal diffusivity

xii

kefr

Trise
Tsink

Tdn’ft

Thermal conductivity

Effective thermal conductivity

Length
Temperature

Temperature rise
Heat sink temperature

Temperature Drift

xiii

CHAPTER 1

INTRODUCTION

1.1 Problem statement

The performance of microelectronic devices is directly dependent on
temperature. If the temperature inside of a device reaches a critical value, failure
of the device can occur. Heat transfer plays a critical role in the performance and
reliability of electronic devices. For given operation conditions even a moderate
reduction of the temperature in the device can significantly improve its lifetime
and performance [1]. For this reason, it is important to know the limits in the
thermal properties of the device that deliver reliable operation along with good
electrical performance.

A high-power transient voltage suppressor (TVS) button diode is the
microelectronic device of focus in this thesis. These electrical devices are used to
protect a circuit from a high voltage surge. When the device is electrically
powered, heat is generated in the silicon diode. As a result, the temperature in
the silicon rises and heat is transferred from the silicon to the heat sinks at both
ends of the button diode assembly. To ensure proper operation of the diode, it is
important that most of the heat created in the silicon is removed, so that the
temperature in the device does not rise over a specific value. This is especially
critical for high-power devices. Since they dissipate more power into heat than

normal devices, they have a higher risk of overheating.

To ensure proper heat transfer, the design of the assembly has to be well
thought out. The materials used for the TVS diode assembly should have good
thermal conductivity in order to help the overall heat dissipation and ensure
proper, reliable functioning of the device. The material with the lowest
conductivity in the diode assembly will control the extent of heat removal from the
silicon diode. In a TVS diode assembly composed of the silicon diode, nickel
plating, solder and heat sinks, the soldering material that connects the silicon
diode to the heat sinks has the lowest thermal conductivity and therefore will
control the extent of the heat transfer. The thermal conductivity of this layer will
determine how much the temperature will rise inside of the assembly. If the
thermal conductivity of the solder layer is too low, heat transfer to the heat sinks
is drastically reduced, resulting in a higher than desired temperature rise in the
diode assembly. Higher temperature rises in the silicon diode are related to
reduced lifetimes and poor diode performance. The objective of this thesis is to
calculate the limits of the thermal diffusivity in the solder layer, such that the
temperature rise inside of the diode does not exceed a critical value. This critical
value of the temperature rise is chosen in such a way that the diode assembly
can meet reliability test criteria. This objective is achieved by using a finite
element program to calculate temperature profiles and transients in the
assembly. The temperature profiles and temperature transients are obtained for
both a continuously powered TVS button diode and for a TVS button diode

subjected to on-off power cycles.

Another common problem with commercially available TVS button diodes
is the presence of solder voids in the assemblies. Voids in the solder are due to
the use of fluxes to improve the wetting of the solid substrate during the soldering
process. If fluxes are used and improper heating takes place while soldering, it
could result in a significant amount of voids due to trapped flux in the solder [2].
Voids are a problem since they not only reduce the mechanical strength of the
solder joint in an assembly, but they can also reduce the effective thermal
diffusivity of the solder, therefore impairing the heat transfer process in the diode
assembly. A secondary objective of this thesis is to use a model to relate thermal
diffusivity to the fraction of voids in the solder, such as to calculate the maximum

amount of voids in the solder that will allow a diode to meet reliability test criteria.

1.2 Thesis organization

This thesis is organized as follows. Chapter 2 presents a brief overview of
diodes. It explains what a diode is and what it is used for. It also contains a brief
introduction to the TVS diode application. This chapter also includes a
description of the diode assembly used for this thesis. It finally discusses different
types of diode reliability testing.

Chapter 3 presents the electrical data of the diode assembly used for this
thesis, along with the equations and the models used to work the problem. This
chapter also presents a list of all the assumptions made while working on this
problem.

Chapter 4 contains all the results obtained. It starts with a verification of

the finite element program used, along with the analytical solution to a simplified

version of the problem. The simulations done are described and the results
obtained are presented and discussed.

Chapter 5 closes the discussion with a statement of the lessons learned
while working on this thesis. All the conclusions reached are presented here and
ideas for future research are presented in this chapter.

The appendixes include program listings, output and input lines. Also
additional data obtained in the form of tables and graphs is presented in this

section.

CHAPTER 2

TRANSIENT VOLTAGE SUPPRESSOR (TVS) DIODES

This chapter presents a discussion of TVS diodes, and a brief discussion
of solid-state physics is included here. References [3] and [4] are suggested to

the reader for a more in depth discussion of solid-state physics.

2.1 Diodes

A diode is formed when a p-type semiconductor is joined with an n-type
semiconductor. When these two materials are joined, the energy bands shift to
equalize the Fermi level throughout the junction. This shift of energy bands
causes what is called a contact potential. This contact potential is an energy
barrier that the electrons will need to surpass in order to cross from the n-type
side into the p-type side. Once equilibrium is formed, electrons on the n-type side
cannot cross to the p-type side because of the energy barrier, as shown in Figure
1.

The Fermi level is offset and the energy barrier height is reduced when a
positive voltage is applied to the p-region of the junction (fonIvard bias), This
results in a flow of carriers across the barrier. The current increases

exponentially with forward bias.

._ .. Contact

\ I I Potential
\

 

 

 

 

 

 

EC

EC
Ef """"""""""""""""""""""""" Ef
EV

 

 

 

 

we
Equilibrium

Figure 1: Equalization of the Fermi level at equilibrium (V=0)

 

 

 

 

 

 

 

 

 

 

 

 

\
E
C \ EC
I5f ...................................... E,
Ev g" k ‘_ EV
p-tYPO n_typ°

Fomard Bias

Figure 2: Reduction in barrier height due to forward bias

When a negative voltage is applied to the p-region of the junction (reverse

bias), the energy barrier increases, and almost no current flows.

 

 

 

 

 

 

 

 

n-type

Reverse Bias

Figure 3: Increase in barrier height due to reverse bias

Since the current flows relatively freely in the fonIvard direction while it can
barely flow in the reverse direction, diodes can be used as one-way valves to
control the amount of current or voltage that can go through to a circuit. Figure 4

shows a typical current vs. voltage characteristic curve for a diode.

 

 

 

 

CURRENT
FORWARD
CURRENT
BREAKDOWN
VQTAGE
V:
_....... g _
r LEAKAGE CURRENT VOLTAGE
AVALANCHE
CURRENT
*REVERSE VOLTAGE

 

 

Figure 4: Typical current vs. voltage characteristic for a diode.

