Domain wall motion across microstructural features in polycrystalline ferroelectric films

Abstract

This paper describes the effect of microstructural features such as grain boundaries and triple points on the pinning of domain wall motion in perovskite Pb(Zr_0.52Ti_0.48)O₃ (PZT) films on polycrystalline SrRuO₃/SrTiO₃ substrates. Spatial variability in the collective domain wall dynamics was assessed using non-linearity mapping via Band Excitation Piezoresponse Force Microscopy (BE-PFM). Collocating the non-linearity maps with triple point locations (as visualized by EBSD) allowed for exploration of the effects that local microstructure (e.g., grain boundary) have on domain wall motion. It was found that the extrinsic behavior varied with both the misorientation angle and the proximity to the grain boundary. The width of influence of individual grain boundaries on the motion of domain walls was a function of the character of the grain boundary; random grain boundaries exhibit deeper minima in α_d/d_33,initial and larger widths of influence  (up to 905 nm) compared to coincident site lattice (CSL) boundaries (up to 572 nm). Additionally, triple points containing larger numbers of random boundaries exhibited non-Rayleigh behavior to greater distances, suggesting that the triple point provides either a deep potential minimum or a region where domain wall motion is unfavorable.

Introduction

The piezoelectric response of ferroelectric materials can be divided into intrinsic and extrinsic sources, where the intrinsic response corresponds to the appropriate average of the single domain single crystal response; extrinsic contributions are those due to motion of mobile interfaces such as phase boundaries or domain walls [1], [2], [3], [4], [5]. The macroscopic properties of polycrystalline perovskites are the ensemble average of many grains and even more domain walls. Calculating the response of ceramics, however, is challenging due to the grain-to-grain coupling, the interactions between the intrinsic and extrinsic contributions, the inherent anisotropy of the piezoelectric response, and incomplete knowledge about how local elastic and electric fields influence domain wall motion. It is thus interesting to explore somewhat simplified systems where the effect of single factors on extrinsic contributions can be quantified.  This paper focuses on the characteristics of individual grain boundaries and triple points on the extrinsic piezoelectric response in lead zirconate titanate (PZT) films, as a model system.

Extrinsic contributions have been reported to decrease near grain boundaries in ferroelectric films and ceramics. Randall et al. demonstrated that the piezoelectric properties of PZT ceramics decreased with decreasing grain size, which was attributed to a change in the domain structure and a reduction in domain wall contributions [6]. Similarly, Griggio et al. reported that an average grain size increase from 110 nm to 270 nm in PZT-based films was accompanied by a doubling of the irreversible dielectric Rayleigh coefficient α_d from 5.3 ± 0.1 cm/kV to 10.6 ± 0.1 cm/kV [7]. α_d is associated with the irreversible motion of domain walls. Grain boundaries have also been reported to influence the ferroelectric switching characteristics [8], [9], [10], [11].

Marincel et al. measured the local impact of single grain boundaries on the irreversible to the reversible Rayleigh coefficient ratios using band excitation piezoresponse force microscopy (BE-PFM). Both reversible d_33,initial and irreversible, α_d, Rayleigh coefficients were calculated from the nonlinear dependence of out-of-plane deflection on increasing applied AC voltage. The ratio of α_d/d_33,initial suggested increased pinning of domain wall motion within 476 nm of a 24 tilt grain boundary in a PbZr_0.52Ti_0.48O₃ (PZT 52/48) film on a bicrystal substrate [12]. The width of  influence of the reduced response at grain boundaries was found to be dependent on both the misorientation angle and the tilt/twist characteristics of the boundary [13].

Among the factors thought to affect the width of influence of a particular grain boundary is the connectivity of the domain structure across the structural discontinuity. Following seminal work by Tsurekawa [14], Mantri reported that for random grain-grain misorientations, domain continuity is dependent on the ability of the material to compensate strain mismatch and minimize the polarization charge at the grain boundary [15]. It was found that a larger uncompensated charge and/or bigger spontaneous polarizations make continuity less energetically favorable.

Fousek et al. studied permissible orientations of ferroelectric domain walls in detail. He noted that uniform strain states should in theory only yield domain walls along planes of mechanical compatibility in the absence of external stress [16]. When no additional elastic strain develops, the domain wall  is deemed a “permissible wall” [16]. If two non-permissible domains meet along a stressed boundary, domain switching is expected to be restricted, as has been noted in grain boundary pinning [16,17]. The domain structure is thus a developing system that acts in response to strain and charge from differently oriented polarizations.

To date, quantitative evaluations of the role of individual grain boundaries on the motion of domain walls are limited, with most of the data pertaining to symmetrical grain boundaries. A more comprehensive set of data is required to better understand the role that grain boundaries exert in pinning extrinsic contributions to the properties. It is speculated that grain boundaries with a shared axis rotation, i.e., Coincident Site Lattice (CSL) boundaries, may facilitate domain wall motion across the grain boundary relative to random grain boundaries. Thus, in this work, the intrinsic and extrinsic contributions to the piezoelectric response were assessed for PZT films deposited onto polycrystalline large-grained SrRuO₃/SrTiO₃ substrates. The substrates allowed many grain boundary orientations to be isolated by Electron Backscatter Diffraction (EBSD) and categorized based on grain boundary angle and shared orientation axes. BE-PFM imaging was used to quantify the local piezoelectric nonlinearities.