Nanosecond domain wall dynamics in ferroelectric Pb(Zr, Ti)O(3) thin films.
ABSTRACT Domain wall motion during polarization switching in ferroelectric thin films is fundamentally important and poses challenges for both experiments and modeling. We have visualized the switching of a Pb(Zr, Ti)O(3) capacitor using time-resolved x-ray microdiffraction. The structural signatures of switching include a reversal in the sign of the piezoelectric coefficient and a change in the intensity of x-ray reflections. The propagation of polarization domain walls is highly reproducible from cycle to cycle of the electric field. Domain wall velocities of 40 m s(-1) are consistent with the results of other methods, but are far less than saturation values expected at high electric fields.
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ABSTRACT: A high speed variation of Scanning Probe Microscopy with continuous image rates on the order of 1 frame per second is applied to investigate the nucleation and growth of individual ferroelectric domains. Movies of consecutive images directly identify nascent domains and their nucleation times, while tracking their development with time and voltage reveals linear domain growth at lateral velocities near 1 mm/s, even faster for nascent domains. Nanoscale maps of nucleation times and growth velocities indicate that domain nucleation and growth are uncorrelated, varying extensively with position. Domain switching dynamics do strongly couple to film defects; for instance, grain boundaries can profoundly pin domain walls, and polarization reversal kinetics are influenced by strain fields near microcracks or in asymmetric specimens. The influence of the onset of switching fatigue is observed as well. These results highlight the importance of updating classical interpretations of ferroelectric switching for truly rigorous models of polarization dynamics. Coupling high speed SPM imaging with in situ activation by voltage or other parameters therefore provides an important methodology to research dynamic surface properties with nanoscale resolution, extendable to a range of materials such as photovoltaics, thermoelectrics, batteries, fuel cells, multiferroics, phase change systems, etc.Journal of the American Ceramic Society 04/2012; 95(4). · 2.43 Impact Factor
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ABSTRACT: Piezoelectric multilayer actuators are technologically important devices used in numerous positioning and force generation applications. During operation, the actuator displacement and force are nonlinearly coupled to the applied electric field, which is often ignored during material characterization. In this study, a novel experimental arrangement is presented that acts like a virtual linear spring, allowing for characterization of the full operational range as a function of applied electric field as well as the true blocking force and impedance matching system stiffness. The macroscopic measurements are contrasted to previous experimental techniques, providing insight into the effect of path dependence on the blocking force.Journal of the American Ceramic Society 06/2014; · 2.43 Impact Factor
- Journal of Materials Research 11/2014; · 1.82 Impact Factor
Nanosecond Domain Wall Dynamics in Ferroelectric Pb?Zr;Ti?O3Thin Films
Alexei Grigoriev,1Dal-Hyun Do,1Dong Min Kim,1Chang-Beom Eom,1Bernhard Adams,2
Eric M. Dufresne,2and Paul G. Evans1
1Department of Materials Science and Engineering, University of Wisconsin Madison, Madison, Wisconsin 53706, USA
2Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
(Received 5 January 2006; published 8 May 2006)
Domain wall motion during polarization switching in ferroelectric thin films is fundamentally
important and poses challenges for both experiments and modeling. We have visualized the switching
of a Pb?Zr;Ti?O3capacitor using time-resolved x-ray microdiffraction. The structural signatures of
switching include a reversal in the sign of the piezoelectric coefficient and a change in the intensity of
x-ray reflections. The propagation of polarization domain walls is highly reproducible from cycle to cycle
of the electric field. Domain wall velocities of 40 ms?1are consistent with the results of other methods,
but are far less than saturation values expected at high electric fields.
DOI: 10.1103/PhysRevLett.96.187601 PACS numbers: 77.80.Fm, 68.37.Yz, 77.84.Dy, 78.47.+p
Improving the present understanding of the structural
dynamics of solids at the nanoscale is an important chal-
lenge in the development of emerging nanotechnologies
based on acoustics, phase transitions, and the coupling of
applied fields to structures. As the relevant length scales
shrink to the nanometer range, the time interval over which
structural transformations occur also decreases and can be
on the order of picoseconds. The relationship between the
space and time scales of structural phenomena in solids is
fundamentally determined by the speed at which elastic
deformations of the crystalline lattice can propagate,
roughly the speed of sound. Reversible effects that can
be found, for instance, in ferroelectric and multiferroic
materials are among the most practically and fundamen-
tally important structural transformations [1,2].
