% Präsentation Photoemission 14. 5. 2007 Matthias Kreier
% see more at http://people.physik.hu-berlin.de/~kreier/

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\usepackage[ngerman]{babel}
\usepackage[latin1]{inputenc}
% \usepackage{ae}

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\title[Determination of Bandstructure by Photoemission]{Determination of the Electronical Bandstructure by Angle Resolved Photoemission}
\subtitle{Research Seminar Surface Physics}
\author{Matthias Kreier}
\institute[Humboldt Universität, AG EES]{Humboldt Universität zu Berlin\\Arbeitsgruppe Elektronische Eigenschaften und Supraleitung}
\date{14. 5. 2007}
\pgfdeclareimage[width=22mm,height=22mm]{titlegraphic}{pic/hulogo} 
\titlegraphic{\pgfuseimage{titlegraphic}}

\begin{document}

\frame[plain]{\titlepage}

\frame{
	\frametitle{Overview}
	\tableofcontents
%	[pausesections]
}

% *************************************************************************** [1]
\section{Motivation}
\begin{frame}
  \frametitle{Bandstructure and Fermi Surface}
  \begin{columns}
    \begin{column}{76mm}  
      \pgfdeclareimage[width=75mm]{gaas}{pic/gaas}
  	  \pgfuseimage{gaas}
    \end{column}
    \begin{column}{1mm}
    \end{column}
    \begin{column}{51mm}
      \pgfdeclareimage[width=50mm]{fermisurface}{pic/fermisurface}
  	  \pgfuseimage{fermisurface}
    \end{column}	
  \end{columns}
\end{frame}

\begin{frame}
  \frametitle{Experimental Results vs. Theory}
  \begin{block}{Photo Electron Spectroscopy on Graphite}
    \pgfdeclareimage[width=\textwidth]{graphite}{pic/graphite}
    \pgfuseimage{graphite}  
  \end{block}
\end{frame}

% *************************************************************************** [2]
\section{Angle Resoved Photoelectron Spectroscopy}
\subsection{Introduction and Basic Principle}

\begin{frame}
\setbeamertemplate{background}{\pgfuseimage{titlegraphic}}
  \frametitle{General Setup}
    \pgfdeclareimage[width=120mm, height=74mm]{1-general}{pic/1-general}
    \pgfuseimage{1-general}
\end{frame}

\begin{frame}
  \frametitle{Step 1: Photoexcitation of the Electron}
  \begin{block}{Transition Propability}
    The probability $\omega_{fi}$ of the transition for an electron from initial state 
    $|\Phi_i \rangle$ to final state $|\Phi_f \rangle$ is given by Fermis Golden Rule:
    $$
    \omega_{fi} = \frac{2\pi}{\hbar} |  \langle \Phi_f | H_{WW} | \Phi_i \rangle |^2 \delta (E_f - E_i - \hbar\omega )
    $$
  \end{block}
  \pause
  \begin{block}{Hamiltonian}
      The interaction between electron and photon is described by the Hamiltonian 
	  $H_{WW}$. In Coulomb gauge and linear approximation it is
	  $$
	  H_{WW} = \frac{e}{2mc} \vec{A} \cdot \vec{p}
	  $$
  \end{block}
  \pause
  \begin{columns}
    \begin{column}{0.46\textwidth}
      \begin{block}{Energy Konservation}
	    $$
	    E_f = E_i + \hbar \omega
	    $$
  	  \end{block}  
    \end{column}
    \begin{column}{1mm}
    \end{column}
    \begin{column}{0.46\textwidth}
      \begin{block}{Momentum Konservation}
	    $$
	    \vec{k_i} = \vec{k_f}
  	    $$
  	  \end{block}
    \end{column}  
  \end{columns}
\end{frame}

\begin{frame}
  \frametitle{Step 2: Transport to the Surface}
   \begin{columns}
    \begin{column}{0.613\textwidth}
	 \begin{block}{Mean Free Electron Path in Bulk Material}
	  \begin{figure}
       \pgfdeclareimage[width=\textwidth]{3-mfw}{pic/3-mfw}
       \pgfuseimage{3-mfw}
	  \end{figure}
	 \end{block}
	\end{column}
    \begin{column}{1mm}
	\end{column}
    \begin{column}{0.35\textwidth}
	 \begin{block}{Limiting Step}
	   At UV excitation energies the mean free path is merely 10 \AA. 
	   One has to care about surface states, clean surfaces that represent 
	   bulk material and UHV conditions. Surface sensitivity can be 
	   used for band deflection by controlled adsorption.
%	   of polar molecules (e.g. H$_2$O).
	 \end{block}
	 \begin{block}{Secondaries}
	  By scattering a spectra of low energy secondary electrons is generated. 
	 \end{block}
	\end{column} 
  \end{columns}
\end{frame}