2.2 Transient Voltage Suppressor (TVS) Diodes

Transient Peak
‘

\

 

 

/
I \\
I \
I \
I \
l \
I \
. r \

IC Failure threshold I \\
TVS Clamping .' \.
Voltage \

Normal operating ___r
voltage

 

 

Figure 5: Voltage transient clamped by TVS diode

TVS diodes are p-n junctions made from silicon. These diodes are
designed to protect vulnerable circuits from damaging voltages. They are used to
dissipate high transient power surges with very short response times. If the
voltage through the diode is higher than a certain value, avalanche breakdown
occurs and the voltage is “clamped” or restrained to that certain value. This
reduces the amplitude of the transient to a nondestructive level. Figure 5 shows a
transient voltage peak being clamped to a safe level by a TVS diode. Due to their
particular application, high amounts of power are created inside of the silicon
diode and consequently high amounts of heat need to be removed from the

diode assembly at any time to maintain the temperature in the assembly at an

acceptable level. The thermal design of the assembly is critical to its

performance. The next section describes the diode assembly.

2.3 TVS Diode Assembly Description

Diode assemblies are made in a wide range of shapes and materials. The
choice of packaging depends on the environment where the diode will be used,
the electrical specifications of the diode, the size of the diode, and the heat
dissipation needed for each specific application. The TVS diode studied in this
thesis is in a button package. This package is composed of slabs of different
materials. The silicon diode is in the middle of the assembly. The area of the
silicon slab is 1.86 x 10'5 m2, and its thickness is 200 pm. The silicon diode is the
only electrically active part in the assembly, and therefore power is only
generated in this slab. To either side of the silicon diode, there is a nickel slab
that is 20 pm thick. The nickel slabs are then followed by solder, used to connect
the diode to copper heat sinks. The solder is 50 pm thick, and is composed of
92.5% lead, 5% tin and 2.5% silver. The copper heat sink is 1000 pm thick.

Thin layers of inter-metallic compounds are formed in each of the material
interfaces. These layers provide the actual bonding between the metals in the
assembly. As the assembly is thermally cycled, these inter-metallic layers
become thicker [5], and could affect the heat transfer characteristics of the diode.
For simplification purposes, it is assumed that these layers are not present in the
diode assembly and the heat transfer in the diode assembly will not be affected

by their presence. The diode assembly as it will be studied is shown in Figure 6.

Diode
C mterlin e

 

 

 

 

 

 

 

 

 

 

 

Cu
Heat Sinks \ : Solder

(92 5% Pb, 5% Sr; 2.5% A9

 

Figure 6: Cross-section of diode assembly

Whenever the diode assembly is subjected to a current, power will be
generated in the silicon. As a result, the temperature in the silicon will rise and
heat flow will occur from the silicon in the middle to the heat sinks at both ends of
the assembly. Since solder is the material with the lowest thermal conductivity in
the assembly, the thermal conductivity of this layer will determine how much the
temperature will rise inside of the assembly. If the thermal conductivity of the
solder is reduced, the heat transfer process is inhibited resulting in a higher than
desired temperature rise inside of the diode assembly. if the thermal conductivity
is low enough, the resulting temperature rise could cause cracks in the solder.
solder fusion or diode performance failure. Cracks in the solder further affect its
ability to dissipate heat, making the device more susceptible to failure [6]. The

solder used in the diode assembly is a ternary alloy, composed of 92.5% Pb, 5%

10

Sn and 2.5% Ag. For this solder alloy, the liquidus and solidus temperatures are
284 and 280°C respectively [7]. Figure 7 shows the ternary phase diagram for
this solder alloy. The high solidus and liquidus temperatures of this alloy are the

main reason it is used as solder in high temperature applications.

 

 

 

 

8
M to
so A
20 Q o

 

O
O
CO

 

 

o 20 4'?) so so 100
3“ Mass % Ag A9

Figure 7: PbISnIAg Ternary Phase Diagram [7]

2.4 Themal Cycling and Power Cycling

Thermo-mechanical fatigue (T MF) is the major cause of failure in
electronic interconnects such as solder. TMF occurs whenever an assembly is

heated or cooled. The materials in the assembly will undergo thermal expansion

11

and contraction. This process will introduce stress into the assembly. The
amount of stress will depend on the thermal coefficient of expansion (T CE) of
each individual material in the assembly. The solder alloy is usually the weakest
part of the assembly and is crucial that it is able to accommodate the stresses
that develop due to mismatches in the TCE of the different materials while the
assembly is thermally cycled. Damage from TMF accumulates affecting the
mechanical properties of the solder. Also the microstmcture of the solder
changes, as the solder is thermally cycled. Coarsening of the microstructure and
growth of the inter-metallic layers can be observed [5]. These changes in
microstructure contribute to the reduced mechanical strength in solder joints
subjected to thermal cycling. In addition, the fatigue life of the joint is reduced,
and crack growth is initiated from the lead rich region close to the inter-metallic
layer [8]. These cracks propagate in the solder until the diode assembly fails.

Since the amount of thermal cycles affect the lifetime of the solder joint,
tests using this principle are widely used to measure the reliability of such joints
in a diode assembly. In a typical thermal cycling test, the assembly is heated
from 25°C to 125°C at a rate of 50°C/min. The assembly then dwells at 125°C for
5 minutes. After this the assembly is cooled down to —55°C at the same ramp
rate of 50°C/min. It then dwells at that lower temperature for 5 minutes. This
cycle (heating, dwelling, cooling, dwelling) is repeated until the assembly fails. An
assembly is considered to fail when its measured resistance is above a preset
value [9].

There is one drawback when using a thermal cycle test. During service,

12

assemblies are really subjected to power cycles instead of temperature cycles.
Power is generated within the electronic device during use, and heat is
transferred from the device into the assembly. This induces a thermal gradient
throughout the whole assembly. Therefore, the TCE mismatch is dependent not
only on the different materials in the assembly, but also on the temperature
gradients created by the power cycles [10]. There exist considerable debate on
whether thermal cycle tests can reproduce the actual failures that occur during
service, where the assemblies are power cycled. This is why some diode
assembly manufacturers prefer to test the reliability of their assemblies using
power cycle tests instead of the more traditional thermal cycle tests. In a typical
power cycle test, the assembly is subjected to a constant current of 60A for 3
seconds, and then the current is turned off for another 3 seconds. This
constitutes one cycle. The cycle is then repeated until the measured resistance
of the assembly is higher than a preset value specific to the assembly. Power
cycling tests are faster and more economical to use than thermal cycle tests [11].
Failures observed in this test are usually due to cracks in the solder that is closer
to the electrical device. These cracks propagate close to the inter-metallic layer

as discussed before. In this thesis, power cycles will be used.

