About the Author ix
Preface xi
1 Basics of Semiconductor 1
1.1 Development of Semiconductors 1
1.2 Analysis of Semiconductors Materials 5
2 Basics of Polymer Materials 9
2.1 Polymer Material 9
2.2 Types and Classification of Polymer Materials 10
2.3 General Properties of Polymer Materials 12
2.4 Summary 13
3 Basics of Elastic Theory 15
3.1 Elasticity 15
3.2 Stress and Strain 15
3.3 Finite Element Method Analysis (FEM Analysis) 16
3.4 Governing Equation of Elastic Body 18
3.5 Law of Elastic Breakage 19
3.6 Plane Stress and Plane Strain 21
4 Stress Evaluations with Defects 23
4.1 Difference from Strength of Materials 23
4.2 Stress Concentration and Stress Intensity Factor 24
5 Basics of Viscoelasticity 27
5.1 About Viscoelasticity 27
5.2 Elasticity, Viscosity, and Viscoelasticity 28
5.3 Stress and Strain Response 29
5.4 Mechanical Model Representing Viscoelastic Properties 32
5.5 Conceptual Formula for Creep and Stress Relaxation 35
5.6 Master Curve and Time-Temperature Conversion Rule 38
5.7 Approximation of Master Curve 39
5.8 Superposition Principle and Basic Equations 40
5.9 Simple Model of Generating Thermal Stress and Strain 41
6 Measurement of Viscoelastic Properties 43
6.1 Dynamic Viscoelasticity 43
6.2 Measurement Method 43
6.3 Complex Modulus and Mechanical Model 44
6.4 Dispersion and Absorption by Frequency 46
6.5 Actual Measurement Example 48
7 Design Issues of LSI Packages 49
7.1 Introduction 49
7.2 Trends and Issues of LSI Packages 51
8 Validity of Viscoelastic Analysis 55
8.1 Introduction 55
8.2 Structure of Laminated Body 56
8.3 Analysis Method 61
8.4 Cooling Experiment of Laminated Body 61
8.5 Analysis Results and Experimental Values 63
8.6 Conclusion 67
9 Application to CSP-μBGA 69
9.1 Introduction 69
9.2 Structure and Modeling of CSP-μBGA 69
9.3 Material Property Values Used for Analysis 70
9.4 Material and Structure Optimization Design by VESAP Analysis 73
10 Thermal Stress and Warpage Behavior During Cooling Process of Three-Layer Laminate 79
10.1 Introduction 79
10.2 Structure of LSI Package 79
10.3 Three-Layer Viscoelastic Laminate Model 80
10.4 Elucidation of Warpage Deformation Behavior by VESAP Analysis 81
11 Warp Deformation Behavior From Heating to Cooling 91
11.1 Introduction 91
11.2 Two-Layer Laminate With Epoxy Resin/FR-4 Substrate 92
11.3 Two-Layer Laminate with Epoxy Resin/Steel 101
11.4 Three-Layer Laminate with Steel/Epoxy Resin/Printed Board 104
11.5 Analysis Experiment of Four-Layer Laminate 108
12 Deformation Prediction Method Considering Curing Shrinkage of Resin 119
12.1 Introduction 119
12.2 Examination the Procedure and the Way of Thinking 120
12.3 Contents of VESAP Analysis 122
12.4 Simple Prediction Formula for Calculating Curing Warpage 123
12.5 Warp Deformation Experiment 128
12.6 Theoretical Prediction of Warpage Deformation due to Hardening and Heat 130
13 Changes in Material Properties and Deformation Behavior Due to Thermal Degradation 133
13.1 Purpose and Background 133
13.2 Experimental Case I 134
13.3 Experiment of Case II 139
14 Simple Evaluation Method for Deformation of Viscoelastic Body 147
14.1 Introduction 147
14.2 Derivation of Simple Formula 147
14.3 Practical Method 151
14.4 Determining the Curing Temperature of the Resin 152
14.5 Effect of Epoxy Resin Thickness on Heat Generation Temperature 153
14.6 Conclusion 156
15 Effect of Cooling Rate on Warpage Behavior of Laminates 159
15.1 Warp Deformation Experiment 159
15.2 VESAP Analysis 160
15.3 Results and Considerations 163
15.4 Final Warp Deformation and Residual Warp Deformation 166
15.5 Estimation Mechanism Between Cooling Rate and Deformation of Laminate 168
15.6 Conclusion 169
Appendix A Development of Viscoelastic Analysis Software (VESAP) 171
A.1 Development Needs and Concepts 171
A.2 Derivation of Basic Formula for Analysis 172
A.3 Contents of the Developed VESAP Software 175
Bibliography 179
Index 185
