% Präsentation Photoemission 10. 12. 2007 in Moskau
% see more at http://people.physik.hu-berlin.de/~kreier/

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\title{Angle Resolved PES on CdHgTe}
\subtitle[Seminar Low Temperature Physics]{Seminar on the Department of Low Temperature Physics and Supra Conductors}
\author{Matthias Kreier}
\institute{Humboldt Universität zu Berlin}
\date{10. 12. 2007}
\pgfdeclareimage[height=22mm]{titlegraphic}{pic/titlepic} 
\titlegraphic{\pgfuseimage{titlegraphic}}

\begin{document}

\begin{frame}[plain]  % das ist eine selbstgebastelte Titelseite, mit Russisch gibt es Tausende Fehlermeldungen
  \setbeamercolor{ueberschrift}{fg=white,bg=blue!70!black!85!red}
  \begin{beamercolorbox}[sep=1mm,wd=\textwidth,center,rounded=true, shadow=true]{ueberschrift}
    \usebeamerfont{frametitle}
    \ru{Определение Электронной Зонной Структуры} $\rm Cd_{X}Hg_{1-X}Te$
	\ru{Методом Угловой Фотоэлектронной Спектроскопии} \\
	\vspace{2mm}
	\usebeamerfont{subtitle}
	\ru{Семинар Кафедры Физики Низких Температур и Сверхпроводимости}
  \end{beamercolorbox}
  \vspace{1mm}
  \begin{center}
    Matthias Kreier
	\vspace{5mm}
	
    \usebeamerfont{institute}
	Humboldt Universität zu Berlin\\
	Arbeitsgruppe Elektronische Eigenschaften und Supraleitung
	\vspace{5mm}
	
    \usebeamerfont{normal}
	10. 12. 2007
	\vspace{5mm}
	
   \pgfuseimage{titlegraphic}
  \end{center}
\end{frame}

%\frame{
%	\frametitle{\ru{Структура речь}}  
%	\tableofcontents   % this would be english ...
%	[pausesections]
%}
\frame{
  \frametitle{\ru{Структура доклада}}  % selbstgebastelte Table of Contents, da Struktur englisch
  \begin{enumerate}
  \item \ru{Мотивация}
  \item \ru{Угловая Фотоэлектронная Спектроскопия}
    \begin{itemize}
	  \item \ru{Введение и базовые принципы}
	  \item \ru{Энергетические соотношения и анализ}
	  \item \ru{Устройство анализатора энергии}
	\end{itemize}
  \item \ru{Качество поверхности, проверка и предсказания}
    \begin{itemize}
      \item Laue transmission pictures
	  \item Surface preparation by cleaving
	  \item Surface check by SEM, AFM and LEED
	\end{itemize}
  \item \ru{Результаты} ARPES \ru{экспериментов на} $\rm CdHgTe$
    \begin{itemize}
      \item Expected spectra and bandstructure
	  \item ARPES results and dispersion
	  \item Interpretation of results
	\end{itemize}  
  \item \ru{Проблема, выводы и перспективы} 
  \end{enumerate}
%	[pausesections]
}

% *************************************************************************** [1]
\section{Motivation}

\subsection{Bandstructure and Fermi Surface}
\begin{frame}
  \frametitle{\ru{Структура зоны и поверхность Ферми}}
  \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}

\subsection{Experimental Results vs. Theory}
\begin{frame}
  \frametitle{\ru{Экспериментальные результаты и теория}}
  \begin{block}{\ru{Спектроскопия фотоэлектронов на графите}}
    \pgfdeclareimage[width=\textwidth]{graphite}{pic/graphite}
    \pgfuseimage{graphite}
  \end{block}
\end{frame}

% *************************************************************************** [2]
\section{Angle Resoved Photoelectron Spectroscopy}

\subsection{General Setup of an ARPES experiment}
\begin{frame}
\setbeamertemplate{background}{\pgfuseimage{titlegraphic}}
  \frametitle{\ru{Устройство} ARPES}
    \pgfdeclareimage[width=120mm, height=70mm]{1-general}{pic/1-generalRU}
    \pgfuseimage{1-general}
\end{frame}

