IEEE Transactions on Electron Devices · 2012 · 22 citations · 15 references
EngineeringMaterials EngineeringMaterials ScienceFinite Element AnalysisFinite Element MethodsHeat TransferComputational ThermomechanicsFinite Element FormulationStrain AnalysisStrain EngineeringStress-strain BehaviorThermal StressesBessel FunctionsFinite Element SimulationSiliconThermal ExpansionThermo-mechanical StressThermomechanical StressThermomechanical Stress AnalysisThrough-silicon Vias
The thermoelastic strains are induced by through silicon vias due to the difference of thermal expansion coefficients between the copper ( ~ 18 ppm / °C) and silicon ( ~ 2.8 ppm /°C) when the structures are exposed to a thermal ramp in the process flow. A compact analytic model (Bessel function) of the strain field is obtained using Kane-Mindlin theory, and has a good agreement with the finite-element simulations. The elastic strains in the silicon in the radial direction and angular direction are tensile and compressive, respectively. The linear superposition of the analytic model of a single via can be used in the multi-via configuration. Due to the interaction of vias, the slightly larger errors of strain occur between the two close vias when the linear superposition is used.
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Thermo-mechanical reliability of 3-D ICs containing through silicon vias
Kuan Lu, Xuefeng Zhang, Suk-Kyu Ryu et al. · 2009 · 208 citations
Engineering, Computer Engineering, Electrical Engineering +17