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\fancyfoot[R]{
	\small
	Poster is available as PDF download:\\
	\textbf{http://tiny.cc/4d1bp}
}
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		\scriptsize
		\textbf{Contact:} A. Hasenkopf\\
		andreas.hasenkopf@physik.uni-regensburg.de\\
		Institut für Experimentelle und Angewandte Physik\\
		Universität Regensburg
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		\centering
		{\Huge\bfseries Investigation of the effect of ring electrodes on the electron beam in the TEM}\\
		{\large\bfseries A. Hasenkopf, J. Thalmair, M. Lohr and J. Zweck}\\
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	\begin{center}
		\large Keywords: \textbf{EMCD, Phase Plate, Differential Phase Contrast, Electron Holography, Lorentz Microscopy}
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\begin{multicols}{3}
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% 	\large

	\mysection{Motivation}

	Electron Magnetic Chiral Dichroism (EMCD, see \cite{emcd_nature}) is an effect observed in the TEM analogous to XMCD. State of the art techniques are based on the so called \textit{intrinsic method} \cite{pd_rubino}. With this method dynamic diffraction effects in the sample are used to obtain two electron waves with a phase difference of $\pi/2$. For this dynamic diffraction a single crystal of magnetic material with special thickness and orientation is required.

	Our goal is to develop a new \textbf{extrinsic} method which works without those requirements. Splitting the beam and introducing the required phase shift in the condenser plane could decrease EMCD measurement periods and would allow the implementation of EMCD measurements in a scanning mode.
%Two electron waves with the required phase difference are generated in the condenser plane. This technique could decrease EMCD measurement periods and would allow the implementation of EMCD measurements in a scanning mode. 

	To realize this method we need a Boersch phase plate integrated in a new condenser aperture design: A \textbf{twin aperture} (fig. \ref{emcd_setup}, see \cite{my_diplom}). During the construction process of our twin aperture we performed investigations on Boersch phase plates and simplified twin apertures to get a better understanding of the effects of those objects on the electron beam.

	\begin{figure}[h]
		\centering
		\subfigure[\small EMCD setup with twin aperture.]{.4\columnwidth}{\label{emcd_setup}\includegraphics[width=\columnwidth]{poster_aperture_twin.png}}
		\subfigure[\small Exploded view of the twin aperture's sandwich.]{.35\columnwidth}{\label{sandwich}\includegraphics[width=\columnwidth]{twinaperture_labeled.png}}


		\caption{\small Schematic drawings of the EMCD setup and exploded view of the twin aperture.}
	\end{figure}

	\mysection{Twin aperture design \& investigated samples}

	Our twin aperture (see fig. \ref{sandwich}) is based on the design of Matsumoto and Tonomura (see \cite{phaseplate}): Instead of a central phase plate supported by three rods we consider two adjacent \textbf{phase plates} in an otherwise non-transparent plane.

	One phase plate is to be on a neutral potential. The second one is to be on a potential fit to cause a phase shift of $\pi/2$ relative to the first one.

	Samples were prepared by depositing Au after electron beam lithography (EBL) on \ce{Si3N4} membranes for investigation in a Tecnai F30. Fig. \ref{simple} shows different samples.

	\begin{figure}[h]
		\label{simple}
		\centering
		\subfigure[\small Concentric: $\diameter_1$=52$\mu$m, $\diameter_2$=32$\mu$m, t=60nm, w=1$\mu$m]{.45\columnwidth}{\label{simple_a}\includegraphics[width=.6\columnwidth]{imc17_fig1.png}}
		\subfigure[\small Adjacent: $\diameter$=52$\mu$m, t=60nm, w=1$\mu$m]{.45\columnwidth}{\label{simple_b}\includegraphics[width=.6\columnwidth]{imc17_fig3a.png}}
		\subfigure[\small Concentric: $\diameter_1$=700nm, $\diameter_2$=300nm, t=60nm, w=50nm]{.45\columnwidth}{\label{simple_c}\includegraphics[width=.6\columnwidth]{imc17_fig5.png}}
		\subfigure[\small Adjacent: $\diameter$=300nm, t=60nm, w=50nm]{.45\columnwidth}{\label{simple_d}\includegraphics[width=.6\columnwidth]{imc17_fig7a.png}}
		\caption{\small Overview of the investigated samples with no applied potential in Lorentz Mode. Outer diameter, thickness \textbf{t} and width \textbf{w} of the ring structures are given in the subfigure captions. The red dashed boxes indicate where line scans (see fig. \ref{linescans}) are performed in direction of the red arrows.}
	\end{figure}

	\mysection{Experiments}

	\textbf{Goals:} \textit{Observation} of beam deflections and phase shifting properties and \textit{Verification} of the phase constancy of phase plates.

