Electrical TEG-Based Monitoring of Metal Diffusion and Reaction-Interlayer Formation in Oxide Dielectrics Using Physics-Informed XGBoost Modeling

Metal atoms or ions originating from interconnects, electrodes, or diffusion-barrier layers can migrate into oxide dielectrics during thermal annealing, causing insulation degradation, leakage-path formation, capacitance variation, and interfacial reaction. This work proposes an electrical test-element-group (TEG)-based monitoring framework that jointly evaluates metal diffusion and reaction-interlayer formation in oxide dielectrics. A Fick–Arrhenius diffusion model is used to calculate a continuous metal concentration profile, while a parabolic reaction model describes the growth of an interfacial reaction layer. The concentration profile and reaction-layer thickness are then coupled to integral resistance and series-capacitance models for adjacent-electrode resistance TEGs and vertical capacitance TEGs, respectively. A physics-informed simulation dataset was generated over a broad range of thermal, material-library, and geometry parameters, and measurement uncertainty was introduced to emulate inline electrical test conditions. XGBoost regression and classification models were then trained to inversely extract the 1% diffusion front, reaction-interlayer thickness, and process-risk class from the simulated electrical responses. With a calibrated material-library feature set, the model achieved an R2 of 0.959 for diffusion-front extraction, an R2 of 0.802 for interlayer-thickness extraction, and a risk-classification accuracy of 93.86%. The results show that resistance TEGs mainly capture lateral conductive-path formation, whereas capacitance TEGs are more sensitive to vertical interlayer formation and dielectric degradation. The proposed framework provides a non-destructive route for monitoring diffusion- and reaction-induced process risks using inline electrical measurements. The present work is based on model-generated datasets; material-specific deployment requires calibration using SIMS, TEM/EDS, XPS, C–V, I–V, or reference TEG data.