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Avoiding Inelastic Strains in Solder Joint Interconnections of IC Devices
Analytical Modeling, Its Role and Significance
Method of Interfacial Compliance
Introduction
Stresses in the Midportion of a Multimaterial Body Subjected to a Change in Temperature
Bimaterial Assembly: Interfacial Shearing Stresses
Bimaterial Assembly: Interfacial Peeling Stresses
Trimaterial Assembly: Interfacial Shearing Stresses
Trimaterial Assembly: Interfacial Peeling Stresses
Numerical Example
Bimaterial Assembly Subjected to Thermal Stress: Propensity to Delamination Assessed Using the Interfacial Compliance Model
Background/Incentive
Strain Energy Release Rate (SERR) Computed Using the Interfacial Compliance Approach
Adequate SERR Specimen’s Length
Numerical Example #1
Numerical Example #2
Probabilistic Approach: Application of the Extreme Value Distribution
Probabilistic Approach: Numerical Example
Appendix A: Convolution of Extreme Value Distribution with a Normally Distributed Variable
Appendix B: A Numerical Integration Example
References
Thermal Stress in Assemblies with Identical Adherends
Introduction
Bell Labs Si-on-Si multi-chip flip-chip Packaging Technology
Simplest Elongated Assembly with Identical Adherends
Assembly with Identical Adherends Subjected to Different Temperatures: Thermal Stresses in a Multileg Thermoelectric Module Design
Motivation
Background
Basic Equation
Theorem of Three Axial Forces
Special Cases
Homogeneously Bonded Assembly
Assembly Bonded at the Ends (Two-Legged TEM)
Midportion of a Long Multilegged Assembly
TEM Designs in Figures 3.11 and 3.12
TEM Designs in Figures 3.11 and 3.12
Design in Figure 3.12 for a High-Temperature Power Generation TEM
Ultrathin and Long (Beam-Like) Legs
Predicted thermal stress in a circular bonded assembly with identical adherends
Motivation
Assumptions
Basic Equation
Solution to the Basic Equation
Large and/or Stiff Assemblies
Normal Stresses in the Bonding Layer
Bow
Bending Stresses in the Adherends
Peeling Stress
Numerical Example
References
Inelastic Strains in Solder Joint Interconnections
Background/Motivation
Assumptions
Shearing Stress
Basic Equation
Boundary Conditions
Elasto-Plastic Solution
Possible Numerical Procedure for Solving the Elasto-Plastic Equations
Predicted Lengths of the Plastic Zones Based on an Elastic Solution
Peeling Stress
Basic Equation
Solution to the Basic Equation
Numerical Example
The Case of a BGA Assembly
Background/Motivation
Basic Equation
Numerical Example #1 (PCB Substrate)
Numerical Example #2 (Ceramic Substrate)
Probabilistic Palmgren-Miner Rule for Solder Materials Experiencing Elastic Deformations
Background/Incentive
Probabilistic Palmgren-Miner Rule
Remaining Useful Life
Rayleigh Law for the Random Amplitude of the Interfacial Shearing Stress
Numerical Example
References
Elevated Stand-Off Heights Can Relieve Thermal Stress in Solder Joints
Background/Motivation
Stresses in a Short Beam Subjected to Bending Caused by its End Offset
Interfacial Stresses in Assemblies with Small Stand-off Heights
Head-In-Pillow Problem
Motivation
Background
Interfacial Stresses and Warpage
Numerical Example
References
Stress Relief in Soldered Assemblies by Using Inhomogeneous Bonds
Background/Incentive
Assembly’s Midportion
Assembly’s Peripheral Portion(s) and Forces at the Boundaries
Interfacial Stresses
Numerical Example
Optimized Design
Optimization Condition
Peripheral Material with a Low Fabrication Temperature
Peripheral Material with a Low Parameter of the Interfacial Shearing Stress
Peripheral Material with a Low Parameter of the Interfacial Shearing Stress and Low Fabrication Temperature
Conclusions
References
Thermal Stresses in a Flip-Chip Design
Background/Incentive
Thermal Stress Model for a Typical Flip-Chip Package Design
Approach
Forces Acting in the Midportion of the Assembly Located at the Design’s Midportion
Peripheral Portions of the Design
Numerical Examples
Design with an Organic Lid: Midportion of the Design
