Phase-Field-Crystal Model: A Tool for Probing Atoms in TSV

Abstract

With the downscaling of interconnection size, material microstructures are becoming more and more significant in 3D through-silicon via (TSV)-based ICs. To consider material behavior and properties at micro/nanoscale for reliability analysis, robust simulation methods considering microstructures are necessary. This chapter introduces the phase-field-crystal (PFC) model, which resolves materials on atomic length scale and diffusive time scale, and discusses its potential to reveal time-dependent microstructures in TSVs at the nanoscale. PFC models are derived by approximations of system free energy based on the classical density functional theory (CDFT). Approximating the correlation functions using polynomial of different orders can describe various crystal structures, e.g., body-centered cubic (BCC) and face-centered cubic (FCC). Moreover, physical fields occurring in the TSV-based 3D integrations, e.g., strain field, magnetic field and electric field, can also be coupled into the PFC models to simulate the responses of microstructures. Finally, PFC models for TSV-based applications, including filler materials such as copper, tungsten and graphene, are briefly introduced.