0
Research Papers

Phase-Field Modeling of Domain Structure Energetics and Evolution in Ferroelectric Thin Films

[+] Author and Article Information
Antonios Kontsos1

Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin TX 78712-0235

Chad M. Landis2

Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin TX 78712-0235landis@mail.utexas.edu

1

Present address: Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104.

2

Corresponding author.

J. Appl. Mech 77(4), 041014 (Apr 16, 2010) (12 pages) doi:10.1115/1.4000925 History: Received July 08, 2009; Revised October 08, 2009; Published April 16, 2010; Online April 16, 2010

A computational model developed based on the phase-field approach is used to model domain structures in ferroelectric thin films and to quantify the effects of strain and applied electric field on the microstructural evolution, and on the induced dielectric, electrostrictive, and piezoelectric film properties. Theoretically predicted vortex-like polydomain and experimentally observed bidomain and monodomain film morphologies are modeled using the continuum phase-field approach. A nonlinear finite element method is used to solve the boundary value problems relevant to ferroelectric thin films. The computed results agree with the Kittel law for specific ranges of film strain. Simulations that track the domain structure evolution and compute ferroelectric thin film properties given the film dimensions and the imposed electromechanical boundary conditions are also reported.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

The types of domain structures in ferroelectric thin films modeled in this article. The arrows designate the direction of polarization vectors. Type (I) corresponds to monodomains in the x-direction, type (II) to bidomains, and types (III)–(V) to different vortex structures. The height of the film is H, and its width is equal to 2L, which corresponds to the domain periodicity in types (III)–(IV). The solids lines inside these models indicate 180 deg and 90 deg domain walls. Periodic boundary conditions are imposed on the broken lines on the side and various electromechanical conditions are chosen for the top and bottom boundaries.

Grahic Jump Location
Figure 2

(a) Excess energy values computed for the monodomain (I), the bidomain (II), and the vortex structures (III–V) of Fig. 1 as a function of the domain periodicity, for two values of film thickness equal to 10l0 and 16l0 and film strain εxx=0.3ε0. (b) Similar results for film strain εxx=0.07ε0.

Grahic Jump Location
Figure 3

Minimum energy equilibrium polarization distributions in the x- and y-directions computed for film strain εxx=0.07ε0. The contour plots are consistent with the data presented in Fig. 2. The solid white arrows designate the direction of polarization vectors and have magnitudes normalized by the spontaneous value P0. Three thickness values are used and are equal to (a) 10l0, (b) 16l0, and (c) 24l0.

Grahic Jump Location
Figure 4

Domain width values that correspond to minimum energy equilibrium solutions for the polarization distributions in ferroelectric thin films are plotted as a function of the square root of film thickness for three different values of film strain. The computed results agree with the Kittel law.

Grahic Jump Location
Figure 5

Excess energy values computed for monodomain structures with polarization vectors in the direction of the applied electric field (i.e., c-domains), bidomain structures with polarization vectors aligned in a direction parallel to the film surface and therefore similar to type (II) of Fig. 1 and polydomain structures for different values of domain periodicity, film thickness equal to 10l0 and two levels of film strain εxx=ε0 and εxx=0.6ε0.

Grahic Jump Location
Figure 11

(a) Normalized strain in the y-direction and (b) normalized stress in the x-direction as a function of applied field in a direction perpendicular to the film surface for several values of film strain, domain periodicity equal to 18l0 and thickness equal to 10l0

Grahic Jump Location
Figure 12

Dielectric behavior of ferroelectric thin films as characterized by the numerical simulations presented in this article for domain periodicity equal to 18l0, film thickness equal to 10l0, and (a) film strain εxx=ε0, which corresponds to a nonpolar domain structure for zero applied field and (b) film strain εxx=0.4ε0 for which a polar structure was obtained for a zero field, as shown in Figs.  1010.

Grahic Jump Location
Figure 6

Evolution of the polarization distributions in the x- and y-directions normalized by the spontaneous polarization for zero applied electric field. The domain periodicity is equal to 18l0, the film thickness equal to 10l0 and the film strain is equal to the spontaneous value. The first two sets of plots correspond to nonequilibrium evolution states and the third one is the equilibrium solution for applied field equal to zero.

Grahic Jump Location
Figure 7

Equilibrium polarization distributions in the x- and y-directions normalized by the spontaneous polarization for zero electric field, domain periodicity equal to 18l0 and film strain εxx=ε0. Three different values of film thickness are used and are equal to (a) 10l0, (b) 14l0, and (c) 16l0.

Grahic Jump Location
Figure 8

Equilibrium polarization distributions in the x- and y-directions normalized by the spontaneous polarization for different values of applied electric field (a) E=0, (b) E=1.0E0, and (c) E=2.066E0. The domain periodicity is equal to 18l0, the film thickness equal to 10l0 and the film strain is εxx=ε0.

Grahic Jump Location
Figure 9

Equilibrium polarization distributions in the x- and y-directions normalized by the spontaneous polarization for different values of film strain. The domain periodicity is equal to 18l0 and the film thickness is equal to 10l0. (a) εxx=0.6ε0, (b) εxx=0.4ε0, and (c) εxx=0.3ε0.

Grahic Jump Location
Figure 10

(a) Electric displacement in the y-direction as a function of applied electric field in the same direction for several values of film strain and for a thin film with domain periodicity equal to 18l0 and thickness equal to 10l0. (b) Effective spontaneous polarization and critical electric field in the y-direction as a function of the film strain.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In