Download Thermal Fatigue Life Prediction of Solder Joints in Avionics

Thermal Fatigue Life Prediction of Solder Joints in Avionics
by Surrogate Modeling
– a Contribution to Physics of Failure in Reliability Prediction
Jonas Arwidson
Norrköping 2013
Linköping Studies in Science and Technology.
Dissertations. No 1521
Thermal Fatigue Life Prediction of Solder Joints in Avionics
by Surrogate Modeling
– a Contribution to Physics of Failure in Reliability Prediction
Jonas Arwidson
Copyright © 2013 Jonas Arwidson, unless otherwise noted.
Department of Science and Technology
Linköping University
Campus Norrköping
SE-601 74 Norrköping, Sweden
Saab AB
Business Area Electronic Defence Systems
Avionics Division
Box 1017
SE-551 11 Jönköping, Sweden
ISBN 978-91-7519-618-3
ISSN 0345-7524
Printed in Sweden by LiU-Tryck, 2013.
Abstract
Manufacturers of aerospace, defense, and high performance (ADHP) equipment
are currently facing multiple challenges related to the reliability of electronic systems.
The continuing reduction in size of electronic components combined with increasing
clock frequencies and greater functionality, results in increased power density. As an
effect, controlling the temperature of electronic components is central in electronic
product development in order to maintain and potentially improve the reliability of the
equipment. Simultaneously, the transition to lead-free electronic equipment will most
probably propagate also to the ADHP industry. Compared to well-proven tin-lead
solder, the knowledge about field operation reliability of lead-free solders is still
limited, as well as the availability of damage evaluation models validated for field
temperature conditions. Hence, the need to fill in several knowledge gaps related to
reliability and reliability prediction of lead-free solder alloys is emphasized. Having
perceived increasing problems experienced in the reliability of fielded equipment, the
ADHP industry has suggested inclusion of physics-of-failure (PoF) in reliability
prediction of electronics as one potential measure to improve the reliability of the
electronic systems.
This thesis aims to contribute to the development of reliable ADHP systems, with
the main focus on electronic equipment for the aerospace industry. In order to
accomplish this, the thesis provides design guidelines for power distribution on a
double-sided printed circuit board assembly (PBA) as a measure to improve the
thermal performance without increasing the weight of the system, and a novel,
computationally efficient method for PoF-based evaluation of damage accumulation in
solder joints in harsh, non-cyclic field operation temperature environments.
Thermal fatigue failure mechanisms and state-of-the-art thermal design and
design tools are presented, with focus on the requirements that may arise from avionic
use, such as low weight, high reliability, and ability to sustain functional during high
vibration levels and high g-forces. Paper I, II, and III describes an in-depth
investigation that has been performed utilizing advanced thermal modeling of power
distribution on a double-sided PBA as a measure to improve the thermal performance
of electronic modules.
Paper IV contributes to increasing the accuracy of thermal fatigue life prediction
in solder joints, by employing existing analytical models for predicting thermal fatigue
life, but enhancing the prediction result by incorporating advanced thermal analysis in
the procedure.
Papers V and VI suggest and elaborate on a computational method that utilizes
surrogate stress and strain modeling of a solder joint, to quickly evaluate the damage
accumulated in a critical solder joint from non-cyclic, non-simplified field operation
iii
temperature profiles, with accuracy comparable to finite element modeling. The
method has been tested on a ball grid array package with SnAgCu solder joints. This
package is included in an extensive set of accelerated tests that helps to qualify certain
packages and solder alloys for avionic use. The tests include -20°C to +80°C and 55°C to +125°C thermal cycling of a statistically sound population of a number of
selected packages, assembled with SnAgCu, Sn100C, and SnPbAg solder alloys.
Statistical analysis of the results confirms that the SnAgCu-alloy may outperform
SnPbAg solder at moderate thermal loads on the solder joints.
In Papers VII and VIII, the timeframe is extended to a future, in which validated
life prediction models will be available, and the suggested method is expected to
increase the accuracy of embedded prognostics of remaining useful thermal fatigue life
of a critical solder joint.
The key contribution of the thesis is the added value of the proposed
computational method utilized in the design phase for electronic equipment. Due to its
ability for time-efficient operation on uncompressed temperature data, the method
gives contribution to the accuracy, and thereby also to the credibility, of reliability
prediction of electronic packages in the design phase. This especially relates to
applications where thermal fatigue is a dominant contributor to the damage of solder
joints.
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Populärvetenskaplig sammanfattning
Tillverkare av elektronik för försvar, flyg, rymd och andra tillämpningar med
krav på hög prestanda och tillförlitlighet står för närvarande inför flera utmaningar.
Över tid så har storleken på elektronik kontinuerligt minskat medan
effektförbrukningen har bibehållits eller ökat. Detta medför krav på mer avancerad
teknologi för att föra bort värmen från elektroniken för att den inte skall överhettas
och/eller tillförlitligheten påverkas negativt. Vidare kommer samma nisch av
elektronikutvecklande industri sannolikt ta steget över till blyfri elektronik som en
följd av ett EU-direktiv om minskning av skadliga ämnen, RoHS-direktivet. Sedan
lång tid har en legering av tenn och bly använts som lod för mekanisk och elektrisk
förbindning av elektronikkomponenter mot deras omgivning. Denna legering är därför
väl beprövad vad gäller tillförlitlighet, och stor erfarenhet finns tillgänglig. För blyfria
lod råder dock för närvarande starkt begränsad tillgänglighet på motsvarande data. Ett
sätt att angripa bristen på tillförlitlighetsdata för blyfria lod är att beräkna
tillförlitlighet och livslängd genom fysikaliska modeller av utmattning och andra
sorters fel: den så kallade Physics-of-Failure (PoF)-metodiken.
Målsättningen med avhandlingen är att bidra till utvecklingen av tillförlitliga
elektronikprodukter framför allt avsedda för flygtillämpningar. Detta görs genom att
närmare studera möjligheterna att hålla kontroll över temperaturen på elektroniken,
samt genom att presentera en ny, beräkningseffektiv metod för att uppskatta förbrukad
livslängd i en lödfog som utsatts för temperaturvariationer.
Teori kring fel som kan uppstå på grund av olika temperaturbelastningar följs av
en genomgång av tillgängliga verktyg för termisk design. Exempel på genomtänkt,
avancerad termisk design av elektronikapparater redovisas med fokus på kravbilden
som finns i flygande tillämpningar, såsom låg vikt, hög tillförlitlighet och höga
vibrationsnivåer. De tre första artiklarna i avhandlingen utgör en detaljerad
undersökning av effekten av att styra placeringen av effektutvecklande
elektronikkomponenter på dubbelsidiga mönsterkort; ett sätt att hålla kontroll över
temperaturen utan att tillföra varken extra vikt eller kostnad.
Övriga artiklar riktar sig mot möjligheten att uppnå ökad precision i skattningen
av förbrukad livslängd i en lödfog som funktion av temperaturrelaterade belastningar.
Första steget mot ökad noggrannhet kan tas genom att integrera avancerad termisk
analys i metoder som tillämpar enkla modeller för utmattning av lödfogar; ytterligare
höjd precision kan åstadkommas genom numeriska beräkningar som dock kräver
omfattande datorkraft och/eller lång beräkningstid. Därför presenteras en
beräkningsmetod som är mycket resurseffektiv jämfört med numeriska lösningar av
v
finita element (FE)-modeller, och samtidigt levererar resultat helt jämförbara med FEberäkningar.
Dessutom redovisas en omfattande serie experiment, vars syfte är att utvärdera
två varianter av blyfria lod i kombination med olika komponenttyper, avseende
användbarhet i flygtillämpningar. I experimenten har ett antal olika typer av
elektronikkomponenter monterats på mönsterkort med dels de två blyfria loden och
även ett ”vanligt” blyat lod för referens, varefter de utsatts för två olika nivåer av
temperaturcykling. Antalet cykler till felutfall har jämförts mellan de olika loden och
komponenttyperna. Resultaten bekräftar andra undersökningar i det att de blyfria loden
uppvisar bättre tillförlitlighet vid måttliga påfrestningar på lödfogarna, medan det
blyade lodet är tåligare vid mer extrema belastningar. Avslutningsvis blickas framåt i
tiden, då möjligen den nya beräkningsmetoden skulle kunna tillämpas i sammanhanget
kontinuerlig bedömning, prognostisering, av kvarvarande liv i elektronik som används.
Det viktigaste bidraget från denna avhandling är värdet av beräkningsmetoden
tillämpad i utvecklingsfasen av en produkt, där den kan bidra till ökad noggrannhet
och därmed vunnet förtroende för predikteringen av livslängd för elektronik. Som en
följd därav kan man närma sig att kunna designa ”rätt från början” och minska antalet
dyrbara omtag i produktutvecklingen.
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Acronyms and Abbreviations
ADHP
BGA
CDI
CFD
COTS
CTE
DSB
FCF
FE
FEM
FNM
IMC
LCM
MEA
PBGA
PoF
PBA
PCB
RoHS
RUL
SAC305
SEDcr
TIM
TRN
Aerospace, defense, and high performance
Ball grid array
Cumulative damage index
Computational fluid dynamics
Commercial off the shelf
Coefficient of thermal expansion
Double-sided PCB
First component to fail
Finite element
Finite element method
Flow network modeling
Intermetallic compound
Life consumption monitoring
More electric aircraft
Plastic ball grid array
Physics of failure
Printed circuit board assembly
Printed circuit board
Restriction of hazardous substances
Remaining useful life
SnAg3.0Cu0.5 solder alloy
Creep strain energy density
Thermal interface material
Thermal resistance network
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List of Papers
The following publications are included in this thesis:
Paper I: J. Johansson, I. Belov, and P. Leisner, “CFD Analysis of an Avionic
Module for Evaluating Power Distribution as a Thermal Management Measure for a
Double-sided PCB,” in Proc. Semi-Therm 2007, San Jose, CA, 2007.
Paper II: J. Johansson, I. Belov, and P. Leisner, “An Experimental Setup for
Validating a CFD Model of a Double-sided PCB in a Sealed Enclosure at Various
Power Configurations,” in Proc. EuroSime 2005, Berlin, Germany, 2005.
Paper III: J. Johansson, I. Belov, and P. Leisner, “Investigating the Effect of
Power Distribution on Cooling a Double-sided PCB: Numerical Simulation and
Experiment,” in Proc. 2005 ASME Summer Heat Transfer Conference, San Francisco,
CA, 2005.
Paper IV: J. Johansson, P. Leisner, J. Lee, D.W. Twigg, and M. Rassaian, “on
Thermomechanical Durability Analysis combined with Computational Fluid
Dynamics Thermal Analysis,” in Proc. ASME International Mechanical Engineering
Congress and Exposition (IMECE 2007), Seattle, WA, 2007.
Paper V: J. Johansson, I. Belov, E. Johnson, and P. Leisner, “A Computational
Method for Evaluating the Damage in a Solder Joint of an Electronic Package
Subjected to Thermal Loads,” Engineering Computations, accepted for publication.
Paper VI: J. Johansson, I. Belov, R. Dudek, E. Johnson, and P. Leisner,
“Investigation on Thermal Fatigue of SnAgCu, Sn100C, and SnPbAg Solder Joints in
Varying Temperature Environments,” Microelectronics Reliability, submitted.
Paper VII: J. Johansson and P. Leisner, “Prognostics of Thermal Fatigue Failure
of Solder Joints in Avionic Equipment,” IEEE Aerospace and Electronic Systems
Magazine, vol. 27, no. 4, Apr. 2012.
Paper VIII: J. Johansson, I. Belov, E. Johnson, and P. Leisner, “An Approach to
Life Consumption Monitoring of Solder Joints in Operating Temperature
Environment,” Proc. EuroSime 2012, Lisbon, Portugal, 2012.
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Author’s contribution to the papers:
Paper I:
70% of the analytic work, and 80% of the writing.
Paper II:
All experimental work, and 90% of the writing.
Paper III:
All experimental work, and 90% of the writing.
Paper IV:
All planning of the collaborative efforts, 50% of computational
experiments, and all of the writing.
Paper V:
All computational experiments, and 90% of the writing.
Paper VI:
30% of the planning of experimental work, 80% of computational
experiments, and all of the writing.
Paper VII: The complete paper.
Paper VIII: All computational experiments, and 90% of the writing.
Publications not discussed in this thesis:
J. Johansson, I. Belov, K. Säfsten, and P. Leisner, “Thermal Analysis of an
Electronic Module with a Double-sided PCB Housed in a 2-MCU Enclosure for
Avionic Applications,” in Proc. IMAPS 2004, Long Beach, CA, 2004.
J. Johansson, I. Belov, K. Säfsten, and P. Leisner, “Thermal Design Evaluation
of an Electronic Module for Helicopter Applications,” CEPA2 Workshop, Paris,
France, 2004.
J. Johansson, “Tools and Methods for Simulation in Thermal Design of
Electronics for use in Harsh Environments,” in Proc. SsoCC ´04, Båstad, Sweden,
2004.
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Acknowledgements
First of all I would like to thank my supervisor Professor Peter Leisner at the
School of Engineering, Jönköping University, for always being positive and
optimistic, able to supply a boost of energy when most needed. Also, many thanks
must be directed to his colleagues, my co-supervisors Dr. Ilja Belov, for continuously
reminding me about the importance of being thorough in every action taken in
research, and Dr. Mats Robertsson, for pursuing this work to the finalized stage,
although long time has passed and his current work situation would in practice not
admit this kind of assignment.