\begin{frame}
  \frametitle{Step 3: Penetration through the surface}
   \begin{columns}
    \begin{column}{0.3\textwidth}
	 \begin{block}{}
       \pgfdeclareimage[width=\textwidth]{4-diff}{pic/4-diff}
       \pgfuseimage{4-diff} \\
	  \small{$\vec{K}$ wave vector in vakuum, $\vec{k}_f $ is wave vector of the final state in crystal}
	 \end{block}
	\end{column}
    \begin{column}{1mm}
	\end{column}
    \begin{column}{0.66\textwidth}  
	 \begin{block}{Dispersion of free Electron}
	  Excited bulk state interacts with free electron state:
	  \setlength{\abovedisplayskip}{0.6mm}
	  $$
	  E_{kin} = \frac{\hbar^2}{2m_e} \vec{K}^2
	  $$
	 \end{block}
	 \begin{block}{Refraction of Electrons at Surface}
	  Parallel component (plus lattice vector $\vec{g}_\|$):
	  \setlength{\abovedisplayskip}{0.6mm}
	  \setlength{\belowdisplayskip}{0.6mm}
	  $$
	  \vec{k}_{i_\|} = \vec{k}_{f_\|} = \vec{K}_{\|} = \sqrt{\frac{2m}{\hbar} E_{kin}} \sin \vartheta 
	  $$
	  Final state energy and perpendicular component:
	  \setlength{\abovedisplayskip}{0.6mm}
	  \setlength{\belowdisplayskip}{0.6mm}
	  $$
	  E_f = \frac{\hbar^2}{2m} (\vec{k}_{f} + \vec{G} )^2 - |V_0|
	  $$
	  \setlength{\abovedisplayskip}{0.6mm}
	  \setlength{\belowdisplayskip}{0.6mm}
	  $$
	  k_{f_\bot} = \sqrt{\frac{2m}{\hbar^2}(E_{kin} + |V_0|) - \vec{G}_\|^2}-G_\bot ~~~~  \vartheta = 0
	  $$
%	  Here $\vec{G}_\|$ could be a reciprocal surface lattice vector.
	 \end{block}
	\end{column} 
  \end{columns}  
\end{frame}

\subsection{Energy Relations and Analysis}
\begin{frame}
  \frametitle{Energy Relations during Measuring Process}
   \begin{columns}
    \begin{column}{0.6\textwidth}
	 \begin{block}{}
       \pgfdeclareimage[width=\textwidth]{5-steps}{pic/5-steps}
       \pgfuseimage{5-steps}
	 \end{block}
	\end{column}
    \begin{column}{1mm}
	\end{column}
    \begin{column}{0.35\textwidth}  
	 \begin{block}{Kinetic Energy}
	  \setlength{\abovedisplayskip}{0mm}
	  $$
	  E_{kin} = \frac{\vec{p}^2}{2m_e} = \frac{m_e}{2} \vec{v}^2
	  $$
	 \end{block}
	 \begin{block}{Lorentz Force}
	  \begin{center}
	   $\vec F=q (\vec E + \vec v \times \vec B)$ 
	  \end{center}
	  \centerline{\textcolor{green!36!black}{$ {\bf B} \le 0.25 \mu T$}}
	 \end{block}
	 \begin{exampleblock}{Example}
	  \setlength{\abovedisplayskip}{0mm}
	  \begin{eqnarray*}
	   \hbar\omega & = & 21.2 \mbox{eV ~~ He-I}\\
	   \Phi & = & 4.8 \mbox{eV ~~~ Au}\\
	   E_{kin} & = & 16.4 \mbox{eV } ~~~ E_F
	  \end{eqnarray*}	 
	 \end{exampleblock}	 
	\end{column} 
  \end{columns}  
\end{frame}  

