Preface
1 Introduction
1.1 Sources of Variations
1.1.1 Process Variations
1.1.2 Environmental Variations
1.1.3 Modeling Variations
1.1.4 Other Sources of Variations
1.2 Components of Variation
1.2.1 Inter-die Variations
1.2.2 Intra-die Variations
1.3 Impact on Performance
2 Statistical Models and Techniques.
2.1 Monte Carlo Techniques
2.1.1 Sampling Probability Distributions
2.2 Process Variation Modeling
2.2.1 Pelgrom's Model
2.2.2 Principal Components Based Modeling
2.2.3 Quad-Tree Based Modeling
2.2.4 Specialized Modeling Techniques
2.3 Performance Modeling
2.3.1 Response Surface Methodology
2.3.2 Non-Normal Performance Modeling
2.3.3 Delay Modeling
2.3.4 Interconnect Delay Models
2.3.5 Reduced-Order Modeling Techniques
3 Statistical Timing Analysis
3.1 Introduction
3.2 Block-Based Timing Analysis
3.2.1 Discretized Delay PDFs
3.2.2 Reconvergent Fanouts
3.2.3 Canonical Delay PDFs
3.2.4 Multiple Input Switching
3.3 Path-Based Timing Analysis
3.4 Parameter-Space Techniques
3.4.1 Parallelepiped Method
3.4.2 Ellipsoid Method
3.4.3 Case-File Based Models for Statistical Timing
3.5 Bayesian Networks
4 Statistical Power Analysis
4.1 Overview
4.2 Leakage Models
4.3 High-Level Statistical Analysis
4.4 Gate-Level Statistical Analysis
4.4.1 Dynamic Power
4.4.2 Leakage Power
4.4.3 Temperature and Power Supply Variations
5 Yield Analysis
5.1 High-Level Yield Estimation
5.1.1 Leakage Analysis
5.1.2 Frequency Binning
5.1.3 Yield Computation
5.2 Gate-Level Yield Estimation
5.2.1 Timing Analysis
5.2.2 Leakage Power Analysis
5.2.3 Yield Estimation
5.3 Supply Voltage Sensitivity
6 Statistical Optimization Techniques
6.1 Optimization of Process Parameters
6.1.1 Timing Constraint
6.1.2 Objective Function
6.1.3 Yield Allocation
6.2 Gate Sizing
6.2.1 Nonlinear Programming
6.2.2 Lagrangian Relaxation
6.2.3 Utility Theory
6.2.4 Robust Optimization
6.2.5 Sensitivity-Based Optimization
6.3 Buffer Insertion
6.3.1 Deterministic Approach
6.3.2 Statistical Approach
6.4 Threshold Voltage Assignment
6.4.1 Sensitivity-Based Optimization
6.4.2 Dynamic Programming
References
Index