2.5 Temperature Rise and Solder Fatigue Lifetime

As discussed in the preceding sections, solder is the most critical part of
the diode assembly. For that reason, the reliability of the solder is a good
indicator of the reliability of the diode assembly itself. It is necessary that the

diode can operate trouble-free for a certain amount of years. To ensure that

13

these conditions are met, the assemblies are subjected to accelerated power or
temperature cycling. In these types of tests the amount of cycles that an
assembly can undertake is directly linked to lifetime in years. Several methods
exist to link the number of cycles to lifetime in field use conditions. But of
particular importance to designers is to have the ability to predict the
performance of their assemblies before they are tested, depending on the
characteristics of the device.

Temperature rise inside of the device is a fundamental key that can be
used to predict the amount of cycles an assembly can undertake. Figure 8 can
be used to calculate how much can the temperature rise in the solder in order to
get a certain amount of cycles. The figure was calculated using eutectic Pb/Sn
solder [12] that has a lower melting range than the high Pb solder discussed
here. Since the solder discussed here has a higher operating temperature than
eutectic solder, using this chart will provide very conservative estimates of the
allowable temperature rise in the solder joint. For a typical automotive application
it is required than more than half the assemblies can undertake 20,000 cycles or
more to be able to qualify the assembly for use in their product. This means that
the temperature rise in the solder cannot exceed 21°C as it is thermally cycled. If
the thermal conductivity in the solder is too low, the temperature rise will exceed
this value and the assemblies will not be qualified. This chart is used in this
thesis to calculate the allowable temperature rise needed to achieve a certain
amount of cycles. This information is used then to determine the lowest value of

thermal diffusivity that the solder layer can have.

14

100000

10000

Number of Power OnIOf'f Cycles

1000
15 20 25 30 35 40 45 50

AT (°C) - Solder Joint Temperature Defined by Power On-Ofl'

 

Figure 8: Number of Cycles as a Function of Solder Temperature Rise [12]

15

CHAPTER 3

HEAT TRANSFER EQUATIONS

3.1 Power generation and temperature in the diode assembly

To calculate temperature transients in the TVS button diode assembly it is
important to understand the power generation in the silicon diode and how it is
affected by temperature. When a current is applied to the TVS diode a voltage

associated with that current develops. Shown in Figure 9 is the current-voltage
characteristic curve for the TVS button diode studied1. The calculations

presented in this thesis are based on this data.
As a result of the applied current, power is generated in the silicon diode.
Power is related to current and voltage by equation 1.
P=IV U)
Where P is the power generated, I is the current applied and V is the voltage.
The power-current characteristic curve for the diode assembly studied is plotted
in Figure 10. When the fonNard current is fixed, power can be represented as a
linear function of temperature. Figure 11 shows this with the forward current fixed

at 60 A.

 

1 Data provided by Dr. J. Lin, of Diotec USA.

16

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3.3 Heat conduction equations

To obtain the temperature profiles of the diode it is necessary to solve the
transient heat conduction equations in each of the diode slabs. The partial

differential equation that describes the heat conduction in the diode is as follows:

(2)

 

Here T is temperature, t is time, x represents distance from the diode centerline,
p is the density, and Cp is the heat capacity. is is the power generated per unit

volume. a is the thermal diffusivity and its related to the thermal conductivity, k,

by equation 3.

a=——— (3)

The heat conduction equation will be solved for each of the different
material slabs, changing the thermal properties accordingly. The values of the
thermal properties for each of the slabs are listed in Table 1. The power
generation term is given in Figure 10 as:

13=-3.58xlO7T+3.12x10‘°[W/m3] (4)
Since power is generated only in the silicon, equation 5 applies only to the silicon

layerz. For all of the other layers:

I3 = O[W/m3] (5)

 

2 Please refer to Figure 8 for diode assembly schematic and dimensions.

20

Table 1: Thermal properties of materials in diode assembly

 

 

 

 

 

 

 

 

 

 

 

 

Thermal Heat Thermal
Density
Conductivity 3 Capacity DifoSiVitY
(kg/m ) 2
(W/m K) (J/kg K) (m ls)
Silicon 108 2330 712 6.51e-5
Nickel 90.7 8885 444 2.30e-5
Solder 45.1 1 1 126 136.3 2.97e—5
C0pper 397 8930 390 1 .14e-4
Air 0.0255 1.22 1.004 2.08e-2
3.4 Boundary Conditions

The following set of boundary conditions will be used in order to solve the

heat conduction partial differential equation:

The initial temperature profile is always known. The initial temperature is

uniform throughout the assembly at time t = Os. The initial temperatures used

are 25°C, 75°C and 125°C.

At the diode centerline (x=0 pm), the temperature gradient is equal to zero.

511:0
dx

Also, there is continuity of heat flux at the material boundaries such that:

at the silicon-nickel interface (x=100 pm)

21

 

 

at the nickel-solder interface (x=120 pm)

dT

dT
—k ._
N: l

= ‘ksolder dx (8)

'Ni solder

at the solder-heat sink interface (x=170 pm)

dT dT
= “kCu
dx dx Cu

solder

(9)

"ksolder

0 Since the conductivity of copper is much larger than the conductivity of solder,
it is a good approximation to keep the heat sink (copper slab) temperature
constant. This means that at the solder-heat sink interface (x=170 pm), (9) is

reduced to:

T = TCu heat sink (10)

3.5 Effect of voids on the solder layer thermal properties

In Table 1, the themal properties listed for solder assume that it is void-
free. If the solder slab contains voids, the voids will have an effect on the therrnai
properties of the solder, specifically the thermal conductivity and the density. The
second objective of this thesis is to identify the amount of solder voids that still
permits reliable operation. To achieve this objective, a model needs to be used to
relate void content and thermal diffusivity in the solder layer.

To describe the effect of the voids on the thermal conductivity, several
models are available. The simplest models treat thermal conduction through
paths of solid medium and voids. There are two such models, the Parallel and
the Serial model. In the parallel model it is assumed that the conduction path in

the porous solid goes through solid and void channels that are parallel to each

22

other, as shown in Figure 12.