\begin{frame}
  \frametitle{Invariance of measured Fermi-Energy on Work Function}
  \begin{columns}
    \begin{column}{0.47\textwidth}
      \begin{block}{Fermi-edge Gold, $\Phi = 4.8$ eV}
	    \begin{center}
          \pgfdeclareimage[width=0.8\textwidth]{gold}{pic/gold}
		  \pgfuseimage{gold}\\
		$E_F = (17.085 \pm 0.004) $ eV
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.47\textwidth}
	  \begin{block}{Fermi-edge Indium, $\Phi=4.12$ eV}
	    \begin{center}	   
          \pgfdeclareimage[width=0.8\textwidth]{indium}{pic/indium}
		  \pgfuseimage{indium} \\
		$E_F = (17.076 \pm 0.005) $ eV
		\end{center}		
      \end{block}
    \end{column}
  \end{columns}
  \begin{alertblock}{}
    The measured Fermi-energy does not depend on the work function of the sample. 
	During the measuring process the entire spectrum is shifted. 
  \end{alertblock}
\end{frame}

\begin{frame}
  \frametitle{Work Function and Energy Relations}
  \begin{columns}
    \begin{column}{0.5\textwidth} 
      \pgfdeclareimage[width=\textwidth]{7-work}{pic/7-work}
	  \pgfuseimage{7-work} \\
	\end{column}
	\begin{column}{2mm}
	\end{column}
    \begin{column}{0.43\textwidth}  
	 \begin{tabbing}
	  $E_i$ \qquad\=energy of initial state\\
	  $E_f$ \>energy of final state\\
	  $E_{VBM}$ \>valence band maximum\\
	  $E_{vac,S}$ \>vacuum level of sample\\
	  $E_{vac,A}$ \>vacuum level of analyser\\
	  $\hbar\omega$ \>photon energy\\
	  $U_b$ \>binding energy\\
	  $E_{thr}$ \>threshold of photo emission\\
	  \textcolor{blue}{$E_{kin,S}$} \>kinetic energy of eletrons\\
	  \>at the sample\\
	  \textcolor{red}{$E_{kin,A}$} \>kinetic energy of eletrons\\
	  \>at analyser\\
	  $U_K$ \>contact potential\\
	  $\Phi_S$ \>work function of sample\\
	  $\Phi_A$ \>work function of analyser\\
	  $E_F$ \>Fermi energy
	  \end{tabbing}
     \end{column}
  \end{columns}  
\end{frame}

\begin{frame}
  \frametitle{Fitting and resulting Band Structure}
  \begin{columns}
    \begin{column}{0.25\textwidth} 
      \pgfdeclareimage[width=\textwidth]{8-mess}{pic/8-mess}
	  \pgfuseimage{8-mess}
	\end{column}
	\pause
	\begin{column}{0.09\textwidth}
      \pgfdeclareimage[width=\textwidth]{arrow}{pic/arrow}
	  \pgfuseimage{arrow}	
	\end{column}
    \begin{column}{0.61\textwidth} 
      \pgfdeclareimage[width=\textwidth]{8-fit}{pic/8-fit}
	  \pgfuseimage{8-fit}	
    \end{column}
  \end{columns}   
\end{frame}

\subsection{Design of an Energy Analyser} % ************

\begin{frame} 
  \frametitle{Retarding and Focussing}
  \begin{columns}
    \begin{column}{0.39\textwidth}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{scienta1}{pic/scienta1}
		  \pgfuseimage{scienta1}
		\end{center}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.53\textwidth}
	  \begin{block}{Preretarding stage}
	    Usually a preretarding stage is used prior to the energy analysis. Electrons 
		enter the analyser with a specified pass energy. One can decelerate (or 
		accelerate) electrons (almost) without changing their absolute energy spread.
%		The energy resolution and intensity of an energy analyser depends its pass energy. 
		Measured kinetic energy:\\ 
		\centerline{$E_{kin,A} = E_{pass} - U_{ret}$}
      \end{block}
	  \begin{exampleblock}{Negative Kinetic Energy}
	  \begin{center}
	   \vspace{1mm}
	   \begin{tabular}{lcr}
	     E$_{kin,S}$ & = & 0.2 eV \\
		 U$_{ret}$   & = & 10.2 eV \\
		 U$_K$       & = & -0.4 eV \\
		 E$_{pass}$  & = & 10 eV \\
		 E$_{kin,A}$ & = & -0.2 eV\\
	   \end{tabular}
	  \end{center}
	 \end{exampleblock}
	\end{column}
  \end{columns}   
\end{frame}

