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DOI: 10.1002/adma.((please add manuscript number))
Ferroelectric Domain Wall Injection
By Jonathan R. Whyte†, Raymond G. P. McQuaid†, Pankaj Sharma‡, Carlota Canalias§,
James F. Scott∆, Alexei Gruverman‡ and J. Marty Gregg†*
†Centre for Nanostructured Media, School of Mathematics and Physics, Queen’s University
Belfast, Belfast BT7 1NN, United Kingdom
‡Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 685880299, USA
§Department of Applied Physics, Royal Institute of Technology, Roslagstullsbacken 21,
10691, Stockholm, Sweden
∆Department of Physics, Cavendish Laboratory, J. J. Thomson Ave., Cambridge, CB3 0HE,
England, UK
Keywords: Ferroelectric, Domain Wall Engineering, Injection, Positioning, Electric Field
Engineering
Recently, there has been an explosion of interest in domain walls as independent
functional entities, with properties distinct from the domains that they delineate[1–14].
Enhanced conductivity along ferroelectric and multiferroic oxide domain walls offers
particular excitement, as new forms of devices can immediately be envisioned, in which
function is entirely related to the presence or absence of conducting domain wall channels.
For example, electric field-induced switching between microstructures where domain walls
connect electrodes and those in which they do not, could create a completely new form of
transistor. Equally, if the number of high conductivity domain walls connecting electrodes
could be changed in a controlled manner, a series of distinct resistance states could be created,
making tuneable memristive devices, of potential in computational applications[15].
In order to realize the opportunity of domain wall electronics, a deep understanding of
transport characteristics and associated physics is undoubtedly needed. Some progress has
been already achieved: following on from the landmark observations by Seidel et al.[2],
atomistic simulations[16] and scanning tunneling microscopy (STM)[17] studies have suggested
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that conductivity results from fundamental alterations in the electronic band structure within
the domain wall. Farokhipoor and Noheda[7] have established the important role of oxygen
pressure during thin film growth. The importance of oxygen vacancies (known to
preferentially aggregate at domain walls[18-20]) has therefore been established as a vehicle for
creating defect-dopant electronic states. Domain wall conductivity in lead zirconate titanate
(PZT) thin films has also been seen to be sensitive to oxygenation[21]. The other major factor
associated with conductivity is the nominal charge state of the domain wall induced by
opposing ‘head-to-head’ or ‘tail-to-tail’ polarization components, presumably due to an
electrostatically driven accumulation of mobile screening point defects[9-11,22-23]. Schröder et
al.[24] demonstrated that photoexcitation could also play a role in their discovery of domain
wall conduction in millimeter thick single crystal lithium niobate (LiNbO3).
While understanding charge transport is a major element in the realization of domain
wall-based electronic devices, the other aspect of behavior that needs to be mastered is the
precise control over where and when domain walls are injected into a system, and how their
subsequent motion is determined. While this kind of capability has been already developed
within the nanomagnetics field[25-32] it is still at its nascent stage in ferroelectric and
multiferroic systems.
Here, we demonstrate how domain wall behavior in uniaxial mesoscale ferroelectric
capacitor structures can be controlled by manipulating the internal electric field landscape
through fabrication of localized structural defects (air holes) of various size, shape and density.
Specifically, we show that local field enhancement zones (the so-called ‘hot-spots’) adjacent
to defects, patterned into the ferroelectric by focused ion beam milling (FIB), allow sitespecific domain nucleation and controllable movement of domain walls. Local regions with
relatively low field intensity (cold-spots) were also found to inhibit domain wall propagation.
Thin single-crystal lamellar slices (thickness ~300 nm) of the uniaxial ferroelectric
KTiOPO4 (KTP)[33-34] with top and bottom surfaces parallel to (010)orthorhombic
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(o),
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machined from a (001)o oriented periodically poled KTP bulk crystal, using focused ion beam
(FIB) milling, and integrated as the dielectric layer into simple coplanar capacitor devices (see
Methods Section). The form of a complete KTP capacitor structure, without any milled
defects, is shown schematically in Fig. 1a. Figure 1b shows PFM amplitude and phase maps
of the remanent domain states in the KTP lamella developing as a function of the potential
difference applied between the two Pt electrodes. What is immediately apparent from this
sequence of images is that, during the switching cycle, domains are nucleated sporadically
and unpredictably. Presumably, at each nucleation site, there is some defect that lowers the
energy barrier required for reverse domain nucleation. However, the important point is that
such nucleation sites are neither well-controlled, nor could their position or critical voltage for
occurrence have been predicted prior to switching.
