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
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