 

Thermal I Solid Phase

Conduction Path

  
 

 

D Voids

Figure 12: Solid and void layout in the Parallel model

On the other hand, the serial model assumes that the conduction path in
the porous solid goes trough solid and void channels that are connected in series
as shown in Figure 13. These two cases represent the upper and lower limits on

the thermal conductivity values.

Thermal I Solid Phase

Conduction Path ‘

  
 

[I Voids

Figure 13: Solid and void layout In the Serial Model

In this thesis the effective thermal conductivity, kerr. of solder with voids is

calculated by using the porosity weighted simple medium (PWSM) model [13].
This model is deducted from a combination of the parallel and the serial models,

and is represented in Equation 12.

e kair + (1‘ E)ksolder (1_ ex )+ k k

k.,,- = k... k (e‘) (11)

air
solder E k solder + (1— e)kair

Here ksdde, and k8,, are the thermal conductivities of the void free solder and air

23

respectively; and e is the void fraction. X is a fitting parameter that describes the
contact between regions of solder in the presence of voids. The contact, X, can
vary from 0 to infinity, corresponding to the void characteristics. For our
calculations X is set to 0.49, which corresponds to spherical voids and indicates
good contact in the conducting medium. Even though the contact has been set to
0.49 for our simulation, thermal conductivity measurements can be made, to
adjust this parameter to pore characteristics different than those assumed here.
Connectivity of the voids, their size and distribution is also critical. If the voids are
connected with each other, it has the same effect as having a larger continuous
void. The heat transfer will be severely impaired when the voids are connected. If
the voids are small and well dispersed heat transfer will occur with ease. This
model assumed that there is no connectivity between voids.

Hu et al. [13] presents actual thermal conductivity data for a porous
Xerogel film that has been fitted successfully with this model. This is shown in
Figure 14.

Figure 15 shows the thermal conductivity for the Pb/Sn/Ag solder as a
function of void content. This figure was calculated using equation 11.

The density of the solder layer is also affected by the presence of voids.

The effective density, pair, is modeled by using a volume average as follows:

[oefir =pair e +psolder(1_ 6) (12)
Where psolder and Pair are the densities of void free solder and air

respectively; and e is the void fraction. Figure 16 shows the density dependence

on void content using Equation 12.

24

 

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Thermal Conductivity (Wlm°C)

Figure 14: Effective thermal conductivity of Xerogel film[13].

25

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3.4 Assumptions

Several assumptions were made to simplify the analysis and solution of

the problem. These assumptions are listed below:

in a real diode assembly, inter-metallic layers are present at all of the material
interfaces. They could contribute to the heat transfer characteristics of the
diode assembly. In this discussion it is assumed that inter-metallic layers do
not play a role in the heat transfer of the diode assembly, and they are not
included as layers in the diode assembly.

The heat sink is perfect, therefore the temperature of the heat sink is always
constant and equal to the ambient temperature.

Heat transfer only occurs in the x direction, from the silicon diode to the heat
sinks at both ends of the assembly. Heat transfer in any other directions is
negligible and will not be taken into account for the calculations.

All the power generated inside of the diode is dissipated as heat. All of the
heat is transferred by conduction.

Voids in the solder layer are spherical, small and are not connected.

The PWSM model correctly describes the relationship between void fraction

and thermal conductivity for the Pb/Sn/Ag solder.

28

CHAPTER 4

RESULTS

4.1 Finite element program

4.1.1 Finite element program Description
In order to solve the heat transfer differential equations discussed in the

previous section, a one-dimensional finite element program3 was used to obtain
temperature profiles and transients for the diode assembly. In depth discussion
of the finite element method can be found in many books and will not be
discussed here. Reading of [20] is recommended if more information about this
method is needed.

In order to calculate the temperature profiles and transients, it is
necessary that the input file contain all the necessary information. The input file
contains the following:

. The physical properties of each material slab: Thermal diffusivity, density,
heat capacity and power generation, as they would appear in the PDE.

. Nodes and elements: The nodes are the places on which the temperature will
be calculated, and an element is a group of nodes. The input file specifies the

total number of nodes, their location and their initial temperature. It also states

 

3 Dr. L. J. Segerlind provided the finite element program used. Appendix A
includes an example input and output file.

29

the total number of elements, and how many nodes exist within each element.
Boundary conditions: The input file specifies the location and type of the
boundary conditions. It can be specified if the boundary condition is a
derivative boundary condition, or a fixed value of temperature at a certain
location. Point heat sources (or sinks) can also be specified. For the problem
discussed in this thesis the temperature gradient is set to zero at the
assembly centerline, and the heat sink temperature is kept constant at
ambient temperature.

The time steps: The input file also has the option of specifying the time step.
The user can define how many time steps are needed and the duration of
each time step. The user can also choose whether to do a forward difference,
a backward difference or a central difference integration to obtain their
results.

Screen and file write controls: This option enables the user to choose how
often the program will record the results on the screen and on the output file.
The user could use different values for the two. So that the program could
write into your output file the nodal values of each time step, while only

showing in the screen the nodal values of temperature every ten time-steps.

Appendix A shows a sample input file, and describes where each of the above

properties or values would be listed.

The output file on the other hand, is a very simple file that only shows the

value of time and the nodal values of temperature at each time. Appendix A also

shows a sample output file.

30

4.1.2 Finite Element Program Verification

To verify that the program provided accurate values, the analytical solution
for the case of only one slab at steady state was obtained and its results were
compared to the numerical solution obtained from the program.

The heat transfer equation for the case of only one slab with heat

generation at steady state is the following:

 

527 aT+b
+ .—

a —O 13
a2 pCp ( >

This equation is a linear ordinary differential equation in temperature and its

solution is widely available. Using the following boundary conditions:
2T— = O at x = O (14)
dc
T = H at x = L (15)

The particular solution of this equation is the following:

 

 

b
H——
T = a {co{ —a x +2
S[ —a ]K PCpa a (16)
co —L
pcpa
For a silicon slab that is 200 mm thick whose center is located at x=0, the

constants for the previous equation are:
H = 298 K
L = 100 ,um
a=2.23 x 10‘6 mz/s
p=2330 kg/m3 (17)
Cp = 712J/kg-K
a =-3.58x107 W».3 -K
b = 3.12x10‘° WM

31

By comparing the temperatures calculated with the analytical solution of
this equation with the temperatures obtained from the FEM program the program
is verified and working as expected. Very little error is introduced by using the
FEM program to calculate these temperature values. To ensure accuracy for the
temperature values calculated with the FEM program, the time steps were varied
to obtain the value of the time step that provided the most accurate results. By
comparing our Analytical solution to the numerical solutions using the different
time steps it was determined that the time steps should be set equal to 0.0036 s.
This time step value provides the smallest errors between results from the
program and the analytical solution of equation using only the silicon slab. Figure
17 shows the percent error of the numerical solution for different values of time
step. Figure 18 shows the comparison between the analytical solution and the

numerical solution obtained from the FEM program.

