In this letter a method to simultaneously measure the physical and the polarization thickness of a 90° domain wall in a ferroelectric perovskite is presented. This method combines accurate atomic force microscopy and piezoresponse force microscopy scans of the same area with little drift and an analysis of the entire scanned area. It is found that the physical thickness is significantly narrower (about seven and a half times) than the polarization thickness in a 90° domain wall in BaTiO3. Evidence of the trapping of defects at such domain walls is also found

Bhattacharya, Kaushik

Franck, Christian

Ravichandran, Guruswami

English

Caltech Authors - Main

APPLIED PHYSICS LETTERS 88, 102907 2006Characterization of domain walls in BaTiO3 using simultaneous atomic
force and piezo response force microscopy
Christian Franck,a Guruswami Ravichandran, and Kaushik Bhattacharya
Division of Engineering and Applied Science, California Institute of Technology, Pasadena,
California 91125
Received 3 November 2005; accepted 31 January 2006; published online 10 March 2006
In this letter a method to simultaneously measure the physical and the polarization thickness of a 90°
domain wall in a ferroelectric perovskite is presented. This method combines accurate atomic force
microscopy and piezoresponse force microscopy scans of the same area with little drift and an
analysis of the entire scanned area. It is found that the physical thickness is significantly narrower
about seven and a half times than the polarization thickness in a 90° domain wall in BaTiO3.
Evidence of the trapping of defects at such domain walls is also found. © 2006 American Institute
of Physics. DOI: 10.1063/1.2185640Ferroelectric materials offer great potential for next gen-
eration high density storage devices, such as nonvolatile ran-
dom memory access and high strain actuators in microelec-
tromechanical systems applications due to their inherent high
dielectric properties and high strain response.1–3 Their mac-
roscopic response to mechanical, electrical and optical loads
is strongly related to their microstructural domain patterns.4,5
The formations and kinetics of these domains are governed
by the underlying atomistic structure, and their interaction
with domain walls and material imperfections. As the size of
the devices reduces to micro- and nano-scale, the motion and
interaction of twin domain walls significantly influences
the overall piezoelectric, optical, and mechanical response of
the device.6 In order to predict and control the phenomeno-
logical behavior of twin wall kinetics, their physical and
electrical properties need to be accurately determined.
Many of the current experimental techniques, including
x-ray diffraction and high-resolution transmission electron
microscopy TEM are capable of imaging domain walls, but
are often unable to provide information about their
polarization.7,8 Also, since these techniques are based on dif-
fraction principles, they only provide averaged information
about the physical twin wall thickness.9 Current far field
techniques are limited in their resolution by the wavelength
of the light and, although near-field techniques such as
NSOM provide useful information, they are still difficult to
use.
An experimental approach for determining the physical
and electrical twin wall thickness in a ferroelectric perovskite
material BaTiO3 by simultaneously using a combination of
atomic force microscopy AFM and piezoresponse force mi-
croscopy PFM is described here. The recorded AFM and
PFM images are quantitatively compared to their respective
displacement and polarization fields using the widely used
and accepted Devonshire–Ginzburg–Landau DGL phenom-
enological model.10–12 As has been shown by Shilo,
Ravichandran, and Bhattacharya9 for the case of PbTiO3, fit-
ting the measured AFM displacement field to the DGL model
by means of a least-squares method produces excellent re-
sults with nanometer resolution. Here, this approach is ex-
tended to include PFM measurements to determine the po-
aAuthor to whom correspondence should be addressed; electronic mail:
christian@caltech.edu
0003-6951/2006/8810/102907/3/$23.00 88, 10290
Downloaded 26 Mar 2006 to 131.215.225.9. Redistribution subject to larization domain wall thickness simultaneously along with
the physical domain wall thickness.
AFM and PFM images are recorded on single crystal
BaTiO3 with dimensions 550.5 mm, initially poled in
the 001 orientation. Figure 1 shows an AFM image of the
typical displacement field of an a100−c001 90°  do-
main interface. Lines have been added to the figure to illus-
trate the location of the twin walls, whereas arrows indicate
the polarization direction as determined by PFM. All AFM
and PFM images are taken in contact mode at room tempera-
ture in ambient air conditions with a Park Scientific Auto-
probe M5 instrument and a DSP lock in amplifier Stanford
Research Systems SR830 equipped with highly doped Si tip
probes Veeco ULCT-AUNM and Veeco MPP-33100
probes. The 90° domain walls were introduced in the crystal
by first heating it above its Curie temperature Tc=105 °C,
and then cooling it down to room temperature. Upon com-
plete cooling, an alternating a-c banded domain pattern is
recorded by means of optical polarized light microscopy,
where the alternating a-c domain sequences are separated by
101-oriented twin walls. Due to the lattice parameter
change at the a-c domain interface, there is a distinct incli-
nation angle of the 100 planes, which can be determined
by a simple geometric calculation as =2 arctancˆ / aˆ−90°,
where cˆ and aˆ are the lattice parameters of the hexagonal
unit cell. In the case for BaTiO3, this angle is typically about
0.6° cˆ / aˆ=1.01.
High resolution AFM and PFM images were taken in the
vicinity of individual 90° twin walls with a lateral step size
in the range of 0.5–1 nm, and typical results are shown in
Figs. 2 and 3, respectively. The center of both the physical
FIG. 1. AFM topography of BaTiO3 showing a typical c-a-c domain
pattern.
© 2006 American Institute of Physics7-1
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102907-2 Franck, Ravichandran, and Bhattacharya Appl. Phys. Lett. 88, 102907 2006and the electrical domain wall coincide for each individual
scan that was taken showing that the drift during and be-
tween the AFM and PFM measurements is negligible. The
strain and polarization fields do not change abruptly in the
vicinity of the twin wall but rather transition smoothly from
one spontaneous value to another. In order to determine the
physical and the polarization twin wall thicknesses, these
scans were compared with those predicted by the DGL8
model, which states that the strain and polarization fields
follow a hyperbolic tangent distribution given by Eqs. 1
and 2 below. The out-of-plane displacement field, however,
follows the integral distribution of the strain field, and is
given by Eq. 3
z = 0 +

