A multivariate parameter analysis of copper pillars eases the design of denser interconnects

Abstract

Electronic packaging increasingly aims at copper pillars as an interconnect concept, because of their benefits for fine pitches, high aspect ratios, high electromigration stability and excellent thermal conductivity. The thermal expansion and high stiffness of the pillars remains a design challenge when building-up more copper volume close to the silicon die. Specific pillar geometries and structured underfills have been suggested but included only few parameter variations. To gain profound insight into the thermo-mechanical aspects of copper pillars we present a parametric finite element approach and an according multivariate analysis of the design space. We chose a 3D slice model to represent a copper pillar matrix and varied height, width and thickness at a constant pitch to consider different aspect ratios and cross sections, and vary the material's CTE and Young's modulus. The general assumption of aiming higher columns without underfill as the most compliant design when controlling for BEoL layer thickness must be rejected. If exploiting the multivariate design space wholly, processing steps may be eliminated, such as structuring an underfill layer. Tailoring the CTE may be used to lower the stress level for a desired aspect ratio, and the ratio of Cu volume to total pillar layer volume should be considered. To accommodate the display of multivariate stress results we propose an appropriate small multiple visualization.