32

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34

4.2 Power-on simulation

4.2.1 Simulation description

In these simulations a constant forward current of 60A was run through a
diode assembly initially at Tsink. This current generates temperature dependent

power in the silicon slab as discussed in the previous chapter. The power
generation along with the thermal properties of each of the slabs and the
boundary conditions are used to solve the differential equations, using the finite
element program. This process is repeated for different values of solder thermal
diffusivity. After gathering temperature transients and profiles for a TVS button
diode assembly initially at 25°C, the simulation is repeated for a diode assembly
initially at 75°C and once more for a diode assembly initially at 125°C. This data
is used to quantitatively describe the effect of the solder effective thermal
diffusivity on:
. The temperature rise of the solder. This parameter is used to predict solder
reliability as discussed in the previous chapters. Temperature rise is defined
in equation 18.
True = Tmax,solder - Ysink (18)
o The maximum temperature in the diode assembly. This parameter is
important since higher temperatures in the diode result in an increase in
fonNard voltage drop, and consequently adversely affecting the performance
of the device.

a The time to reach steady state, or if solder fusion temperature is reached

35

before reaching a steady state, the time to failure.

4.2.2 Temperature transients for “on” cycles

Lowering the thermal diffusivity of the solder layer has several effects on
the temperature transients. The temperature rise in the diode increases as the
thermal diffusivity of the solder decreases. A change of 20% in the thermal

diffusivity of the solder doubles the temperature rise in the solder layer. The
temperature rise for a diode with one“: 1.25 x 10'5 m2/s is greater than 21°C. This

presents a problem for applications that require the diode assembly to last more
than 20,000 cycles. As previously discussed in Chapter 2, if a device is to last
that long in a test, the temperature rise could not exceed 21°C. If the application
requires a lower amount of cycles to pass a reliability test, the solder can have a
lower value of the thermal diffusivity. Care should be taken though to avoid
values of the solder thermal diffusivity that are lower than one“ = 4.51 x 10'6 m2/s,
After this value is reached, most of the heat generated becomes trapped inside
of the silicon and nickel layers. As a result of the low conductivity in the solder
layer, the temperature rise in the diode assembly is too extreme and the
temperature in the solder layer reaches the melting temperature. At this point
failure occurs due to solder fusion. The following figures show how decreasing
the thermal diffusivity of the solder layer affects the transients for a diode with

Tsink=25°C4. When the heat sink temperature is increased at constant solder

thermal diffusivity, the maximum temperature profiles are increased

 

4 Power on temperature transients for Tsink=75°C and Tsmk=125°C are included
in Appendix B

36

proportionally to the increase in the heat sink temperature. This effect is minimal

if compared to the effect of decreasing the thermal diffusivity of the solder layer.

37

 

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The maximum temperature at steady state increases with decreasing
solder thermal diffusivity. The maximum temperature inside of the silicon diode
also rises as the heat sink temperature is increased. Decreasing this temperature
is of major importance since diode lifetimes decrease with increasing
temperature. Higher temperatures in the silicon diode can lead to an undesired
increase in the fonlvard voltage drop and a reduction in its current handling
affecting the performance of the diode. Even a moderate reduction in the
maximum temperature can significantly improve device lifetime and performance
[6].

As shown in Figure 24, steady state could not be achieved for diodes with

solder thermal diffusivity lower than 6.66 x 10'6 m2/s, since solder fusion occurs

before a steady state can be achieved. The time needed to reach steady state
increases when the void content is increased, but it decreases while raising the
sink temperature for a diode with a constant amount of solder voids. This is
expected, since the power generation decreases with increasing temperature.
The effect of the heat sink temperature is more important when the thermal
diffusivity of the solder is higher. When the thermal diffusivity of the solder is low,
the time needed to reach steady state is very similar regardless of heat sink

temperature.

4.2.3 Temperature profiles

The simulations show that the thermal diffusivity of the solder layer also
has an effect on the temperature profiles inside the TVS button diode assembly.

The temperature profile in the silicon part of the diode is not linear due to the

44

power generation in that layer. As the thermal diffusivity of the solder layer
decreases, more heat becomes trapped inside of the silicon and nickel layers
and the temperature inside the silicon and nickel layers becomes more uniform.
The temperature profile changes, becoming more linear as the solder thermal
diffusivity is reduced. The temperature profile at steady state becomes almost
constant in the silicon layer as the solder reaches the thermal diffusivity limit

before solder fusion occurs. The following figures show how the solder thermal

diffusivity affects the temperature profiles for a diode at Tsink=25°05.

 

5 Appendix C includes temperature profiles for a diode assembly at higher sink
temperatures.

45

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The temperature gradient in the solder becomes larger as the solder

thermal diffusivity decreases. In the limit case of Gaff: 4.51x10'6 m2/s, the

gradient becomes as large as 5°C/pm. Temperature gradients are a major
source of stress in the solder joint. A gradient so large could lead to thermal
shock, where fracture or cracks can grow and propagate in the solder layer
resulting in failure of the TVS diode assembly. By increasing the thermal
diffusivity in the solder layer, excessive temperature gradients in the solder layer
can be avoided, helping to increase the overall lifetime and thus the reliability of

the TVS diode assembly.
4.3 Power cycle testing

4.3.1 Simulation description

In the Power Cycle Test (PCT) simulation, the fonlvard current is kept at
60A for three seconds, and then it is turned off for another three seconds. This
cycle is applied to a diode assembly initially at 25°C. During the On part of the
cycle the current generates temperature dependent power in the silicon slab as
shown previously. During the Off part of the cycle, there will be no current, and
therefore no power generated within the silicon. This on-off cycle will be repeated
until a steady oscillation is obtained. The power generation and the thermal
properties of each slab and the boundary conditions are used to solve the
differential equations. This process is repeated for different values of the solder
thermal diffusivity. After gathering temperature transients for the diode assembly

initially at 25°C, the process is repeated for a diode assembly at 75°C and then

52

for a diode assembly at 125°C.
In this section of the chapter, we describe quantitatively the effect of the
solder void content on:
. The number of cycles needed to obtain a steady oscillation when the diode is
cycled.
- The amplitude of the temperature oscillations when the diode is cycled at
steady-state. The oscillation amplitude is defined as:
amplitude = T Si,max — T Si,min (19)
. The temperature drift in the solder when the diode is cycled. The drift of
oscillations is defined as:

Dr 1ft = Isoldermean - Tsink (20)

4.3.2 Temperature transients for on-off cycles

When the diode assembly undergoes power cycling, the cyclic fluctuation
in temperature creates stresses and strains that can initiate crack growth in the
solder. These cracks propagate and ultimately can cause failure of the TVS
button diode assembly.