I would like to thank many people at Saab AB, though especially M. Sc. Bengt
Rogvall and Dr. Ingemar Söderquist for initiating this project and believing in my
capability of performing this kind of work, and M. Sc. Mats Johansson for always
listening and being supportive, and for providing valuable feedback during the writing
of the thesis. Doctors Håkan and Kristina Forsberg have been perfect role models and
provided inspiration when mostly needed.
The financial support from the KK foundation and Saabs Teknikråd is gratefully
acknowledged, as this enabled the studies.
My brother, Docent Jonny Johansson, has been more important to me than he
could imagine, all the way through. I would also like to thank my parents for
reminding me in times of trouble, that there might be other things in life that are more
important than completion of this work.
Ten years have passed since I initiated the work that is summarized in this thesis.
It might be that a sense of emptiness will emerge after concluding the work, which has
from time to time, and especially in the final stage, been quite intense. However,
during these years a wonderful woman came into my life, and subsequently two
amazing little copies of both of us. I believe these three incredibly important people
could earn increased attention from now on, and replace the potential sense of
emptiness with meaning and delight. Shortly before defending this thesis, we decided
on using Marias family name for all of us, which should explain the inconsistency with
“Johansson” and “Arwidson”.
xi
xii
Contents
1
INTRODUCTION ............................................................................................. 1
1.1
1.2
1.3
2
THERMAL CHALLENGES FOR AVIONIC EQUIPMENT ......................................... 2
RELIABILITY OF LEAD-FREE ELECTRONICS ..................................................... 3
OBJECTIVE, SCOPE, AND DELIMITATIONS ........................................................ 4
THERMAL MANAGEMENT OF AVIONIC EQUIPMENT ...................... 7
2.1
2.2
2.3
2.3.1
2.4
2.5
3
HEAT TRANSFER FUNDAMENTALS ................................................................... 7
THERMALLY INDUCED FAILURE MECHANISMS.............................................. 10
THERMAL DESIGN TOOLS .............................................................................. 12
Uncertainty in Simulations ................................................................... 15
STATE-OF-THE-ART THERMAL MANAGEMENT IN AVIONICS ......................... 16
MANAGING POWER DISTRIBUTION ................................................................ 21
RELIABILITY PREDICTION ...................................................................... 27
3.1
3.2
3.3
3.4
3.4.1
3.4.2
ADVANCED THERMAL ANALYSIS INCORPORATED IN THERMAL FATIGUE LIFE
PREDICTION ................................................................................................... 29
PHYSICS OF FAILURE IN RELIABILITY PREDICTION OF SOLDER JOINTS ......... 33
ACCELERATED THERMAL CYCLING TESTS OF SURFACE MOUNT PACKAGES
WITH SAC, SN100C, AND SNPB SOLDER PASTE............................................ 36
SURROGATE MODELING OF DAMAGE ACCUMULATION IN SOLDER JOINTS ... 37
Data Preparation .................................................................................. 40
Algorithm for Estimation of Accumulated Damage .............................. 42
4
PROGNOSTICS OF REMAINING USEFUL LIFE OF ELECTRONIC
EQUIPMENT................................................................................................... 49
5
CONCLUDING SUMMARY AND CONTRIBUTION TO THE FIELD . 53
5.1
5.2
5.3
THERMAL MANAGEMENT .............................................................................. 53
PHYSICS OF FAILURE IN RELIABILITY PREDICTION OF SOLDER JOINTS ......... 54
FUTURE WORK ............................................................................................... 55
REFERENCES ................................................................................................................. 57
THE PAPERS ................................................................................................................... 65
xiii
1
Introduction
The history of aviation had a remarkable beginning. Only six years after the first
successful flights of the Wright brothers in December 1903, the Frenchman Henri
Blériot flew across the English Channel. Another five years from that, scout planes
performed reconnaissance in World War I, shortly followed by the creation of small
forces of fighter planes that engaged in aerial combat and bombing raids [1].
Simultaneous to the first long jumps of aviation, the evolution of electronic
equipment was initialized when the Englishman John A. Fleming invented the Fleming
valve, which today is called a diode. Three years later, in 1906, the American Lee D.
Forest developed the diode further to what is currently called the triode, which
amplifies the voltage of an incoming signal, for example from a radio antenna. This
invention eventually enabled radiotelephone equipment for use in aircrafts; although
heavy and voluminous, this represented the first electronic equipment for use in
aircrafts, named avionics.
After the initial steps of the evolution of electronics, not much happened with the
technology on which radio (1910´s), television (1930´s), and the electronic computer
(1940´s) was based. By the time jet propulsion was emerging as the dominating
technique to enable forward motion of aircrafts, in 1947 the transistor was invented
[2]. The transistor was more reliable, smaller, lighter, and consumed less power than
the vacuum tube, and had soon replaced the vacuum tube in electronic equipment,
including avionics. This represented path-breaking development of technology and the
beginning of an avalanche in utilization of electronics.
In the early 1960´s, the single transistor was extended by the invention of the
integrated circuit, and in 1965 Gordon Moore made his famous prediction that the
number of transistors on a single chip would double every year the following ten
years. With some adjustments, Moore’s prediction extended much longer than to 1975,
and is still valid, and even extended to “More than Moore", which includes
diversification of the parts that can be integrated in one electronics package [3].
Currently, the size of a transistor on a silicon integrated circuit is in the scale of
101 nanometers, and single-molecule transistors are produced, which are made of
carbon nanotubes and silicon nanowires with diameter of less than ten nanometers [4],
[5]. Thus, the expression avalanche in electronics design might be justified considering
a technology developing from vacuum tubes to nanotubes in just about half a century.
With regards to airborne electrical equipment, a modern aircraft may be equipped with
hundreds of avionic units, with functionality ranging from passenger entertainment, to
safety-critical flight control systems.
1
Chapter 1
The downsizing of electronics has also led to the need of a multi-scale approach
in product development, both considering time and geometry. To minimize the power
dissipation in a transistor, the switch rise and fall time is optimized, gaining a few
nanoseconds, while the component must prove a lifetime of many years. The size of
the transistors on an integrated circuit is in the range of 10 nanometers, whereas the
length scale of the entire component package is several centimeters.
Another challenge currently arises from the increased complexity in product
development, since multiple technology areas need to develop simultaneously and
collaboratively. New materials are continuously developed, and in the development of
integrated circuits, chemistry, metallurgy, physics, electronics, and mechanics
engineers need to cooperate. Profound requirements are put on the quality of the
product and the design process, including robustness to altered boundary conditions,
and reliability. A large number of tests are to be performed on every component and
system, including thermal, mechanical, moisture, vibration, shock, chemical, and
electrical tests, as well as combinations hereof [3].
Each active transistor within an electronic component generates heat due to
switching losses and electrical resistance in the semiconductor. Hence, the continuing
reduction in size of electronic components, concurrent with increasing clock
frequencies and greater functionality, result in increasing volumetric heat generation
and surface heat fluxes in many products. As an effect, keeping temperature levels of
electronic components within their maximum ratings is central in electronic product
development, affecting all levels of the electronic product hierarchy, from the chip to
the complete system.
The restriction of hazardous substances (RoHS) directive [6] limits the use of
lead in the manufacture of various types of electrical and electronic equipment. The
knowledge about field operation reliability of lead-free solders is still limited, as well
as the availability of models for prediction of service life of the solder joints.
Combined with low-volume manufacturing of potentially safety-critical equipment,
many manufacturers of electronics for the aerospace, defense, and high performance
(ADHP) equipment are therefore currently exempt from the RoHS directive. However,
manufacturers of commercial off the shelf (COTS) electronic components have since
several years converted to producing lead-free electronics. Since ADHP manufacturers
often utilize COTS electronic components, the transition to lead-free electronic
equipment will most probably propagate also to manufacturers of electronic equipment
for avionic applications. Accordingly, the need to fill in several knowledge gaps,
including reliability and reliability prediction of lead-free solder alloys, is emphasized.
1.1
Thermal Challenges for Avionic Equipment
The thermal challenges that emerge from the downsizing of electronics are
common to most electronic equipment. For avionic applications, the measures to
overcome these challenges are however constrained by the obvious and strong driving
forces to minimize weight, and maximize reliability.
Avionics applications can be divided into military and civilian applications,
where military applications have historically represented the driving force in the
2
Introduction
evolution of avionics. In the past, design of military electronic equipment embodied
the cutting edge in technology, as military applications represented more than 50% of
the total semiconductor market in the 1960´s [7]. Currently, ADHP applications
represent approximately 2% of the semiconductor market [8] and thus render no
interest of major semiconductor manufacturers to make such parts.
Therefore, COTS electronic components designed for computers, consumer, and
telecommunications applications, which today represent more than 75% of the
semiconductor market, are used to a growing extent in ADHP applications. From a
thermal perspective, high-performance COTS components are often cooled by adding
a fan-cooled heatsink with spring-loaded attachment to the top surface. This is
adequate for stationary computers that are subjected to insignificant vibration loads
during its lifetime. However, for military and/or avionic applications, this would not
be a feasible design due to multiple reasons such as weight, volume, and vibration
levels. Instead, focus might be set on minimizing contact resistance to a cooling
surface, optimizing heat conduction, and affecting the power distribution on the
printed circuit board assembly (PBA) in collaboration with electronic design
engineers.
For avionic applications, the trend of more electric aircraft (MEA) generates
additional thermal management challenges, as an increasing amount of avionic
systems are employed in harsh environments, subject to large variations in ambient
temperatures, external thermal loads generated by nearby high-power dissipating
equipment, and inherently transient internal power dissipation [9].
1.2
Reliability of Lead-Free Electronics
Facing the transition to Pb-free electronics, the ADHP industry currently needs to
know that utilized electronic packages can be qualified for field operation with
sufficient reliability and lifetime. In the research community, large effort has been put
on determining whether lead-free solder can replace the well-proven tin-lead solder
with regards to thermal fatigue life [10]–[14]. This process is however difficult to
complete, due to lack of field data on the large number of lead-free solder alloys that
exist on the market, variation of the alloy composition of a specific solder alloy
between different suppliers, and high dependence of initial microstructure, and thus
reliability, on manufacturing parameters.
During product development for avionic applications, the electronic packages
must be qualified for field operating conditions that vary depending on the specific
location of the equipment (for example in zones with controlled or uncontrolled
environment in an aircraft). In qualification of a certain package type for different
thermal environments, accelerated testing is the predominating method, although
acceleration factors for lead-free solder joints are still largely unknown. Emphasized
by observations of degraded reliability during operation testing of U.S. Army systems,
incorporation of physics-of-failure (PoF) in reliability prediction of electronics
currently attracts a lot of attention by the military and aerospace industry [15]. Until
recently, the physics-of-failure contribution to reliability prediction defined in
industrial handbooks such as MIL-HDBK 217F [16], extended to calculations of
3
Chapter 1
thermal cycles to failure, based on simplified analytical correlations. However, in a
recent industrial standard [17], a number of physical failure mechanisms are defined,
as well as suggestions on how to evaluate them. Specifically for thermal loading of
solder joints, it is recommended to employ finite element (FE) analysis in order to
evaluate damage accumulation during one thermal cycle, and subsequently calculate
the number of cycles to failure [17]–[20]. Obviously, this assumes reduction of field
conditions to cyclic loading, which might result in reduced accuracy of the predicted
lifetime. Evaluation of damage accumulation in solder joints for field conditions
without temperature data reduction is a task that still poses a large challenge for fullscale FE analysis, in terms of computational resources.
In case the expected operating environment is known, but not explicitly
expressed as a combination of thermal cycles, rainflow cycle counting can be applied
to convert the application environment to temperature cycles and half-cycles [21].
Subsequently, constitutive laws can be applied along with FE analysis and fatigue laws
to predict the thermal cycling reliability [22], [23]. However, the cycle-counting
approach contains assumptions regarding the ratio between dwell time at a certain
temperature level and the ramp time for each counted cycle [24], [25].
Hence, compared to the cycle-counting approach, improved accuracy of the
computed damage in solder joints would be achieved using uncompressed temperature
data as input to the same lifetime prediction method. As a consequence of the
increased transient variation of thermal loads expected from the MEA trend, it may
furthermore be beneficial to employ advanced thermal analysis such as computational
fluid dynamics (CFD) to supply detailed temperature data as input for the FE analysis.
However, direct usage of FE analysis for evaluation of accumulated damage in a
solder joint from uncompressed temperature data would lead to long computational
time, and require large computational resources. Therefore, there is a need for a
computationally more efficient method to assist designers in quick evaluation of the
accumulated damage in solder joints for non-modified operating temperature profiles.
1.3
Objective, Scope, and Delimitations
The power density of electronic components is ever escalating [26], thereby
continuously creating new challenges to the avionics industry with regards to
reliability. The use of commercial off the shelf (COTS) electronic components in
avionic applications brings lead-free electronics, which has been insufficiently verified
with regards to long-term reliability, closer to the avionic industry. Today, the impact
of this evolution on field reliability of avionic equipment is at large unknown. One
measure that has been proposed in order to increase the knowledge in this area is to
introduce physics of failure (PoF) in reliability prediction [17].
The objective with this thesis is twofold: To study and analyze thermal
challenges for avionic equipment and investigate power distribution on an avionic
printed circuit board assembly (PBA) as a thermal management measure, and to
address the identified need of physics of failure in reliability prediction in the product
design phase of avionic equipment by testing the following hypothesis:
4
Introduction
It is possible to develop a method that provides rapid evaluation of damage
accumulation in solder joints in field temperature conditions, such that:
It utilizes non-cyclic, non-compressed temperature data of anticipated
field operation temperature environment.
It provides accuracy comparable to three-dimensional finite element
(FE) analysis.
