First‐Principles and Deep Potential Study of Dielectric Properties and Doping Mechanisms in BaTiO ₃ ‐Based Perovskites

ABSTRACT

This study presents a comprehensive theoretical investigation of the electronic structure, temperature‐dependent dielectric properties, and defect‐mediated doping mechanisms in BaTiO ₃ ‐based perovskite ceramics, employing density functional theory (DFT) calculations integrated with deep neural network potential molecular dynamics simulations. First‐principles calculations using the Vienna Ab initio Simulation Package (VASP) with the GGA+U methodology ( U _eff = 4.2 eV for Ti 3d states) provided accurate structural parameters, electronic band structures, and defect formation energies. A high‐fidelity deep potential was constructed using the DeePMD‐kit framework based on 15 247 DFT‐calculated configurations, achieving exceptional accuracy with energy RMSE of 0.87 meV/atom and force RMSE of 115 meV/Å. Critically, we demonstrate that conventional VASP/DFPT calculations on small 2 × 2 × 2 supercells severely underestimate dielectric constants ( ε _r ≈ 120 for pure BaTiO ₃ ), while large‐scale deep potential molecular dynamics on 10 × 10 × 10 supercells (5000 atoms) yields values ( ε _r ≈ 2100 at room temperature, 298 K) in quantitative agreement with experiments (1700–2000), validating the necessity of large‐scale simulations for accurate dielectric property predictions. The computational results reveal fundamentally distinct doping mechanisms: acceptor doping with Mg ²⁺ (1.5 mol% at Ti‐sites) creates [Mg ^″ _Ti −V _O ^•• ] defect‐dipole complexes with a binding energy of 0.53 eV, inducing compositional heterogeneity that transforms the sharp first‐order ferroelectric transition into a diffuse phase transition, yielding a room‐temperature dielectric constant of ε _r ≈ 3400 (at 298 K) and a temperature coefficient of capacitance (TCC) of approximately ±12% across the X8R evaluation range, approaching X8R compliance. Donor doping with La ³⁺ (2 mol% at Ba‐sites) raises the room‐temperature permittivity to ε _r ≈ 3800 and enhances the peak dielectric constant but preserves the sharp Curie transition with TCC exceeding +200%, failing X8R compliance. The amphoteric dopant Y ³⁺ exhibits 72% B‐site versus 28% A‐site occupancy (Δ E _site = +0.35 eV), giving a room‐temperature dielectric constant of ε _r ≈ 3100, while producing a broadened but insufficiently suppressed peak with TCC of approximately +35% near the diffuse maximum, also exceeding X8R limits at this concentration.