To exert control over the spatial location of nucleation sites we engineer heterogeneity
in the developed electric field (as informed by finite element modeling) via FIB milled holes
into the lamella. Through indirect hysteresis measurements, McQuaid et al.[35] and McMillen
et al.,[36] rationalised measured changes in domain wall mobility by local enhancement or
denudation of the electric field in BaTiO3 ferroelectric wires patterned with notches and
antinotches. However, the precise way in which engineered electric field heterogeneity
influences domain nucleation, and subsequent wall mobility, has not been explicitly
visualized until now.
Figure 2a illustrates the local field variations associated with circular holes cut into
the KTP lamellae within the interelectrode gap, when a potential difference is applied to the
capacitor electrodes. A scanning electron microscope (SEM) image of a real KTP capacitor
sample with two sets of FIB-fabricated circular hole defects, reflecting those modeled in Fig.
2a, is shown in Fig. 2b. Modeling indicates that there is a dramatic field enhancement on
either side of the holes, parallel to the electrodes, and associated field reduction above and
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below them, in regions closer to the electrodes, due to the relative distribution of high and low
permittivity regions (KTP and air respectively).
The KTP lamella originated in a monodomain state due to the bulk crystal being prepoled, shown in Fig. 2c. One second voltage pulses were then applied, in the opposite sense to
the initial poling voltage (in steps of 10 V) and a PFM image of the whole lamella was
captured between each pulse application. Reverse domains first appeared after the application
of the 70V pulse (Fig. 2c). Importantly, the position in which the reverse domains nucleated
correlated strongly with the position of the field hotspots as modeled in Fig. 2a, clearly
suggesting that the increased field intensity adjacent to the FIB-machined holes was
responsible for inducing the site-specific nucleation observed.
To gain greater insight into the exact locations and critical voltages at which reverse
domain nucleation (or initial injection of domain wall pairs) occurred, the slow scan axis of
the PFM was disabled to allow a single lateral line just above the defects to be continually
scanned. After poling the lamella back to the monodomain state, a series of switching voltage
pulses of increasing magnitude (10V increments) was then applied during the PFM line scan
acquisition. The form of the experiment is illustrated schematically in Fig. 3a. This
methodology allowed the position of nucleation events to be mapped immediately after the
application of each voltage pulse. Figure 3b shows the PFM amplitude signal from the single
line scan and how the information on that line scan changes as voltage pulses of increasing
magnitude were successively applied. The exact points at which voltage pulses were supplied
can be seen in the image by the sporadic ‘white’ lines of noise, suspected to result from
electrostatic interactions between the cantilever and electrodes during the application of the
larger voltage pulses.
Domain wall pairs (where each pair appears as a single dark line in the PFM amplitude
image) first appeared after a 1 second 60V pulse had been applied (note that one of the
domain wall pairs, successfully injected initially, later backswitched). Correlation between the
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domain nucleation sites and modeled local field hot-spots is illustrated in Fig. 3c. As can be
seen, domain wall injection events occur exactly at the points at which hot-spots in field are
predicted. Note also that these hot-spot related nucleation events occur at the expense of any
other sporadic reverse domains of the kind seen in Fig. 1c.
Alternative shape designs for FIB-milled holes (and associated variations in local field
inhomogeneity) were then examined. One such design consisted of four right-angled triangles
arranged in a square formation (Fig. 4). This was of particular interest, as field modeling
suggested a notably strong local field enhancement adjacent to the most acute of the vertex
angles of the triangular holes (Fig. 4a). If local field variations were genuinely responsible for
inducing reverse domain creation, then in this structure the first nucleation events would be
expected in-between the sharp vertices of the triangles.
To test this prediction, voltage pulses of incrementally increasing amplitude were
applied to the single-domain KTP lamella with triangular holes. Remnant domain states were
imaged by lateral PFM after each pulse application. First, it was found that domain nucleation
occurred at a lower voltage (50V) than that in KTP lamellae with the circular holes described
above. Second, from Fig. 4b, which shows the domain growth after a 60V pulse, it is clear
that nucleation events have been initiated adjacent to the most acute vertex of the triangular
holes i.e. the point at which the highest local electric field was expected. It was also observed
that this defect design pinned propagation of the domain wall through the center of the sample
as larger voltage pulses were applied, thus preventing the needle domain from reaching one of
the electrodes (Fig 4b).
