Numerical Simulation and Mechanism Analysis of Through-Silicon Via (TSV) Filling Using an Arbitrary Lagrange-Eulerian (ALE) Method

Abstract

A physicochemical model for electroplating copper in through-silicon vias (TSVs) is proposed to investigate the filling mechanism. Finite element method (FEM) and multifrontal massively parallel sparse direct solver (MUMPS) are employed to solve the numerical model. The motion of the fluid/solid interface (electrolyte/metal interface) is tracking using the Arbitrary Lagrange-Eulerian (ALE) method. Compared to other models, the diffusion, adsorption, desorption and incorporation of the additives (accelerator and suppressor) and ions (cupric ion and chloride ion) are included in this model. Simultaneously, the deactivation of the accelerator and the process parameters for copper deposition are also considered in the model. Numerical simulations are performed for filling the Ø 40 μm × 140 μm blind vias. The "Δ", "V", "8", and extreme bottom-up filling models are achieved by verifying the component of plating baths. A good match is achieved qualitatively between the simulated profiles and the real-world filling experiments.