Reliability Physics and Engineering

1 Introduction 2 Materials and Device Degradation 2.1 Material/Device Parameter Degradation Modeling 2.1.1 Material/Device Parameter Decreases With Time 2.1.2 Material/Device Parameter Increases With Time 2.2 General Time-Dependent Degradation Models 2.3 Degradation Rate Modeling 2.4 Delays in the Start of Degradation 2.5 Competing Degradation Mechanisms 3 From Material/Device Degradation to Time-To-Failure 3.1 Time-To-Failure 3.2 Time-To-Failure Kinetics 4 Time-To-Failure Modeling 4.1 Flux-Divergence Impact on Time-To-Failure 4.2 Stress Dependence and Activation Energy 4.3 Conservative Time-To-Failure Models 4.4 Time-To-Failure Modeling Under High Stress References 5 Gaussian Statistics - An Overview 5.1 Normal Distribution 5.2 Probability Density Function 5.3 Statistical Process Control References 6 Time-To-Failure Statistics 6.1 Lognormal Probability Density Function 6.2 Weibull Probability Density Function 6.3 Multimodal Distributions 6.3.1 Multimodal Distribution (Separated In Time) 6.3.2 Mixed Multiple Failure Mechanisms References 7 Failure Rate Modeling 7.1 Device Failure Rate 7.2 Average Failure Rate 7.2.1 Lognormal Average Failure Rate 7.2.2 Weibull Average Failure Rate 7.3 Instantaneous Failure Rate 7.3.1 Lognormal Instantaneous Failure Rate 7.3.2 Weibull Instantaneous Failure Rate 7.4 Bathtub Curve 7.5 Failure Rate for Electronic Devices References 8 Accelerated Degradation 8.1 Metastable States 8.2 Impact of Temperature on Degradation Rate 8.3 Free-Energy of Activation 8.4 Impact of Stress and Temperature on Degradation Rate 8.4.1 Real Versus Virtual Stresses 8.4.2 Impact of Stress on Materials/Devices 8.5 Accelerated Degradation Rates References 9 Acceleration Factor Modeling 9.1 Acceleration Factor 9.2 Power-Law Versus Exponential Acceleration 9.3 Cautions Associated with Accelerated Testing 9.4 Conservative Acceleration Factors References 10 Ramp-To-Failure Testing 10.1 Ramp-To-Failure Testing 10.2 Linear Ramp-Rate 10.2.1 Linear Ramp with Exponential Acceleration 10.2.2 Linear Ramp with Power-Law Acceleration 10.3 Breakdown/Rupture Distributions 10.4 Cautions Associated With Ramp-To-Failure Testing 10.5 Transforming Breakdown/Rupture Distributions Into Constant-Stress Time-To-Failure Distributions 10.5.1 Transforming Breakdown/Rupture Distribution Time-To-Failure Distribution Using Exponential Acceleration 10.5.2 Transforming Breakdown/Rupture Distribution to Time-To-Failure Distribution Using Power-Law Acceleration 10.6 Constant-Stress Lognormal Time-To-Failure Distributions From Ramp Breakdown/Rupture Data 10.6.1 Exponential Acceleration 10.6.2 Power-Law Acceleration 10.7 Constant-Stress Weibull Time-To-Failure Distributions From Ramp Breakdown/Rupture Data 10.7.1 Exponential Acceleration 10.7.2 Power-Law Acceleration References 11 Time-To-Failure Models for Selected Failure Mechanisms in Integrated Circuits 11.1 Electromigration (EM) 11.2 Stress Migration (SM) 11.2.1 SM in Aluminum Interconnects 11.2.2 SM in Copper Interconnects 11.3 Corrosion 11.3.1 Exponential Reciprocal-Humidity Model 11.3.2 Power-Law Humidity Model 11.3.3 Exponential Humidity Model 11.4 Thermal-Cycling/Fatigue Issues 11.5 Time-Dependent Dielectric Breakdown (TDDB) 11.5.1 Exponential E-Model 11.5.2 Exponential 1/E - Model 11.5.3 Power-Law Voltage V-Model 11.5.4 Exponential - Model 11.5.5 Which TDDB Model to Use 11.5.6 Complementary Electric-Field and Current-Models 11.6 Mobile-Ions/Surface-Inversion 11.7 Hot-Carrier Injection (HCI) 11.8 Negative-Bias Temperature Instability (NBTI) References 12 Time-To-Failure Models for Selected Failure Mechanisms In Mechanical Engineering 12.1 Molecular Bonding in Materials 12.2 Origin of Mechanical Stresses in Materials 12.3 Elastic Behavior of Materials 12.4 Inelastic/Plastic Behavior of Materials 12.5 Important Defects Influencing Material Properties 12.5.1 Vacancies 12.5.2 Dislocations 12.5.3 Grain Boundaries 12.6 Fracture Strength of Materials 12.7 Stress Relief in Materials 12.8 Creep-Induced Failures 12.8.1 Creep Under