First-principles modeling of ferroelectric capacitors via constrained displacement field calculations

First-principles modeling of ferroelectric capacitors presents several technical challenges due to the coexistence of metallic electrodes, long-range electrostatic forces, and short-range interface chemistry. Here we show how these aspects can be efficiently and accurately rationalized by using a finite-field density-functional theory formalism in which the fundamental electrical variable is the displacement field D. By performing calculations on model Pt/BaTiO₃/Pt and Au/BaZrO₃/Au capacitors we demonstrate how the interface-specific and bulk-specific properties can be identified and rigorously separated. Then, we show how the electrical properties of capacitors of arbitrary thickness and geometry (symmetric or asymmetric) can be readily reconstructed by using such information. Finally, we show how useful observables such as polarization and dielectric, piezoelectric, and electrostrictive coefficients are easily evaluated as a byproduct of the above procedure. We apply this methodology to elucidate the relationship between chemical bonding, Schottky barriers and ferroelectric polarization at simple-metal/oxide interfaces. We find that BO₂-electrode interfaces behave analogously to a layer of linear dielectric put in series with a bulklike perovskite film while a significant nonlinear effect occurs at AO-electrode interfaces.