	For all experiments samples were approx. 20$\mu$m away from the eucentric height's plane and potentials of 0V, 5V and 20V have been picked from data sets, if not otherwise stated. Only in Lorentz mode all samples were investigated. Using DPC and holography only the sample shown in fig. \ref{simple_c} was investigated.

%In this section different TEM techniques are used to observe the effect of a supplied potential. Because the PCBs (printed circuit board) for mounting the membranes are too thin the membranes are for all experiments approx. 20$\mu$m away from the eucentric height's plane. From each data set three line scans have been choosen (0V, 5V and 20V), if not otherwise stated.

	In \textbf{Lorentz Mode} samples were strongly defocussed for improved observability.

	\begin{figure}[h]
		\label{linescans}
		\centering
		\noindent
		\subfigure[\small Concentric: $\diameter_1$ 52$\mu$m, $\diameter_2$ 32$\mu$m, t=60nm, w=1$\mu$m]{.44\columnwidth}{\label{linescans_a}\includegraphics[width=\columnwidth]{data/imc_poster_scan_a_cropped.png}}
		\subfigure[\small Adjacent: $\diameter$ 52$\mu$m, t=60nm, w=1$\mu$m]{.44\columnwidth}{\label{linescans_b}\includegraphics[width=\columnwidth]{data/imc_poster_scan_b_cropped.png}}
		\subfigure[\small Concentric: $\diameter_1$ 700nm, $\diameter_2$ 300nm, t=60nm, w=50nm.]{.44\columnwidth}{\label{linescans_c}\includegraphics[width=\columnwidth]{data/imc_poster_scan_c_cropped.png}}
		\subfigure[\small Adjacent: $\diameter$ 300nm, t=60nm, w=50nm.]{.44\columnwidth}{\label{linescans_d}\includegraphics[width=\columnwidth]{data/imc_poster_scan_d_cropped.png}}
		\caption{\small Line scans for different supplied potentials across the ring structures as indicated in fig. \ref{simple}.}
	\end{figure}

	\begin{itemize}
		\item All samples show distict effect known from biprisms.
		\item All samples show variation in observed ring thickness w due to the application of potentials.
		\item Samples with large structures (see fig. \ref{linescans_a} and \ref{linescans_b}) show Fresnel fringes with strong dependency on supplied potential.
		\item Structures connected to a neutral potential show also effects caused by mirror charges, if the other structure is supplied with a potential.
		\item Samples with small structures (see fig. \ref{linescans_c} and \ref{linescans_d}) show no dependency of Fresnel fringes on supplied potential.
		\item For higher magnification and different microscope settings (eucentric height, focus, beam convergence, etc.) Fresnel fringes show different dependency behavior (compare fig. \ref{concentric_28mu_fringes} and \ref{linescans_a}).
	\end{itemize}


	%As expected all structures supplied with a voltage show beam deflections as known from biprisms. As one can see these effects are stronger for the large $\mu$m-scaled structures (see fig. \ref{linescans_a} and \ref{linescans_b}). These large structures show a potential dependent dark and bright margin, respectively. 

	%The effects caused by structures without a supplied voltage can be explained by treating the arrangements as a capacitor. Thus on the ring initially connected to mass mirror charges are gathered. As the supplied potential on the other ring is positive the mirror charges cause a negative potential.

	%The small nm-scaled structures do not show that kind of margin; but still beam deflections are observable. Due to thermal drift of the samples, the linescans of fig. \ref{linescans_c} are aligned relative to the gap between the rings and the linescans of fig. \ref{linescans_d} are aligned absolute to the center points of the rings.

