Validated multiphysics simulation of die-scale co-planarity and mass transport limitations in copper pillar electroplating

Abstract

In advanced wafer-level packaging, achieving co-planarity of copper (Cu) pillars is essential for device yield and reliability, yet remains challenging due to non-uniform current distribution and localized mass transport limitations during electroplating. We present an experimentally validated, computationally efficient simulation strategy that couples multi-physics modeling of fluid dynamics, mass transport, and Butler–Volmer kinetics with a novel geometric approximation, enabling full die-scale predictions at a fraction of the computational cost of direct modeling. Complex layouts are partitioned into an N × N grid, with dense bump regions represented as equivalent circular electrodes, allowing accurate resolution of local current density and Cu²⁺ depletion effects. Across multiple layouts, simulated maximum and minimum bump heights deviate from experimental measurements by <1.5 %, confirming the model’s predictive capability. Analysis reveals that non-uniformity is driven by a spatially dependent transition from kinetic control to mass-transport control in densely patterned regions. Requiring only layout geometry as input, the method provides a practical tool for early-stage design screening and process optimization, reducing costly experimental iterations in advanced packaging development.