Phase Field Simulation of Domain Switching Dynamics in Multi-axial Lead Zirconate Titanate Thin Films

Open Access
Britson, Jason Curtis
Graduate Program:
Materials Science and Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
March 04, 2015
Committee Members:
  • Long Qing Chen, Dissertation Advisor
  • Clive A Randall, Committee Member
  • Venkatraman Gopalan, Committee Member
  • Michael T Lanagan, Special Member
  • Ferroelectrics
  • Phase Field
  • Domain Switching
  • Thin Films
  • PZT
The defining characteristic of ferroelectric materials is their ability to be switched between energetically equivalent polarization states. This behavior has led to an interest in ferroelectrics for a wide range of bulk and thin film applications such as mechanical actuators and ferroelectric random access memory devices. Ferroelectric switching depends on domain wall motion, however, and is critically influenced by the existence of defects such as dislocations and preexisting domains. Domain wall motion in thin film applications can be controlled by individual local defects due to the reduced length scale of the system. This dissertation describes the impact of preexisting ferroelastic domains and misfits dislocations in coherent (001)-oriented Pb(Zr0.2,Ti0.8)O3 (PZT) thin films on the switching response and domain structure. A phase field model based on the Landau-Ginzburg-Devonshire theory that accounts for the electrostatic and mechanical interactions is used to describe domain structures in ferroelectric PZT thin films. To solve the governing equations a semi-implicit Fourier-Spectral scheme is developed that accommodates boundary conditions appropriate to the thin film geometry. Errors are reduced in the solutions at the film edges through extensions to the model developed to correct the Fourier transform around stationary discontinuities at the thin film edges. This correction is shown to result in increased accuracy of the phase field model needed to appropriately describe dynamic switching responses in the thin film. Investigation of switching around preexisting ferroelastic domains showed these defects are strong obstacles to switching in PZT thin films. Directly above the ferroelastic domain the magnitude of the required nucleation bias underneath a tip-like electrode was found to be elevated compared to the required bias far from the domain. Locally both the piezoelectric and dielectric responses of the thin film were found to be suppressed, which is in agreement with previously reported experimental results. Modeling results also showed that built in electric fields and long range strains around the ferroelastic domains were responsible for the observed property changes. During switching embedded ferroelastic domains were shown to arrest 180° ferroelectric switching by forming partially stabilized charged 90° domain walls in which the local bound charge was accommodated by substantial broadening of the domain wall. This led to the charged interface remaining stable over a modest range of applied biases and necessitated a larger switching bias than required far from the ferroelastic domain. This result may explain previously observed experimental difficulty poling PZT thin films around ferroelastic domain structures. Ferroelastic domains were then modeled around misfit dislocations in coherent thin films to better quantify interactions between two common types of elastic defects. Isolated misfit dislocations relieving compressive strain in the thin film were found to locally stabilize ferroelastic domains due to the creation of in-plane tensile stresses around the dislocations. Ferroelastic domains in thinner films extended completely to the free surface of the thin film, while in films with larger thicknesses only small, wedge-shaped domains were observed. The transition between the two domain structures with film thickness is shown to be well reproduced with transmission electron microscopy results. Calculations of the total free energy and its derivatives in the system show the transition has the characteristics of a first order transition at the critical thickness. These results show how dislocations may stabilize the wide range of observed domain structures based on the local stress environment around the dislocation. Dynamic responses of ferroelastic domains around dislocations were found to be reduced through elastic interactions. Inclusions of dislocations near the substrate interface reduced both the real part of the dielectric response and the loss tangent, indicating misfit dislocations are strong pinning centers in thin films. A method to separate the domain wall and lattice contributions to the total response is proposed and used to show that the reduction in response is due to decreases in the domain wall mobility around the dislocations caused by the local non-uniform stress state. This provides insight into the causes of reduced responses in ferroelectric thin films that is then used to demonstrate a film geometry that maximizes the local dielectric response in the system. This work provides insight into switching in ferroelectric thin films around specific common elastic defects and provides a basis for investigating the impact of other classes of defects that are difficult to isolate and study experimentally. For instance, point defects such as oxygen vacancies around moving domain walls could be more easily studied with phase field models. Further, phase field modeling creates a method to quantitatively rank the impact of various defect types on ferroelectric switching. By studying common defects, efforts to produce high quality devices by minimizing defect concentration can be focused on eliminating the most critical defects.