Its computational efficiency is significantly higher than FE analysis.
The thermal challenges are addressed in chapter 2, by presenting fundamentals of
heat transfer, thermal fatigue failure mechanisms, and state of the art thermal design
and design tools, with focus on the requirements that may arise from avionic use. For
example, such requirements comprehend low weight, high reliability, and ability to
sustain functional during high vibration levels and high g-forces, which all affect the
feasibility of some thermal management measures. Paper I, II, and III provide an indepth investigation utilizing advanced thermal modeling of power distribution on a
double-sided PBA as a measure to improve its thermal performance.
The need in the design phase for quick evaluation of damage accumulation in
solder joints is addressed in chapter 3. With regards to thermal fatigue of solder joints,
the current state-of-the-art physics-based reliability prediction comprises simplifying
the thermal loads, to cyclic loading with assumptions regarding the ratio between
dwell times and temperature ramp times. Following this, analytical life prediction
models are employed to calculate the number of cycles to failure. Hence, one step to
take in order to increase the potential accuracy of the prediction would be to employ
the same analytical life prediction models, but enhance the accuracy by including
advanced thermal analysis in the procedure (paper IV).
Reliability engineers would benefit from a life prediction model that was
validated for non-cyclic temperature variations at field operation temperature levels.
The maximum possible accuracy of the life prediction would then be achieved by 3-D
finite-element (FE) modeling of stress and strain during a number of anticipated
typical field operation temperature profiles. Even without fully validated life
prediction models, this kind of calculation would today bring higher credibility to the
lifetime prediction, and supply increased understanding of the impact of different
temperature profiles. However, FE modeling can require large computational
resources and long calculation time. Therefore, a computational method is proposed
that utilizes surrogate stress and strain modeling of a solder joint, to quickly deliver
damage evaluation for a solder joint subjected to a non-cyclic, non-simplified field
operation temperature profile. This is treated in Papers V and VI.
Much research is ongoing to create constitutive laws for the emerging lead-free
solder alloys [19], [27], [28]. Extending the horizon further, to a future when validated
life prediction models will be available, the suggested computational method is
expected to enable increased accuracy of embedded prognostics of remaining useful
thermal fatigue life of a critical solder joint. Chapter 4 presents an overview of
prognostics of electronics, and a brief description of the potential prognostics
5
Chapter 1
application of the suggested method, with more details provided in Papers VII and
VIII.
There is a multitude of failure modes, mechanisms and locations in all levels of
avionic equipment. With regards to evaluation of damage accumulation, this work has
however been limited to focus on thermal fatigue of solder joints. A concluding
summary of the work, reflecting on the contributions to the field, ends this thesis.
6
2
Thermal Management of
Avionic Equipment
2.1
Heat Transfer Fundamentals
Heat transfer is the science that seeks to predict the transfer of energy that takes
place between material bodies as a result of a temperature difference [29]. There are
three modes of heat transfer: conduction, convection, and radiation.
Conduction is the transfer of energy within a body due to a temperature gradient.
The energy is conducted from the high-temperature region to the low-temperature
region (see Figure 1). In its simplest form, one-dimensional heat flow by conduction is
calculated as:
q cond
tA
,
l
where l is the length of the conducting path, A is the area of the conducting path,
the thermal conductivity of the body, and t is the temperature difference.
Figure 1. One-dimensional, steady-state conduction heat flow [30].
7
(1)
is
Chapter 2
For the three-dimensional case, conduction heat transfer is expressed as an
energy balance for an infinitesimal element, such that (in Cartesian coordinates):
x
T
x
y
T
y
z
T
z
q
cp
T
t
(2)
where the left hand side describes the net transfer of thermal energy into the control
volume and the energy generated within the infinitesimal element, and the right hand
side is the change in thermal energy storage in the element.
Convection is the energy transfer from a body to a fluid, which might be gas or
liquid. A difference is noted between forced convection, where the fluid is propelled
by a fluid accelerating device such as a fan, and natural convection, where the motion
of the fluid is initiated by a change of density due to heating of the fluid (see Figure 2).
The force that arises from this phenomenon is called buoyancy force. The energy
transferred by convection is calculated as:
q conv
hA(Ts
Tamb )
(3)
where h is the convection heat transfer coefficient that depends on the properties and
velocity of the fluid, A is the area of the heat dissipating surface, Ts is the temperature
of the surface, and Tamb is the temperature of the ambient air.
Figure 2. Temperature and velocity distributions for natural convection in air
near a heated vertical surface. Upward movement of hot air (a). Distributions at
arbitrary vertical location (b). is the distance at which the velocity and the
temperature reach ambient surrounding conditions [31].
8
Thermal Management of Avionic Equipment
Thermal radiation is when a surface emits electromagnetic radiation as a result
of its temperature. The frequency of the radiation depends on the absolute temperature
of the radiating device; however for the temperature range possible for electronics to
operate within, thermal radiation mainly occurs in the infrared frequency range. The
energy transferred between two bodies by radiation can be calculated as:
q rad
F FG A(Ts
4
4
(4)
Tamb )
where F is an emissivity function, FG is a geometric “view factor” function, is the
Stefan-Boltzmann constant (5.669 10-8 W/m2 K4), A is the area of the radiating
surface, Ts is the radiating surface temperature, and Tamb is the temperature of the
receiving surface.
Depending on the application, any of the three energy transfer modes can be the
dominant mode for removing the energy, and thus the heat, from the electronic
equipment. In Table 1, a coarse estimation of thermal conductivity and convective heat
transfer coefficient values is provided.
Table 1. Approximate values of conductivity and convection heat transfer
coefficients for different heat transfer modes.
Heat transfer mode
Conduction in solids
Thermal Conductivity
(W/(m K))
0.13-2000
Heat transfer
2
coefficient (W/(m K))
Reference
[32]
Natural convection in gases
5-15
[33]
Forced convection in gases
15-250
[33]
Natural convection in liquids
50-100
[33]
Forced convection in liquids
100-2000
[33]
Boiling liquids
2500-35000
[29]
In ground applications, e.g. stationary computers, the critical components may be
cooled by conduction to a heatsink, which is in turn cooled by forced convection.
Other options exist for removing the heat dissipated by current high-performance
processors, but ultimately the heat is transferred to the surrounding air by forced or
natural convection. Ground applications can of course be divided into a vast number of
categories, ranging from the automotive industry, through military equipment, to
handheld devices, such as mobile phones, but the general principle of conduction plus
convection cooling remains.
Avionics applications may utilize the same cooling principles as ground
equipment. In avionics, however, constraints are posed on the cooling solutions in
terms of e.g. minimized weight, extreme reliability requirements, and environmental
requirements such as harsh temperature levels, high levels of vibration, and lowdensity cooling air at high altitudes.
In space, the main principle for cooling of electronic equipment differs
completely from the previously mentioned applications, due to the absence of air.
Radiation is the only mechanism that transports heat to and from a spaceship or a
satellite. Therefore, control of the temperature of the electronics is realized by
carefully utilizing radiating and reflecting surfaces on the hull of the vehicle.
9
Chapter 2
2.2
Thermally Induced Failure Mechanisms
In order to encounter the problems that arise in avionics as a result of thermal
loading, a basic understanding of failure mechanisms is needed. A failure mechanism
is the mechanical or chemical mechanism that causes the failure mode, which is often
a short or open electric circuit, at a specific location – the failure site.
Although failure modes are often identified on system level, the failure
mechanisms are active on the lowest hardware level – the failure site may often be
located within an electronic component, or at the interface between the component and
the PCB. The connections between electronics reliability and thermal loading are
extremely complex and cannot in general be represented by analytical correlations,
which provide an unambiguous answer to the lifetime of a certain component, subsystem, or system.
On all failure sites of an avionic system (from on-chip to system of systems), a
diversity of failure mechanisms and failure modes exist, which may eventually cause
breakdown of system functionality. In Table 2, the failure mechanisms are shown,
which account for the majority of failures in electronic systems, classified according to
the packaging level where the respective failure mechanism may occur.
Table 2. Failure sites, modes, and mechanisms at different packaging levels of
electronic systems (modified from [34]).
Packaging level
Failure site
Die metallization
Failure mode
Short circuit
Open circuit
Breakdown
Level 0 (chip and on-chip sites)
Level 1 (parts and components that
cannot be disassembled and
reassembled with the expectation
that the item would still work)
Gate-oxide
Die
Transistor
Between die and
molding compound
Level 3 (enclosure, chassis, drawer,
and connections for PBAs)
Level 4 (entire electronic system)
Level 5 (multi-electronic systems and
external connections between
different systems)
Change of leakage current
Crack
Short circuit
Delamination
Bond wire
Open circuit
Encapsulant interface
Capacitors
Delamination
Short circuit
Open circuit
Short circuit
Open circuit
Short circuit
Solder joint
Level 2 (printed circuit board (PCB),
and interconnects connecting the
components to the PCB)
Short circuit
Printed-through hole/
Via
Printed circuit board
(PCB)
Metallization shorts
Lead pad
Loss of polymer strength
Open circuit
Trace
Open circuit
Connection
Open circuit (often
intermittent)
10
Failure mechanism
Electrochemical migration
Electromigration
Electrical overstress (EOS)
Electrostatic discharge (ESD)
Time-dependent dielectric
breakdown (TDDB)
Hot carrier
Crack initiation and propagation
Contact migration
Crack initiation and propagation;
popcorning
Bond lift due to mechanical
overstress
Corrosion
Corrosion
Dielectric breakdown
Thermal fatigue, vibration fatigue
Tin whisker growth
Thermal fatigue
Electrochemical migration
Conductive-filament formation
Electrochemical migration
Glass transition
Corrosion
Corrosion
Electromigration
Mechanical wearout, corrosion,
fretting
Thermal Management of Avionic Equipment
Some of the failure mechanisms seen in Table 2 are not clearly dependent on
temperature, for example corrosion [35]. However, below follows short descriptions of
the most clearly thermally induced failure mechanisms.
Delamination
The reliability of general multilayer microelectronic devices is influenced by the
interfacial strength (adhesion) and resistance to fracture (debonding) of the many
bimaterial interfaces. Residual stresses, thermo-mechanical cycling and mechanical
loading may drive time dependent fracture in the multilayer structures, allowing for
ionic contaminants to cause corrosion-induced failures, or immediate electrical failure
by sheared or cratered wire bonds [36].
When two joined materials are subject to thermal loads, stresses can be produced
at the material interfaces due to coefficient of thermal expansion (CTE) mismatch
between the materials. These stresses may cause delamination of the materials and
hence affect overall reliability of the system [37].
Apart from differences in CTE, defects in the attachment layer may cause
interfacial debonding. One common defect is voids embedded in the packaging of the
component. Voids can form from melting anomalies associated with oxides or organic
films on the bonding surfaces, trapped air in the attachment, local non-wetting,
outgassing, and attachment shrinkage during solidification [38]. For plastic
encapsulants, which are inherently hygroscopic, moisture present in the layers can lead
to premature failure and reduced lifetimes of these devices. The “popcorning” failure
mechanism appears at high temperature, such as during the reflow soldering assembly
process, when the moisture vaporizes and expands, generating high stresses that may
cause delamination [39].
Bond wire fatigue
Mainly due to the differences in CTE mentioned above, the bond wires that
electrically connect the chip to the leadframe are subject to mechanical fatigue when
exposed to thermal cycling. The interfacial strength between the bond wire and the
bond pad can be reduced by diffusion-induced brittle intermetallic phases or Kirkendal
voids at the interface.
Thermal fatigue of solder joints
Thermal fatigue of solder joints occurs when the CTE of the PCB differs from
that of the electronic component attached to the PCB, and the assembly is subject to
temperature variations. Shear strain imposes stress in the solder joint, and the slow
process of temperature variation leads to stress relaxation primarily by creep strain
within the solder joint. Repeated stress relaxation leads to solder fatigue, crack
initiation, and crack propagation until electrical failure is a fact. Figure 3 shows
schematically the principal failure sites in a solder ball subject to thermal fatigue loads.
Evidence of thermal loadings can be found in the microstructure of the solder
joint. Both grain coarsening and growth of intermetallic compounds (IMC) between
the copper pad and the bulk solder can be indicators of thermal cycling material
degradation [40], [41]. Figure 4 shows an example of a BGA solder ball with
Sn3.0Ag0.5Cu solder alloy, before and after harsh thermal cycling between -55°C and
11
Chapter 2
+125°C. Before thermal cycling, no grains can be distinguished, whereas after thermal
cycling, grain boundaries are visible using differential interference-contrast filtering on
an optical microscope.
Figure 3. Schematic presentation of main failure sites in a solder ball subject to
thermal fatigue loads.
50µm
50µm
Figure 4. Optical microscopy image of SAC305 solder ball after manufacturing
(left), and after 2257 thermal cycles between -55°C and +125°C (right).
Differential interference contrast filtering enhanced by increased contrast level
reveals that there are no visible grain boundaries before thermal cycling, while
grains are clearly visible after thermal cycling.
2.3
Thermal Design Tools
In the different product development phases, various types of thermal evaluations
are required. In the quotation phase, there is a need for a quick approximation of the
thermal performance of a device; during the conceptual design phase a tool is needed
that can make time-efficient estimates for comparing different thermal designs. In the
detailed design phase, there is a need for more detailed thermal simulations, which are
able to identify potential hot spots and evaluate different ways of mitigating these. For
use in these design phases, six classes of tools have been identified:
Hand calculations
Spreadsheets
12
Thermal Management of Avionic Equipment
Flow network modeling (FNM)
Computational fluid dynamics (CFD)
Finite element method (FEM)
Experiments
A summary of the identified thermal design tools, with examples of tools in each
classification as well as significant features, is presented in Table 3. In the following,
the variety of tools is described somewhat more in detail.