\begin{frame} 
  \frametitle{Energy Dispersion inside Spherical Condensator}
    \pgfdeclareimage[width=0.98\textwidth]{scienta2}{pic/scienta2}
	\centerline{\pgfuseimage{scienta2}}
\end{frame}


\begin{frame}
  \frametitle{Angle Resolution by Mapping of Entrance Point}
    \pgfdeclareimage[width=0.93\textwidth]{scienta3}{pic/scienta3}
    \pgfuseimage{scienta3} 
\end{frame}

\begin{frame}
  \frametitle{Resolution of Spherical Analyser}
  \begin{columns}
    \begin{column}{0.59\textwidth}
        \pgfdeclareimage[width=\textwidth]{principle}{pic/principle}
		\pgfuseimage{principle} 
    \end{column}
    \begin{column}{0.38\textwidth}
	  \begin{block}{Potentials on hemispheres}
	    For transmission of electrons with initial emergy $E_0$ along a path 
		with $R_0 = (R_{in} + R_{out})/2$ the potential has to be
		$$
		V_{out} = E_0[3-2(R_0/R_{out})]
		$$
		$$
		V_{in} = E_0[3-2(R_0/R_{in})]
		$$
      \end{block}
	  \begin{block}{Resolution}
	    $$
		\frac{\Delta E}{E_{pass}} = \frac{w}{2R_0} + \alpha^2
		$$
		\begin{center}
	      \begin{tabular}{cl}
		  w & width entrance slit\\
		  $\alpha$ & acceptance angle\\
		 \end{tabular}
		\end{center}
      \end{block}	  
    \end{column}
  \end{columns}
\end{frame}

% *************************************************************************** [3]
\section{Zero Gap Semiconductor}
\subsection{Survey in Gray Tin}

\begin{frame}
  \frametitle{Survey of Narrow-Gap Semiconductors: $\alpha$-Sn}
  \begin{block}{}
    \begin{enumerate}
	  \item[(I)]  cruical magnetoresistance measurements on n-type 
				  material by Ewald's group which showed no anisotropy at 4 or 77 K 
				  but a dominance of electrons of (111) symmetry at 200 K
	  \item[(II)] measurements of conductivity, Hall effect and susceptibility at 
				  temperatures above 150 K, which demonstrated an activation energy of 0.08 eV
	  \item[(III)] measurement of an electron mass of 0.02 $m_0$ which was inconsistent with 
				  a small ($\rm \Gamma_8^{+} - \Gamma_7^{-}$) gap
	  \item[(IV)] pressure measurements which gave a high-temperature pressure 
	              coefficient consistens with conduction band minima at the L point
	  \item[(V)]  pressure measurements on conductivity and Hall effect at low temperatures 
				  which were inconsistent with the presence of (111) electrons and also 
				  of (000) electrons in a $\rm \Gamma_7^{-}$ \it extremum
	\end{enumerate}
  \end{block}
  \begin{columns}
    \begin{column}{0.47\textwidth} 
	  \begin{alertblock}{}
	    No conventional positive-gap band structure could fit all of these criteria.
	  \end{alertblock}
	\end{column}  
    \begin{column}{1mm} 
	\end{column}  
    \begin{column}{0.47\textwidth}
	  \begin{exampleblock}{}
	   {\scriptsize
	    William Paul \& Steven Groves:
		{\it Band Structure of Gray Tin}, 1963, 
		{\rm Phys. Rev. Lett. {\bf 11} 194 } }
	  \end{exampleblock}
	\end{column}  
  \end{columns}
\end{frame}

\begin{frame}
  \frametitle{Inverted Bandstructure}
  \begin{columns}
    \begin{column}{0.6\textwidth}   
          \pgfdeclareimage[width=\textwidth]{neggap1}{pic/neggap1}
		  \pgfuseimage{neggap1}   
	\end{column}  
    \begin{column}{1mm} 
	\end{column}  
    \begin{column}{0.35\textwidth}
	  \begin{block}{$\alpha$-Sn paper}
	   Results for HgTe was in S. Groves thesis, but statement about it was 
	   taken out of {\it PRL} paper in case speculations on this material 
	   they had not measured themselves would jeopardise publication.
	  \end{block}
	  \begin{block}{ZnS semiconductors}
	   bandgap definition:
	   $$
	   \rm E_0 = E(\Gamma_6) - E(\Gamma_8)
	   $$
	   \centerline{(direct bandgap)}
	  \end{block}
	\end{column}  
  \end{columns}
\end{frame}