FIB-milled hole defects not only produce regions of enhanced field strength but also
cause localized field reduction, or ‘cold-spots’. While ‘hot-spots’ have been seen to induce
domain nucleation, it was expected that cold-spots could significantly impede domain wall
propagation. This expectation was tested by monitoring the motion of domain walls under an
applied planar electric field using in-situ PFM[37] imaging in a KTP lamellar capacitor
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structure with two pairs of FIB-milled triangular holes (Fig. 5). The modeled electric field
distribution for this pattern under an applied bias is shown in Fig. 5a. After application of a 5
second 110V pulse, the regions above and below each defect remained unswitched. These
unswitched domains resided in the cold-spot regions of the lamella (Fig. 5b) showing very
clear correlation with the field models. Again the slow scan axis was disabled and a single
line on the lamella was continually scanned by the PFM. The scan line was situated just below
one of the triangular defects and across the two domain walls of an unswitched domain,
shown by the highlighted region in Fig. 5b. As the scan progressed with time, DC voltage was
applied in the reverse direction to grow this domain. Several image lines were obtained before
the applied voltage value was increased in 1V increments, allowing the movement of the
domain walls to be monitored.
Figure 5c shows the amplitude signal acquired from the single line PFM scan. As the
scan progresses (top of image to bottom) the in-situ applied voltages increased from 11V to
22V. The domain wall on the right hand side can be seen to freely propagate further right
under applied bias. In contrast, the domain wall on the left-hand side of the image remained
almost stationary. The average distance moved by each domain wall at each voltage is shown
in Fig. 5d.
Comparison of the position of the domain walls and the modeled electric field
landscapes shown in Fig. 5e, suggests that the right domain wall in Fig. 5c is close to a region
where it should experience a significantly larger electric field than the left hand wall. Any
subsequent movement of the right hand wall further to the right takes it past the local hotspot,
but beyond that the field level experienced is still relatively high. For the left domain wall a
very significant lateral movement would be required for it to reach a region of comparable
field intensity. Overlayed on Fig. 5e are the spatial extents of the domain walls’ motions.
Clearly, the left hand domain wall has remained pinned in a region of field denudation, while
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the right hand domain wall has experienced reasonable fields over the entire course of its
propagation.
From all of the above discussions, it is clear that the introduction of the low
permittivity defects into KTP lamellae dramatically alters the domain switching dynamics.
The manner in which switching behavior is altered is driven by heterogeneities in the local
electric field related to the fabricated defects: domain walls are predictably injected into the
lamellae at defect-determined locations that correlate with areas of local field enhancement. In
addition, propagation and pinning of the domain walls strongly depend on the local field
distribution defined by the shape and mutual arrangement of the fabricated defects. These
observations highlight that the design of field heterogeneity could represent an important tool
for manipulating the injection, position and movement of domain walls in any future ‘domain
wall electronics’ - based devices.
Experimental
Sample preparation. Thin single-crystal KTP lamellar slices (thickness ~300 nm) were
machined using a single beam FEI200TEM FIB, from a periodically poled KTP bulk crystal
fabricated by Canalias. A micromanipulator-controlled fine glass needle was used to remove
the lamellae from the bulk crystal and position it across a 2 µm interelectrode gap of a
(sputter-coated) platinised passive MgO substrate with a pre FIB-milled electrode design
similar to that of McQuaid et al. [38]. Defect pattern files were created in CleWin3 and
imported into NanoBuilder on a FEI Nova 600 DualBeam system for automated milling of
holes. Samples were then annealed in air at 300oC - 400oC for 6 hours for lamellae with or
without defects respectively, to expel gallium ion contamination [39] whilst minimising
chemical alterations of the KTP [40]. The gallium oxide residing on lamellar surfaces was
removed via 3 minutes of etching in 3 M HCl solution, resulting in a high quality surface
topography suitable for PFM domain imaging. Using electron-beam-induced-deposition of
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platinum on the same dual beam system, the lamellae were secured in place on each edge
parallel to the interelectrode gap. The electron beam dissociates a precursor gas (MeCpPtMe3)
to deposit platinum at the electron beam target whilst residual fragments are expelled from the
vacuum chamber. Finally each electrode of the sample was conductively secured with silver
paste onto a glass slide with macroscopically patterned sputter-coated platinum electrodes,
enabling application of voltage across the sample whilst being positioned under an Atomic
Force Microscope scanner head.
Field modelling. Modeling of the local field distribution between the coplanar electrodes of
the capacitor structures was performed using the ‘QuickField Finite Elements Analysis
System’. Low frequency dielectric properties of KTP, found by Bierlein and Arweiler [41],
were used as material parameter inputs for these finite element models.