Table 3. Classification of thermal design tools.
Classification
Hand calculations
Tool
Thermal Resistance Network
(TRN)
Spreadsheets
Microsoft Excel
Flow Network Modeling
(FNM)
MacroFlow
Computational
Dynamics (CFD)
Coolit, Flotherm, Icepak,
MacroFlow,
Thermal
Desktop, ANSYS, Flovent
Fluid
Finite Element Method
(FEM)
ANSYS, Matlab,
Multiphysics
Comsol
Experiments
Physical prototypes, burn-in
tests
Features
Rapid solutions.
Renders a good overview of influence of
different designs on thermal performance.
Handles advanced mathematical and
engineering functions.
Macros
Graphics capabilities
Data table formatting
Efficient for solving complex TRN:s.
Design of different types of air- or liquidcooled electronics systems.
Quick evaluation of system-level thermal
design.
Flow constraints important.
No component temperature predictions –
only system level.
Detail-level simulations and analyses of
heat transfer and fluid flow.
Extensive
calculation
times
when
modeling with high level of detail.
Detail-level
analysis
of
primarily
conduction cooling.
Thermal stress analysis.
The classic way of evaluating a product
design.
Requires knowledge of measurement
techniques.
Hand Calculations
In an early stage of product design, in the stage of the company trying to win an
order to develop a certain product, a quick estimation of the thermal performance of
the product would be appreciated. Here, hand calculations can be utilized. Given the
total dissipated power, a rough estimation of the mechanical design of the avionic
device, and the thermal boundary conditions, thermal resistance networks (TRN) that
represent the different heat transfer paths within the system can be modeled. A TRN
may provide rather accurate predictions of relative heat transfer efficiency when
comparing different design alternatives.
13
Chapter 2
Spreadsheets
When TRN:s get too complex to calculate by hand – many thermal resistances in
parallel that lead to areas of different temperatures is the most common case for
avionic equipment – there is an option to use spreadsheets to handle the large number
of equations that should be solved simultaneously. Spreadsheets handle advanced
mathematical and engineering functions, and provide graphical capabilities for
displaying results.
Flow Network Modeling
A tool that could be used for more detailed analyses, still in the early phase of
product design, is flow network modeling (FNM). FNM is a generalized methodology
to calculate system-wide distributions of flow rates and temperatures in a network
representation of a cooling system. Practical electronics cooling systems can be
considered as networks of flow paths through components such as screens, filters,
fans, ducts, bends, heat sinks, power supplies, and card arrays [42]. To be able to use
FNM, empirical correlations of the impact on the flow from these components are a
prerequisite. This technique does not give the detail level results for predicting
component temperatures, but in order to quickly estimate average temperatures of subsystems and compare the heat transfer efficiency of different designs, FNM is a useful
tool. For avionic applications, FNM may prove useful in evaluation of the cooling air
system in an aircraft, while it may not add much value in thermal design evaluation of
a single avionics enclosure.
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a tool that performs calculations of flow,
heat, and mass transfer in complex geometries, at any level ranging from electronic
component design to heating, ventilation, air conditioning and refrigeration (HVAC)
flows in e.g. buildings. The main issue with CFD is that extensive calculation times
are required when the detail level gets high. At present, much effort is put on
developing systems for transferring CAD-data directly to the CFD software, including
automatic simplifications of detailed geometries in order to accelerate the CFD
calculations.
Finite Element Method
The main use of finite element method (FEM) has traditionally been analysis of
mechanical stress and deformation, although conduction heat transfer can also be
included in the calculations. Software packages are also available, which combine
FEM and CFD solvers, in order to model coupled physical phenomena that can be
described by partial differential equations. For example, thermoelectric cooling
coupled with all three modes of heat transfer could be analyzed.
Experiments
By many considered the only true way of estimating temperatures within a
system, experimental measurements might however not be the obvious way to retrieve
correct data. The environmental specifications have to coincide with the actual
operating conditions, and the experimental setup should correspond to reality.
14
Thermal Management of Avionic Equipment
The final design tool, classified under experiments, is the burn-in test, in which
the finalized device is exposed to severe environmental loading while operating. The
purpose of the burn-in test is to identify errors that might occur in the initial stage of
the bathtub curve [38], which is further described in chapter 3 below. Burn-in should
be carefully balanced though; firstly, as this procedure is a kind of accelerated test it is
of vital importance to ascertain that failure mechanisms that may occur during the
burn-in also may occur in real operating conditions. Secondly, caution must be taken
not to damage fully functional parts and shorten the lifetime of the device. With
regards to thermal fatigue of solder joints, currently available lifetime prediction
models may supply an adequate estimation of the consumed life during a number of
burn-in cycles. A lot of experimental data has been published, and constitutive laws
for creep rate have been derived, which comprise harsh thermal loading that is the case
during burn-in testing. However, addressing the impact on lifetime of the simultaneous
thermal and vibrational loading is not possible with the information available today.
In practice, all of the tools above except the burn-in test can be used for dynamic
as well as static temperature predictions. The precision in transient calculations varies
accordingly with the tool used, and the design stage in which the calculations are
performed.
2.3.1
Uncertainty in Simulations
When a CFD simulation is initiated to predict airflow and heat transfer in an
electronic system, many approximations as compared to real-life physical components
are introduced. Together, these approximations may cause the result to differ
substantially from reality. Lasance [43] summarizes the errors from the input data and
from the numerical setup to a final error, which is in the order of 20%. It should be
noted, that when speaking of percentage errors in temperature, the temperature rise
relative the ambient temperature or the temperature of the cooling air must be referred
to. In [44], a methodology to follow before initiating a CFD simulation is proposed as
seen in Figure 5.
15
Chapter 2
1. Problem definition
2. Physical/computational
domain
3. Computational grid
4. Model selection
5. Material selection and
properties
6. Boundary conditions
(BC)
7. Solution strategy
8. Post-processing
Objectives of model?
Degree of accuracy needed?
Model part of, or full system?
Geometry created in CFD or imported from CAD?
Two- or three-dimensional or axi-symmetric?
Can symmetry be used?
Type of mesh?
Regions in need of finer mesh?
Isothermal, conjugate, or conduction only problem?
Laminar/turbulent, steady/unsteady, compressible or
incompressible flow?
Near-wall function?
Influence of buoyancy and/or radiation?
Thermal properties independent of absolute
temperature?
PCB:s - use effective thermal conductivity?
Isotropic or orthotropic properties?
Simplification by symmetry, cyclic or periodic BC?
Are all BC:s known?
Convection BC:s possible?
Algorithm?
Higher order interpolation scheme needed?
Convergence time?
Do the results make sense?
Refinement needed?
Problem objectives satisfied?
Figure 5. General methodology before running CFD [44].
2.4
State-of-the-Art Thermal Management in Avionics
Examining different cooling technologies, it is easy to start to compare heat flux
capacity. However, it must not be forgotten that the critical component might be a lowpower component, which due to its placement on the PBA gets too hot, faces too large
temperature gradients, or experiences too high thermally induced mechanical loading
due to its size. Since the significant metrics a thermal design engineer must meet are
junction and solder joint temperatures, the main feature to compare between different
cooling technologies is not heat flux capacity, but applicability for the current cooling
requirement [45]. This chapter explores important thermal and practical attributes of
current state-of-the-art cooling schemes. In Table 4, a reviewing list of various cooling
16
Thermal Management of Avionic Equipment
technologies is provided, with significant features of each technology identified.
Technology maturity and the applicability for use in avionics applications are graded
from 1 to 5, where 1 means emerging or unsatisfactory, and 5 denotes mature or
outstanding.
Table 4. Review of cooling technologies.
Cooling technology
Heat pipes
Spray cooling
Jet impingement
Immersion cooling
Phase transformation
solid-fluid
Phase transformation
for thermal energy
storage
Forced convection
direct air cooling
Thermoelectric cooler
Hybrid cooling
Managing power
distribution
Significant features
Functionality independent
of orientation
Highly efficient heat
removal. Wetting of
electronics however
requires a need for
electrical isolation.
Used in some thermal
interface materials to
minimize thermal contact
resistance
Useful for capacitive
storage of heat at transient
temperature extremes
Possible only when the
cooling air is noncontaminated
Electronic refrigerator with
low efficiency
Multiple thermal interface
resistances
Distribute heat sources as
evenly as possible
Maturity
4
Avionic use
3
Reference
[33]
3
3
[29]
[46], [47]
4
3
[48]
4
4
3
2
5
5
4
1
[45]
5
5
[45]
5
5
[49]
Heat Pipes
Heat pipes belong to the passive cooling technologies. A heat pipe is an
evacuated, vacuum-tight envelope, outer diameter from 3 mm and up, with a wick
structure on the inside (see Figure 6). It contains a small amount of working fluid,
which in the isothermal state is uniformly distributed over the wick structure by
capillary forces. When heat is applied anywhere on the heat pipe, the working fluid at
this location vaporizes. Since the envelope is evacuated, the vaporized working fluid
spreads immediately over the entire volume inside the heat pipe to establish uniform
pressure in the contained volume. At the condenser area, the vaporized working fluid
is condensed into the wick structure releasing its latent heat of vaporization, and is
returned to the evaporating area by capillary forces. Heat pipes operate independent of
gravity, although the performance is maximized when the orientation is vertical and
the capillary forces are assisted by gravity to transport the working fluid back to the
area of vaporization [50]. Functionality can be negatively affected by g-forces
exceeding 5 g [51], wherefore implementation in avionics should be treated with great
care.
17
Chapter 2
Figure 6. Heat pipe function [52].
Spray Cooling/Fluid Jets
Spray cooling and fluid jets both uses fluid impingement directly onto the
electronics for heat removal. Spray cooling utilizes small droplets that evaporate from
the heat-dissipating surface, whereas jet impingement consists of a number of jet
streams that create a continuous fluid film on the surface, thereby transporting the heat
away by convection to the fluid. Comparisons made in [46] indicate a higher
efficiency of jet streams in terms of the ratio between dissipated heat and power
consumed by the fluid pumping system. Using deionized water as a coolant, heat
fluxes as high as 300 W/cm2 at 80 C surface temperature could be removed from the
5.0 8.7 mm2 surface of a diode. Water can be used as the coolant provided that the
components are electrically isolated from the fluid, but in return water has much
higher heat capacity than the dielectric fluids that may be impinged directly onto
electrically conductive surfaces. Both these technologies represent high-efficiency and
high-complexity cooling solutions, which may be utilized in avionic applications
unless no other option provides adequate cooling. Reliable fluid pumping systems are
required, and filtering techniques to avoid clogging of nozzles, which could result in
catastrophic temperature levels.
Immersion cooling
A PBA can be fully submerged in a container of dielectric fluid. The need for
electrical isolation excludes water as coolant, which otherwise would have been highly
efficient considering heat removal capacity. As an example, the power supply unit
(PSU) for a radar array for the F-18 fighter is liquid-cooled in a flow-through cooling
system design. The total power dissipation of the PSU is 400 W, and the maximum
temperature of the device is 75 C at an inlet temperature of the cooling fluid of 15 C
[48].
Phase transformation solid-fluid
Due to the increased volumetric heat flow in electronics, continuous research is
carried out to minimize thermal contact resistance between the heat source and the
cooling system. Thermal interface materials (TIM) are available, which when heated
change phase from solid to liquid. This means that when the heat source starts heating
up, the TIM wets the surface of the heat source, enabling optimal thermal contact. It is
18
Thermal Management of Avionic Equipment
vital to realize that the contact pressure between the cooling system and the heat
source should preferably remain constant at both phases. This may be enabled by a
spring-loaded attachment of the heat source to the cooling system, which may be
possible in avionic systems in case the heat source has relatively low weight, such as
switching transistors in power converters for electric motor drive.
Phase transformation for thermal energy storage
The power dissipated by an avionic system may not be uniform over time, as is
neither the environmental conditions. Phase transformation of for example a
polyalcohol material or paraffin can be used as a capacitive storage of heat dissipated
under worst-case conditions. Research is currently ongoing to improve the low thermal
conductivity of such materials, which is limiting the usage of this technology in
avionic applications [49].
Forced convection direct air cooling
Direct air cooling of the electronic components and the PCBs, is an efficient,
light-weight, and cheap cooling solution. Drawbacks for avionic use are the
requirements put on the cooling air such as content of moisture, particles, and oil, as
well as reduced cooling capacity at high altitudes, and the common operational mode
with loss of cooling air. Furthermore, since the PBAs do not require mounting on a
card carrier for conductive heat removal, which also acts as mechanical stabilizer, the
PBAs may need to be mechanically reinforced to reduce the impact of vibration.
Historically, thermal design for cooling electronics at high altitudes has been a
matter of design tolerance. With a large margin between the operating temperatures
and the maximum temperature, it has been accepted that the margins are smaller at
high altitudes, but still within the allowed design space. As design margins are
shrinking, this is currently not good enough. The problem can be overcome by
introducing fully pressurized cooling systems for all the critical electronics, but this
adds great complexity, and increased cost and weight. Instead, higher flow of air
through the cooling system has to be admitted when the air density decreases [53].
This way the impact of altitude on the cooling capacity is reduced, though not kept
constant.
