Simulation of TSV Protrusion in 3DIC Integration by Directly Loading on Coarse-Grained Phase-Field Crystal Model

Abstract

As thermal management in 3DIC integration becomes increasingly important in advanced semiconductor node processes, novel experimental and modeling approaches are in great demand to reveal the critical material issues involving multiscale microstructures that govern the behavior of through-silicon-via (TSV) protrusion. Here, a coarse-grained phase-field crystal model properly coupled with mechanics through the atomic density field is used to simulate the formation of polycrystalline structures and protrusion of nano-TSVs from the atomic scale. TSVs with different grain structures are directly loaded, and protrusion/intrusion profiles are obtained along with displacement, stress, and strain fields. Thermodynamic driving forces from external loadings and the mismatch of Young’s modulus between adjoining grains as well as detailed displacement and strain distributions are ascribed to control the complex deformation in TSVs. TSVs with sizes up to around 30 nm and an aspect ratio of 4 are successfully investigated, and a further increase in the size and aspect ratio to cover the micrometer range is feasible, which lays down a solid basis toward a multiscale material database for simulation inputs to the design of TSV-based 3DIC integration and relevant electronic design automation (EDA) tools.

Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

“…The Finite element method (FEM) emerged as a particularly suitable framework for solving the APFC model's equations [16,60,77,78], besides being also employed in PFC studies in the first place [79][80][81][82][83]. Indeed, it conveniently discretizes PDEs while exploiting inhomogeneous and adaptive meshes.…”

Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

“…The Finite Element Method (FEM) emerged as a particularly suitable framework for solving the APFC model's equations [16,58,67,68], besides being also employed in PFC studies in the first place [69][70][71][72][73]. Indeed, it conveniently discretizes partial differential equations (PDEs) while exploiting inhomogeneous and adaptive meshes.…”