\subsection{Alloys of CdTe and HgTe}
\begin{frame}
  \frametitle{Bandgap for $\rm CdTe$, $\rm HgTe$ and $\rm Cd_XHg_{1-X}Te$}
  \begin{columns}
     \begin{column}{0.33\textwidth}
      \pgfdeclareimage[width=\textwidth]{gaas2}{pic/gaas2}
	  \pgfuseimage{gaas2}	
	\end{column} 
    \begin{column}{1mm} 
	\end{column} 	
    \begin{column}{0.63\textwidth}   
      \pgfdeclareimage[width=0.8\textwidth]{cd-hg}{pic/cd-hg}
	  \centerline{\pgfuseimage{cd-hg}}\\
      \begin{block}{}
	   \begin{tabular}{ccc}
		 \bf CdTe &\bf property & \bf HgTe  \\[0.5ex]
		 0,675  & Phillips-Van Vechten ionicity f$_i$  & 0,68 \\
		 6.488  & lattice constant   & 6.445 \\
		 1.56   & gap    & -0.283 \\
	   \end{tabular}
	  \end{block}
	\end{column}	
  \end{columns} 
\end{frame}

\begin{frame}
  \frametitle{$\rm Cd_XHg_{1-X}Te$}
  \begin{columns}
    \begin{column}{0.4\textwidth}
	 \begin{center}
      \pgfdeclareimage[width=\textwidth]{8-fit}{pic/8-fit}
	  \pgfuseimage{8-fit}\\
	  inverted bandstructure of HgTe,\\ measured with ARPES
	 \end{center} 
	\end{column} 
    \begin{column}{1mm} 
	\end{column} 	
    \begin{column}{0.57\textwidth}   
      \begin{block}{Properties}
        CdTe and HgTe are consolute. 
		The bandgap can be free adjusted. The alloys have a high electron 
		mobility and a high optic absorption coefficient.
	  \end{block}
      \begin{block}{Fabrication}
	   \begin{itemize}
	   	 \setlength{\itemsep}{0mm}
	     \item modified Bridgeman technique
%		 \item liquid phase epitaxy (LPE)
		 \item molecular beam epitaxy (MBE)
	   \end{itemize}
	  \end{block}
      \begin{block}{Application}
	   \begin{itemize}
	   	 \setlength{\itemsep}{0mm}
	     \item dual-band infrared detectors with high quantum efficiency 
		       (simultaneous detection in the MWIR and LWIR)\\
		 \item CCD-array for IR-astronomy
	   \end{itemize}
	 \end{block}	  
	\end{column}	
  \end{columns} 
\end{frame}

% *************************************************************************** [4]
\section{Measurements and Results}
\subsection{Preparation}

\begin{frame}
  \frametitle{Samples of $\rm Cd_XHg_{1-X}Te$}
  \begin{columns}
    \begin{column}{0.5\textwidth}  
      \begin{block}{}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{samples}{pic/samples}
		  \pgfuseimage{samples}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.34\textwidth}
	  \begin{block}{Data of Samples}
	    \vspace{1mm}
	    \begin{tabular}{clr}
		 \bf Nr. & \bf\quad X & \bf weight  \\[0.5ex]
		 \rm Ia  & 0,07   & 127 mg \\
		 \rm Ib  & 0,07   & \\
		 \rm II  & 0,4    & 130 mg \\
		 \rm IIIa& 0,2    &  92 mg \\
		 \rm IIIb& 0,2    &  67 mg \\
		 \rm IV  & 0,183  & 129 mg \\
		 \rm V   & 0,1955 & 248 mg \\
		 \rm VI  & 0,105  & 109 mg \\
		\end{tabular}
	    \vspace{1mm}
      \end{block}
	  \begin{center}
        \pgfdeclareimage[width=40mm]{zns}{pic/zns}
		\pgfuseimage{zns}
	  \end{center}	  
	\end{column}
  \end{columns}  	  
\end{frame}