Thermoelectric cooler
A thermoelectric cooler (TEC) uses the temperature difference that arises when
an electric current flows through a circuit in which two different metals are joined
(Peltier effect). In electronics cooling applications, this effect can be used primarily to
cool point sources of heat. One way of rating a TEC is to study the coefficient of
performance (COP) of the TEC, defined as the ratio of transferred heat to input power
[33]. The COP of a TEC is often low, in the range of 1 [54], compared to larger scale
machines such as air conditioners or refrigerators with a COP of 3 to 5. Hence, TEC
have nearly no use in avionic equipment since the total power dissipated in the unit
will increase significantly.
19
Chapter 2
Hybrid cooling
Hybrid cooling is a comprehensive term for cooling schemes, which incorporates
more than one cooling technology, e.g. liquid cooling in combination with liquid-to-air
heat exchanger. Examples of hybrid cooling schemes are shown in Figure 7 [45], [55].
For all of these designs, the liquid may be replaced by air, providing greatly reduced
cooling capacity, but also substantially less weight, complexity, and cost. The leftmost
solution is the most economical design, providing fair temperature gradients at
moderate power loads. For example, at approximately 50 W dissipated into a heat
sink/card carrier with the approximate dimensions 250x200x4 mm3, a total
temperature rise in the range of 7°C can be expected from the wedge clamp; 2-3°C in
the contact resistance between card carrier and the card-edge heat exchanger, and 45°C in the card carrier. Since this design assumes a solid card carrier, commonly
aluminum, this detail supplies thermal mass, which helps to reduce the transient
temperature rise in case the cooling system temporarily is disabled. The other designs
provide more efficient cooling of the electronics, but also greater complexity of the
system, and reduced capability to handle loss of cooling, which is a common
requirement to sustain for a limited time in avionic applications.
Figure 7. Avionics hybrid cooling schemes [55].
Price and Short [56] describes the thermal design of an airborne computer chassis
situated in an electronics pod, which is suspended from the fuselage by pylons. The
computer consists of 24 PBAs that are mounted in card slots in the chassis (see Figure
8), dissipating in total 400 W. The PBAs are cooled by conduction to pin fin heat sinks
integrated in the top and in the bottom of the chassis, cooled by forced convection
20
Thermal Management of Avionic Equipment
obtained by a fan included in the unit. The design approach utilized to enable
operation at low air pressure was to define the maximum allowable cooling air supply
temperature, ranging from 55 C at sea level, to 26 C at 13,700 m altitude.
Figure 8. Exploded view of air-cooled computer chassis [56].
2.5
Managing Power Distribution
In contrast to the elaborated computer enclosure briefly discussed above, a costfree and weight-free measure to improve the thermal performance of electronics,
regardless of air density and all other environmental loads, is available by managing
power distribution on a double sided PBA. Papers I, II, and III provide an in-depth
investigation of this thermal management measure. The avionic unit studied in this
context consists of three PBAs, housed in a 2 Modular Concept Unit (MCU, ARINC
600 standard) sealed enclosure, including one double-sided PBA (DSB). The PBAs in
the unit are cooled by thermal conduction to the walls of the enclosure. Ultimately, the
heat is removed from heatsinks integrated in the enclosure walls by forced convection
cooling air (see Figure 9).
21
Chapter 2
Figure 9. Avionic enclosure studied in the context of managing power distribution
(left), and double-sided PBA, mounted to enclosure side wall, with 24 individually
controlled power sources on each side of the PCB (right).
Evaluation of different power configurations has been formulated as a problem of
determining non-dominated designs, as exemplified in Figure 10. Assume that the
system performance depends on r discrete design variables q1,…, qr representing a
point q = (q1,…, qr) of an r-dimensional space D. Let Q = QT QS be a finite set of
feasible alternatives or designs, where QT D is a set of designs to be explored
satisfying the design variable constraints based on technical specification due to
production and/or application reasons, and QS D is a set of designs for which state
variable constraints are satisfied, e.g. thermal constraints. Let also
Y ={ym , m = 1,...,M} be a finite set of attributes (e.g. performance criteria), which are
considered to be minimizing.
A design p Q is called a non-dominated design [57], [58] if there exists no
design q Q, such that
ym (q)
ym ( p) for all m 1,..., M ,
(5)
and
ym0 (q)
ym0 ( p) for at least one m0
1,..., M .
22
(6)
Thermal Management of Avionic Equipment
Max case temperature (fluid side), oC
(HS side [W], fluid side [W]) = (24, 6)
95
94
93
8
92
5
1
91
90
2
89
4
7
88
86
87
88
3
89
90
91
92
93
94
95
o
Max case temperature (HS side), C
Figure 10. Domination graph: arrows are directed from dominating designs
toward dominated designs.
An experimental setup has been created that enables full control of the power
dissipated by each component placed on the DSB, as seen in Figure 11. The initial
investigations have been conducted on DSB with uniform power configuration, that is,
the same power is applied to every component on one side of the DSB. For the nonuniform power configurations shown in Figure 12, high-power components on the
primary side of DSB are placed opposite to low-power components on the secondary
side, and vice versa. Such a configuration is considered reasonable to keep the
components on each side of DSB as cool as possible. In this study, power
configurations including components with equal power forming relatively large groups
on the board have been analyzed. The highlighted power configuration in Figure 12
results in the lowest maximum temperature on the DSB.
CFD simulated temperatures of each power configuration are shown in Figure 13
and a comparison between measured and simulated temperatures for the power
configuration highlighted in Figure 12 are provided in the contour plots seen in Figure
14. In an environment of 55°C cooling air supplied at a rate of 6.7 g/s to the 2MCU
enclosure, with 39 W of power dissipated by other PBAs in the enclosure, and 36 W
dissipated by DSB, managing power distribution between the sides of the PCB results
in up to 5.5°C decrease of the maximum temperature of the included components.
23
Chapter 2
Figure 11. Screenshot of software for power distribution control.
high-power components on HS side
high-power components on fluid side
Figure 12. Evaluated DSB symmetrical power configurations with 30 W
dissipated on HS side and 6 W dissipated on the fluid side of the PBA. The arrow
highlights the most preferable power configuration with regards to maximum
temperature.
24
Thermal Management of Avionic Equipment
Air flow
direction
Figure 13. Surface temperature of the DSB fluid side for symmetrical power
configuration with 30 W on HS side and 6 W on fluid side.
Figure 14. Contour plots of measured case temperatures (left), versus simulated
temperatures (right) on the DSB fluid side with the most preferable power
configuration with regards to maximum temperature.
Having identified the importance of utilizing advanced thermal analysis in order
to calculate temperature distribution within electronic equipment, the next step of the
work for this thesis aimed to incorporate CFD analysis in physics-based lifetime
prediction. This is covered in the next chapter.
25
Chapter 2
26
3
Reliability Prediction
The IEEE defines reliability as “The ability of an item to perform a required
function under stated conditions for a stated period of time.” [59]. Reliability
predictions for avionic equipment are often based on traditional methods, such as
presented in Military Handbook (MIL-HBK) 217 [16]. In this type of methods,
reliability is determined by calculating a constant failure rate, or its reciprocal the
mean time between failures (MTBF), of each component and sub-system comprising
the total system. The “bathtub curve” shown in Figure 15 illustrates the failure rate as
a function of time. Initially, manufacturing defects and/or defect electronic
components may cause high failure rate. These imperfections are identified and
eliminated as a result of the burn-in test briefly discussed in Section 2.1; a test that
every unit is exposed to prior to shipping out to the customer. Subsequent to its early
failures, a robust product will thrive in a period of low, near constant failure rate with
intrinsic failures that occur randomly. Finally, mechanical, chemical, or electrical
failures due to wear-out start to increase as the product approaches its lifetime.
Failure rate
Burn in
Useful life
Wear out
Time to wearout failure
Constant failure rate
Time
Figure 15. The “bathtub curve” illustrating the failure rate over time, with high
initial failure rate due to imperfections in the electronic components or in the
manufacture of the equipment, followed by a period of constant failure rate due
to random failures during the useful life of the equipment, and increasing failure
rate when approaching the end of life of the equipment.
27
Chapter 3
The models applied for traditional prediction of reliability due to thermal failure
mechanisms are based on the Arrhenius law, which states that the failure rate depends
exponentially on the steady-state temperature of the analyzed component, such that
p
E a kT
Ae
(7),
where p is the failure rate, A is a constant, Ea is the activation energy for the
analyzed failure mechanism, and k is Boltzmann´s constant.
From this, the “10 C rule” has been derived, which implies that a decrease of the
steady-state temperature by 10°C increases the life of an electronic component by a
factor of two. This might be true for some failure mechanisms at a limited range of
temperatures. However, as general statement about the component failure rate, which
depends on a number of failure mechanisms and wear-out mechanisms, the 10 C rule
does not apply. Some failure mechanisms have a temperature threshold below which
the mechanism is not active at all, while others are even suppressed at elevated
temperatures [60]. In the temperature range -55°C to +150°C, most of the reported
failure mechanisms are not due to high steady-state temperature. They either depend
on temperature gradients, temperature cycle magnitude, or rate of change of
temperature [38]. Hence, a more elaborated method would be required to increase the
confidence in the reliability predictions, which in a better way captures the physics
behind each failure mechanism. This can be achieved by utilizing a life prediction
model to assess the time to wearout failure as seen in Figure 15. This will be further
covered in chapter 3.2 below.
One step towards physics-based life prediction was taken in the MIL-HBK 217,
when thermal cycling fatigue was included by employing the Coffin-Manson model
[61],
1
Nf
1
2 2
c
(8),
f
where Nf is the mean number of temperature cycles to failure,
is the cyclic strain
range, f = 0.325 is the fatigue ductility coefficient, and c = -0.442 is the fatigue
ductility exponent for standard eutectic SnPb solder. The cyclic strain range
depends on the difference in coefficient of thermal expansion (CTE) between the
component and the PCB, the cyclic temperature extremes, distance from neutral point
(commonly the center of the package), and stand-off height.
In a multitude of papers (e.g. [58], [62], [63]), variants of the Coffin-Manson
thermal fatigue prediction model have been experimentally validated for different
types of electronic components, hole-mounted as well as surface-mount attached,
different PCB composition, etc. The predominating modification of the CoffinManson model has been made by Engelmaier [64] in that he made the constant c
variable such that, for SnPb solders,
28
Reliability Prediction
c
0,442 6 10 4 Tsj 1,74 10
2
ln 1
360
td
(9)
where Tsj is the mean solder joint cycling temperature, and td dwell time (in minutes)
at the temperature extremes.
However, most real geometries cannot be accurately represented by this model.
Many effects like deformation of board and component, multiaxial distribution of
strain, the part of the strain that results from local CTE mismatch between the solder
alloy and copper pads, and the complicated inelastic character of solder deformation
can probably not be included in a similar model.
Hence, since this analytical technique does not fully take into account the physics
behind the failure mechanisms, correlation to thermal cycling tests is required for each
package type under consideration [65]. Furthermore, the non-periodic temperature
fluctuations experienced during field usage of a product cannot be captured by this
model. Instead, periodic behavior must be extracted from the measured data [66], and
unknown distortion of the input data is thus introduced.
3.1
Advanced Thermal Analysis incorporated in Thermal
Fatigue Life Prediction
In particular when power cycling plays a vital role for the temperature of the
equipment, advanced thermal analysis may improve the accuracy of physics-based
lifetime prediction. Paper IV presents research collaboration with Boeing Phantom
Works, in which a lifetime prediction tool has been extended to allow analysis of
electronics in a complex thermal environment. An option has been added to read
‘snapshots’ of the result from a transient CFD analysis and use them as a basis for the
thermal fatigue analysis.
The tool calculates the fatigue life of a printed circuit board assembly (PBA) in
an avionic unit under combined vibration and cyclic thermal and power loads.
Individual component lifetime under combined operation environments are evaluated
in terms of component cumulative damage indices (CDI). CDI for each individual
environment is the ratio of number of cycles required for that environment to the life
cycles that the solder joint can sustain under that specific environment. The CDI
evaluation does not distinguish the sequence of damage between thermal and
vibration, so the total CDI is obtained by summing the CDI due to vibration and the
CDI due to thermal cycling (Miner’s rule) [67]. The Engelmaier model is applied to
calculate the thermal fatigue life of the solder joints in the assembly.
As an example, the process utilized to analyze the lifetime of an avionic PBA is
presented. The initial step is a transient thermal analysis of the unit in which the PBA
is located. The different operating modes of the unit are modeled and analyzed using a
commercially available CFD tool, which generates a time history of the temperature at
all points within the unit and PBA, as shown in Figure 16.
29
Chapter 3
Figure 16. Typical transient temperature profile at various points of the avionic
unit.
The second step comprises exporting temperatures from the transient temperature
analysis to the lifetime prediction tool. The temperatures calculated by the global
analysis are mapped to the PBA mounted within the box, yielding the temperature
distribution of the PBA as functions of time, see Figure 17. The lifetime prediction
tool utilizes Equations (8) and (9) together with the transient temperature profile
converted to temperature cycles and half-cycles, to assess the lifetime of each lead and
solder joint included in the PBA. The thermomechanical fatigue level of leads and
solder joints within the unit are reported as a cumulative damage index (CDI). CDI
from one of the operating modes defined for the PBA is shown in Figure 18.
Figure 17. Temperature of PBA at different points of time.
30
Reliability Prediction
Figure 18. CDI from thermomechanical fatigue.
Lifetime prediction of solder joint due to vibration is performed separately. The
environment can be seen in Figure 19, in which the continuous random vibration
spectrum specified for the location of the unit is presented. This vibration environment
would be applied to the PBA for 5 hours, according to the specification. Subjected to
this vibration spectrum, 16 modes of natural frequencies have been identified causing
board deflection to take into account for the fatigue calculations. The 5 first modes can
be seen in Figure 20. The CDI due to vibration, shown in Figure 21, is added to form
an overall CDI based on Miner’s rule. The total CDI is presented in Figure 22.
