Controlled creation and displacement of charged domain walls in ferroelectric thin films

Charged domain walls in ferroelectric materials are of high interest due to their potential use in nanoelectronic devices. While previous approaches have utilized complex scanning probe techniques or frustrative poling here we show the creation of charged domain walls in ferroelectric thin films during simple polarization switching using either a conductive probe tip or patterned top electrodes. We demonstrate that ferroelectric switching is accompanied - without exception - by the appearance of charged domain walls and that these walls can be displaced and erased reliably. We ascertain from a combination of scanning probe microscopy, transmission electron microscopy and phase field simulations that creation of charged domain walls is a by-product of, and as such is always coupled to, ferroelectric switching. This is due to the (110) orientation of the tetragonal (Pb,Sr)TiO3 thin films and the crucial role played by the limited conduction of the LSMO bottom electrode layer used in this study. This work highlights that charged domain walls, far from being exotic, unstable structures, as might have been assumed previously, can be robust, stable easily-controlled features in ferroelectric thin films.

electrostatic charges accumulated during scanning, extrinsic contributions due to tiny domain wall motion, real enhanced lateral piezoelectric response at these DWs, or due to the inherent error in the method involving shift and change of tip/contact resonance mode. Apart from that, turning the sample by 90° causes a vanishing of the lateral PFM signal (see Supplementary Fig. S1) confirming the restriction of the polarization to the [100] and [010] directions.
Combining the PFM data with the known sample orientation and polarity of the applied switching bias allows us to reconstruct the domain structure (Fig. 1f). The switched rectangle changed both the in-plane and the out-of-plane phase and therefore has polarization opposite to the as-grown film. The secondary domain changed only the in-plane phase and its polarization therefore points up and against the original in-plane state. This creates a 90° DW between the primary and the secondary domain (1 in Fig. 1f) and inevitably also a head-to-head CDW between the outer boundary of the secondary domain and the as-grown domain (2 in Fig. 1f).
More detailed switching experiments were done in order to closer investigate the formation mechanism of the secondary domain. As can be seen from the lateral amplitude (Fig. 2a,b) the position of the secondary domain is strictly limited to one side of the switched area, towards the [110] direction. This position was neither affected by changing the slow scan direction (indicated by arrows) to create a trailing field effect 14,28 , nor by the orientation of the switched area. Also the size of the switched area doesn't influence the size of the secondary domain which is created even in the case of switching along one single line (Fig. 2c). Increasing the voltage while scanning with the same speed results in a further displacement of the CDW (Fig. 2d). At 2 V no switching could be observed. This agrees well with the extrapolated displacement of the CDW, s, with respect to the applied voltage where no displacement is expected below 2.6 V (Fig. 2e).
With the aim of revealing the cross-sectional view of domain walls, an area was switched by PFM and a FIB cut was performed in the (001) plane to obtain a perpendicular section through the domain walls. Figure 3a shows a close-up of the PFM amplitude image with the corresponding scanning TEM (STEM) cross-sectional image where the DWs observed in STEM are correlated with the PFM. High Resolution TEM (HRTEM) and the corresponding filtered image of the same region are shown in Fig. 3b. They reveal a strongly distorted region of about 1 nm width due to elastic strain evidencing a ferroelastic domain wall. A more in-depth analysis of the structural details by HRSTEM is in progress but beyond the scope of this study. Figure 3c-f shows the switching process obtained by phase field simulation (details in Methods) wherein the field is applied between the small top electrode and the continuous bottom electrode mimicking the situation found in PFM or under a narrow electrode. Since no reliable phase field parameters for PST are available at the moment, we demonstrate the fundamental switching mechanism on well tested model of prototypical ferroelectric BaTiO 3 . The details in switching process may differ between the two materials, but the qualitative features of side domain nucleation is clearly robust which we tested by variation of simulation parameters such as temperature and electrostriction coefficients. A lateral electric field component, E L , at the electrode edges induces nucleation of the secondary domain which inevitably faces the as-grown state in a head-to-head arrangement. The simulation assumes purely dielectric material and therefore cannot result in free carrier compensated CDWs but still demonstrates the principle of the in-plane switching process. The lateral electric field, which must be present to create and displace the observed CDWs, will always appear in the vicinity of a PFM tip or electrode edge. However, as this field is highly inhomogeneous, it would rapidly decrease in the lateral direction and is usually negligible around distances corresponding to the film thickness. As the observed secondary domain is much larger (~500 nm) than the film thickness (70 nm) this excludes the field inhomogeneity at the PFM tip or the electrode edges as the only contribution to the CDW formation. In fact the secondary domain propagates to a larger distance only if a high resistivity bottom electrode is taken into account, where slowly redistributing electric charges create an in-plane potential drop during switching, as is the case for the phase field simulations presented here (Fig. 3d-f).
The mechanism demonstrated both experimentally and by the simulation can be understood as follows: Switching an area of the as-grown single domain film by 180° flips the polarization downwards thereby pushing the positive polarization charge to the bottom electrode. The switched polarization charge needs to be compensated by charge carriers transported through the LSMO electrode. However, the resistivity of high quality (001) plane LSMO is reported to be as large as 1000 μ Ω cm at room temperature 29 , orders of magnitude higher than The understanding of the mechanism involved in the creation of the secondary domain offers us the possibility to control its behavior. The strict connection of the CDW to the switched area was confirmed by PFM on the bare surface, causing the CDW to move or disappear if the switched area is changed or removed, respectively (see Supplementary Fig. S2). In order not to depend on the PFM tip for the creation of the CDW, low conductivity Pt line electrodes were prepared by electron beam induced deposition from a precursor gas, which allows control of the length of the switched region 31,32 . As added schematically to the actual topography image in Fig. 4a, the PFM tip was placed on one side of the electrode and only used to locally apply the voltage, without any scanning. A train of pulses of 0.1 s (Fig. 4c-e) was used to successively create, move and annihilate a CDW. The corresponding lateral PFM amplitude is shown in Fig. 4b-e where the superposed frame indicates the electrode area. Starting from the initial single domain state (Fig. 4b) a short voltage pulse is applied causing the area below the electrode to switch and the accompanying CDW to appear (Fig. 4c, indicated by arrow). An additional pulse of the same polarity causes a progression of the CDW (Fig. 4d) whereas a pulse of opposite polarity enables a reset of the structure to its initial state (Fig. 4e). This demonstrates the reproducibility and reversibility of this process offering a practical method to control the CDW.
The most intriguing property of CDWs presented in several previously published works 5,6,13,14,16 is the CDW conductivity. We therefore scanned CDW regions with conductive AFM. However, enhanced conductivity was not found. Here it is necessary to emphasize, that conductivity of CDWs is not a guaranteed property. It is well established today that CDW conductivity is controlled by several factors beside the intrinsic conductivity. For instance, the contact barriers in reverse bias and associated contact resistances can in principle prevent entirely observation of conduction even if the CDW itself is conducting 16 . Moreover, even intrinsic conductivity of CDWs is not guaranteed. First principles calculations on similar compound PbTiO 3 33 show that, with increasing charging, CDWs will experience band splitting and pass through conducting state attaining finally again to an insulating state when they are strongly charged. Also defect compensation, which should not play an important role at room temperature, but which in principle suppresses CDW conductivity, cannot be entirely excluded. Last, but not least, CDWs can always acquire a shape which does not provide complete conductive path between electrodes. Evidently, the possible reasons for not having directly observed enhanced conduction are manifold. Identification of the exact cause is a new challenge which however exceeds the scope of this paper. On the other hand, this doesn't limit the validity of the described mechanism which represents an alternative, convenient method to create charged domain walls.