The present understanding of steady-state and quasi-
steady-state ferroelectric phenomena including polariza-
tion hysteresis is already satisfactory as a result of exten-
sive experimental and theoretical studies [1,3,4]. The
dynamics of polarization switching, however, are largely
unexamined at small lengths and short times. The motion
of polarization domain walls presents a challenge for the-
ory and modeling because of the span of length and time
scales involved, which can range from domain wall widths
of 1 nm or less to devices sizes in length, and from pico-
seconds to microseconds in time. The switching process in
a ferroelectric thin film occurs in three steps: the nucleation
of a reversed polarization domain, domain propagation in
the direction of the electric field,and lateral domain growth
in the direction perpendicular to the electric field . At
progressively higher electric fields, the speed of polariza-
tion switching scales with the magnitude of the electric
field but apparently is limited by the propagation velocity
of elastic deformations in crystals, which is several kms?1
in single crystals of perovskite-type ferroelectrics .
Experimental studies with present techniques, primarily
piezoelectric force microscopy (PFM) and electrical mea-
surementsofthe displacement current, have established the
utility of this three-step model [7–10]. Although these
studies have considerably broadened what is known about
switching phenomena in ferroelectrics, they have not vi-
sualized the process dynamically at scales appropriate for
describing domain wall motion in large electric fields.
A unique combination of spatial and time resolution is
experimentally available using synchrotron x-ray scatter-
ing, which presently achieves resolutions of less than
60nm in space and lessthan 1ps in time in separate experi-
ments [11,12]. We have applied a combination of time-
resolved scattering and x-ray microdiffraction to study the
structural dynamics of polarization switching in ferroelec-
trics. We investigated polarization switching in a ferroelec-
tric capacitor consisting of a 400-nm-thick tetragonal
Pb?Zr0:45Ti0:55?O3(PZT) film between a uniform grounded
SrRuO3(SRO) bottom electrode and a 200 ?m-diameter
polycrystalline SRO top electrode. The epitaxial PZT and
bottom SrRuO3electrode layers were deposited by off-axis
sputtering . The SRO electrodes allowed the PZT
capacitor to operate for more than 1010switching cycles
without polarization fatigue . The remnant polarization
measured with 1 kHz triangular electric field pulses was
2Pr? 104 ?C=cm2. The electric field in the PZT film was
applied in the surface-normal ?001? direction, which is the
direction of the remnant polarization.
The ferroelastic distortion of ferroelectrics allows struc-
tural techniques to probe the remnant polarization quanti-
tatively. In PZT crystals, the (002) and (00?2) x-ray Bragg
reflections of the tetragonal phase correspond to opposite
polarization states and can differ in intensity by 30% or
more [15,16], which is a result of the noncentrosymmetric
unit cell of ferroelectrics. X rays of 10 keV photon energy
from an undulator insertion device at sector 7 of the
Advanced Photon Source were focused to a 115 nm spot
by Fresnel zone plate optics. The fundamental time reso-
lution for experiments using synchrotron radiation was set
by the duration of individual x-ray pulses arising from the
passage of single bunches of electrons through magnetic
PRL 96, 187601 (2006)
12 MAY 2006
© 2006 The American Physical Society
insertion devices . At the Advanced Photon Source,
successive 100 ps x-ray bunches are separated in time by
153 ns. A limit of 1:15 kms?1on the highest velocities
measurable using time-resolved microdiffraction can be
obtained by considering time dependent scattering mea-
surements at two locations separated by the spatial resolu-
tion. With larger distances, significantly higher speeds, up
to those exceeding the speed of sound (?4 kms?1for
PZT) could be measured.
To perform a time-resolved study of polarization switch-
ing, an electrical pulseapplied to the ferroelectric capacitor
was synchronized with x-ray pulses arising from a single
circulating electron bunch. The diffracted x rays were
collected with an avalanche photodiode detector with suf-
ficient time resolution to resolve individual x-ray pulses
. At each point in scans of delay time between the
electric field pulse and the x-ray probe, 1000 electric field
cycles were applied to the samplewith an overall repetition
rate of 10 kHz. The acquisition electronics were gated so
that only photons scattered during these pulses contributed
to the measured intensity.
