Reliability physics and engineering: Time-to-failure modeling

469 Pages·2019·5.086 MB·English

by  McPherson J.W.

J. W. McPherson
Reliability
Physics and
Engineering
Time-To-Failure Modeling
Third Edition
Reliability Physics and Engineering
J. W. McPherson
Reliability Physics
and Engineering
Time-To-Failure Modeling
Third Edition
J.W.McPherson
McPhersonReliabilityConsulting,LLC
Plano,TX,USA
ISBN978-3-319-93682-6 ISBN978-3-319-93683-3 (eBook)
https://doi.org/10.1007/978-3-319-93683-3
LibraryofCongressControlNumber:2018955282
©SpringerNatureSwitzerlandAG2013,2019
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The best idea that I have ever had
—marrying my wife Victoria
Preface
All engineers could benefit from at least one course in Reliability Physics &
Engineering.Itisverylikelythat,startingwithyourveryfirstengineeringposition,
youwillbeasked—howlongisyournewlydevelopeddeviceexpectedtolast?This
textbook was designed to help answer this fundamentally important question. All
materialsanddevicesareexpectedtodegradewithtime,soitisverynaturaltoask—
howlongwillthedevicelast?
Theevidenceformaterial/devicedegradationisapparentlyeverywhereinnature.
Afreshcoatingofpaintonahousewilleventuallycrackandpeel.Doorsinahouse
can become stuck due to the shifting of the foundation. The new finish on an
automobile will oxidize with time. The tight tolerances associated with finely
meshed gears will deteriorate with time. Critical parameters that are associated
with precision semiconductor devices (threshold voltages, drive currents, intercon-
nectresistances,capacitorleakages,etc.)willdegradewithtime.Inordertounder-
standthelifetimeofthematerial/device,itisimportanttounderstandthereliability
physics (kinetics) for each of the potential failure mechanisms and then be able to
developtherequiredreliabilityengineeringmethodsthatcanbeusedtoprevent,or
atleastminimizetheoccurrenceof,devicefailure.
Reliability engineering is a fundamental part of all good electrical, mechanical,
and civil engineering designs. Since proper materials selection can also be a
critically important reliability factor, reliability engineering is also very important
tomaterialsscientists.Reliabilityisdistinguishedfromqualityinthatqualityusually
referstotime-zerocomplianceorconformanceissuesforthematerial/device.Reli-
ability refers to the time dependence of material/device degradation. All devices
(electrical and/or mechanical) are known to degrade with time. Measuring and
modeling the degradation rate, the time to failure, and the failure rate are the
subjectsofreliabilityengineering.
Manyelectricalandmechanicaldevices,perhapsduetoperformanceand/orcost
reasons,pushtheirstandardoperatingconditions(useconditions)veryclosetothe
intrinsic strength of the materials used in the design. Thus, it is not a question of
whether the device will fail, but when. Reliability engineering methods permit the
vii
viii Preface
electricalengineer,armedwithacceleratedtestingdata,toclaimwithconfidencethat
anewlydesignedintegratedcircuitwilllastatleast10yearsunderspecifiedvoltage
and temperature operating conditions. Reliability engineering methods permit the
mechanical engineer to claim that the newly designed engine will last for
180,000milesat3000rpmwithanoilchangerequiredevery6000miles.Reliability
engineeringmethodspermitthecivilengineertoclaimthatanewlydesignedbridge
should last at least 75 years under specified environmental and use conditions.
Reliability engineering methods enable the materials scientist to select a cost-
effective material which can safely withstand a specified set of high-temperature
andhigh-stressuseconditionsformorethan10years.
This textbook provides the basics of reliability physics and engineering that are
needed by electrical engineers, mechanical engineers, civil engineers, biomedical
engineers, materials scientists, and applied physicists to help them to build better
devices/products. The information contained within should help all fields of engi-
neeringtodevelopbettermethodologiesformorereliableproductdesigns,reliable
materials selections, and reliable manufacturing processes—all of which should
help to improve product reliability. A mathematics level through differential equa-
tions is needed. Also, a familiarity with the use of Excel spreadsheets is assumed.
Anyneededstatisticaltrainingandtoolsarecontainedwithinthetext.Whiledevice
failureisastatisticalprocess(thusmakingstatisticsimportant),theemphasisofthis
book is clearly on the physics of failure and developing the reliability engineering
tools required for product improvements during device-design and device-fabrica-
tionphases.
Plano,TX,USA J.W.McPherson
Acknowledgments
I would like to thank the many excellent engineers and scientists that I had the
pleasure of working with and learning from during my three-decade career with
Texas Instruments. Also, I am very appreciative of the ideas developed during
stimulatingdiscussionswithmanycolleaguesinreliabilityphysicsandengineering
within industry, universities, and national laboratories. I will be forever grateful to
