Computational Modeling of Polarization Coupling in Lead-Free Ferroelectric Bilayers BaTiO₃/BiFeO₃ and Hf₀.₅Zr₀.₅O₂/BiFeO₃

Ferroelectric multilayers offer versatile opportunities for tuning dielectric and electronic properties, but they also present challenges in understanding electrostatic and mechanical interactions at interfaces. A computational investigation of lead-free ferroelectric bilayers BaTiO₃/BiFeO₃ (BTO/BFO) and Hf₀.₅Zr₀.₅O₂/BiFeO₃ (HZO/BFO) was conducted at 300 K by using combined Landau–Ginzburg–Devonshire and semiconductor models. Coupled nonlinear equations describing electrostatic potential, charge density, polarization, and field distribution were solved in MATLAB for 120 nm layers with 180° head-to-tail domains. The model predicts spontaneous polarizations of 52.43 µC cm⁻² (HZO), 24.37 µC cm⁻² (BTO), and 75.77 µC cm⁻² (BFO), with corresponding permittivity of 2.526×10⁻¹⁰ F m⁻¹, 9.033×10⁻¹⁰ F m⁻¹, and 5.236×10⁻¹¹ F m⁻¹, respectively. Simulations of BTO/BFO indicate strong interfacial polarization coupling and nonlinear dielectric response, while HZO/BFO exhibits stable polarization switching under external bias. Hysteresis and permittivity–field relationships analyzed in Mathematica reveal asymmetric switching behavior characteristic of bilayer systems. The simulations predict interface-controlled ferroelectric phenomena and guide experimental investigations involving thin film growth, structural analysis, and ferroelectric measurements.