Design with an Organic Lid: Peripheral Portion of the Design
Design with a Copper Lid: Midportion of the Design
Design with a Copper Lid: Peripheral Portions of the Design
Is 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 System
Effect of the Underfill Glass Transition Temperature
Background
Assumptions
Thermally Induced Forces and Interfacial Stresses
Thermally Induced Forces in the Midportion of a Long Flip-Chip/Substrate Assembly
Distributed Thermally Induced Forces
Interfacial Shearing Stresses
Numerical Example
References
Assessed Interfacial Strength and Elastic Moduli of the Bonding Material from Shear-Off Test Data
Background/Incentive
Basic Equation
Solution to the Basic Equation
Interfacial Shearing Stress
Shear Modulus of the Bonding Material
Numerical Example
Possible Characterization of the Solder Material Properties
CONCLUSION
References
Board-Level Dynamic Tests
Background
Drop Testing
Role Of Modeling
Linear Response
Nonlinear Response
Solder Joints
Board-Level Testing
Conclusions
Appendix A: Exact Solution to the Problem of the Nonlinear Dynamic Response of a PCB to the Drop Impact during Board-Level Drop Tests
A.1. Background/Initiative
A.2. Assumptions
A.3. Kinetic and Strain Energies
A.4. Condition of Nondeformability of the PCB Support Contour
A.5. Stress (Airy) Function
A.6. In-plane (membrane) Stresses and Strains
A.7. Parameter of Nonlinearity
A.8. Basic Equation and Its Solution
A.9. Vibration Amplitude
A.10. Effective Initial Velocity
A.11. Nonlinear Frequency
A.12. Bending Moments
A.13. Equivalent Static Loading
A.14. Numerical Example
References
Appendix References
Failure-Oriented-Accelerated-Testing and Multiparametric Boltzmann–Arrhenius–Zhurkov Equation
Accelerated Testing
FOAT, Its Significance, Attributes, and Role
Multiparametric BAZ Equation
Temperature Cycling: Predicted Time-to-failure
Incentive for Mechanical Prestressing of Accelerated Test Specimens
Background/Incentive
Basic Equations
Boundary Conditions
Solutions to the Basic Equations
Constants of Integration
Numerical Example
Accelerated Testing of Solder Joint Interconnections: Incentive for Using a Low-Temperature/Random- Vibrations Bias
Background/Incentive
Methodology
Reduction to Practice
Calculation Procedure
Numerical Example
Testing Facility and Procedure
Conclusion
Possible Next-Generation QT
Appendix A: Elastic Stability of the Specimen as a Whole
Appendix B: Approximate Formula for the Interfacial Peeling Stress and Elastic Stability of the Compressed Component #1
References
Probabilistic Design for Reliability
Background/Incentive
PDfR and its “ten commandments”
Design for Reliability of Electronic Products: Deterministic and Probabilistic Approaches
Some simple PDfR examples
Adequate Heat Sink
Reliable Seal Glass
Extreme Response in Temperature Cycling
The Total Cost of Reliability could be Minimized: Elementary Example
Required Repair Time to Assure the Specified Availability
Background/Incentive
Analysis
Numerical Example
Conclusion
Burn-in Testing of Electronic and Photonic Products: To BIT or not to BIT?
Background/Initiative
Objective
Information Based on the Available BTC
Conclusion
APPENDIX A: RELIABILITY OF AN ELECTRONIC PRODUCT COMPRISED OF MASS-PRODUCED COMPONENTS
A.1. Summary
A.2. Background/Incentive
A.3. Analysis
A.3.1. Analytical Bathtub Curve (Diagram)
A.3.2. Statistical Failure Rate
A.3.3. The Case When Random SFR isNormally Distributed
A.3.4. The Case When Random SFR is Distributed in Accordance with the Rayleigh Law
A.3.5. Probability of Nonfailure
A.4. Conclusions
References
Appendix References
Fiber Optics Systems and Reliability of Solder Materials
Background/Objective
Fiber Optics Structural Analysis (FOSA) in Fiber Optics Engineering: Role and Attributes
Fibers Soldered into Ferrules
Thermal Stresses in a Cylindrical Soldered TriMaterial Body with Application to Optical Fibers
Background/Incentive
Analysis
Numerical Example
Conclusion
References
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