Summary
We have shown by the combination of vertical and lateral PFM data that switching (110) oriented epitaxial tetragonal ferroelectric thin films results in the creation of a secondary domain accompanied by a charged domain wall. This is attributed to the inhomogeneity of the electric field at sharp electrode edges in combination with the low conductivity of the bottom electrode. Both effects together cause the build-up of a lateral electric field able to switch and propagate the in-plane polarization component of the weakly tetragonal material, hence forming a charged domain wall. Furthermore, our investigations evidenced that the creation and dimension of the charged domain wall are determined by the characteristics of the applied voltage during the 180° switching of the film. Combining this with a low conductivity top electrode allows for a precise control of the position of the switched area and simultaneously of the charged domain wall. Moreover, the presented system is based on STO as a substrate material which can be grown as a buffer layer on Si and therefore might allow the realization of these structures on Si platform as well. These results represent a further step in the ongoing effort to precisely tune domain structures as building blocks of envisioned 'nanoelectronics' .

Methods
Thin films were fabricated by pulsed laser deposition on (110) plane STO substrates (Crystec GmbH, Germany) after etching in buffered HF and annealing at 900 °C in air. Using a laser fluence of ~1 J/cm 2 , conditions for growth of the bottom electrode La 0.67 Sr 0.33 MnO 3 (LSMO) layer and the ferroelectric Pb 0.6 Sr 0.4 TiO 3 layer were T S = 625 °C, p O2 = 0.14 mbar, f = 2 Hz and T S = 575 °C, p O2 = 0.25 mbar, f = 3 Hz, respectively.
PFM was performed on an Asylum Research Cypher with Ti/Ir coated ASYELEC-01 silicon probes with a force constant of 2 N/m.
Focused ion beam (FIB) cutting was conducted with a ZEISS NVision using a 30 kV acceleration voltage and beam current from 700 pA down to 40 pA after having deposited a protective carbon coating of 1 μ m.
Transmission electron microscopy (TEM) was carried out with a Tecnai Osiris instrument using an acceleration voltage of 200 kV.
The two-dimensional phase field model (results in Fig. 3) was adopted from ref. 16 and modified as follows. Since Landau energy coefficients of PST are not known, the original coefficients of (110) tetragonal BaTiO 3 from ref. 16, but at temperature 353 K, where tetragonality is smaller due to proximity to the paraelectric phase, were used. The free charge in the bulk of the 60 nm × 2.1 μ m rectangular film is excluded, i.e. the material is assumed to be an ideal dielectric. The top (110) surface is mechanically free and has a 100 nm long ideal electrode where a 70 ns electric potential pulse with smooth edges is applied. The rest of the top surface contains fixed screening charge that fully compensates the charge of the [110] component of the spontaneous polarization. The bottom boundary is clamped to a rigid plane without a strain mismatch. Full bottom electrode is assumed as a non-ideal one dimensional conductor with defined electron drift and diffusion. The electron concentration was chosen as 10 19 cm −3 and mobility was varied in order to mimic the effect of the limited conductivity. When the mobility is < 10 −24 cm 2 /(Vs) (note that mobility must be considered relatively to the simulation time) the secondary domain always propagates to a distance larger than the film thickness. Zero potential and constant electrode charge is defined 1 μ m from the switching event. Note that the 50-100 nm long secondary domain appears always even in the case with an ideal bottom electrode, but it retracts and disappears after the switching event. In reality it could be pinned and survive, i.e. the secondary domain could be possibly observed even when using high quality bottom electrodes.