	%Due to the low magnification (see figs. \ref{linescans_a} and \ref{linescans_b}) and the small dimensions of the interference fringes no fringes are observed in the line scans  of the large structures. Taking a closer look at a sample similar to that shown in fig. \ref{simple_a} also reveals interference fringes for all supplied potentials (see fig \ref{concentric_28mu_fringes}).

	\begin{figure}[h]
		\label{concentric_28mu_fringes}
		\centering
			\subfigure[\small 0 V]{.3\columnwidth}{\label{closeup_a}\includegraphics[width=\columnwidth]{imc17_concentric_28mu_00v.png}}
			\subfigure[\small 20 V]{.3\columnwidth}{\label{closeup_b}\includegraphics[width=\columnwidth]{imc17_concentric_28mu_20v.png}}
			\subfigure[\small Line scans]{.5\columnwidth}{\label{closeup_c}\includegraphics[width=\columnwidth]{imc17_concentric_fringe_scan.png}}
		\caption{\small Close up of a sample similar to the sample seen in fig. \ref{simple_a}. (a) and (b) show the sample for supplied potentials of 0V and 20V. (c) shows line scans across both images as indicated by the red dashed box in (a).}
	\end{figure}
	
	%In the close up (see fig. \ref{concentric_28mu_fringes}) the dependency of the fringe intensity on the supplied potential is inverted. This different behavior of a similar sample may be explained by a different adjustment of the TEM (eucentric height, under- or overfocus, convergent or divergent beam, etc.).

	%For all samples the ring width w observed in the images changed as a result of the beam deflection caused by the einzel lens. 

	\begin{figure}
		\label{dpc_schema}
		\centering
			\subfigure[\small Schematic of detector ring segments.]{.3\columnwidth}{\label{dpc_outer}\includegraphics[width=\columnwidth]{dpc_outer.png}}
			\subfigure[\small Image taken by ring segment detectors (0V).]{.3\columnwidth}{\label{dpc_img}\includegraphics[width=\columnwidth]{data/dpc/imc17_dpc.png}}\\
			\subfigure[\small No beam shift. Beam is centered.]{.25\columnwidth}{\label{dpc_c}\includegraphics[width=\columnwidth]{dpc_field_0.png}}
			\subfigure[\small Beam is shifted by magnetic field.]{.25\columnwidth}{\label{dpc_d}\includegraphics[width=\columnwidth]{dpc_field_1.png}}
			\subfigure[\small Beam is shifted by magnetic field.]{.25\columnwidth}{\label{dpc_e}\includegraphics[width=\columnwidth]{dpc_field_2.png}}
			\caption{\small Schematic drawings of the DPC detector unit. (a) Definition of the x- and y-axes of the detector. The segments labeled with \textbf{+} and \textbf{-} show which segments contribute to the differential signal in x-direction. (b) Image of the sample with red and blue dashed boxes indicating directions of x- and y-axes in the image. (c),(d),(e) Beam shift (red arrows) caused by in-plane \textbf{magnetic} fields (blue arrows) resulting in differential DPC signal. DPC signals are caused by in-plane \textbf{electric} fields in an analogous way (imagine electric fields are rotated 90° in (d) and (e)). Source: \cite{pd_uhlig}}
	\end{figure}

	For \textbf{Differential Phase Contrast} measurements the sample was in the focal plane.

% 	\begin{figure}[h]
% 		\label{dpc_holo}
% 		\centering
% 		\subfigure[\small Image taken by ring segment detectors (0V).]{.4\columnwidth}{\label{dpc_img}\includegraphics[width=\columnwidth]{data/dpc/imc17_dpc.png}}
% 		\subfigure[\small Hologram (20V).]{.4\columnwidth}{\label{holo_img}\includegraphics[width=\columnwidth]{data/holo/20v-holo.png}}
% 		\caption{\small (a) Image of the sample with red and blue dashed boxes indicating the x- and y-axes of the DPC detector (b) Hologram showing a segment of the central ring on a potential of 20V.}
% 	\end{figure}

	\begin{itemize}
		\item DPC shows strong edge effects at the rim of the ring material.
		\item All DPC signals have a linear background. For a supplied potential of 20V the background has been fitted by a green dashed line.
		\item In regions outside the ring arrangements and inside the central ring the signal corresponds with the background level.
		\item Application of a potential results in an offset from the background level in the area between the rings depending on the potential difference.
	\end{itemize}

	%As one can see from fig. \ref{dpc} the DPC signal shows strong fluctuations in the region of the ring material. In the remaining free regions (outside outer ring, within inner ring) the DPC signal shows a smooth linear behavior. If no potential is applied to the central ring the DPC signal is a straight line in these regions. If a potential is supplied the signal shows in the region between the rings an asymmetric offset due to the different directions of the electric field in the linescan.

