#
2008 APS March Meeting

## Volume 53, Number 2

##
Monday–Friday, March 10–14, 2008;
New Orleans, Louisiana

### Session Q38: Focus Session: Ferroelectric Films and Finite Size Effects

11:15 AM–2:15 PM,
Wednesday, March 12, 2008

Morial Convention Center
Room: 230

Sponsoring
Unit:
DCMP

Chair: Max Stengel, University of California, Santa Barbara

Abstract ID: BAPS.2008.MAR.Q38.1

### Abstract: Q38.00001 : Imaging ferroelectric polarization by electron holography

11:15 AM–11:51 AM

Preview Abstract
Abstract

####
Author:

Hannes Lichte

(Technische Universitaet Dresden)

Understanding solids means analysis of the arrangement of the
different
atoms, e.g. at interfaces, and the intrinsic electric and
magnetic fields,
as well as the resulting charge distribution. This is
particularly important
for functional materials, such as semiconductors, ferroelectrics and
ferromagnetics. There is a variety of tools answering these
questions
partially. In particular since correction of aberrations [1],
Transmission
Electron Microscopy (TEM) offers a lateral resolution below 0.1nm
hence can
locally analyze position and species of atoms e.g. at interfaces.
The most
severe drawback is that the phase of the electron wave is not
accessible by
conventional imaging methods, and therefore phase-modulating
peculiarities
of the object such as electric and magnetic fields are invisible.
However,
these are measurable by TEM-holography rendering both amplitude
and phase
distributions produced by the object. For an overview see e.g. [2].
The electron phase $\varphi $ is modulated by the electric potential
$V(x,y,z)$ as $\varphi (x,y)=\sigma \int\limits_{object}
{V(x,y,z)dz} $ with
interaction constant $\sigma $. In ferroelectrics, the
polarization $\vec
{P}$ contributes with a phase shift $\varphi _{pol} (\vec
{r})=\frac{\sigma
}{\varepsilon _0 }\int\limits_{object} {\left[ {\int\limits_{\vec
{r}0}^{\vec {r}} {\vec {P}(x,y,z)} d\vec {r}} \right]dz} $ with
respect to a
reference point $\vec {r}0$, chosen in field-free space; $\vec
{r}=(x,y)$ is
the coordinate perpendicular to $z$-direction. Therefore, the
projected
in-plane polarization $\vec {P}_{proj} (\vec
{r})=\int\limits_{object}
{\left[ {\int\limits_{\vec {r}0}^{\vec {r}} {\vec {P}(x,y,z)}
d\vec {r}}
\right]dz} $ would be determined from a phase image. However, the
polarization is partly compensated by \textit{compensating
charges }at surfaces, interfaces and domain
boundaries, which contribute with a corresponding potential
distribution.
The net effect is found in the phase image reconstructed from an
electron
hologram. Meanwhile, specific ferroelectric effects are found on
micrometer
and nanometer, even at atomic dimensions.
[1] M. Haider et al., Nature 392 (1998) 768. [2] H. Lichte et
al., Ann. Rev.
Materials Research 37 (2007), 539

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2008.MAR.Q38.1