Although, in principle, the time resolution is set by the
duration of a single x-ray bunch, the actual sensitivity of
time-resolved x-ray microdiffraction to transient structural
changes in PZT is a function of several experimental de-
tails. Piezoelectricity is the fastest of the structural re-
sponses of ferroelectrics to applied electric fields, and
can be used to measure an upper limit on the effective
time resolution of the experiment. To probe the piezo-
electric distortion, the lattice spacing of PZT in the ?001?
direction was measured as a function of the delay between
the probing x-ray bunch and in 8 Velectrical pulses. Each
data point had an uncertainty in intensity due to counting
statistics of less than 10%. At the onset of the electric field,
the Bragg reflection shifted to a lower 2? angle, commen-
surate with the expansion of the PZT lattice expected when
the polarization and electric field are parallel (Fig. 1). In
addition to the transient structural change during the pulse
there was a long term shift in 2? after a large number of
unipolar voltage pulses corresponding to a strain of
?0:05%, which we attribute to charging of the PZT thin
film. The maximum transient strain, 0.18%, is in itself
interesting for potential applications utilizing lattice dis-
tortions to modify electronic or magnetic structures
[19,20]. From strain measurements, we conclude that the
electric field applied to the ferroelectric capacitor was
lower than what would be expected given the pulse voltage
and film thickness. For 18 V pulses the electric field
estimated using the strain was 230 kVcm?1, based on a
piezoelectric coefficient of 53 pmV?1obtained in low-
Bipolar electrical pulses switch the direction of the
remnant polarization when the field exceeds the coercive
electric field. With 18 V pulses, the intensity contrast
between the two remnant states was 30% indicating that
the polarization reversed during the pulse. The time de-
pendence of the PZT (002) Bragg reflection is shown in
detail in Fig. 2(a) during polarization switching in response
to a ?18 V voltage pulse. The polarization direction is
reset prior to this pulse using a positivevoltage pulse of the
same magnitude. Turning on the negative voltage first
shrinks the PZT lattice along the c axis, shifting the
Bragg reflection to a higher 2? angle. Hundreds of nano-
the 2? angle of the PZT (002) Bragg reflection as a function of
the delay time after the onset of an 8 V electrical pulse. The
effective time resolution of the measurement, corresponding to
the 90% to 10% transition time, is 620 ps.
Time-resolved x-ray microdiffraction measurement of
FIG. 2 (color).
reflection as a function of ?–2? and time during the switching
of the remnant polarization by a ?18 V pulse to the capacitor.
(b) Applied voltage as a function of time during polarization
switching. (c) X-ray intensity as a function of time plotted from
the data of part (a) along the line with 2? ? 34:83?. Points a and
b denote the times of the beginning and end, respectively, of the
structural signal associated with polarization reversal. The shift
in absolute values of 2? between Figs. 1 and 2 is the difference in
the alignment of the x-ray diffractometer.
(a) The intensity of the PZT (002) Bragg
PRL 96, 187601 (2006)
12 MAY 2006
seconds later, the (002) reflection moves to a lower
2? angle. The points a and b in Fig. 2(b) mark be-
ginning and end of the scattering signature of the reversal
of the piezoelectric response. With bipolar voltage pulses
of smaller magnitude, the remnant polarization was not
switched and the intensity of the Bragg reflection was
unchanged before and after the electrical pulses. The dif-
ference in the Bragg angles of the reflections before and
after the switching pulse is consistent with charging at the
ferroelectric/electrode interfaces .
