Effects of interface dislocations on properties of ferroelectric thin films

https://doi.org/10.1016/j.jmps.2007.01.011Get rights and content

Abstract

Effects of interfacial dislocations on properties of thin-film ferroelectric materials, such as the self-polarization distribution, Curie temperature, dielectric constant and the switching behaviors, are investigated via the system dynamics based on the Landau–Devonshire functional. Dislocation generation in the film is found to reduce the overall self-polarization and the Curie temperature. The spatial variations are both very strong, particularly in the immediate neighborhood of the dislocation cores. In agreement with previous results based on a stationary model, a dead layer exists near the film/substrate interface, in which the average self-polarization is much reduced. Moreover, it is evident from our results that interface dislocations play an important role in suppressing the remnant polarization and the coercive field of the polarization.

Introduction

Much work has been done recently on nano-scale ferroelectric thin films because of their remarkable properties that make them very useful in electro-optic, pyroelectric, and piezoelectric devices, as well as ultra-high-density nonvolatile memories (Haeni et al., 2004; Fong et al., 2004; Streiffer et al., 2002; Balzar et al., 2004). It is well known that properties of ferroelectrics in the bulk and thin-film forms may be significantly different, depending on the combined effects of film surfaces, depolarization field, film/substrate interfaces, epitaxial stress and the external electric field, etc (Catalan et al., 2005; Sinnamon et al., 2002; Wesselinawa et al., 2005; Scott et al., 2005; Wang et al., 2003). In this regard, misfit dislocations introduces a large stress field superimposing on the epitaxial stresses to significantly affect the physical properties of the film. Related investigations constitute an active area of thin-film research.

Dislocation structure formed in BaTiO3 grown on SrTiO3 substrate has been analyzed by using X-ray and transmission electron microscopy, and determined the critical thickness of the misfit dislocation generation (Suzuki et al., 1999). They also confirmed that the misfit relaxation depended on the presence of dislocations. Similar investigations have been carried out and result showed that misfit dislocations were very important on the stability of the polarization field (Sun et al., 2004; Chu et al., 2004). The dielectric properties of ferroelectric thin film also depended on internal stresses and dislocation-type defects (Li et al., 2001; Canedy et al., 2000). Using the phase-field model, effects of interfacial dislocations on the polarization distribution and domain structure of ferroelectric thin film have been investigated (Hu et al., 2003). They also developed a method to predict the evolution of a domain structure in a ferroelectric thin film with an arbitrary spatial distribution of dislocations. However, the effects of the depolarization field and the near-surface eigenstrain relaxation could not be readily taken into account within this approach. Another concern also arose from the non-linear nature of the model, which did not always admit a unique solution.

In our previous work (Wang and Woo, 2005; Zheng et al., 2006a), we adopted the time-dependent Ginzburg–Landau equation approach to investigate the self polarization distribution near misfit dislocations, successfully including the effects of relaxation of the surface effect and the depolarization. The existence of a dead layer near the film/substrate interface was confirmed (Haun et al., 1987). However, the dielectric constant was assumed to be spatially uniform. This assumption is inconsistent with the spatially varying polarization field, on which the dielectric constant is functionally dependent. Besides, among many of the most important properties of a ferroelectric thin film, only the spontaneous polarization distribution was discussed.

In this paper, effects of interfacial dislocations on the self-polarization, Curie temperature and dielectric constant are considered as functions of temperature and film thickness. The spatial variations of the self-polarization, the depolarization, and the extrapolation length are specifically taken into account. This is done via the finite-difference solution of the evolution equation derived from a thermodynamic model in which the free energy is constructed with the help of the Landau–Devonshire functional. The interface dislocations effects on the remnant polarization and the coercive field of ferroelectric thin film also is investigated. The results are discussed and the observations concluded.

Section snippets

The free energy equation

We consider a single-domain ferroelectric thin film on a compliant substrate, which undergoes a cubic to tetragonal (tetragonal to cubic) phase transformation on cool-down (heat-up). We use a coordinate system in which the x-axis is parallel to [1 0 0], the y-axis to [0 1 0], and the z-axis to [0 0 1], where the film in the x- and y-directions extend to infinity, the film surface and the film/substrate interface are on the z=h and z=0 planes, respectively, h being the film thickness (Fig. 1). A

The finite difference method and the Runge–Kutta method

The evolution of the self-polarization field P is obtained by numerically solving the time-dependent Ginzburg–Landau Eq. (2.5) subject to the electric and mechanical boundary conditions. We adopt the second-order finite difference method for spatial integration and the fourth-order Runge–Kutta method for time integration to solve Eq. (2.5) in this work (Wang and Zhang, 2006). The ferroelectric thin film is considered as a stack of layers, each of which has a finite thickness Δz with physical

Simulation results and discussions

To be specific, we consider a PbTiO3 thin film on a rigid LaAlO3 substrate. We use as an approximation material constants for the Landau free energy, the electrostrictive coefficients and the elastic properties for bulk materials from the literatures (Lakovlev et al., 2002; Pertsev et al., 1998; Streiffer et al., 2002; Li et al., 2002b). We consider that this approximation should be sufficient for our discussion.