When performing PCT cycles, the numerical simulations show that the
number of cycles needed to obtain a steady oscillation increases as the thermal
diffusivity of the solder layer decreases. Though, this number remained

unaffected by changes in sink temperature. It is not possible to obtain a steady
oscillation when one“: 4.51 x 10’6 m2/s regardless of heat sink temperature. When

the thermal diffusivity of the solder layer decreases, the power generates heat

and the temperature keeps on increasing in the assembly, and the heat has no

53

way of reaching the assembly’s heat sink leading to a further increase in the

temperature. The following figures show the effect of the solder thermal diffusivity

on the temperature transients for a diode assembly at Tsjnk =25°C undergoing a

power cycling tests.

 

6 Appendix D includes power cycling temperature transients for a diode at higher
heat sink temperatures.

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59

The amplitude of the steady state oscillations increases slightly by the

decreasing the thermal diffusivity of the solder layer. The amplitude of the

oscillations goes from 7°C for one“ = 2.98 x 10’5 mzls and goes up to 10°C for (Xeff

= 6.66 x 10'6 m2/s. Oscillations of large amplitude in the solder temperature are

bad for the assembly, since large repetitive changes in temperature accumulate
stress in the solder joint and can lead to diode failure. It is desirable that these
temperature oscillations are kept with minimal amplitude to obtain improved
devices that can meet reliability test criteria.

An important aspect in the reliability of the TVS diode assembly is the drift
temperature. The drift in temperature represents the temperature difference
between the solder joint and the environment temperature. Increases in drift
temperature are a cause for ooncem since the lifetime of the assembly

decreases as the drift temperature increases. The simulations show that the drift

in the temperature increases with decreasing one“. A decrease of 20% in the

solder thermal diffusivity nearly doubles the drift temperature. High drift
temperatures mean that a high temperature gradient exists when the diode is
going through power cycling. Higher temperature gradients can result in crack
formation and propagation or thermal shock and failure of the device. The
diffusivity of the solder has to be maintained at a maximum to avoid high drift
temperatures during cycling.

When the diode undergoes power cycling and the solder has reduced
thermal diffusivity, the heat dissipation process is inhibited, allowing for higher

temperatures in the diode assembly. On the other hand, when the solder has a

60

high thermal diffusivity, heat dissipation occurs without problem, allowing the
temperature in the assembly to recover almost to its initial temperature during the
off part of the cycle. Using a solder of high thermal diffusivity helps to avoid
oscillations of large amplitude and also helps to reach steady oscillations in less
time. The reduction in temperature inside of the diode assembly will in turn help

to achieve longer lifetimes and better performance in reliability tests.

4.4 Solder voids and thermal diffusivity

‘ “’3 f; Solder region with

 

‘..p-,..‘.

Figure 36: Solder voids in a commercially available diode

61

Solder voids are a common occurrence in commercially available diode
assemblies. Figure 36 shows a commercially available diode that has been pried
opened. When the diode is opened, some areas become loose through the
silicon glass, and other areas become loose through the solder. When the solder
has a low void content, the diode breaks open through the silicon. If the diode is
filled with voids it will break open from the solder layer. Voids make the diode
assembly mechanically weak and affect the thermal properties of the assembly,
drastically reducing the thermal diffusivity of this layer. As discussed in the
previous sections, even a slight reduction in thermal diffusivity can cause
reliability problems. Therefore, it is necessary to use a model to relate the
thermal diffusivity data to solder void content. Using this model one can calculate
the maximum amount of voids that can still deliver the desired thermal diffusivity
needed to have good reliability of the TVS diode assembly.

The thermal conductivity and the density models described in Chapter 3
were used to calculate thermal diffusivity as a function of solder void content. The
following figure illustrates how the thermal diffusivity of the solder decreases with
void content.

When voids in excess of 33% are present, (when the thermal diffusivity of
the solder drops lower than 1 .25 x 10'5 mzls) the temperature rise will be higher

than 21°C, and the diode assembly will not meet the requirements to pass a
20,000 cycle reliability test.
Although it would be unpractical to have a solder with such a high

concentration of voids, It is important to point out that solder fusion will occur for

62

nWifil IV» .«dbmp Blu¢lu “b.- /

 

a diode in the power-on mode when voids in excess of 78% are present. For
solders with lower melting point this critical void content will be lower. These
critical void concentrations will decrease slightly when the environment
temperature is higher The presence of voids in the solder layer increases the
time needed to achieve a steady state in the power-on mode. This time nearly
doubles with an increase in void content of only 20%. Steady state cannot be

achieved when voids in excess of 78% are present in the solder layer due to

solder fusion7.

 

7 78% is the amount of solder voids needed to reach solder fusion at Tsink=25°C.
When Tsink is higher this critical amount of voids will be lower.

63

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64

The temperature gradient in the solder layer is also greatly affected by the
amount of voids this layer contains. The temperature gradient in the solder has
the tendency to double every time the void concentration is increased by 20%.

The number of cycles (and therefore the time) needed to reach steady
oscillations in the power on-off cycles steadily increases while increasing solder
void content.

The temperature drift is the characteristic that is most affected by the
presence of voids in the solder layer of the TVS button diode assembly while it
undergoes power cycling. The drift is almost doubled with an increase in solder
voids of only 20%. Since a larger temperature drift is equivalent to a shorter
lifetime, it is desirable to reduce the amount of voids in the solder layer.

The effect of changing the heat sink temperature was minimal for most of
the simulations, even though increasing the sink temperature increased the
steady state temperature profiles in the diode assembly. The heat sink
temperatures used yield similar oscillation amplitudes, and require the same
amount of cycles to reach a steady oscillation state. Lowering the heat sink
temperature (environment) will help reduce some of the reliability problems, since
the overall temperature profiles will be reduced by doing so. However, reducing
the amount of voids is a better option since the steady temperature profiles are
much more dependent on the void content than on the heat sink temperature,
and in many occasions the service conditions will require to operate the

assembly at elevated environment temperatures.