Figure 19. Vibration environment for PBA.
31
Chapter 3
Figure 20. Natural frequencies of PBA.
Figure 21. CDI from vibration.
Currently, tools are at hand that incorporate thermal analysis embedded in the
lifetime prediction software. However, the thermal analysis models are quite basic, and
generally do not include CFD analysis to correctly model fluid flows. In more complex
cases, such as presented in Paper IV, it may be convenient to integrate advanced
thermal analysis software for lifetime prediction purposes. Hence, the lifetime
prediction tool has been modified to use result files from any thermal analysis tool as
input data for thermal fatigue prediction.
32
Reliability Prediction
Figure 22. Total CDI from vibration and thermomechanical fatigue.
There is a drawback with incorporating advanced thermal analysis in lifetime
prediction tools, besides the obvious increase of computational load. Operating any
progressive software tool requires substantial knowledge about the mechanisms that
are simulated. Hence, the operator of such a comprehensive tool should preferably be
experienced in a number of engineering disciplines such as mechanical fatigue,
lifetime prediction, and thermal modeling.
Furthermore, a general word of caution needs to be acknowledged as the
computational tools get increasingly powerful: The results are never more accurate
than the input data provided to the tool. Considering the case presented above, the
environments to which the unit is assumed subject are based on the specified operating
environments and loads. Great care needs to be taken to spread the understanding of
the difference between assumed and real life environmental loads.
3.2
Physics of Failure in Reliability Prediction of Solder
Joints
In section 2.1 of the thesis, a notion of the multitude and variation of thermally
induced failure mechanisms is conveyed. In order to conceive the impact of these
mechanisms on the factual reliability, understanding the physics behind the failure
mechanisms is of vital importance. In the mid-1990-s, CALCE Electronic Products
and Systems Center defined a new life prediction method utilizing the Physics-ofFailure process [68]. An overview of the Physics-of-Failure process is shown in Figure
23, where the chain can be seen of retrieving detailed information of all geometries,
materials, production processes, field environments, etc., to use as input for
performing analyses of manufacturability, lifetime, and performance, which result in
risk mitigating solutions to enable a more reliable product.
33
Chapter 3
The Physics-of-failure (PoF) Design & Qualification Process
Design-Fix-Build-Test methodology
Stakeholders
Inputs
Internet
Databases
Integrators
Suppliers
Environments
Storage, transport,
usage
Materials
PWB, solders,
adhesives, heat sinks
Assemblers
Parts
ASICs, memories,
FPGAs, processors, etc.
Researchers
Regulatory
Agencies
Product
Analysis
Outputs
Manufacturability analysis
“Risk Mitigation
Solutions”
Laminate formation, solder joint formation,
etching, plating
Architecture
Production
Process
“Stress” analysis
Global
Temperature,
vibration, shock,
moisture, EMI
Operational
Parameters
Life Cycle
Profile
Local
Lead, solder,
PTH/vias, trace,
laminate
Failure analysis
Defect
identification
Failure
identification
Stress
management
Design
tradeoffs
CFF, delamination, fiber debonding, lead
fatigue, solder fatigue, via fatigue
Soldering, laminating,
screen printing, plating,
etching, etc.
Product and
supply chain
evaluation
Performance analysis
Failure models
Cross-talk, delay time, failed circuit
identification
Screening
conditions
Process
Wearout, overstress
Tests
Sensitivity analysis
HALT, HASS, ESS, etc.
Evaluate product failure due to variations in
environmental and architectural parameters
Accelerated
test
Health
management
solutions
Figure 23. Physics-of-Failure process [69].
With regards to the impact of temperature variations on lifetime, mathematical
models have been developed to estimate the number of thermal cycles to failure.
However, these always contain simplifications to a varying degree, and since there are
a variety of failure mechanisms as previously shown, great care should be taken to
understand the background of the models before applying them in reliability
prediction. It is crucial to remember a few factors that make life prediction of solder
joints a complex task [23]:
Solder joints differ from each other (distance from neutral point, height,
geometry, metallurgy).
Initial microstructure of the solder alloy varies.
Substrate finishes and component finishes. Intermetallic compounds
(IMC) vary with soldering process.
Many possible failure mechanisms: Grain/phase coarsening, grain
boundary sliding, matrix creep, micro-void formation and linking,
resulting in crack initiation and crack propagation.
Non-linear, and temperature dependent mechanical behavior of solder.
Strictly speaking, creep processes take place above -40 C, which is
approximately half of the homologous temperature, which the is absolute
temperature melting point.
34
Reliability Prediction
Failure criterion might vary (intermittent electrical opens that are difficult
to detect; mechanical or electrical damage).
The failure location in a specific solder joint may vary depending on the
above variations.
The existing life prediction models for specifically thermal fatigue of solder
joints can be classified in three groups, listed in the order of increased complexity
[70]: Analytical models, Constitutive law + fatigue law models, and Damage
mechanics based models. The analytical models, primarily represented by the
Engelmaier model [64] and its modifications, are simple to implement, but they
include too little detail to utilize for higher accuracy reliability prediction purposes.
The Constitutive law + fatigue law models, such as the strain energy partitioning
method (SEPM) [27] and the Accumulated strain energy density (SEDcr) approach
[18], [19] which will be further discussed below, provide more accurate predictions
with less restriction than the analytical models. The damage mechanics based models,
including the Disturbed state concept (DSC) [28] and the computationally more
efficient Reduced accelerated DSC (RADSC) [71], may provide the highest prediction
accuracy. However, the implementation and computational effort is considerably
higher for the damage mechanics based models than for the other two classes of
models.
Secondary creep is often assumed the main damage mechanism for thermal
fatigue of solder alloys [18]–[20], [23]. FE calculated volume-averaged SEDcr based
on secondary creep, is in a number of publications used to quantify the damage
accumulation process in solders [18], [19], [70], [72], [73]. Constitutive laws for creep
strain rate as a function of stress and temperature include double-power law and
hyperbolic-sine law [23]. The power law can be expressed as follows:
d s
dt
AII
T
n II
exp
Qa , II
kT
AIII
T
n III
exp
Qa, III
kT
,
(10)
and the hyperbolic-sine law:
d s
dt
where
n
C III , IV sinh
exp
d s
is the steady state creep strain rate,
dt
Qa
,
kT
(11)
is the applied stress, k is the
Boltzmann’s constant, T is the absolute temperature, Q is the activation energy, n
denotes stress exponents, A and C are constants, and prescribes the stress level above
which the sinh-dependency dominates the calculated creep strain rate. Both
constitutive laws capture the change in creep mechanism that takes place at certain
stress levels denoted with the roman numbered subscript II through IV.
Implementing either of these models in FE calculations, the accumulated creep
strain can be estimated, and utilized in a fatigue law. Currently, SEDcr is widely
accepted as damage metric for life prediction. SEDcr is calculated by multiplying the
creep strain by the applied stress.
35
Chapter 3
In the recent standard for physics of failure in reliability prediction ANSI/VITA
51.2 [17], a model is advised that belongs to the constitutive law + fatigue law class of
models. It utilizes SEDcr as damage metric [18], and a very simple fatigue law to
evaluate the lifetime. This method is recommended for life prediction, even though it
has not been validated for field operation temperature levels. Furthermore, since the
standard suggests expressing the anticipated field temperature in terms of cycles, the
temperature data will be simplified with regards to ramp rates and dwell times. Even
though this standard represents a large step towards physics-based reliability
predictions, it is apparent that much work remains until thermal fatigue life prediction
of solder joints can be performed with full confidence in the results. One way to
approach completion of the process is to perform various kinds of reliability tests and
publish as much details from the tests as possible, as has been done in Paper VI, and
further described in section 3.3 below.
Ideally, a life prediction model would be available that was validated for noncyclic temperature variations. Indeed, even without fully validated life prediction
models, this kind of calculation might bring higher credibility to the prediction results,
and supply increased understanding of the impact of different temperature profiles.
However, comprehensive FE modeling of stress and strain in a solder joint in noncyclic temperature environment can require large computational resources and long
calculation time. Therefore, a computational method has been proposed that quickly
evaluates the damage accumulated in a solder joint exposed to a non-cyclic, nonsimplified field operation temperature profile with accuracy comparable to FE
modeling.
3.3
Accelerated Thermal Cycling Tests of Surface Mount
Packages with SAC, SN100C, and SnPb Solder Paste
Accelerated thermal cycling tests have been performed with the twofold aim to
contribute to development of models for evaluation of damage accumulation, and to
provide further experimental data to assist in qualification of certain package types and
lead-free solder alloys. Paper VI describes the tests, which have been performed on a
range of surface-mount electronic component packages that could be considered for
avionic applications, mounted with SAC305, SN100C, and Sn62Pb36Ag2 solder
paste. The composition of each tested solder alloy is provided, as well as detailed
manufacturing parameters and geometries of each electronic package. From the
experimental results and FEM assisted interpretation thereof, engineering guidelines
have been generated regarding selection of packages and solder alloys for avionic
applications. One of the 48 PBAs subjected to the tests is shown in Figure 24, showing
the ten different component types that have been included in the tests.
36
Reliability Prediction
QFN48
0402RES
BGA256
BGA49
QFN72
LGA133
1206RES
BGA1152
TSOP48
QFP304
Figure 24. Printed circuit board assembly subjected to thermal cycling tests.
The accelerated thermal cycling tests comprise nearly 12000 cycles in -20°C to
+80°C environment, and more than 6000 cycles of -55°C to +125°C temperature
variation. The results confirm the feasibility of the lead-free solder alloys in -20°C to
+80°C thermal cycle, as well as the benefit of softer SnPb-alloys when subjected
to -55°C to +125°C temperature cycling. The effect of die size on thermal cycling
reliability of a full-array BGA component has been quantified with the help of Weibull
graphs and FE analysis. The accelerated test results have been related to field
environments found in avionic applications.
In agreement with other published results [11], [13], [23], SAC305 PBGA256
has been selected to be a viable candidate both for controlled and uncontrolled thermal
environments.
3.4
Surrogate Modeling of Damage Accumulation in
Solder Joints
When the dependency of one or more response variables on one or more design
variables is not possible to express analytically, and experiments or FE simulation is
considered too time consuming for practical utilization, measures such as model
reduction methods or surrogate modeling can be applied. Model reduction methods
that take into account nonlinear response have been demonstrated, for example on
advanced calculations of crack propagation in elastic-plastic media [74]. While these
methods assume computationally efficient reduced FE modeling in the calculations,
surrogate modeling takes one step further in that more simple methods are utilized for
the response evaluation. Surrogate modeling has two primary applications: design
optimization, and design space approximation. One way to create a surrogate model
37
Chapter 3
for design space approximation is to design a response surface by interpolating the
values of the response variables between the results of a limited number of
experiments with design variables set to cover the design space. Different interpolation
schemes can be applied to estimate the response between the data points included in
the experiments [75].
The novel computational method presented in Paper V, and further elaborated in
Paper VI, provides relatively fast evaluation of accumulated damage in a critical solder
joint of an electronic package on a PCB, with accuracy comparable to computationally
demanding FE simulations. Linearly interpolated FE-simulation-based response
surfaces are utilized to create a surrogate model for design space approximation. The
method includes the following: a simulation-based design-of-experiment (DoE)
procedure that utilizes thermal load limits for the solder joint, an analytic method to
improve the data resolution, construction of linearly interpolated surfaces from the FE
model response, and computation of accumulated damage in a solder joint for field
temperature conditions.
Due to unavoidable singularities in stress values delivered by numerical solution
at the interface between the copper pad and solder [76], [77], a published procedure
has been utilized to estimate accumulated creep strain energy density (SEDcr) in a ball
grid array (BGA) solder joint [18]. Briefly, SEDcr is volume-averaged in a region
comprising a 25 m thick layer of solder at package or board interface, depending on
where the largest damage accumulation is expected, with at least two finite elements
across the thickness.
The creep strain energy density is computed for each time interval tn , tn 1 ,
n 0,1,... of a discretized operating temperature profile, through multiplying the
calculated creep strain by the average of the equivalent stresses at the beginning and at
the end of each time interval. The computation is performed for each finite element in
the region of the solder joint where the damage accumulation is largest.
In order to calculate both the creep strain accumulated during the time interval
tn , tn 1 , and the equivalent stress at the end of the same time interval, the following
input data is required: the temperature at the beginning and at the end of the time
interval, and the equivalent stress at the beginning of the time interval. The calculation
procedure is described with the three graphs provided in Figure 25.
The graph seen in Figure 25 (a) highlights the operating temperature Tn , the
neutral temperature Tsf of the solder joint, von Mises or equivalent stress n , and
accumulated creep strain n , for time intervals tn 1, tn and tn , tn 1 . These time
intervals are translated to FE time intervals 0,2t FE , t FE tn 1 tn , shown in Figure
25 (b) and Figure 25 (c), respectively. Temperatures T1 and T2 in Figure 25 (b)
correspond to Tn 1 and Tn in Figure 25 (a), whereas T1 and T2 in Figure 25 (c) reflect
Tn and Tn 1 , respectively. The neutral temperature T0 is defined such that the slope
between T0 and T1 creates the equivalent stress 1 at time tFE . The equivalent stress
in Figure 25 (b), represent n and n in
2 , and the accumulated creep strain
Figure 25 (a), while 2 and seen in Figure 25 (c), correspond to n 1 and n 1 ,
respectively.