	%The effect of a supplied potential on the slope of that line is negligible as it is a gradient in the background intensity of the images recorded by the DPC detectors.

	\begin{figure}[h]
		\label{dpc}
		\centering
		\subfigure[\small Linescan (red box)]{.44\columnwidth}{\label{dpc_a}\includegraphics[width=\columnwidth]{data/dpc/imc17_dpc_scan_a.png}}
		\subfigure[\small Linescan (blue box)]{.44\columnwidth}{\label{dpc_b}\includegraphics[width=\columnwidth]{data/dpc/imc17_dpc_scan_b.png}}
		\caption{\small Linescans across the sample as indicated in fig. \ref{dpc_img} along the x- and y-axes of the corresponding DPC differences. The green dashed lines highlight the background in both line scans for a supplied potential of 20V.}
	\end{figure}

	With the \textbf{Holography} technique the same frame showing a segment of the central ring (see fig. \ref{holo_img}) was investigated. For holography the sample was in the focal plane.

	\begin{figure}[h]
		\label{holo}
		\centering
		\subfigure[\small Hologram (20V).]{.4\columnwidth}{\label{holo_img}\includegraphics[width=\columnwidth]{data/holo/20v-holo.png}}\\
		\subfigure[\small Phase image (0V)]{.4\columnwidth}{\label{holo_a}\includegraphics[width=\columnwidth]{data/holo/00v-phase.png}}
		\subfigure[\small Phase image (20V)]{.4\columnwidth}{\label{holo_b}\includegraphics[width=\columnwidth]{data/holo/20v-phase-rings-box.png}}
		\subfigure[\small Line scans of phase images]{.5\columnwidth}{\label{holo_c}\includegraphics[width=\columnwidth]{data/holo/20v-linescan.png}}
		\caption{\small (a) Hologram showing a segment of the central ring on a potential of 20V. (b),(c) Phase images for the potentials 0V and 20V. The color range [black,white] represents the numeric range [0,2$\pi$[. The red dashed curves in (c) highlight the shape of the central ring. The blue dashed box indicates where line scans in the phase images have been taken. (d) Line scans.}
	\end{figure}

	\begin{itemize}
		\item Application of a potential results in rapid phase changes in radial direction in the region between the rings.
		\item In the area occupied by ring material application of a potential shows no significant change in behavior of the phase.
		\item In the free area surrounded by the central ring changes in phase are significantly reduced.
	\end{itemize}


	%. If no potential is supplied, the ring structures are almost not  recognizable. One only sees a linear gradient in the phase image. Within the central ring the slope is slightly altered. Applying a potential transforms the gradient to a radial one. The slope of that gradient is increased in the region between the rings and shows a different algebraic sign. In the regions enclosed and occupied by the central ring the slope is strongly decreased such that the phase is almost constant in the region enclosed by the central ring as predicted in \cite{phaseplate}. 

	\mysection{Conclusions}

	Effects caused by 5V potentials are rather small: At about this value the Fresnel fringes exceed background intensity (see fig. \ref{linescans}). Thus the potential supplied to the phase plate should not exceed 5V. As pointed out in \cite{my_diplom} a potential of $<$3V should be sufficient to result in a phase shift of $\approx\pi/2$ and fulfill requirements for EMCD assuming a primary electron energy of 300keV and ring electrodes with a thickness of 100nm.

	DPC and holographic measurements show no or little spatial variation in phase within the central ring (phase plate) for high voltages as expected from the theoretical phase constancy \cite{phaseplate}.

	%Lorentz Microscopy and DPC measurements show strong edge effects (bright/dark margin and fluctuation, respectively).

	For the manufacturing of the twin aperture we declude that the diameter for the phase plates should be chosen to be larger than the diameter of the apertures in order to cut off the shown edge effects. This has one further advantage: In EBL processes one has more tolerances regarding beam displacements.

	Due to the dimensions of our \ce{Si3N4} membranes we choose these diameters: 56$\mu$m for the apertures and 58$\mu$m for the phase plates. Thus allowing several $\mu$m of free space between phase plates.

% \begin{multicols}{2}
 \scriptsize
%  	\mysectionnonum{Acknowledgment}
%  
%  	\begin{itemize}
%  		\item Johannes Thalmair -- Electron Holography
%  		\item Matthias Lohr -- Differential Phase Contrast
%  	\end{itemize}
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