The time at which the remnant polarization switched
varied with the position of the beam on the thin film
capacitor due to the finite speed of the growth of polariza-
tion domains. We have defined the switching time for each
position to be the period of time between the onset of the
electric field pulse and the midpoint of the polarization
switching structural transient a-b. Assuming that the
growth of domains in which the polarization has switched
begins at the onset of the electric field, the switching time
defined in this way corresponds to the time needed for a
polarization domain wall to travel from the nucleation site
to the measurement position. The structural transient asso-
ciated with polarization switching can be observed using
the time dependence of the intensity of x rays scattered to a
fixed point in reciprocal space near the (002) Bragg reflec-
tion [Fig. 2(c)]. Measurements of the diffracted intensity as
a function of time at different positions of the x-ray probe
show that the switching time depends on the position
(Fig. 3). The data presented in Figs. 2 and 3 support the
assumption that the spatial distribution of nucleation sites,
directions of domain growth, and domain wall velocities
do not change significantly from one switching cycle to
another. If the opposite were true, the structural signature
associated with switchingwouldbesmeared overthe entire
The locations of polarization domain nucleation sites,
domain growth directions, and domain wall velocities can
be summarized on a map of the polarization switching time
as a function of position [Fig. 4(a)]. The color scale in
Fig. 4(a) corresponds to the time at which the midpoint of
the a-b switching transient occurred at each point. The
distribution of nucleation sites is not random, as would be
expected based on homogenous nucleation [7,22,23], but
rather is limited to a few widely separated locations. In
Fig. 4(a) the polarization domain grows essentially from a
single nucleus. Previous studies of polarization kinetics
indirectly suggest a far higher nucleation rate than we
have observed [4,7,9]. The area of the region shown in
Fig. 4(a) is 400 ?m2, much larger than the 1 ?m2area that
is typically thought to contain a single nucleation site for
polarization reversal . The low nucleation rate, corre-
sponding to only several hundred nuclei in the entire
with 2? ? 34:83?at several positions on the capacitor. Each
curve is labeled with the distance from the position of the first
measurement. The intensities at each position of the beam are
Time dependence of the x-ray intensities measured
FIG. 4 (color).
20 ?m2area of the thin film capacitor. The earliest and latest
switching times are red and blue, respectively. It was not pos-
sible to unambiguously assign switching times to the white areas.
(b) Polarization switching time as a function of a distance along
the arrows shown in the inset. The solid line is a linear fit giving
a 40 ms?1domain wall velocity. The error bars correspond to
the uncertainty associated with assigning the switching time.
(a) Polarization switching times in a 20 ?
PRL 96, 187601 (2006)
12 MAY 2006
device, can be explained by a strong heterogeneity of the
nucleation of reversed domains, perhaps at structural de-
fects or even at the probe tip contacting the device .
The reproducibility of the domain wall motion between
cycles of the electric field also suggests that the nucleation
of reversed domains is not homogenous across the device.
The challenge of predicting domain dynamics is in part a
result of the inability of theoretical descriptions, including
Kolmogorov-Avrami models, to separate the relative im-
portance of nucleation and domain wall motion in switch-
ing kinetics. Based on the parameters of these models, the
switching process kinetics is commonly described as being
determined either by the rate of nucleation or by the speed
of domain walls [4,22]. The problems in distinguishing
between these phenomena leads to difficulty in forming
the connection between atomic scale simulations, includ-
ing molecular dynamics studies of domain wall motion
, and the larger-scale models needed for entire devices.
The parameters of the three-step model of switching ki-
netics can be probed quantitatively and independently us-
ing the polarization switching map in Fig. 4(a). The do-
main wall velocity can be estimated using the portion of
Fig. 4(a) in which domains propagate without interference
from nearby nucleation centers. Crystallographic anisot-
ropy does not appear to influence the polarization domain
growth under these conditions.
A linear fit to a plot of the polarization switching time as
a function of position gives an average domain wall veloc-
ity of 40 ms?1for ?18 V electric pulses [Fig. 4(b)].
Although 40 ms?1is far below the limit set by elastic
deformation, it is in reasonable agreement with recent
experiments using PFM [7,25]. A domain wall velocity
of ?1 ms?1in electric fields of 78 kVcm?1was deduced
from the evolution of domains following a series of electric
field pulses . Higher electric fields and smaller capacitor
sizes are expected to yield considerably higher speeds for
domain walls and could potentially shift the relative im-
portance of nucleation and domain wall motion. Velocities
near the speed of sound may not be reachable within the
range of electric fields available below the breakdown
field, 1.0 to 1:6 MVcm?1for these films.
These time-resolved synchrotron x-ray microdiffraction
experiments establish the reproducibility of the polariza-
tion switching process and the heterogeneity of polariza-
tion reversal in these ferroelectric thin films in the nano-
second time regime. Furthermore, synchrotron x-ray mi-
crodiffraction with the time resolution demonstrated in this
letter is capable of quantifying transient structural pro-
cesses at speeds up to those associated with the propaga-
tion of elastic deformations in crystals. The potential ap-
plications of this approach to ultrafast dynamics are not
limited only to ferroelectric polarization switching, but in-
clude also a wide range phenomena, such as ferromagnetic
and antiferromagnetic domain wall motion, the propaga-
tion of thermal waves in nanostructured materials, and
the relationship between magnetism and polarization in
This work was supported by the U.S. Department of
Energy, Office of Basic Energy Sciences, under Grant
No. DE-FG02-04ER46147. C.B.E. acknowledges support
from NSF DMR-0313764 and ECS-0210449. Use of the
Advanced Photon Source was supported by the U.S.
