Supporting Online Material for:
Watching Domains Grow: In-situ studies of polarization switching by combined Scanning
Probe and Scanning Transmission Electron Microscopy
Hyejung Chang1, Sergei V. Kalinin1, Seung Y. Yang2, P. Yu2, S. Bhattacharya3, Ping P. Wu3,
Long Q. Chen3, R. Ramesh2, Stephen J. Pennycook1, and Albina Y. Borisevich1
1
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN
37831, USA
2
Department of Materials Science and Engineering and Department of Physics,
University of California, Berkeley, CA 94720, USA
3
Department of Materials Science and Engineering, Penn State University,
University Park, PA, 16802, USA
*To whom correspondence should be addressed. E-mail: albinab@ornl.gov
I. Methods
In situ STEM imaging:
A Nanofactory Instruments Scanning Tunneling Microscope (STM) double tilt holder
(nr0819) was used in a STEM (FEI Titan S 80-300) operated at 300 kV. A schematic of the
holder is shown in Fig. S1(a). β-tilt is achieved with the cradle tilt by piezoelectric motion of the
motor shaft connected to a cradle wing spring. The sapphire ball slides against the cradle wing
spring. A W tip for the STM probe was fixed on the 3 dimensionally moveable end of a
piezotube in the holder. The cross-section TEM sample glued on a Mo grid (Fig. S1(b)) was
loaded on the cradle acting as a counter electrode. Bias was applied through the
electrochemically prepared W-tip to the outer edge of the sample in the domain boundary region.
Fig. S1. A schematic of (a) STM double tilt holder and (b) sample cross-section geometry with respect to
the W-tip.
Phase field modeling:
The evolution of polarization distribution and thus the ferroelectric domain structure of a
BiFeO3 film are simulated by solving the Time Dependent Gizburg-Landau (TDGL) Equations:
Pi  x, t 
t
 L
F
 Pi  x, t 
(i  1, 2,3),
(1)
where Pi is the polarization vector, x is coordinate, t is time, L is the kinetic coefficient related to
domain wall mobility, and F is the total energy containing the bulk chemical, gradient, elastic
and electrostatic energy. The detailed expression for the total free energy and the values of the
coefficients can be found in our previous publications 1,2.
Eq.(1) is solved numerically using semi-implicit Fourier spectral method3. In the bismuth
ferrite nano-wire simulation, a matrix of 128 x x128 x x 64 x domain with periodic boundary
conditions along x1 and x2 axes is applied. The film thickness hf = 14 x .
A ferroelectric nanowire structure oriented along [110] direction is simulated to mimic
the experimental sample geometry. The thickness of the nanowire is taken as hf = 14 nm and the
width is 30 nm. The elasticity equation for the nanowire mechanical boundary condition 4 is
solved using the iterative perturbation method for elastically inhomogeneous systems by setting
the elastic constants zero for the vapor phase, so the stress-free boundary conditions along the
surfaces of an island are automatically satisfied.
The tip-induced potential distribution was represented as,
 appl   a
r0
( x1  x 0 ) 2  ( x 2  y 0 ) 2  r0
2
(2)
where a is the voltage applied on the surface of thin film with the conductive tip, ( x 0 , y 0 ) is the
tip location and r0 is the effective radius, and x1, x2 are the coordinates on the surface. The
electric potential on the bottom surface of film is kept at zero.
II. Image of domain wall
Two out of 12 possible <110> pseudocubic projection of BiFeO3 have vertical {110}
domain wall planes, and thus we see the domain wall as a sharp line (Fig. S2(a)). But eight of
them are not perfectly vertical to the domain wall plane, so in these cases we see an inclined
domain wall plane showing a finite width as shown in Fig. S2(b).
Fig. S2. Atomic models of possible <110> pseudocubic projection of BiFeO3 showing {110}
planes (pink).
III. Strain contour by mechanical contact
Mechanical contact between the W-tip and the BFO film causes strain contrast in the
TEM image, see Fig. S3. The irregular shape of the contour and its penetration to the substrate
are at first glance similar to the image of the domain observed in Fig. 3. However, the
indentation-related contrast in Fig.S3 has elastic, not ferroelastic nature, and thus several
important differences with Fig.3 can be pointed out. First of all, there is no apparent indentation
of the tip into the sample in the dataset in Fig.3. Second, multiple strain contours (strain fringes)
are formed in Fig.S3 that do not have a well-defined shape such as contrast in Fig.3; the lines are
also not continuous across the existing domain walls. Third, the contrast extends into the STO
substrate. And, last but not least, the contrast in Fig. S3 developed instantaneously, while
contrast in Fig.3 took tens of minutes to evolve after initial application of bias, which rules out
piezoelectric effect induced strain contours.
Fig. S3. Sequential TEM images showing the evolution of strain contours induced by mechanical
contact between the W-tip and the BFO film.
Supporting movie 1.
An in situ STEM movie shows dynamic nucleation and growth of a ferroelastic domain from the
contact surface between the BFO film and the W tip. The new domain preferentially forms at the
site having an acute angle between the surface and the domain wall. It grows asymmetrically due
to pinning by the pre-existing domain wall on the left. The domain wall on the right hand side
blocks the growth for a while, but it is passed through relatively easily compared to the left hand
domain wall. The image size is 2.35ⅹ2.35 um2.
References
[1] Zhang, J. X.; Li, Y. L.; Wang, Y.; Liu, Z. K.; Chen, L. Q.; Chu, Y. H.; Zavaliche, F.; Ramesh,
R. J. Appl. Phys. 2007, 101, (11), 052909.
[2] Zhang, J. X.; Li, Y. L.; Choudhury, S.; Chen, L. Q.; Chu, Y. H.; Zavaliche, F.; Cruz, M. P.;
Ramesh, R.; Jia, Q. X. J. Appl. Phys. 2008, 103, (9), 094111.
[3] Chen, L. Q.; Shen, J. Computer Physics Communications 1998, 108, (2-3), 147-158.
[4] Zhang, J. X.; Wu, R.; Choudhury, S.; Li, Y. L.; Hu, S. Y.; Chen, L. Q. Appl. Phys. Lett. 2008,
92, (12), 122906.