The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films

Recent experimental measurements of large flexoelectric coefficients in ferroelectric ceramics suggest that strain gradients can affect the polarization and permittivity behaviour of inhomogeneously strained ferroelectrics. Here we present a phenomenological model of the effect of flexoelectricity on the dielectric constant, polarization, Curie temperature (T-C), temperature of maximum dielectric constant (T-m) and temperature of the onset of reversible polarization (T-ferro) for ferroelectric thin films subject to substrate-induced epitaxial strains that are allowed to relax with thickness, and the qualitative and quantitative predictions of the model are compared with experimental results for (Ba0.5Sr0.5)TiO3 thin films on SrRuO3 electrodes. It is shown that flexoelectricity can play an important role in decreasing the maximum dielectric constant of ferroelectric thin films under inhomogeneous in-plane strain, regardless of the sign of the strain gradient.

Studies of switching kinetics in ferroelectric thin films

Experimental studies are reported concerning the importance of interfacial capacitance (including electrode screening, space-charge layers, and/or chemically discrete dead layers). on domain switching behaviour in thin films of ferroelectric lead zirconate-titanate (PZT), strontium bismuth tantalate (SBT), and barium strontium titanate (BST). Emphasis is placed upon studies at applied field values very near the coercive field E, asymmetry in fatigue for positive and negative polarity coercive fields, and in the case of BST, of the coexistence of ferroelectric and paraelectric phases Studies of dielectric loss show important correlations between tan 6 and fatigue (polarization decrease) as a function of bipolar switching cycles N. This is a priori not obvious, since the former is a linear response and the latter, a nonlinear response. Modelling of enlarged interfacial,space-charge layers in PZT films and chemically distinct dead (paraelectric) layers in BST films shows contradictory tendencies of coercive-voltage changes with the growth of passive layers.

The effect of tungsten trioxide thin films at ferroelectric-electrode boundaries on fatigue behaviour

A conventional thin film capacitor heterostructure, consisting of sol-gel deposited lead zirconium titanate (PZT) layers with sputtered platinum top and bottom electrodes, was subjected to fatiguing pulses at a variety of frequencies. The fatigue characteristics were compared to those of a similarly processed capacitor in which a ~20nm tungsten trioxide layer had been deposited, using pulsed laser deposition, between the ferroelectric and upper electrode. The expectation was that, because of its ability to accommodate considerable oxygen non-stoichiometry, tungsten trioxide (WO3) might act as an efficient sink for any oxygen vacancies flushed to the electrode-ferroelectric boundary layer during repetitive switching, and hence would improve the fatigue characteristics of the thin film capacitor. However, it was found that, in general, the addition of tungsten trioxide actually increases the rate of fatigue. It appears that any potential benefit from the WO3, in terms of absorbing oxygen vacancies, is far outweighed by it causing dramatically increased charge injection in the system.

Maximum of dielectric permittivity caused by structural transition in ferroelectric BaTiO3-SrTiO3 superlattices

We invoke the onset of dislocations along the BaTiO3-SrTiO3 interface as reported by Wunderlich et al. to explain the non-monotonic behaviour of the dielectric permittivity as a function of superlattice periodicity and the less than four-fold in-plane symmetry at the dielectric maximum. At a periodicity of about 10/10, depending on composition and growth mechanism, several groups report a maximum of dielectric permittivity. In addition to that we observe in-plane symmetry less than tetragonal for 10/10 superlattices by HR-XRD, in contrast to initial low-resolution data from Tabata et al. thus challenging the assumption of unrelaxed strain all the way through the superlattice. The aim of this article is to link both effects to the increasing volume fraction of conducting layers close to the interface in series with the superlattice layers.

Switching dynamics in ferroelectric thin films: An experimental survey

We have conducted a broad survey of switching behavior in thin films of a range of ferroelectric materials, including some materials that are not typically considered for FeRAM applications, and are hence less studied. The materials studied include: strontium bismuth tantalate (SBT), barium strontium titanate (BST), lead zicronate titanate (PZT), and potassium nitrate (KNO3). Switching in ferroelectric thin films is typically considered to occur by domain nucleation and growth. We discuss two models of frequency dependence of coercive field, the Ishisbashi-Orihara theory where the limiting step is domain growth and the model of Du and Chen where the limiting step is nucleation. While both models fit the data fairly well the temperature dependence of our results on PZT and BST suggest that the nucleation model of Du and Chen is more appropriate for the experimental results that we have obtained.

