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Avoiding Inelastic Strains in Solder Joint Interconnections of IC Devices

Analytical Modeling, Its Role and SignificanceMethod of Interfacial ComplianceIntroductionStresses in the Midportion of a Multimaterial Body Subjected to a Change in TemperatureBimaterial Assembly: Interfacial Shearing StressesBimaterial Assembly: Interfacial Peeling StressesTrimaterial Assembly: Interfacial Shearing StressesTrimaterial Assembly: Interfacial Peeling StressesNumerical ExampleBimaterial Assembly Subjected to Thermal Stress: Propensity to Delamination Assessed Using the Interfacial Compliance ModelBackground/IncentiveStrain Energy Release Rate (SERR) Computed Using the Interfacial Compliance ApproachAdequate SERR Specimen’s LengthNumerical Example #1Numerical Example #2Probabilistic Approach: Application of the Extreme Value DistributionProbabilistic Approach: Numerical ExampleAppendix A: Convolution of Extreme Value Distribution with a Normally Distributed VariableAppendix B: A Numerical Integration ExampleReferencesThermal Stress in Assemblies with Identical AdherendsIntroductionBell Labs Si-on-Si multi-chip flip-chip Packaging TechnologySimplest Elongated Assembly with Identical AdherendsAssembly with Identical Adherends Subjected to Different Temperatures: Thermal Stresses in a Multileg Thermoelectric Module DesignMotivationBackgroundBasic EquationTheorem of Three Axial ForcesSpecial CasesHomogeneously Bonded AssemblyAssembly Bonded at the Ends (Two-Legged TEM)Midportion of a Long Multilegged AssemblyTEM Designs in Figures 3.11 and 3.12TEM Designs in Figures 3.11 and 3.12Design in Figure 3.12 for a High-Temperature Power Generation TEMUltrathin and Long (Beam-Like) LegsPredicted thermal stress in a circular bonded assembly with identical adherendsMotivationAssumptionsBasic EquationSolution to the Basic EquationLarge and/or Stiff AssembliesNormal Stresses in the Bonding LayerBowBending Stresses in the AdherendsPeeling StressNumerical ExampleReferencesInelastic Strains in Solder Joint InterconnectionsBackground/MotivationAssumptionsShearing StressBasic EquationBoundary ConditionsElasto-Plastic SolutionPossible Numerical Procedure for Solving the Elasto-Plastic EquationsPredicted Lengths of the Plastic Zones Based on an Elastic SolutionPeeling StressBasic EquationSolution to the Basic EquationNumerical ExampleThe Case of a BGA AssemblyBackground/MotivationBasic EquationNumerical Example #1 (PCB Substrate)Numerical Example #2 (Ceramic Substrate)Probabilistic Palmgren-Miner Rule for Solder Materials Experiencing Elastic DeformationsBackground/IncentiveProbabilistic Palmgren-Miner RuleRemaining Useful LifeRayleigh Law for the Random Amplitude of the Interfacial Shearing StressNumerical ExampleReferencesElevated Stand-Off Heights Can Relieve Thermal Stress in Solder JointsBackground/MotivationStresses in a Short Beam Subjected to Bending Caused by its End OffsetInterfacial Stresses in Assemblies with Small Stand-off HeightsHead-In-Pillow ProblemMotivationBackgroundInterfacial Stresses and WarpageNumerical ExampleReferencesStress Relief in Soldered Assemblies by Using Inhomogeneous BondsBackground/IncentiveAssembly’s MidportionAssembly’s Peripheral Portion(s) and Forces at the BoundariesInterfacial StressesNumerical ExampleOptimized DesignOptimization ConditionPeripheral Material with a Low Fabrication TemperaturePeripheral Material with a Low Parameter of the Interfacial Shearing StressPeripheral Material with a Low Parameter of the Interfacial Shearing Stress and Low Fabrication TemperatureConclusionsReferencesThermal Stresses in a Flip-Chip DesignBackground/IncentiveThermal Stress Model for a Typical Flip-Chip Package DesignApproachForces Acting in the Midportion of the Assembly Located at the Design’s MidportionPeripheral Portions of the DesignNumerical ExamplesDesign with an Organic Lid: Midportion of the DesignDesign with an Organic Lid: Peripheral Portion