Predictive Modeling of TCV-Cu Protrusion Under Thermal Cycling

Abstract

Through-ceramic-via copper (TCV-Cu) in direct-plated-copper (DPC) substrates can protrude during thermal cycling, threatening package planarity and interconnect reliability. This work develops a coupled thermo-mechanical framework that links transient temperature histories to out-of-plane deformation via a calibrated creep law for electroplated Cu. A 3-D finite-element model resolves the via shoulder and Cu/ceramic corner while enforcing realistic interface constraints and elastic heterogeneity. Creep parameters are identified by inverse optimization against 32 ramp-dwell thermal profiles using weighted least squares reflecting profilometer repeatability and registration uncertainty. The residual plots show no systematic bias, and leave-one-profile-out cross-validation confirms predictive robustness. Mechanistic analysis reveals stress-creep synergy during heating produces CEEQ pulses and peak protrusion, whereas high-temperature dwells and slow cooling govern residual buildup. A persistent ring-like stress hotspot forms at the via shoulder and Cu/ceramic interface corner. Sensitivity studies indicate faster ramps increase peak but reduce residual protrusion, while longer dwells amplify residuals; array pitch and modulus contrast modulate hotspot intensity. The results yield actionable process-window guidance for ramp rate, dwell duration, and layout, providing a compact, data-validated predictor for TCV-Cu protrusion in advanced packaging.