Origin of Ferroelastic domains in Free-Standing Single Crystal Ferroelectric Films

The origin of the unusual 90 degrees ferroelectric/ferroelastic domains, consistently observed in recent studies on mesoscale and nanoscale free-standing single crystals of BaTiO3 [Schilling , Phys. Rev. B 74, 024115 (2006); Schilling , Nano Lett. 7, 3787 (2007)], has been considered. A model has been developed which postulates that the domains form as a response to elastic stress induced by a surface layer which does not undergo the paraelectric-ferroelectric cubic-tetragonal phase transition. This model was found to accurately account for the changes in domain periodicity as a function of size that had been observed experimentally. The physical origin of the surface layer might readily be associated with patterning damage, seen in experiment; however, when all evidence of physical damage is removed from the BaTiO3 surfaces by thermal annealing, the domain configuration remains practically unchanged. This suggests a more intrinsic origin, such as the increased importance of surface tension at small dimensions. The effect of surface tension is also shown to be proportional to the difference in hardness between the surface and the interior of the ferroelectric. The present model for surface-tension induced twinning should also be relevant for finely grained or core-shell structured ceramics.

Domains in Ferroelectric Nanodots

Almost free-standing single crystal mesoscale and nanoscale dots of ferroelectric BaTiO3 have been made by direct focused ion beam patterning of bulk single crystal material. The domain structures which appear in these single crystal dots, after cooling through the Curie temperature, were observed to form into quadrants, with each quadrant consisting of fine 90° stripe domains. The reason that these rather complex domain configurations form is uncertain, but we consider and discuss three possibilities for their genesis: first, that the quadrant features initially form to facilitate field-closure, but then develop 90° shape compensating stripe domains in order to accommodate disclination stresses; second, that they are the result of the impingement of domain packets which nucleate at the sidewalls of the dots forming “Forsbergh” patterns (essentially the result of phase transition kinetics); and third, that 90° domains form to conserve the shape of the nanodot as it is cooled through the Curie temperature but arrange into quadrant packets in order to minimize the energy associated with uncompensated surface charges (thus representing an equilibrium state). While the third model is the preferred one, we note that the second and third models are not mutually exclusive.

The influence of Notches on Domain Dynamics in Ferroelectric Nanowires

The extent to which notches inhibit axial switching of polarization in ferroelectric nanowires was investigated by monitoring the switching behavior of single crystal BaTiO(3) wires before and after patterning triangular notches along their lengths. Static zero-field domain patterns suggested a strong domain-notch interaction, implying that notches should act as pinning sites for domain wall propagation. Surprisingly though, notches appeared to assist, rather than inhibit, polar switching. The origin of this effect was rationalized using finite element modeling of the electric field distribution along the notched wire; it was found that the air gap associated with the notch acted to enhance the local field, both in the air, and in the adjacent region of the ferroelectric. It seems that this local field enhancement outweighs any pinning interactions.

The Effect of Antinotches on Domain Wall Mobility in Single Crystal Ferroelectric Nanowires

Changes in domain wall mobility, caused by the presence of antinotches in single crystal BaTiO3 nanowires, have been investigated. While antinotches appeared to cause a slight broadening in the distribution of switching events, observed as a function of applied electric field (inferred from capacitance-voltage measurements), the effect was often subtle. Greater clarity of information was obtained from Rayleigh analysis of the capacitance variation with ac field amplitude. Here the magnitude of the domain wall mobility parameter (R) associated with irreversible wall movements was found to be reduced by the presence of antinotches - an effect which became more noticeable on heating toward the Curie temperature. The reduction in this domain wall mobility was contrasted with the noticeable enhancement found previously in ferroelectric wires with notches. Finite element modeling of the electric field, developed in the nanowires during switching, revealed regions of increased and decreased local field at the center of the notch and antinotch structures, respectively; the absolute magnitude of field enhancement in the notch centers was considerably greater than the field reduction in the center of the antinotches and this was commensurate with the manner in, and degree to, which domain wall mobility appeared to be affected. We therefore conclude that the main mechanism by which morphology alters the irreversible component of the domain wall mobility in ferroelectric wire structures is via the manner in which morphological variations alter the spatial distribution of the electric field.