\begin{frame}
  \frametitle{Crystal Quality - Laue Images}
  \begin{columns}
    \begin{column}{0.7\textwidth}    
	  \begin{block}{Polaroid and Simulation}
	    \begin{center}	   
          \pgfdeclareimage[width=\textwidth]{laue}{pic/laue}
		  \pgfuseimage{laue} 
		\end{center}		
      \end{block}  
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.25\textwidth}	
	  \begin{block}{Sample \rm Ib}
	    \begin{center}	   
		  $\rm Cd_{0.07}Hg_{0.93}Te$ \\[1mm]
          \pgfdeclareimage[width=\textwidth]{sample3}{pic/sample3}
		  \pgfuseimage{sample3}\\
		  \setlength{\tabcolsep}{0.7mm}
	      \begin{tabular}{rr}		  		
			thickness: & 620 $\mu$m\\
		    weight:    & 81 mg\\
		  \end{tabular}
		\end{center}
	  \end{block}
	  \vspace{10mm}
	\end{column}
  \end{columns}  	
\end{frame}




\begin{frame}
  \frametitle{Surface Preparation - Cleavage Mechanism}
  \begin{columns}
    \begin{column}{0.394\textwidth}
      \begin{block}{}
	    \begin{center}
          \pgfdeclareimage[width=0.8\textwidth]{orlowski}{pic/orlowski}
		  \pgfuseimage{orlowski}\\
		  cleavage chamber by \\
		  N. Orlowski, assembled 2000
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.45\textwidth}
	  \begin{block}{}
	    \begin{center}	   
          \pgfdeclareimage[width=0.8\textwidth]{sample1}{pic/sample1}
		  \pgfuseimage{sample1}\\[1mm] 
          \pgfdeclareimage[width=0.8\textwidth]{sample2}{pic/sample2}
		  \pgfuseimage{sample2}\\
		  cleavage in sample holder
		  \end{center}		
      \end{block}
	\end{column}
  \end{columns}  
\end{frame}


\subsection{Measurement Results}

\begin{frame}
  \frametitle{Surface Quality after Cleavage}
  \begin{columns}
    \begin{column}{0.53\textwidth}
      \begin{block}{SEM Image}
	    \begin{center}
          \pgfdeclareimage[width=0.9\textwidth]{sem}{pic/sem}
		  \pgfuseimage{sem}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.4\textwidth}
	  \begin{block}{LEED Image}
	    \begin{center}	   
          \pgfdeclareimage[width=43mm,height=36.4mm]{leed}{pic/leed}
		  \pgfuseimage{leed}
  	    \end{center}		
      \end{block}
	  \begin{alertblock}{Reasons for LEED}
		\begin{itemize}
		  \item craggedness of cleavage
		  \item spot size electron beam
		  \item failure in apparature
		\end{itemize}	  
	  \end{alertblock}
	\end{column}
  \end{columns} 
\end{frame}

\begin{frame}
  \frametitle{BESSY Measurements at BUS Beamline, $\hbar\omega = 80$ eV}
    \pgfdeclareimage[width=\textwidth]{cdhgte1}{pic/cdhgte1}
    \pgfuseimage{cdhgte1}  
\end{frame}

\begin{frame}
  \frametitle{Dispersion in Valence Band? Gap? Peak Position?}
  \begin{columns}
    \begin{column}{0.3\textwidth}
      \begin{block}{BESSY $h\nu = 40 $ eV}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{gap-bessy1}{pic/gap_bessy1}
		  \pgfuseimage{gap-bessy1}\\
		  $\rm Cd_{0.18}Hg_{0.82}Te$\\
		  26. 1. 2007
		\end{center}  
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.3\textwidth}	
      \begin{block}{BESSY $h\nu = 80 $ eV}
	    \begin{center}	  
          \pgfdeclareimage[width=\textwidth]{gap-bessy2}{pic/gap_bessy2}
		  \pgfuseimage{gap-bessy2}\\
		  $\rm Cd_{0.4}Hg_{0.6}Te$\\
		  3. 2. 2007		  
		\end{center} 		  
      \end{block}	  
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.3\textwidth}
      \begin{block}{He-I $h\nu = 21.2 $ eV}
	    \begin{center}	  
          \pgfdeclareimage[width=\textwidth]{gap-he}{pic/gap_he}
		  \pgfuseimage{gap-he}\\
		  $\rm Cd_{0.2}Hg_{0.8}Te$\\
		  8. 3. 2007		  
		\end{center} 		  
      \end{block}	
	\end{column}
  \end{columns} 
\end{frame}

