Zone-Based Thermo-Mechanical Gradient Mapping in Cu–Cu Bonded 3D Stacked Die Packages for Reliability Analysis
摘要
In vertically stacked die architectures with direct Cu–Cu bonding, localized mechanical and thermal gradients play a critical role in interconnect reliability under thermal cyclingThermal cycling. Traditional global warpage or average energy metrics often fail to capture spatial amplification effects that drive early failures. This study introduces a zone-based thermo-mechanical gradient framework for a 3D stacked die structure with two siliconSilicon dies connected by a 35 × 35 copper pillar array. Copper pillar height (10–30 µm) is parametrically varied to assess its influence on stress distribution and energy localization under JEDEC JESD22-A104D thermal cyclingThermal cycling. The array is segmented into center, mid-array, and edge zones, reflecting distinct constraint conditions. Stress Amplification Index, Strain Localization Index, and Energy Gradient Index are applied to quantify deviations from global behavior. The results provide insight into height-dependent gradient transitions, supporting interconnect geometry optimization and layout-aware design for advanced Cu–Cu bonded packaging in next-generation electronics.