PhysicsProfessorsE.GarnessPurdom(GuilfordCollege),Yung-LiWang(Florida
StateUniversity),andEdwardDesloge(FloridaStateUniversity)beingoutstanding
role models during my earliest physics education. I benefited greatly from interac-
tionswithtwoNobelPrizeWinnersinphysics:PaulDirac(FloridaStateUniversity)
andJackKilby(TexasInstruments).
ix
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 PhysicsofDegradation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1 Degradation. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 5
2 RiseofEntropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 MetastableStates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4 GibbsPotential/Free-Energy(ABriefReview). . . . .. . . . . . . . .. 10
5 RelationshipBetweenIncreasedGibbsPotential
andDecreasedStability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6 DissipativeWork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
7 ReachingLowerGibbsPotential. . . . . . . . . . . . . . . . . . . . . . . . . 23
8 ImperfectMaterials/Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9 NuclideDegradation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Bibliography. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 31
3 Time-DependenceofMaterialsandDeviceDegradation. . . . . . . . . 33
1 Materials/DeviceDegradation. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Material/Device-ParameterDegradationModeling. . . . . . . . . . . . 34
2.1 Material/Device-ParameterDecreaseswithTime. . . . . . . 36
2.2 Material/Device-ParameterIncreaseswithTime. . . . . . . . 39
3 GeneralTime-DependentDegradationModels. . . . . . . . . . . . . . . 42
4 DegradationRateModeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5 DelaysintheStartofDegradation. . . . . . . . . . . . . . . . . . . . . . . 45
6 CompetingDegradationMechanisms. . . . . . . . . . . . . . . . . . . . . 50
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 FromMaterial/DeviceDegradationtoTime-to-Failure. . . . . . . . . . 59
1 Time-to-Failure(TF). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2 Time-to-FailureKinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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xii Contents
5 Time-to-FailureModeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
1 Flux-DivergenceImpactonTime-to-Failure. . . . . . . . . . . . . . . . 67
2 StressDependenceandActivationEnergy. . . . . . . . . . . . . . . . . . 71
3 ConservativeTime-to-FailureModels. . . . . . . . . . . . . . . . . . . . . 75
4 Time-to-FailureModelingUnderHigh-Stress. . . . . . . . . . . . . . . 77
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Bibliography. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 80
6 GaussianStatistics:AnOverview. . . . . . . . . . . . . . . . . . . . . . . . . . 81
1 NormalDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2 ProbabilityDensityFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3 StatisticalProcessControl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 91
7 Time-to-FailureStatistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
1 LognormalProbabilityDensityFunction. . . . . . . . . . . . . . . . . . . 93
2 WeibullProbabilityDensityFunction. . . . . . . . . . . . . . . . . . . . . 97
3 MultimodalDistributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.1 MultimodalDistribution(SeparatedinTime). . . . . . . . . . 100
3.2 MixedMultipleFailureMechanisms. . . . . . . . . . . . . . . . 103
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Bibliography. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 107
8 FailureRateModeling. . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 109
1 DeviceFailureRate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2 AverageFailureRate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.1 LognormalAverageFailureRate. . . . . . . . . . . . . . . . . . 111
2.2 WeibullAverageFailureRate. . . . . . . . . . . . . . . . . . . . . 112
3 InstantaneousFailureRate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.1 LognormalInstantaneousFailureRate. . . . . . . . . . . . . . . 113
3.2 WeibullInstantaneousFailureRate. . . . . . . . . . . . . . . . . 114
4 BathtubCurve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5 FailureRateforElectronicDevices. . . . . . . . . . . . . . . . . . . . . . . 116
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Bibliography. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 124
9 AcceleratedDegradation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
1 ImpactofTemperatureonDegradationRate. . . . . . . . . . . . . . . . 125
2 ImpactofStressandTemperatureonDegradationRate. . . . . . . . 127
3 AcceleratedDegradationRates. . . . . . . . . . . . . . . . . . . . . . . . . . 130
4 FreeEnergyofActivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 RealVersusVirtualStresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Bibliography. .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 136