38
Reliability Prediction
T
Tn+1
n
n-1
Tn
Tsf
n+1
n+1
Tn-1
n
tn-1 tn
(a)
T2
1
0
t
T
T
T2
T0
T1
tn+1
2
tFE
2tFE
1
T1
T0
2
0
t
(b)
tFE
2tFE
(c)
t
Figure 25. Transition from operating temperature (a) to FE time interval;
transition from time interval t n 1 , t n (b), and from time interval t n , t n 1 (c).
Depending on whether the temperature in the beginning of each time interval is
below or above Tsf (see Figure 25 (a)), the electronic package either contracts or
expands relative to the PCB. As a consequence, the equivalent stress in the end of each
time interval may differ by orders of magnitude, even at similar initial equivalent
stress magnitudes at the beginning of the time intervals, and similar temperature slopes
from Tn 1 to Tn , and Tn to Tn 1 , respectively. Translated to the FE time interval as
shown in Figure 25 (b) and Figure 25 (c), the equivalent stress 2 , resulting from the
initial equivalent stress 1 followed by similar temperature slopes from T1 to T2 ,
would significantly differ for the two situations.
Assumptions and simplifications accompanying the proposed method are
provided in detail in Paper V. The method is realized in two steps: data preparation, in
which the surrogate model is created, and, computation of accumulated damage caused
by thermal loads by utilizing the surrogate model.
39
Chapter 3
3.4.1
Data Preparation
The data preparation comprises the following steps:
1) Identify the solder joint that accumulates the largest thermomechanical
damage by FE modeling of the electronic component of interest.
2) Assess thermal load limits, and create a simulation plan that adequately
covers the identified range of thermal loads. Perform a sequence of short
FE simulation runs according to the plan, and store the model response in
data files.
3) Create response surfaces by linear interpolation between the data points.
4) Increase the data resolution to improve the quality of the response
surfaces.
From a practical viewpoint, the data preparation phase takes some time.
However, most of the described processes, such as creating the simulation plan based
on thermal load limits, performing the FE simulation runs, creating response surfaces,
and increasing the data resolution, can be automated via appropriate scripting that
enables co-operation between e.g. Matlab and the FE solver. Such automation is partly
implemented for the results reported in this thesis. Specifically, Python scripting is
employed to schedule the simulation runs in Abaqus 6.9, and programming in Matlab
R2011b has been done to generate interpolants and increase the data resolution.
The thermal load limits are defined by the extreme operating temperatures, Tmax
and Tmin , the maximum temperature change T max for the chosen time step, and the
maximum difference T01max between the operating temperature Tn , and the
concurrent neutral temperature T0 n expected during the lifetime of the solder joint.
The purpose of the simulation plan is to generate a sufficient number of data
points to accurately compute the damage metric. The results of the simulations are
stored in one data file for each finite element within the region of the solder joint
where damage accumulation is largest. In every simulation run, the FE model is
computed with a three-temperature profile (T0 , T1, T2 ) , as can be seen in Figure 25 (b)
and Figure 25 (c), returning the associated output quantities 1 , 2 and , which are
unique for every finite element within the evaluated region.
A simulation flow for data generation is shown in Figure 26. The resulting data
points are represented by ordered sets that correspond to N simulation runs:
(T0 j , T1 j , T2 j , 1 j , 2 j , j ) , j 1,2,..., N . The thermal load limits Tmax , Tmin , T01max ,
T max should be utilized such that the interpolated response surfaces would be able
to handle all possible operating temperature profiles that the solder joint may
experience during its lifetime. Every difference between T1 j and T0 j will correspond
to the difference between the current neutral temperature of the solder joint and the
operating temperature, and every difference between T1 j and T2 j will correspond to
the temperature increment in the operating temperature profile during each time
interval tn , tn 1 , n 0,1,... .
40
Reliability Prediction
Thermal load limits:
T min , T max , T 01 max , T max
Selection of three temperatures
(T0 j ) N
(T1 j ) N
1
T0 j [T1j
T1 j
T01max,T1j
1
(T2 j ) N
1
T01max]
[ T min , T max ]
T2 j [T1 j
T max,T1 j
j
T max]
1,2,..., N
Automated finite element
simulation runs
Collection of data points:
(T0 j , T1 j , T2 j , 1 j , 2 j , j )
j 1,2,...,N
Figure 26. Simulation flow for data generation.
3.4.1.1
Revised Data Structure
The symmetric, “spider-like” structure of the data as depicted in Figure 26 has
provided a reliable base for designing the response surfaces utilized in the original
version of the method. Although redundant data points has been created due to the
resulting, non-physical extension of neutral temperature levels, this has been
considered feasible for the data required for a limited span of operating temperatures.
However, in order to enable evaluation of thermal fatigue for an extended temperature
range, the data structure had to be revised. Rather than a symmetrical structure of
T01max linked to T1 j , the neutral temperature now originates from a defined range of
T0 n temperatures, as shown schematically in Figure 27. The novel data structure,
introduced in Paper VI, gives threefold reduction in the number of initial simulation
runs, compared to the previously reported data structure.
41
Chapter 3
T0
T1
T2
Figure 27. Schematic representation of new data structure for three-temperature
data points.
3.4.2
Algorithm for Estimation of Accumulated Damage
The proposed method calculates the volume-averaged accumulated SEDcr within
the evaluated region of the solder joint, during arbitrary thermal loading within the
above estimated limits. A flowchart of the computational algorithm is presented in
Figure 28.
The computational process begins with setting parameters n 0, 0, m 0, and
Wm 0 , m 1,2,...M , to assume stress-free conditions and no accumulated creep strain
energy density in the identified solder joint at time t0 = 0. Index n represents a discrete
time point tn where accumulated damage in the solder joint is evaluated, n = 0,1,2,… .
For each time interval tn , tn 1 , n 0,1,2,... the three-temperature points
(T0 n, m , Tn , Tn 1) are formed. For n > 0, the current element-wise stress-free
int
int
temperature T0 n, m is set by evaluating interpolants T pos
or Tneg
for each element m
from the evaluated region, at the query location (Tn , n ,m ) . Which interpolant to
evaluate depends on whether the element-wise stress-free temperature T0 n 1, m is
higher or lower than the temperature Tn at the end of the previous time interval.
Subsequently, the von Mises stress n 1, m and the accumulated creep strain
are retrieved by evaluating interpolants S int and E int , respectively, at the query
location (T0 n, m , Tn , Tn 1) . Notice, while temperatures Tn and Tn 1 are shared by all M
n 1, m
finite elements, the current stress-free temperature T0 n, m is unique for each element m,
m 1,2,...M .
The SEDcr accumulated during the time interval tn , t n
calculated, such that
Wn 1,m
( n 1,m
2
n,m )
1
is then
(12)
n 1, m .
42
Reliability Prediction
The total element-wise SEDcr Wm accumulated by the time tn 1 is summated,
and subsequently applied to calculate the volume-averaged total SEDcr WVA ,
accumulated by the time t n 1 ,
WVA
Wm Vm
m 1,2,..., M
Vm
m 1,2,..., M
,
(13)
where Vm is the volume of finite element m.
Initialize algorithm with n
0, 0, m
0, Wm
0,
m = 1,2,…,M.
Form three-temperature point
interpolant evaluation,
int
(Tn , n, m ), if
T pos
T0 n, m
T0 n,m , Tn , Tn 1 , by
Tn
T0 n
1, m
int
(Tn , n, m ), if Tn
Tneg
T0 n
1, m
Tn , if n
&n
0
&n
0
0
m = 1,2,…,M.
Retrieve equivalent creep strain and equivalent stress
by interpolant evaluation, and calculate accumulated
SEDcr for time interval t n , t n 1 ,
n 1, m
E int T0 n, m , Tn , Tn 1 ,
n 1, m
S int T0 n , m , Tn , Tn 1 ,
Wn 1, m
m
n 1, m
n, m
2
n 1, m ,
1,2,..., M .
Calculate total accumulated SEDcr in each element,
Wm
Wl , m
l 1, 2,..., n 1
, m = 1,2,…,M.
Calculate volume-averaged accumulated SEDcr, and
proceed to next time step,
WVA
n
Wm
m 1, 2,..., M
Vm
Vm
m 1,2,..., M
,
n 1
Figure 28. Computational algorithm for calculation of volume-averaged
accumulated SEDcr.
43
Chapter 3
As can be seen in Equations (10) and (11), the creep strain rate depends
nonlinearly on the absolute temperature and the equivalent stress. Therefore, linear
interpolation between the data points might not result in acceptable accuracy, unless
the data is adequately resolved. Thus, in order to generate adequate data resolution
without requiring an impractical number of simulation runs, an analytical method to
increase the number of data points has been developed.
Within the estimated thermal load limits reported in this work, the equivalent
stress in the solder joint has been found near-linearly dependent on temperature, due to
linearly elastic properties of all materials in the FE model except for solder. A new
data point (T0new , T1new , T2new , 1new , 2new , new ) can therefore be enabled, where 1new and
new
2
are generated by linear interpolation between two numerically calculated data
points, where only one of the three temperature parameters differs. Subsequently,
Equation (10) or (11) can be applied to deliver new . Details on the procedure for
improvement of data resolution are provided in Paper V.
In order to identify the solder joint that accumulates the largest damage, FE
simulation of a relatively mild accelerated test with a lead-free PBGA256 component
attached to an FR-4 PCB as seen in Figure 29 has been performed. The results have
been compared with the failure location observed in diagonally cross-sectioned
components that have been exposed to a thermal cycling test (see Figure 30). Failure
analysis has furthermore served to reveal the failure mode, thereby increasing the
confidence in the assumptions and simplifications made in the FE model.
A coarsely meshed quarter-symmetry 3-D FE model with equal mesh on all
solder joints identifies the solder joint with the largest damage accumulation correctly.
The highest concentration of accumulated creep strain energy density is located in the
solder at package interface, in agreement with the experimental results. Next, a
detailed octant-symmetry 3-D FE model is created, with local mesh refinement on the
solder joint that accumulates the largest SEDcr (see Figure 31).
Figure 29. PBGA256 component under thermal cycling test.
44
Reliability Prediction
Figure 30. Optical microscopy image of crack in solder joint coinciding with die
corner; arrow indicates crack location near the solder joint-to-component bond
pad interface.
Figure 31. Octant symmetry FE model, including mesh and composition; zoom in
on detailed mesh on critical solder joint, with 25 m thick evaluated region;
SEDcr distribution in lower part of the figure confirms failure location seen from
experiments.
45
Chapter 3
A number of problems have been encountered and mitigated during the
development of the suggested method. More pronounced singularity-behavior has been
observed in the solder at the package interface, which has led to non-physical stress
relaxation at high temperature dwell, and troubles in obtaining stable values from the
surrogate model of T0 n, m for some of the finite elements. Furthermore, insufficient
precision of the FE-calculated volume-averaged stress data obtained from the
simulation runs in the data preparation phase, has led to miscalculation of the stress in
vicinity of the neutral temperature. Details on the measures taken to mitigate these
phenomena are provided in Paper V and Paper VI.
The final result is that SEDcr is computed more than two orders of magnitude
faster than FE simulations with the same operating temperature profiles. Comparisons
between SEDcr calculated with the proposed method and FE simulation for an
example of field temperature profile is shown in Figure 32. Figure 33 shows the same
for the -20°C to +80°C thermal cycling test, as well as the difference in accumulated
SEDcr between FE and the proposed method. It can be seen, that the agreement
between the results predicted with the suggested computational method and the FE
simulations, converges to approximately 4%.
Operating Temperature, C
80
70
60
50
40
30
20
0
2000
4000
6000
8000
10000
12000
14000
10000
12000
14000
Time, sec
Acc. energy density, J/m3
300
250
Surr. model
FE
200
150
100
50
0
0
2000
4000
6000
8000
Time, sec
Figure 32. Example of field temperature profile (top), and accumulated creep
strain energy density: FE simulation vs. surrogate modeling method (bottom).
46
Reliability Prediction
100
Operating temperature, C
80
60
40
20
0
-20
-40
0
1
2
3
4
5
6
7
Time, sec
6
x 10
4
3
Acc. energy density, J/m
4
3T
FE
Surr. model
FE
5
8
x 10
4
3
2
1
0
0
1
2
3
4
5
6
7
Time, sec
8
x 10
4
10
Diff. in acc. energy density, %
8
6
4
2
0
-2
-4
-6
-8
-10
0
1
2
3
4
Time, sec
5
6
7
x 10
4
Figure 33. TC temperature (top), predicted SEDcr to compare the surrogate
modeling method for evaluation of damage accumulation with FE simulation
(middle), and difference between FE and the surrogate modeling method in
accumulated SEDcr (bottom).
The method is believed to be general in terms of application to different
electronic packages, as far as validated life prediction models are available. The
requirement to the FE model is that it is capable to identify the solder joint that
accumulates the largest thermomechanical damage, and predict the right failure
location. Therefore, the quality of the results delivered by the proposed computational
47
Chapter 3
method depends on the quality of the FE model. The added value with the proposed
method is that various non-cyclic field temperature profiles, taken in any sequence,
can be quickly evaluated in the design phase, provided that appropriate data
preparation has been performed according to described routines.
Besides the revised data structure, further improvements of the method are
presented in Paper VI. In order to resolve singularity-related problems, it has been
found necessary to implement T0-limit control, and stress relaxation at hightemperature dwell to maintain adequate accuracy for increased temperature range.
Due to its ability for time-efficient operation on uncompressed temperature data,
the developed method might contribute to the accuracy of reliability prediction of
electronic packages. This especially relates to applications where thermal fatigue is a
dominant contributor to the damage of solder joints and where time dependent
analysis, such as creep analysis, is involved.
