Markov model describing progressive degradation of local percolation path in thin oxides

Abstract

Time-Dependent Dielectric Breakdown (TDDB) remains a critical reliability challenge in advanced CMOS technologies using thin /High-k oxides. While extensive research focused on the formation of conductive filaments and the physics and statistics of soft breakdown and hard breakdown events, the intermediate wear-out phase — where a localized leakage path gradually increases in conductivity — has not been thoroughly analyzed or modeled. Firstly, this work addresses this gap by experimentally isolating and analyzing the wear-out phase with a Machine learning-assisted analysis, revealing key statistical features of wear-out and its dependence on stress voltage. Secondly, a Monte Carlo-implemented Markov model is used to simulate the localized degradation of a one-defect percolation path by means of a thermally activated defect creation and deactivation/annealing process, governed by an Arrhenius-like transition probability function. Simulations qualitatively reproduce the observed experimental degradation trends, with discrepancies in voltage dependence and initial defect accumulation, highlighting the need for a more nuanced approach, including statistical distributions of atomic bond strengths.