2
w tanh x − x0
w/2  , 1
pz = p0 +
p
2
wp tanh x − x0
wp/2
 + px − x0 , 2
uz = u0 +

2
w lncosh x − x0
w/2 	 + x − x0 , 3
where x describes the coordinate of the surface plane per-
pendicular to the twin-wall trajectory on the surface, and can
be expressed as
x = x cos  + y sin  , 4
where  is the angle between the sample’s x axis and the x
axis. The center location of the twin wall physical and elec-
trical along the x axis is prescribed by x0; u0 and p0 are
arbitrary initial displacement and polarization constants, 
and p are material constants,  and p are arbitrary free
FIG. 2. High resolution AFM image and its best-fit DGL simulation for the
displacement field of the domain wall in BaTiO3.
FIG. 3. High resolution PFM image and its best-fit DGL simulation for the
polarization field of the domain wall in BaTiO3.
Downloaded 26 Mar 2006 to 131.215.225.9. Redistribution subject to sample rotations, and w and wp are the displacement and
polarization twin wall thicknesses, respectively. The factor of
2 in Eqs. 1–3 arises from the projection of the x axis
onto the s axis twin-wall trajectory.
The unknown parameters, x0, u0, p0, , p, , , p, and
w and wp are determined by fitting Eqs. 2–4 to the respec-
tive full field AFM and PFM images by a least-squares fitting
procedure. Figures 2 and 3 show typical AFM and PFM im-
ages and the best fit simulations superimposed in the vicinity
of a 90° twin wall. The physical and polarization twin wall
thicknesses are determined to be w=9.8±0.3 nm and
wp=76.1±11.2 nm. In particular, the polarization domain
walls are observed to be much wider than the displacement
domain walls in BaTiO3.
In order to ensure the accuracy of the determined param-
eters, the accuracy of each simulation fit is determined by
calculating the average per point error of each data fit by the
following expressions:
eu =