Constant-Load/Stress Conditions 12.8.2 Creep Under Constant-Strain Conditions 12.9 Crack-Induced Failures 12.9.1 Stress Raisers/Risers at Crack Tips 12.9.2 Strain-Energy Release Rate 12.9.3 Fast Fracture/Rupture 12.10 Fatigue-Induced Failures 12.10.1 Fatigue for Materials (No Pre-Existing Cracks) 12.10.2 Low-Cycle Fatigue 12.10.3 High-Cycle Fatigue 12.10.4 Fatigue for Materials (With Pre-Existing Cracks) 12.11 Adhesion Failures 12.12 Thermal-Expansion Induced Failures 12.12.1 Thermal Expansion 12.12.2 Constrained Thermal Expansion 12.12.3 Thermal-Expansion Mismatch 12.12.4 Thin Films on Thick Substrates 12.13 Corrosion-Induced Failures 12.13.1 Dry Oxidation 12.13.2 Wet Oxidation 12.13.3 Impact of Stress on Corrosion Rates References 13 Conversion of Dynamical Stresses Into Effective Static Values 13.1 Effective Static-Stress Equivalent Values 13.2 Effective Static-Stress Equivalent Values When Using Power-Law TF Models 13.3 Effective Static-Stress Equivalent Values When Using Exponential TF Models 13.4 Conversion Of A Dynamical Stress Pulse Into A Rectangular Stress Pulse Equivalent 13.4.1 Effective Rectangular Pulse Stress-Equivalent Values for Power-Law TF Models 13.4.2 Effective Rectangular Pulse Stress-Equivalent for Exponential TF Models 13.4.3 Numerical Integration 13.5 Effective Static-Temperature Equivalents 13.6 Mission Profiles 13.7 Avoidance of Resonant Frequencies 14 Increasing the Reliability of Device/Product Designs 14.1 Reliability Enhancement Factor 14.2 Electromigration Design Considerations 14.3 TDDB Design Considerations 14.4 NBTI Design Considerations 14.5 HCI Design Considerations 14.6 Surface Inversion Design Considerations 14.7 Creep Design Considerations 14.7.1 Creep in Rotors 14.7.2 Creep in Pressurized Vessels 14.7.3 Creep in Leaf Springs 14.7.4 Stress Relaxation in Clamps/Fasteners 14.8 Fatigue Design Considerations 14.8.1 Fatigue in Storage Vessels 14.8.2 Fatigue in Integrated Circuits 15 Screening 15.1 Breakdown/Strength Distribution for Materials and Devices 15.2 Impact of Screening Stress on Breakdown Strength 15.2.1 Screening Using Exponential TF Model 15.2.2 Screening Using Power-Law TF Model 15.3 Screening Effectiveness 15.3.1 Screening Effectiveness Using Exponential TF Model 15.3.2 Screening Effectiveness Using Power-Law TF Model 16 Heat Generation and Dissipation 16.1 Device Self-Heating and Heat Transfer 16.1.1 Energy Conservation 16.1.2 General Heat Flow Equation 16.2 Steady-State Heat Dissipation 16.3 Effective Thermal Resistance 16.4 General Transient Heating and Heat Dissipation 16.4.1 Effective Thermal Resistance Revisited 16.4.2 Heat Capacity 16.5 Modeling Dynamical Heat Generation and Dissipation 16.5.1 Thermal Relaxation 16.5.2 Thermal Rise with Constant Input Power 16.5.3 Thermal Rise and Relaxation with Single Power Pulse 16.5.4 Thermal Rises and Relaxations with Periodic Power Pulses 16.6 Convection Heat Transfer 16.7 Radiation Heat Transfer 16.8 Entropy Changes Associated With Heat Transfer References 17 Sampling Plans and Confidence Intervals 17.1 Poisson Distribution 17.1.1 Poisson Probability for Finding Defective Devices 17.1.2 Poisson Sample-Size Requirements 17.2 Binomial Distribution 17.2.1 Binomial Probability for Finding Defective Devices 17.2.2 Binomial Sample-Size Requirements 17.3 Chi-Square Distribution 17.3.1 Chi-Square Confidence Intervals 17.3.2 Chi-Square Distribution for Defect Sampling 17.4 Confidence Intervals for Characteristic Time-To-Failure and Dispersion Parameters 17.4.1 Normal Distribution Confidence Intervals 17.4.2 Lognormal Distribution Confidence Intervals 17.4.3 Weibull Distribution Confidence Intervals 17.4.4 Chi-Square Distribution Confidence Intervals Average Failure Rates References Appendix A: Useful Conversion Factors Appendix B: Useful Physical Constants Appendix C: Useful Rough Rules-Of-Thumb Appendix D: Useful Mathematical Expressions Appendix E: Useful Differentials and Definite Integrals Appendix F: Free-Energy Appendix G: t(1-alpha/2,nu) Distribution Values Appendix H: chi2(P,nu) Distribution Values Index