We first consider the polarization field near a b=a[1¯00] single edge dislocation,

Summery and conclusions

The time-dependent Ginzburg–Landau equation of a ferroelectric thin film with interfacial dislocations is solved numerically using a finite-difference scheme. Taking into account the inter-dependence of the polarization and depolarization fields, as well as the surface effect, effects of interfacial dislocations on ferroelectric thin films are investigated. We obtain the self-polarization field around a single edge misfit dislocation at different temperatures, and determine the dead region

Acknowledgments

This project was supported by Grants PolyU5312/03E, 5322/04E and GU164. Co-author BW is also grateful for grants from the National Science Foundation of China (Nos. 50232030, 10172030 and 10572155) and the Science Foundation of Guangzhou Province (2005A10602002).

References (40)

  • Y.L. Li et al.

    Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films

    Acta Mater.

    (2002)
  • J.W. Matthews et al.

    Defects in epitaxial multilayers: I. Misfit dislocations

    J. Cryst. Growth

    (1974)
  • D. Balzar et al.

    Defect-related lattice strain and the transition temperature in ferroelectric thin films

    Phys. Rev. B

    (2004)
  • Z.G. Ban et al.

    Optimization of the tenability of barium strontium titanate films via epitaxial stresses

    J. Appl. Phys.

    (2003)
  • A.M. Bratkovksy et al.

    Formation and rapid evolution of domain structure at phase transitions in slightly inhomogeneous ferroelectrics and ferroelastics

    Phys. Rev. B

    (2002)
  • C.L. Canedy et al.

    Dielectric properties in heteroepitaxial Ba0.6Sr0.4TiO3 thin film: Effect of internal stresses and dislocation-type defects

    Appl. Phys. Lett.

    (2000)
  • G. Catalan et al.

    Phys. Rev. B

    (2005)
  • M.W. Chu et al.

    Impact of misfit dislocations on the polarization instability of epitaxial nanostructured ferroelectric perovskites

    Nat. Mater.

    (2004)
  • D.D. Fong et al.

    Ferroelectricity in ultrathin perovskite films

    Science

    (2004)
  • H. Haeni et al.

    Room-temperature ferroelectricity in strained SrTiO3

    Nature (London)

    (2004)
  • M.J. Haun et al.

    Thermodynamic theory of PbTiO3

    J. Appl. Phys.

    (1987)
  • J.P. Hirth et al.

    Theory of Dislocation

    (1982)
  • S.Y. Hu et al.

    Effect of interfacial dislocations on ferroelectric phase stability and domain morphology in a thin film—a phase-field model

    J. Appl. Phys.

    (2003)
  • Hull, D., Bacon, D., 2001. Introduction to Dislocations, fourth ed. Butterworth-Heinemann,...
  • J.Y. Jo et al.

    Coercive fields in ultrathin BaTiO3 capacitors

    Appl. Phys. Lett.

    (2006)
  • R. Kretchmer et al.

    Surface effects on phase transitions in ferroelectrics and dipolar magnets

    Phys. Rev. B

    (1979)
  • Hao Li et al.

    Dependence of dielectric properties on internal stresses in epitaxial barum strontium thin film

    Appl. Phys. Lett.

    (2001)
  • Y.L. Li et al.

    Effect of electrical boundary conditions on ferroelectric domain structures in thin films

    Appl. Phys. Lett.

    (2002)
  • S. Lakovlev et al.

    Doping and thickness effects on dielectric properties and subswitching behavior of lead titanate thin films

    Appl. Phys. Lett.

    (2002)
  • D.C. Lupascu

    Fatigue in Ferroelectric Ceramics and Related Issues

    (2004)
  • Cited by (31)

    • Influence of dislocations on domain walls in perovskite ferroelectrics: Phase-field simulation and driving force calculation

      2022, International Journal of Solids and Structures
      Citation Excerpt :

      Dislocations in bulk ferroelectrics are still hardly studied. The remnant polarization and the coercive electric field of ferroelectrics are known to be strongly influenced by dislocations (Alpay et al., 2004; Zheng et al., 2007). Nevertheless, a recent study shows that the influences vary with the dislocation density in bulk ferroelectrics (Wu et al., 2013b).

    • Screw dislocation equations in a thin film and surface effects

      2016, International Journal of Plasticity
      Citation Excerpt :

      Dislocations play an important role in plastic deformation and other mechanical behaviors even at small scales (Shen, 2008; Fertig and Baker, 2009). Due to the large surface to volume ratio, the mechanical and electrical properties of thin films can be very different from the bulk counterparts (Freund and Suresh, 2004; Zheng et al., 2007), and it becomes more necessary to take the surface effects into account. In general, thin film materials display strong size-effects: smaller is stronger.

    View all citing articles on Scopus
    View full text