PFM domain imaging. PFM measurements were obtained from both Queen’s University
Belfast (QUB) and the University of Nebraska – Lincoln (UNL). PFM measurements
displayed in Fig. 1 were carried out in QUB whilst the remaining images were obtained from
UNL. A Veeco Dimension 3100 AFM system with a Nanoscope IIIa controller, modified for
PFM measurements using a EG&G 7265 lock-in-amplifier, was used in QUB. Here an
oscillating voltage of 1 VRMS at a frequency of 20 kHz was applied to a Nanosensors PPPEFM cantilever (force constant ~2.8 N/m). The system used at UNL was a commercial
Asylum Research MFP-3D system operated in single frequency PFM mode. MikroMasch
DPE 18 cantilevers with an oscillating amplitude of 2 VPP at a frequency of 39 kHz from an
Agilent Technologies 33220A Function/Arbitraty Waveform Generator were used in this case.
DC voltages were applied to lamellae using a Keithley 237 High Voltage Source Measure
Unit. In pulsed experiments, pulses applied were of 1 second duration.
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Acknowledgements
The authors thank J. F. Einsle for helpful insight into creating high quality defect patterns in
lamellae. In addition, the authors acknowledge financial support from the Materials World
Network (MWN) scheme involving the Engineering and Physical Sciences Research Council
in the UK (EP/H047093/1) and the National Science Foundation in the USA (DMR-1007943).
International networking support from The Leverhulme Trust (F/00 203/V) is gratefully
acknowledged. JMG, RGPMcQ and JRW acknowledge support from the Department of
Employment and Learning (DEL).
Received: ((will be filled in by the editorial staff))
Revised: ((will be filled in by the editorial staff))
Published online: ((will be filled in by the editorial staff))
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Figure 1: Experimental setup and sporadic nature of switching in unpatterned KTP
lamella. (a) 3D schematic of experimental setup showing the lamella placed across a 2µm
gap between Pt electrodes, with <001>o axis perpendicular to the interelectrode gap edge
and <100>o parallel to it; the lamella is secured in position with electron beam deposited
platinum. The PFM cantilever tip scans across the surface yielding domain images. (b)
Lateral PFM amplitude (left) and phase (right) images of remnant domain states after the
application of voltage pulses of various amplitude and polarity; domain nucleation events
across the lamella are random.
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Figure 2: Domain nucleation in KTP lamellae with patterned circles. (a) Electric field
model of KTP lamella with milled circles under 60V applied between coplanar electrodes
(top and bottom) showing the creation of field hot-spots left and right of the defects and
cold-spots above and below. (b) SEM image of a KTP lamella with milled circular defects
(c) PFM images of amplitude (left) and phase signals (right) showing a mono-domain
state from 0-60V (top) and domain nucleations aligned with the field hot-spots post
application of 70V (bottom) (white circles superimposed to show positions of holes).
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Figure 3: Domain wall injection through defect-induced generation of the local field hotspots. (a) Schematic of experimental setup with red highlighted region showing the
position of the scan line. (b) Amplitude image showing the observation of new domain
wall pairs which appear to be in line with the field hot-spots shown in Figure 2a. (c) PFM
amplitude profile showing domain walls (minima in amplitude) with corresponding
modeled E-field values showing that the positions of nucleated domain walls coincide
with the location of field hotspots.
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Figure 4: Single nucleation event from field hot-spots near triangular defects. (a) Electric
field model of KTP lamella under the application of 100 V with field hotspots positioned
at inside vertices of triangular holes. (b) Amplitude (left) and phase (right) images show
the appearance of a new domain nucleating from one of the hot-spots post application of
60 V, implying that the production of field hotspots can control the exact location of
reverse domain nucleation.
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Figure 5: Effect of local field inhomogeneity on domain wall movement. (a) Electric field
model of triangular defects. (b) Phase information of the remnant domain state post
application of 5 second 110V pulse and with the phase information overlaid on sample
topography; a schematic of the cantilever tip continually scanning one line (in red) whilst
field is applied is also shown. (c) Amplitude PFM image of the red line in (b) showing the
difference in the propagation of the two domain walls as voltage is increased. (d) The
magnitude of the left and right domain walls’ displacement from their original position as
a function of voltage applied. The displacement was calculated using the average domain
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wall position at each voltage. (e) The modeled local field values of scan position with the
relative movements of the domain walls showing that the extent of domain wall
movement is directly correlated with the field intensities experienced during propagation.
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