Department of Energy, Office of Science, Office of Basic
Energy Sciences, under Contract No. W-31-109-Eng-38.
 A. Gruverman, O. Auciello, and H. Tokumoto, Annu. Rev.
Mater. Sci. 28, 101 (1998).
 G. Lawes et al., Phys. Rev. Lett. 95, 087205 (2005).
 J. Li, B. Nagaraj, H. Liang, W. Cao, Chi.H. Lee, and
R. Ramesh, Appl. Phys. Lett. 84, 1174 (2004).
 A.K. Tagantsev, I. Stolichnov, N. Setter, J.S. Cross, and
M. Tsukada, Phys. Rev. B 66, 214109 (2002).
 E. Fatuzzo, Phys. Rev. 127, 1999 (1962).
 R.C. Miller and G. Weinreich, Phys. Rev. 117, 1460
 A. Gruverman, B.J. Rodriguez, C. Dehoff, J.D. Waldrep,
A.I. Kingon, R.J. Nemanich, and J.S. Cross, Appl. Phys.
Lett. 87, 082902 (2005).
 T. Tybell, P. Paruch, T. Giamarchi, and J.-M. Triscone,
Phys. Rev. Lett. 89, 097601 (2002).
 H.M. Duiker, P.D. Beale, J.F. Scott, C.A. Paz de Araujo,
B.M. Melnick, J.D. Cuchiaro, and L.D. McMillan,
J. Appl. Phys. 68, 5783 (1990).
 P.K. Larsen, G.L.M. Kampschoer, M.J.E. Ulenaers, and
G.A.C.M. Spierings, Appl. Phys. Lett. 59, 611 (1991).
 Y. Suzuki, A. Takeuchi, H. Takano, and H. Takenaka, Jpn.
J. Appl. Phys. 44, 1994 (2005).
 A.M. Lindenberg et al., Science 308, 392 (2005).
 C.B. Eom et al., Science 258, 1766 (1992).
 C.B. Eom et al., Appl. Phys. Lett. 63, 2570 (1993).
 C.A. Wallace, J. Appl. Crystallogr. 3, 546 (1970).
 D.-H. Do, P.G. Evans, E.D. Isaacs, D.M. Kim, C.B. Eom,
and E.M. Dufresne, Nat. Mater. 3, 365 (2004).
 S.H. Lee, A.L. Cavalieri, D.M. Fritz, M.C. Swan, R.S.
Hegde, M. Reason, R.S. Goldman, and D.A. Reis, Phys.
Rev. Lett. 95, 246104 (2005).
 A. Grigoriev, D.-H. Do, D.M. Kim, C.-B. Eom, B. Adams,
E.M. Dufresne, and P.G. Evans, Mater. Res. Soc. Symp.
Proc. 902E, T06 (2005).
 Y.-A. Soh, P.G. Evans, Z. Cai, B. Lai, C.-Y. Kim,
G. Aeppli, N.D. Mathur, M.G. Blamire, and E.D.
Isaacs, J. Appl. Phys. 91, 7742 (2002).
 Y.Kato,R.C. Myers,
Awschalom, Nature (London) 427, 50 (2004).
 L. Pintilie and M. Alexe, J. Appl. Phys. 98, 124103 (2005).
 Y. Ishibashi, Jpn. J. Appl. Phys. 31, 2822 (1992).
 D.J. Jung, K. Kim, and J.F. Scott, J. Phys. Condens.
Matter 17, 4843 (2005).
 Y.-H. Shin, V.R. Cooper, I. Grinberg, and A.M. Rappe,
Phys. Rev. B 71, 054104 (2005).
 H. Fujisawa, M. Shimizu, and H. Niu, Jpn. J. Appl. Phys.
43, 6571 (2004).
PRL 96, 187601 (2006)
PHYSICAL REVIEW LETTERS
12 MAY 2006