of the DesignDesign with a Copper Lid: Midportion of the DesignDesign with a Copper Lid: Peripheral Portions of the DesignIs it Really Important that the Entire Underchip Area is Encapsulated (“Underfilled”)?Stress Relief in an FC Design Due to the Application of an Inhomogeneous Solder Joint SystemEffect of the Underfill Glass Transition TemperatureBackgroundAssumptionsThermally Induced Forces and Interfacial StressesThermally Induced Forces in the Midportion of a Long Flip-Chip/Substrate AssemblyDistributed Thermally Induced ForcesInterfacial Shearing StressesNumerical ExampleReferencesAssessed Interfacial Strength and Elastic Moduli of the Bonding Material from Shear-Off Test DataBackground/IncentiveBasic EquationSolution to the Basic EquationInterfacial Shearing StressShear Modulus of the Bonding MaterialNumerical ExamplePossible Characterization of the Solder Material PropertiesCONCLUSIONReferencesBoard-Level Dynamic TestsBackgroundDrop TestingRole Of ModelingLinear ResponseNonlinear ResponseSolder JointsBoard-Level TestingConclusionsAppendix A: Exact Solution to the Problem of the Nonlinear Dynamic Response of a PCB to the Drop Impact during Board-Level Drop TestsA.1. Background/InitiativeA.2. AssumptionsA.3. Kinetic and Strain EnergiesA.4. Condition of Nondeformability of the PCB Support ContourA.5. Stress (Airy) FunctionA.6. In-plane (membrane) Stresses and StrainsA.7. Parameter of NonlinearityA.8. Basic Equation and Its SolutionA.9. Vibration AmplitudeA.10. Effective Initial VelocityA.11. Nonlinear FrequencyA.12. Bending MomentsA.13. Equivalent Static LoadingA.14. Numerical ExampleReferencesAppendix ReferencesFailure-Oriented-Accelerated-Testing and Multiparametric Boltzmann–Arrhenius–Zhurkov EquationAccelerated TestingFOAT, Its Significance, Attributes, and RoleMultiparametric BAZ EquationTemperature Cycling: Predicted Time-to-failureIncentive for Mechanical Prestressing of Accelerated Test SpecimensBackground/IncentiveBasic EquationsBoundary ConditionsSolutions to the Basic EquationsConstants of IntegrationNumerical ExampleAccelerated Testing of Solder Joint Interconnections: Incentive for Using a Low-Temperature/Random- Vibrations BiasBackground/IncentiveMethodologyReduction to PracticeCalculation ProcedureNumerical ExampleTesting Facility and ProcedureConclusionPossible Next-Generation QTAppendix A: Elastic Stability of the Specimen as a WholeAppendix B: Approximate Formula for the Interfacial Peeling Stress and Elastic Stability of the Compressed Component #1ReferencesProbabilistic Design for ReliabilityBackground/IncentivePDfR and its “ten commandments”Design for Reliability of Electronic Products: Deterministic and Probabilistic ApproachesSome simple PDfR examplesAdequate Heat SinkReliable Seal GlassExtreme Response in Temperature CyclingThe Total Cost of Reliability could be Minimized: Elementary ExampleRequired Repair Time to Assure the Specified AvailabilityBackground/IncentiveAnalysisNumerical ExampleConclusionBurn-in Testing of Electronic and Photonic Products: To BIT or not to BIT?Background/InitiativeObjectiveInformation Based on the Available BTCConclusionAPPENDIX A: RELIABILITY OF AN ELECTRONIC PRODUCT COMPRISED OF MASS-PRODUCED COMPONENTSA.1. SummaryA.2. Background/IncentiveA.3. AnalysisA.3.1. Analytical Bathtub Curve (Diagram)A.3.2. Statistical Failure RateA.3.3. The Case When Random SFR isNormally DistributedA.3.4. The Case When Random SFR is Distributed in Accordance with the Rayleigh LawA.3.5. Probability of NonfailureA.4. ConclusionsReferencesAppendix ReferencesFiber Optics Systems and Reliability of Solder MaterialsBackground/ObjectiveFiber Optics Structural Analysis (FOSA) in Fiber Optics Engineering: Role and AttributesFibers Soldered into FerrulesThermal Stresses in a Cylindrical Soldered TriMaterial Body with Application to Optical FibersBackground/IncentiveAnalysisNumerical ExampleConclusionReferences

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