i,j
N
umxi,yj − usxi,yj2
N
, 5
ep =


i,j
N
pmxi,yj − psxi,yj2
N
, 6
where N is the total number of xi and yj data points that
comprise the total set of NxN points, um and us, pm and ps are
the measured and simulated displacements and polarizations,
respectively, and eu and ep are the average per point errors
for the fitted displacement and polarization fields.
Figures 4 and 5 show the average per point error plotted
versus the twin wall thickness for the physical and polariza-
tion twin walls, respectively. These plots are generated by
first fitting the complete image to the best-fit simulation and
then varying w and wp over a wide range of possible values.
This shows that the average per point error of the simulation
is smallest for the determined twin wall thicknesses and sys-
tematically increases away from it, thereby verifying the ac-
curacy of the fit. The dashed lines in Figs. 4 and 5 represent
e+e /N, which is the sum of the average per point error and
the average noise level per point, which is represented by
FIG. 4. Average per point error of the best-fit displacement field simulation
over a range of domain wall thicknesses. The dashed line shows the sum of
the average per point error and the average noise level per point, which is an
estimation of the fitting error.e /N.
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102907-3 Franck, Ravichandran, and Bhattacharya Appl. Phys. Lett. 88, 102907 2006To further ensure the accuracy of these results, multiple
AFM and PFM images were taken in the vicinity of indi-
vidual twin walls and the standard deviations 	w and 	wp
were calculated. The standard deviation of the physical twin
wall thickness is found to be 	w=0.3 nm, while the corre-
sponding standard deviation of the polarization domain wall
thickness is determined to be 	wp=11.2 nm. In order to un-
derstand the large value for the standard deviation of the
polarization twin wall thickness, the possibility of dependen-
cies of the twin wall thickness on i excitation voltage, ii
excitation frequency, and iii tip geometry are evaluated and
the results are shown in Table I. None of these factors ap-
pears to have an influence on the polarization domain wall
thickness. In particular, the fact that two different tip geom-
etries of different radii 10 nm and over 30 nm give iden-
tical results shows that the large observed width in the PFM
is not an artifact of the distortion of the domain wall under
the influence of the PFM tip.
This study extends the methodology developed by Shilo
and co-workers wherein the entire scanned image is fit to the
DGL model to obtain a domain wall thickness to accurately
determine both the physical and polarization thickness of the
domain wall.9 It is demonstrated that this method provides
accurate and reliable measurements.
The most important finding of this study is that the po-
larization width of a 90° domain wall in BaTiO3 is signifi-
FIG. 5. Average per point error of the best-fit out-of-plane polarization field
simulation over a range of domain wall thicknesses. The dashed line shows
the sum of the average per point error and the average noise level per point,
which is an estimation of the fitting error.
TABLE I. Summary of PFM measurements as a function of excitation am-
plitude, excitation frequency and tip geometry.
Tip Voltage Frequency
Polarization thickness
nm
Mean
nm
Std. Dev.
nm
MPP 2.5 V 5 kHz 79.5±3.2
MPP 2.5 V 5 kHz 74.0±3.1
MPP 2.5 V 17 kHz 68.4±0.6 78.7 10.6
MPP 2.5 V 17 kHz 93.1±0.6
MPP 2.5 V 17 kHz 68.4±0.6
MPP 2.5 V 17 kHz 93.1±0.6 72.9 13.7
ULCT 2.5 V 17 kHz 67.8±0.6
ULCT 2.5 V 17 kHz 62.3±0.7
MPP 2.5 V 5 kHz 79.5±3.2
MPP 2.5 V 5 kHz 74.0±3.1
MPP 3.5 V 5 kHz 87.8±3.5 78.6 17.0
MPP 4.5 V 5 kHz 87.1±1.7
Average: 76.1 11.2Downloaded 26 Mar 2006 to 131.215.225.9. Redistribution subject to cantly thicker about 7.5 times than the physical width.
Physically, the domain wall is found to be very sharp ap-
proximately 10 nm, consistent with previous studies and ex-
isting theory. However, the polarization switch takes place
over a much larger distance, approximately 75 nm. This is
consistent with the recent careful analysis of 90° domains
using the DGL theory.13 Further, it has recently been shown
using ab initio studies14 in PbTiO3 and DGL theory ex-
tended to include semiconductor effects in BaTiO3 that
there is an electrostatic potential drop across a 90° domain
wall. Further, this potential drop causes the formation of a
charge double layer and attracts defects, including oxygen
vacancies to the domain wall. Consequently, the electrostatic
effects extend over long distances, thereby giving rise to
wider polarization domain walls. This study shows direct
experimental evidence of the disparity between physical and
polarization widths in ferroelectric materials.
Significant variation was found in thickness of domain
walls between different regions though the errors in indi-
vidual measurements were small. It is accepted by now that
90° domain walls trap defects, including dopants and oxygen
vacancies, and such defects widen the domain wall.9,15–17
The variations we have observed are consistent with this
mechanism.
Finally, theoretical studies13,15,17 have shown that the do-
main walls may bend close to free surfaces and have struc-
tures different from the bulk. Our observations, specifically
the independence of observations with tip geometry and ap-
plied voltage, suggest that these do not significantly affect
our conclusions. However, a more detailed study with a
broader range of tip geometries and a fitting with a more
complete theory will be used in the future to gain further
insight into this issue.
The authors gratefully acknowledge the financial support
of the U.S. Army Research Office DAAD-19-01-1-0517.
They thank Dr. D. Shilo for his help with the experimental
investigation.
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Characterization of domain walls in BaTiO3 using simultaneous atomic force and piezo response force microscopy

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Characterization of domain walls in BaTiO3 using simultaneous atomic force and piezo response force microscopy

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