65

4.5 Summary of Results

The following tables summarize the results obtained from all of the

simulations.

Table 2: Steady-state temperature rise In the solder for different values of

thermal diffusivity at different heat sink temperatures

 

Tsink=25°C | Tsink=75°C | Tsink=125°C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(leff (mzls) Void % Temperature Rise (°C)
2.98 x 10'5 0 5.68 5.88 6.07
1.63 x 10'5 20 13.05 13.5 13.96
1.33 x 10‘5 30 18.32 18.95 19.59
1.31 x 10'5 31 18.98 19.63 20.29
1.25 x 10'5 33 20.3 21.08 21.79
1.08 x 10'5 40 26.47 27.39 28.3
6.66 x 10’5 60 66.4 68.71 71.02
4.51 x 10*5 72 148.21 153.37 158.53

 

66

 

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Table 3: Critical values of themal diffusivity and the corresponding solder

void concentrations

 

Thermal DiffusivityNoids for Tn-se = 21°C

 

 

 

 

 

 

 

 

 

 

 

 

 

Tsink(°C) aefi (mzls) Void %
25 1.25 x 10'5 33
75 1.25 x 10'5 33
125 1.25 x 10'5 33
Thermal DiffusivityNoids for solder fusion
Tsink(°C) aefi (m2/s) Void %
25 3.51 x 10'6 73
75 3.48 x 10'6 76
125 4.51 x 10J<3 72

 

 

 

Table 4: Time needed to reach steady state for different values of thermal

diffusivity at different heat sink temperatures

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tsink=25°C Tsink=75°C] Tsink=125°C

(leff (mi/s) Void % Time to Steady State (s)

2.98 x 10'5 0 6.048 6.048 6.048
1.63x10’5 20 12.132 12.132 12.132
1.33 x 10'5 30 16.416 16.416 16.416
1.31 x 10'5 31 16.956 16.956 16.956
1.25x10'5 33 18.108 18.108 18.108
1.08 x 10'5 40 23.004 23.004 23.004
6.66 x 10'6 60 54.72 54.72 54.72
4.51 x 10'6 72 119.52 119.52 119.52

 

68

 

Table 5: Temperature gradient in the solder layer for different values of

thermal diffusivity at different heat sink temperatures

 

 

 

 

 

 

 

 

 

 

Tsink=25°C l Tsmk=75°c | Tsink=125°C
def, (m2/s) Void % Temp. Gradient in Solder (°C/um)
2.98x10‘5 0 0.11 0.12 0.12
1.63 x 10'5 20 0.26 0.27 0.28
1.33 x 10'5 30 0.37 0.38 0.39
1.31 x 10'5 31 0.38 0.39 0.41
1.25 x 10'5 33 0.39 0.42 0.44
1.08 x 10'5 40 0.53 0.55 0.57
6.66 x 10'6 60 1.32 1.37 1.42
4.51 x 10'6 72 2.96 3.06 3.17

 

 

 

 

 

 

 

Table 6: Number of cycles needed to achieve steady state for different

values of thermal diffusivity at different heat sink temperatures

 

 

 

 

 

 

 

 

 

 

 

 

 

Tsink=25aC I Tsink=75°C Tsink=125°C
aefi (m2/s)f Void % # of Cycles until Steady Oscillation
2.98 x 10‘5 0 1 1 1
1.63 x 10'5 20 2 2 2
1.08 x 10'5 40 3 3 3
1.01 x 10'5 43 4 4 4
6.66 x 10’6 60 6 6 6

 

69

 

 

 

 

Table 7: Oscillation amplitude for different values of thermal diffusivity at

different heat sink temperatures

 

 

 

 

 

 

 

 

 

 

 

 

Tsink=25°C [Tsink=75°C | Tsink=125°C
aeff (m2/s) Void % Amplitude of Steady Oscillation (°C)
2.98 x 10'5 0 7.66 7.74 8.00
1.63 x 10'5 20 8.55 8.85 9.15
1.08 x 10'5 40 8.80 9.10 9.40
1.01 x 10'5 43 8.87 9.10 9.40
6.66 x 10'6 60 9.00 9.10 9.40

 

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Table 8: Temperature drift for different values of thermal diffusivity at

different heat sink temperatures.

 

 

 

 

 

 

 

 

 

 

 

 

Tsink=25°C I Tsink=75°C I Tsink=125°C
aefi (mzls) Void % Drift at Steady Oscillation (°C)
2.98 x 10'5 0 5.11 5.29 5.47
1.63 x 10'5 20 9.72 10.50 10.39
1.08 x 10'5 40 16.66 17.24 17.82
1.01 x 10'5 43 18.43 18.86 19.49
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73

CHAPTER 5

CONCLUSION

5.1 Conclusion

This thesis has explored the effect of the thermal diffusivity of the solder
layer on the heat transfer and reliability of a TVS button diode assembly.
Reducing the thermal diffusivity of the solder layer can result in very high
temperature rises in the diode assembly, which are detrimental to its lifetime and
reliability. Maintaining the value of the solder thermal diffusivity at a high value
will not only ensure proper performance, but also ensure reliable operation.
Solder voids in the solder layer can reduce the effective thermal diffusivity of this
layer. This results in an increase in temperature and a decrease in lifetime of the
diode. Therefore, reliable operation also depends on maintaining a low amount of
voids in the solder layer.

It is concluded that a TVS diode assembly should have solder with a
thermal diffusivity of 1.25 x 10'5 m2/s or more in order to last more than 20,000

cycles in a reliability test. This value corresponds to 33% voids in the solder

layer. Solder fusion will occur whenever the thermal diffusivity of the solder layer

falls below 3.51 x 10'6 m2/s or 78% solder voids.

5.2 Future Research

For future research, it suggested to explore the effect of the thermal

74

diffusivity of the solder on other popular testing methods such as the accelerated
thermal cycling test (ATC). The effect of solder voids in combinations of power
and temperature cycling can also be studied.

Another improvement that can be made over the calculations presented
here is to add calculations for the therrno-mechanical stress in the diode
assembly such as to calculate reliable estimates of the lifetime of a diode
assembly.

It is also important to investigate the effect of the solder voids on the
thermal mismatch of nickel and silicon, since silicon-nickel delamination is also a
known failure mechanism for the diode assembly.

