Numerical Simulation And Design Of Experiments Of Thermo-mechanical Stress For Through Silicon Vias Interconnect

Through silicon vias (TSVs) technology, as a key technology, has been widely usedin microelectromechanical system of three-dimensional (3D) chip integration because oftheir advantages of high device speed and small package size. Copper interconnect lineis one of typical interconnect lines in the TSV technology. Thermal-mechanical coupledconstitutive law including strain gradient is established first and then emedded into theABAQUS software with User-defined Material Mechanical Behavior for thermal stressanalysis. The parameterized finite element model, the design of experiments methodand numerical optimization techniques are proposed to study the TSV structureoptimimzation based on the established constitutive law. The main work andconclusions are as follows:(1) The thermal stress and strain distributions of the full-filled copper interconnectand copper interconnect with Polymer filling are investigated, the result show that bothpotential failure occurs in the corner interface between copper and other materials,where the thermal stress exceeds the yield strength of copper. Compared to thefull-filled copper TSV interconnect, the TSV interconnect with Polymer filling morelikely fail due to thermal expansion coefficient mismatch.(2) Thermal-mechanical coupled constitutive law including strain gradient whichemedded into the ABAQUS software with User-defined Material Mechanical Behavioris used on thermal induced stress analysis in TSV interconnect. Meanwhile, the resultswhich compared with the idealized elastic-plastic interconnect model show that axialstress is in good agreement, and the analytical solution obtained radial stress is muchsmaller. The different radius and scaling of the copper-filled TSV interconnect, sizeeffect is significant in the center and interface at the top, thermal stress significantlyincrease when the feature size of TSVs close to sub-micron. The radius of TSVs has asignificant impact on Hydrostatic stress, when via radius is smaller than10μm, largerHydrostatic stress were found in the center location of TSVs. Induced voids may appearalong the center of the TSVs which agreement with experimental results. The thermalstress is closely related to the relative ratio of via depth to via radius. Further analysis show that the stress concentration regions change with the aspect ratio increasing. Whenaspect ratio is greater than10, the stress concentration area migrates to the centerlineregion, at the same time the thermal stress increases significantly.(3) Design of experimental and single design response optimization areinvestigated for the designs of the TSV interconnect structure based on parameterizedfinite element model. Material Intrinsic effect based on the strain gradient which has asignificant effect on the thermo-mechanical properties of TSV interconnect must bedesigned with sufficient attention. The optimization results show that, in the case of thesame initial model, different optimization methods will receive different optimalsolution. The choice of optimization technology has a significant impact on the results,because the structural optimization of TSVs with multi-peak characteristics, the designspace of TSV interconnects is large.