Thermal Stress and Strain in Microelectronics Packaging

'1. Thermomechanics for Electronics Packaging.- 1.1 Introduction.- 1.2 Fundamental Equations of Thermoelasticity for Electronics Packaging.- 1.2.1 Assumptions.- 1.2.2 Fundamental Equations of Thermoelasticity.- 1.3 Governing Equations of Thermoelasticity for Electronics Packaging.- 1.3.1 Coupled Thermoelasticity.- 1.3.2 Coupled-Quasi-Static Thermoelasticity.- 1.3.3 Uncoupled-Quasi-Static Thermoelasticity.- 1.3.4 Theory of Isotropic Thermal Stresses.- 1.3.5 Temperature-Dependent Strain Energy Density.- 1.4 Boundary Value Problems for Electronics Packaging.- 1.5 Thermoelastic Example Problems for Electronics Packaging.- 1.5.1 Chip on a Semi-infinite Substrate.- 1.5.2 Chip on a Finite Substrate.- 1.6 Analysis of Stress.- 1.6.1 Three-dimensional Stress State.- 1.6.2 Two-dimensional Stress State.- 1.7 Analysis of Strain.- 1.7.1 Three-dimensional Strain State.- 1.7.2 Two-dimensional Strain State.- 1.8 Geometric Nonlinearity.- 1.8.1 Strain Components in Lagrangian Coordinates.- 1.8.2 Strain Components in Eulerian Coordinates.- 1.8.3 Large-Deflection Example Problem for Electronics Packaging.- 1.9 Material Nonlinearity.- 1.9.1 Hyperelasticity.- 1.9.2 Plasticity.- 1.9.3 Viscoelasticity.- 1.9.4 Viscoplasticity.- 1.9.5 Creep.- 1.10 Summary and Recommendations.- References.- 2. Thermal Expansivity and Thermal Stress in Multilayered Structures.- 2.1 Introduction.- 2.2 Analysis.- 2.3 Spreadsheet Calculation of Stress in N Layers.- 2.3.1 The Axisymmetric Assumption.- 2.4 Conclusion.- References.- 3. Thermal Stresses in Anisotropic Multilayered Structures.- 3.1 Introduction.- 3.2 Elasticity of an Orthotropic Layer Referred to the Global Coordinates of the Laminate.- 3.3 Thermal Stress Problem of a Rectangular Laminate.- 3.4 Stress Functions: Interface and Boundary Conditions.- 3.5 Generalized Plane Deformation of a Laminated Strip.- 3.6 The Principle of Complementary Virtual Work.- 3.7 Polynomial Approximations of the Stress Functions.- 3.8 Differential Equations and Boundary Conditions for the Coefficient Functions.- 3.9 Determination of the Deformation Parameters B, C, and O.- 3.10 Solution of the Eigenvalue Problem.- 3.11 Isotropic and Specially Orthotropic Laminates.- 3.12 Thermal Stress in the Vicinity of a Curved Free Edge.- 3.13 Layered Beams.- 3.14 Refinement and Regression of the Polynomial Approximation.- 3.15 Measures of the Criticality of the Interlaminar Stresses.- 3.16 Examples: Three-Layer Anisotropic Laminates and Isotropic Beams.- 3.17 Concluding Remarks.- Nomenclature.- Appendix 3A.- References.- 4. Transient Thermal Stresses in Multilayered Devices.- 4.1 Introduction.- 4.2 Transient Heat Transfer Solutions.- 4.3 Variational Principle for the Thermoelasticity Problem.- 4.4 Asymptotic Thermal Stress Distribution Near Free Edge.- 4.4.1 Homogeneous Asymptotic Solution.- 4.4.2 Particular Asymptotic Solution.- 4.5 Formulations of Hybrid Singular Element.- 4.5.1 Formulation.- 4.5.2 Verification of the Special Hybrid Element.- 4.6 Green's Function Integration Method.- 4.7 Transient Behaviors of Multilayered Devices.- 4.8 Design Based on Transient Thermal Stresses.- 4.8.1 Crack Initiation.- 4.8.2 Thermal Fatigue.- 4.9 Discussion and Summary.- References.- 5. Temperature Dependence of Thermal Expansion of Materials for Electronics Packages.- 5.1 Introduction.- 5.2 Theory.- 5.3 Experimental.- 5.4 Results and Discussion.- 5.4.1 Ceramics.- 5.4.2 Metals.- 5.4.3 Sandwiches (Cu-Invar-Cu and Cu-Mo-Cu).- 5.4.4 Organic Boards and Packages.- 5.5 Summary.- References.- 6. Thermal Stress Considerations in Die-Attachment.- 6.1 Introduction.- 6.2 Properties of Die-Attach Materials for Various Applications.- 6.3 Analytical Consideration of Thermal Stresses in Die-Attach.- 6.3.1 Timoshenko and Other Models.- 6.3.2 Calculation of Maximum Die Stress.- 6.3.3 Suhir's Model.- 6.3.4 Numerical Calculation of Die Stress.- 6.4 Die Stress Measurement.- 6.4.1 Pie