For a calculation that better approximates reality the inter-metallic layers
could be added into the model Also, since heat transfer for this application mainly
occurs in one direction, this was the case studied here, but the other dimensions
can be also be added. Other suggestion is to verify the relationship of solder
voids and thermal diffusivity by experimental means, and make adjustments to
the model presented as necessary.

Finally, because of environmental constraints there is growing interest in
the application of other soldering materials that are lead-free, these materials

could also be studied using a similar analysis.

75

APPENDICES

76

APPENDIX A
FINITE ELEMENT PROGRAM SAMPLE INPUT AND OUTPUT FILES

77

Sample Input File:

 

# of nodes, # of

 

"Silicon Diode with Linear Heat Generation” elements, # of
"Lumped" 4' materials
3029.3

 

 

 

0,1,1
108,0,0,1658960
90.7.0.0,3944940

45.185,0,0,1516473.8

0.000000,356.6648
0.000005,356.6591
0.000010,356.6419
0.000015,356.6132
0.000020,356.5731
0.000025,356.5215
0.000030,356.4585
0.000035,356.384
0.000040,356.298
0.000045,356.2006
0.000050,356.0916
0.000055,355.971 1
0.000060,355.8391
0.000065,355.6955
0.000070,355.5403
0.000075,355.3737
0.000080,355.1954
0.000085,355.0055
0.000090,354.8041
0.000095,354.591
0.000100,354.3663
0.000105,354.0929
0.000110,353.8218
0.000115,353.5528
0.000120,353.2859
0.000130,352.2212
0.000140,351.1615
0.000150,350.1056
0.000160,349.0522
0.000170,348
1 ,2,1 \
2,3,1

3,4,1

4,5,1 >—

5,6,1
6,7,1
7,8,1

 

Type of

Material 30“"??0’

 

 

 

 

 

 

 

\ Properties

 

 

Node location and initial
temperature.

 

 

 

 

 

 

J

 

 

Material in each node

 

 

78

8,9,1
9.10.1
10,11.1
11,12,1
12,13,1
13,14,1
14,15,1
15,16,1
16,17,1
17,18,1
18,19,1
1920.1
2021.1
21.222
22.232
23,242
24,252
2526.3
2627.3
2728.3

30

28,293

29.30%

1 ,0.0 /
1 ,83,0.00001
40,9,CDMChk

 

 

 

Material in each node,
Continued

 

 

 

Boundary Conditions

 

 

 

/

 

 

Number of time steps and time
step duration

 

 

 

 

File write and screen write
control

 

 

Sample Output File

.00009

354.5503
354.5467
354.5359
354.5179
354.4927
354.4604
354.421 1
354.3747
354.3215
354.2615
354.1948
354.1215
354.0417
353.9556
353.8633
353.7648

 

 

 

Time. t

 

 

 

 

 

Nodal values of Temperature
at time t

 

 

 

79

353.6604
353.5503
353.4346
353.31 34
353.1 87
353.0262
352.8516
352.6636
352.463
351 .6147
350.7367
349.8366
348.922
348

 

 

 

Nodal values of Temperature
at time t. continued

 

 

_/

80

 

APPENDIX B

TEMPERATURE TRANSIENTS FOR “POWER-ON” TESTS. TsmK=75°C AND
T3|NK=125°C

81

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91

APPENDIX C

TEMPERATURE PROFILES FOR “POWER-ON” TESTS. Tsmx=75°C AND
Tame-425°C

92

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103

APPENDIX D

TEMPERATURE TRANSIENTS FOR POWER ON-OFF CYCLES. TsmK=75°C
AND TsmK=125°c

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BIBLIOGRAPHY

113

—L

BIBLIOGRAPHY

. R. Puchert, A. Banlvolff, M. VoB, U. Menzel, J. W. Tomm, and J. Luft,

“Transient Then'nal Behavior of High Power Diode Laser Arrays” IEEE Trans.
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K. Subramanian and J. G. Lee, “Physical Metallurgy in Lead Free Electronic
Solder Development,” JOM, vol.55, no. 5, pp. 26-32, May 2003.

M. Shur. Introduction to Electronic Devices. New York: John Wiley and Sons,
1996, pp. 188-213.

B. Streetman and S. Banerjee. Solid State Electronic Devices. New Jersey:
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J. H. L. Pang, K. H. Tan, X. Shi, and Z. P. Wang, “Thermal Cycling Aging
Effects on Microstructural and Mechanical Properties of a Single PBGA
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. J. Evans and J. Y. Evans, “Packaging Factors Affecting the Fatigue Life of

Power Transistor Die Bonds,” IEEE Trans. Comp. Packag. Manuf. Technol.,
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. http://wwwmetallurgy.nist.govlghase/solder/aggbsn.html

B. Rodgers, J. Punch, J. Jarvis, P. Myllykoski, and T. Reinikainen, “Finite
Element Modelling of a BGA Package Subjected to Themial and Power
Cycling,” IEEE Inter Society Conference on Thermal Phenomena, pp. 993-
1000, June 2002.

J. H. L. Pang, D. Y. R. Chong, and T. H. Low, "Thennal Cycling Analysis of
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114

10.E. Davitt, F. A. Stam, and J. Barrett, "The effect of Power Cycling on the
Reliability of Lead free Surface Mount Assemblies,” IEEE Trans. Comp.
Packag. Technol., vol. 24, no. 2, pp. 241-249, June 2001.

11.P. Towashirapom, G. Subbarayan, B. Mcllvanie, B. C. Hunter, D. Love, and
B. Sullivan, “Predictive Reliability Models Through Validated Correlation
Between Power Cycling and Thermal Cycling Accelerated Life Tests,”
Soldering and Surface Mount Technology, vol. 14, no. 3, pp. 51 -60, 2002.

12.R. D. Gerke and G. B. Kromann, “Solder Joint Reliability of High l/O Ceramic
Ball Grid Arrays and Ceramic Quad-Flat—Packs in Computer Environments:
The PowerPC 603W and PowerPC 604TM Microprocessors,” IEEE Trans.
Comp. Packag. Technol., vol. 22, no. 4, pp 488-496, Dec. 1999.

13.0. Hu, M. Morgen, P. S. Ho, A. Jain, W. N. Gill, J. L. Plawsky, and P. C.
Wayner, Jr., "Thermal Conductivity Study of Porous Low-k Dielectric
Materials,” App. Physics Letters, vol 77, no. 1, pp. 145-147, July 2000.

14.A. Constantinides and N. Motsufi, Numerical Methods for Chemical Engineers
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