Analysis of Dielectric Prebreakdown of High-k Stacking Polycrystalline MIM by Stochastic Trap-Clusters Growing and Percolation-Based Transportation

We propose a method to analyze the dielectric prebreakdown (DB) which is based on: 1) charge transport; 2) stochastic trap-cluster generations; and 3) percolation in a metal–insulator–metal (MIM) stacked polycrystalline high-
${k}$
capacitor of TiN–TiO2–ZrO2–TiO2–TiN. We assume that measured dielectric leakage current until the breakdown is comprised of transient transports under static fields: direct tunneling, trap-assisted tunneling (TAT), and inelastic tunneling. The charge transports induce trap generation and formation of stochastic trap-cluster. The generated trap-cluster amplified the stress-induced leakage current (SILC). One of the clusters can be expanded and electrically link the cathode and anode throughout the dielectric to form a critical path. We can model the current through this path analytically by partition function and percolation. By careful analysis of measured time-dependent dielectric leakage currents, we found that prebreakdown is most related to SILC and inelastic tunneling at a low electric field (< 4 MV/cm).