Phase-field simulation of defect transport, current evolution and piezoelectric response in dielectric and ferroelectric oxides

In this study, we used the phase-field model to study the defect transport, resistance degradation behavior, current-voltage characteristics and piezoelectric responses in a number of representative dielectric and ferroelectric oxides including SrTiO3, BaTiO3, and Pb(Zr1-xTi x)O3. The effects of electric field strength, domain orientations, domain structures as well as grain boundaries on the distribution and evolution of ionic/electronic space charges and leakage currents were systematically investigated.;We developed the electrochemical transport model to study the ionic/electronic space charge profiles and local electric potential distribution at equilibrium state and their evolutions under applied biases in a sandwiched Ni|SrTiO 3|Ni capacitor configuration by solving the coupled transport equations for space charges and Poisson equation for electric potential using the Chebyshev collocation algorithm. We introduced the possibility of polaron-hopping between Ti3+ and Ti4+ at the dielectric/electrode interfaces using the Butler-Volmer equations. The simulated space charge and electric potential profiles at steady state agreed with recent experiment observations. The contribution of ionic transport and polaron-hopping to the resistance degradation based on phase-field simulations and experimental studies were compared and analyzed.;We proposed a model to study the resistance degradation behavior of ferroelectric oxides in the presence of ferroelectric spontaneous polarization by combining the phase-field model of ferroelectric domains and non-linear diffusion equations for ionic/electronic transport. We took into account the non-periodic boundary conditions for solving the electrochemical transport equations and Ginzburg-Landau equations using the Chebyshev collocation algorithm. We considered both single domain configuration and multi-domain structure consisting of 180° and 90° domain walls relative to a thin film BaTiO3 single crystal orientated to the normal of the electrode plates (Ni) in a single parallel plate capacitor configuration. The capacitor was subjected to a dc bias of 0.5V at room temperature. The effect of domain orientations and multi-domain structures on the defect and leakage current evolution was investigated. The simulated field-dependence of characteristic time of degradation was compared with other theoretical model.;Using the model developed above, we further studied current-voltage (I-V) responses in bulk BaTiO3 ferroelectric oxides. The polarization-modulated rectifying I-V characteristics in Cu|BaTiO3|Cu single parallel plate capacitor were studied. The effects of polarization induced metal/ferroelectric interfacial charges, the dopant concentrations and the defect screening levels on the I-V behaviors and rectification ratios were systematically investigated.;We investigated the effect of grain boundary interface of donor-state on defect and leakage current evolution in SrTiO3 constrained by Ni electrodes based on a back-to-back double Schottky barrier model. The formation of depletion regions along the grain boundary acted as barriers to the cross-transport of charge defects. A variety of conditions including the dopant concentration, the depletion width and the number of grain boundaries and their effect on resistance degradation were studied.;Phase-field model was also employed to understand the piezoelectric response of hypothetic single-crystal PbZr1-xTixO3 (PZT). We obtained the dependence of piezoelectric coefficient (d 33) on PbTiO3 compositions (x) near the morphotropic phase boundary (MPB) composition of PZT. The piezoelectric response of single crystal PZT from phase-field simulation, of single crystal based on thermodynamic calculation and of polycrystalline PZT from literatures have been compared and analyzed. The relation between multi-domain structure of the poled PZT single crystal and the enhancement of d33 near the MPB composition was discussed.