\begin{frame}
  \frametitle{Cleavage Quality - Satellites of Hg5d$_{3/2}$}
  \begin{columns}
    \begin{column}{0.3\textwidth}
      \begin{block}{BESSY $h\nu = 40 $ eV}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{5d-3}{pic/5d_3}
		  \pgfuseimage{5d-3}\\
		  $\rm Cd_{0.18}Hg_{0.82}Te$\\
		  26. 1. 2007
		\end{center}  
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.3\textwidth}	
      \begin{block}{BESSY $h\nu = 80 $ eV}
	    \begin{center}	  
          \pgfdeclareimage[width=\textwidth]{5d-1}{pic/5d_1}
		  \pgfuseimage{5d-1}\\
		  $\rm Cd_{0.4}Hg_{0.6}Te$\\
		  3. 2. 2007		  
		\end{center} 		  
      \end{block}	  
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.3\textwidth}
      \begin{block}{He-I $h\nu = 21.2 $ eV}
	    \begin{center}	  
          \pgfdeclareimage[width=\textwidth]{5d-2}{pic/5d_2}
		  \pgfuseimage{5d-2}\\
		  $\rm Cd_{0.2}Hg_{0.8}Te$\\
		  8. 3. 2007		  
		\end{center} 		  
      \end{block}	
	\end{column}
  \end{columns}
  \vspace{1.5mm}
  {\tiny 
    X. Yu, L. Vanzetti, G. Haugstad, A. Raisanen, A. Franciosi: 
	{\it Inequivalent sites for Hg at the HgTe (110) surface}. Surf. Sci {\bf 275}, 92-100, (1992)
  }
\end{frame}



% *************************************************************************** [5]
\section{Summary and Outlook}
\subsection{Summary}

\begin{frame}
  \frametitle{Conclusion}
  \begin{columns}
   \begin{column}{0.45\textwidth} 
     \pgfdeclareimage[width=\textwidth]{ar65}{pic/ar65}
	 \pgfuseimage{ar65}  
   \end{column}  
   \begin{column}{0.5\textwidth}  
   \begin{block}{Photo Electron Spectrosopy}
    \begin{itemize}
     \item powerfull technique to determine bandstructure and electronic properties of solids
     \item detected electrons easy to analyse
     \item surface sensitive
     \item UHV conditions inevitable
    \end{itemize}
   \end{block}
   \pause
   \begin{block}{$\rm Cd_XHg_{1-X}Te$}
    \begin{itemize}
     \item first angle resolved measurement
     \item inverted bandstructure - zero gap
     \item complicated (110) surface preparation
    \end{itemize}
   \end{block}
  \end{column}
 \end{columns}  
\end{frame}

\subsection{Outlook}
\begin{frame}
 \frametitle{Outlook}
 \begin{columns}
  \begin{column}{0.6\textwidth}   
  \begin{block}{Measurement}
    \begin{itemize}
     \item Laue pictures of measured crystals
     \item LEED at WESPHOA chamber
     \item EDX for composition
	 \item automatic nitrogen refill system
	 \item measurements at BESSY training beamline with syncrotron light and new Scienta
	 \item cooled cleavage
    \end{itemize}
  \end{block}
  \begin{block}{More Samples ...}
    \begin{itemize}
     \item samples of already grown $\rm Cd_xHg_{1-X}Te$ crystals from Hr. Sölle
     \item growth of new $\rm Pb_xZn_{1-X}Te$
	 \item more samples from Moscow
    \end{itemize}
  \end{block}
  \end{column}
  \begin{column}{0.35\textwidth} 
    \pgfdeclareimage[width=\textwidth]{ar65-2}{pic/ar65-2}
	\pgfuseimage{ar65-2}    
  \end{column}  
 \end{columns}   
\end{frame}

\begin{frame}
  \begin{center}
    \Large Thanks for your attention!
  \end{center}
\end{frame}

\end{document}

\end{document}