48
4
Prognostics of Remaining Useful
Life of Electronic Equipment
Historically, diagnostics and prognostics of remaining useful life (RUL) have
often been implemented for critical structural components of a system. Electronic
equipment has been a minor part of the system, and the lifetime of the electronics has
been judged much longer than the most critical mechanical components. Currently,
however, the function of such equipment relies more and more on electronics,
embedded in various locations of the system. Simultaneously, essentially depending on
the use of commercial off the shelf (COTS) electronics in more rugged applications
than the original intention, the lifetime of the electronics is decreasing.
Consequently, prognosticating the remaining useful life of electronic equipment
is a research area that currently attracts attention. Accuracy of life prediction tools has
become critically important, due to increased reliability requirements on absolute
numbers, instead of traditional relative comparison [23]. As an outcome of this, the
interest increases of, for instance, aircraft manufacturers, to continuously monitor RUL
of line replaceable units for avionic use, thus achieving significant potential to provide
safer, more reliable, and cost-effective avionic systems [78].
Much research is currently ongoing to define methods and models to correctly
predict RUL of electronics, with all levels of failure modes taken into consideration.
As an outcome of the above attempts, four wide-ranging categories of implementation
of prognostics can currently be found in literature:
A.
Monitor failure precursors: Performance parameters are monitored, such
as voltage levels, and switching time constants, that may indicate impending failures
[79];
B.
Introduce expendable devices: Implement fuses and “canaries” into the
system; a prognostic cell that fails earlier than the system, and thus provides advance
warning of a failure [80];
C.
Microstructural analysis: Removal and cross-sectioning of expendable,
dummy component solder joints. The grain size and the rate of change of intermetallic
growth may reveal the state of the solder joint [81].
D.
Life consumption monitoring (LCM): use physics-of-failure models,
applied on measured environmental and thermal loads, to compute RUL of the
equipment [24], [82].
Each of the above categories has its individual advantages and limitations,
further discussed in Paper VII. However, the concept of merging two or more of these
49
Chapter 4
approaches, achieving fusion prognostics [83], is currently of high interest in the
research community [84], [85].
Similar reduction of field operation temperature data as described in the context
of reliability prediction has been suggested for real-time fatigue calculation of solder
joints [86]. The benefit gained by instead implementing the computational method
previously presented in this thesis, is the potential of increased accuracy of the
prediction of remaining useful life of the monitored system. It has to be noted,
however, that this would require validated combinations of constitutive laws for
calculation of the damage metric, and life prediction models in which to apply the
damage metric.
A prognostic unit embedded in the host system needs to be miniaturized, reliable,
robust, and independent of external power supply over long periods of time.
Furthermore, it should be “invisible” for the host system, not to adversely affect the
traditional mean time between failures (MTBF) calculations, which supposedly
accompany the initial quotation documents.
The Physics-of-Failure process has been adapted for utilization in prognostics
applications according to the flowchart given in Figure 34 [87]. After identification of
which parameters to monitor during usage of the product, by utilizing fault tree
analysis and failure mode, mechanisms, effects, and criticality analysis (FMMECA)
followed by virtual reliability assessment, applicable sensors are introduced in the
system. The acquired data is simplified to minimize memory space needed for storage,
and make the data compatible with the requirements of each PoF model.
Step 1: Conduct failure modes, mechanisms and effects analysis
Step 2: Conduct a virtual reliability assessment to assess the failure
mechanisms with earliest time to failure
Step 3: Monitor appropriate product parameters
environmental (e.g. shock, vibration, temperature, humidity)
operational (e.g. voltage, power, heat dissipation)
Step 4: Conduct data simplification to make sensor data suitable for
stress and damage models
Step 5: Perform stress and damage accumulation analysis
Step 6: Estimate the remaining life of the product
Is the
remaining-life
acceptable?
Continue
monitoring
Schedule a maintenance action
Figure 34. Physics of Failure process applied for life consumption monitoring
(LCM) [87].
50
Prognostics of Remaining Useful Life of Electronic Equipment
The novel comprehensive method for prognostics of thermal fatigue failure of
solder joints suggested in Paper VII, is summarized in Figure 35. Steps 1 through 3 are
performed in advance, while steps 4 and 5 are executed in real time. From a global
CFD simulation in the first step, and the following global reliability prediction of the
PBAs included in the system in step 2, the first component to fail (FCF) is identified.
A temperature sensor is introduced near FCF in the third step. Using data from
the CFD simulation, and information about the state of the host unit (on/off), the
correct temperature offset between the temperature measured at the sensor location,
and the average FCF temperature, is calculated. This gives the true time history of the
temperature of FCF.
As opposed to the existing Physics of Failure-method shown in Figure 34, the
suggested method for evaluation of damage accumulation utilizes unrefined
temperature data as input to the real-time, in situ RUL calculations performed in the
fourth step.
In the fifth step, data reduction, by means of ordered overall range (OOR)
method and rainflow algorithm [24], is performed to save the general temperature time
history for future analysis, development of products for similar environments, and
design of accelerated tests. Also, as can be seen in Figure 35, the logged temperature
profile is used to verify the initial assumptions of temperature time history. The
accuracy of the prognosticated remaining useful life depends on the level of details
captured in the model, and the level of confidence from validation efforts.
Action
Output
1. Global transient
computational fluid
dynamics (CFD)
analysis
Expected time
history of
temperature
2. Global durability
analysis
First component
to fail (FCF)
3. Introduce
temperature sensor
at FCF
True time
history of FCF
temperature
4. Real-time local
RUL calculations
for FCF
Remaining
thermal fatigue
life
5. Data reduction
and storage
FCF temperature
history logged
for future use
Figure 35. Suggested method for thermal fatigue prognostics of solder joints.
51
Chapter 4
Since the prognostic system is transparent to the host system, the initial reliability
calculations for the host system will remain unaffected. The proposed computational
method also enables use of a low-end computer to perform the remaining useful life
(RUL) calculations. Thereby power consumption is minimized, and reliability is
maximized.
In Paper VIII, the surrogate modeling approach for estimation of accumulated
damage in solder joints has been taken one step further towards future realization in
life consumption monitoring applications. Implementation routines are discussed, and
effects on the prediction accuracy of data resolution and other factors have been
investigated. An avionic application scenario presented for a PBGA256 component
serves to highlight implementation routines, which have been found realizable under
the following assumptions:
Initially, all solder joints are considered stress-free.
Being a frequent assumption for thermal fatigue of lead-free solders,
secondary creep is the chosen damage mechanism [20], [23], [88].
Other damage mechanisms for thermal fatigue, such as time-independent
plasticity and primary creep, are not addressed.
The hyperbolic-sine law is employed as constitutive model for creep rate
calculation [23].
Accumulated creep strain energy density (SEDcr) is used as damage
metric [19], [70]. A number of lifetime prediction models show good
correlation to thermal cycling experiments with this damage metric [88],
[89]. Although with certain limitations, SEDcr may furthermore quantify
the damage accumulation not only for termal cycling tests, but also for
operating temperature conditions [19], [90].
Computed SEDcr is volume-averaged in a 25 m thick interfacial layer of
the solder joint, at the solder-to-component interface [76].
Linear interpolation between data points obtained by initial simulation
runs is applied to create the response surfaces. Accuracy issues are
mitigated by employing an analytic method to improve the data resolution.
The accuracy of prediction with the proposed method is evaluated by
relating the computed results to FE simulated results.
Uncertainty investigation of the deformation constants in the constitutive
law is out of scope of this thesis, as is robustness to production induced
variations of for example solder joint geometry and solder microstructure.
The surrogate modeling approach will provide added value to life
consumption monitoring by increasing the accuracy of, specifically,
thermal fatigue life consumption of solder joints.
A data resolution has been determined that forms the base for response surfaces
that provide prediction accuracy comparable to 3-D FE simulations. Even though the
suggested approach has to be carefully validated, the vision is that it can be combined
with other LCM methods and deliver improved prediction accuracy of remaining
thermal fatigue life.
52
5
Concluding Summary and
Contribution to the Field
The main contributions in this thesis to development of avionic equipment are
threefold: Design guidelines for power distribution on a double-sided PBA, a novel,
computationally efficient method for evaluation of damage accumulation in solder
joints in harsh, non-cyclic field operation temperature environments, and the results
from thermal cycling tests of electronic packages intended for avionic applications,
assembled with SAC305, Sn100C, and SnPbAg solder alloys.
5.1
Thermal Management
It has been concluded that the thermal performance of avionic equipment can be
improved by utilizing power distribution between the sides of a double-sided PBA.
Paying attention to this opportunity in an early stage of product design can render costand weight-free thermal enhancement of the system. The reported CFD-based
methodology can be applied as part of concurrent development and contribute to the
trend in development of design tools that enable co-design of electrical and thermal
layout of printed circuit boards.
Quantitatively, in an environment of 55°C cooling air supplied at a rate of 6.7 g/s
to the outside of a sealed avionic enclosure, with 39 W of power dissipated by other
PBAs in the enclosure, and 36 W dissipated by a double-sided PBA attached to the
enclosure side wall, managing power distribution between the sides of the doublesided PBA results in up to 5.5°C decrease of the maximum case temperature of the
included components.
Bridging the gap between thermal management and reliability prediction, the
benefit of incorporating advanced thermal analysis in physics-based lifetime prediction
has been highlighted and elaborated. Results have been presented from a collaborative
research project, in which a physics-based lifetime prediction tool has been extended
to allow for analysis of electronics in a complex thermal environment. Signifying one
step towards physics of failure in reliability prediction, this methodology is expected
to be introduced shortly in the development of avionic products.
53
Chapter 5
5.2
Physics of Failure in Reliability Prediction of Solder
Joints
Representing the key contribution of this thesis, a novel computational method
has been presented that utilizes surrogate stress and strain modeling of a solder joint to
enable quick evaluation of thermal fatigue damage, such that:
-
It utilizes non-cyclic, non-compressed temperature data of anticipated field
operation temperature environment.
On the tested various temperature profiles, it provides accuracy within 4%
compared to 3-D FE analysis.
Its computational efficiency is two orders of magnitude higher than FE analysis.
The added value with the proposed method is that various operating (non-cyclic)
temperature profiles, taken in any sequence, can be quickly evaluated in the design
phase. Due to its ability for time-efficient operation on uncompressed temperature
data, the method gives contribution to the practicable accuracy, and hence the
credibility, of reliability prediction of electronic packages. Effects of data resolution,
which forms the base for response surfaces utilized in the surrogate model, on the
prediction accuracy have been investigated, as well as other factors. A data resolution
has been determined that provides prediction accuracy comparable to 3-D FE
simulations on the tested temperature profiles. The method has been tested on a fullarray BGA256 package subjected to -20°C to +80°C thermal cycles, as well as to
representative avionics field temperature profiles. It is however expected to be general
in terms of application to different electronic packages, assuming that validated life
prediction models are available for each solder alloy and relevant geometry of the
critical solder joint that has to be identified in advance.
The potential future application of the computational method as a means for
embedding real-time prognostics of remaining useful life in avionic equipment has
also been elaborated in the thesis. A review of prognostics and health management
methods for electronics has been provided, and a procedure to enable increased
accuracy of in situ, real-time prognostics has been suggested. A proposed realization in
avionics has been discussed, including implementation routines. Even though the
suggested approach has to be carefully validated, the vision is that it can be combined
with other life consumption monitoring methods and deliver improved prediction
accuracy of remaining useful life of electronics.
Experimental data has been provided from accelerated thermal cycling tests for
qualification of lead-free electronic packages and solder alloys for use in avionics. The
tests were performed in -20°C to +80°C and -55°C to +125°C environments. The
results confirm similar tests in that the lead-free solder alloys perform better in -20°C
to +80°C thermal cycle, while the benefit of softer SnPb-alloys is seen at higher levels
of strain in the solder joints. Employing Weibull analysis combined with FE analysis,
the effect of die size on thermal cycling reliability of a full-array BGA component has
been quantified. The accelerated test results have been related to field environments
found in avionic applications.
In the context of reliability prediction, especially assuming that the reliability and
design engineering disciplines collaborate in the early stages of product development,
54
Concluding Summary and Contribution to the Field
the computational method may have its strongest impact. Most clearly pronounced for
applications where thermal fatigue is a dominant contributor to the damage of solder
joints, utilization of the method may assist to bring product development one step
closer to “First time right” design. As a consequence, this would imply a reduction of
the number of expensive iterations in product design.
5.3
Future Work
Full understanding and complete modeling capabilities of the physics of failure
of electronic equipment is a great challenge that will require a lot of research. Small
steps are continuously taken to increase the knowledge in this area that is of increasing
importance to the ADHP industry. The experimental data provided in this thesis,
supplemented by further in-depth failure analysis of the test vehicles, will provide one
such step in that it will contribute to increased understanding of crack propagation in
solder joints in different thermal environments. Concerning reliability prediction, the
suggested computational method should be verified against FE modeling of multiple
solder joint geometries.
If, in the future, necessary understanding of the physics of failure would be
established, a new design space would open concerning reliability and maintenance of
electronic systems. In avionic units it could be commercially interesting to include
sensors that monitor the environmental loads, and indicate when service or exchange
of the unit is due. The surrogate modeling method presented in this thesis is expected
to contribute to the accuracy of LCM of avionic equipment. However, since thermal
fatigue of solder joints is but one out of a variety of failure mechanisms that may
define the lifetime of avionic equipment, the suggested method has to be combined
with other LCM methods.
55
Chapter 5
56
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The Papers
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