\subsection{Step 1: Photoexcitation of the Electron}
\begin{frame}
  \frametitle{\ru{Первый шаг: Фотовозбуждение электрона}}
  \begin{block}{\ru{Вероятность перехода}}
    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}{\ru{Гамильтониан}}
      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}{\ru{Сохранение энергии}}
	    $$
	    E_f = E_i + \hbar \omega
	    $$
  	  \end{block}  
    \end{column}
    \begin{column}{1mm}
    \end{column}
    \begin{column}{0.46\textwidth}
      \begin{block}{\ru{Сохранение импульса}}
	    $$
	    \vec{k_i} = \vec{k_f}
  	    $$
  	  \end{block}
    \end{column}  
  \end{columns}
\end{frame}

\subsection{Step 2: Transport to the Surface}
\begin{frame}
  \frametitle{\ru{Второй шаг: Транспорт фотоэлектронов к поверхности}}
   \begin{columns}
    \begin{column}{0.70\textwidth}
	 \begin{block}{\ru{Средний свободный пробег электронов в твёрдом 
	                   веществе в зависимости от энергии}}
	  \begin{figure}
       \pgfdeclareimage[height=60mm]{3-mfw}{pic/3-mfw}
       \pgfuseimage{3-mfw}
	  \end{figure}
	 \end{block}
	\end{column}
    \begin{column}{1mm}
	\end{column}
    \begin{column}{0.28\textwidth}
	 \begin{block}{\ru{Ограничения метода}}
	   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. 
	 \end{block}
	 \begin{block}{\ru{Вторичные электроны}}%Secondaries
	  By scattering a spectra of low energy seconda- ry electrons generates.
	  %\ru{Из за соударении генериются спектра малоэнергих вторичных электронов}
	 \end{block}
	\end{column} 
  \end{columns}
\end{frame}

\subsection{Step 3: Penetration through the surface}
\begin{frame}
  \frametitle{\ru{Третий шаг: Проникновение через поверхность}}
   \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}{\ru{Дисперсия свободных электронов}}
	  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}{\ru{Отражение электронов на поверхности}}
	  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 during Measuring Process}
\begin{frame}
  \frametitle{\ru{Энергетические соотношения во время измерения}}
   \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}{\ru{Кинетическая энергия}}
	  \setlength{\abovedisplayskip}{0mm}
	  $$
	  E_{kin} = \frac{\vec{p}^2}{2m_e} = \frac{m_e}{2} \vec{v}^2
	  $$
	 \end{block}
	 \begin{block}{\ru{Сила Лоренца}}
	  \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}{\ru{Пример}}
	  \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}  

\subsection{Invariance of measured Fermi-Energy on Work Function}
\begin{frame}
  \frametitle{\ru{Зависит ли измеренная энергия} E$_F$ \ru{от работа выхода?}}
  \begin{columns}
    \begin{column}{0.47\textwidth}
      \begin{block}{\ru{Золота}, $\Phi = 4.8$ 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}{\ru{Индий}, $\Phi=4.12$ 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}{}
    \ru{Измеренная величина энерги Ферми не зависит от работы выхода материала образца.}
	\ru{Целая спектра сместилось во время измерения.} 
  \end{alertblock}
\end{frame}

\subsection{Work Function and Energy Relations}
\begin{frame}
  \frametitle{\ru{Работа выхода и отношения энергий}}
  \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}

\subsection{Fitting and resulting Band Structure}
\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 - Retarding and Focussing}
\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}

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

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

\subsection{Design of an Energy Analyser - Resolution of Spherical Analyser}
\begin{frame}
  \frametitle{\ru{Разрешение сферического анализатора}}
  \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{Surface Quality, Preparation, Expectations}
\subsection{Overview of gotten Samples}
\begin{frame}
  \frametitle{\ru{Образцы} $\rm Cd_XHg_{1-X}Te$}
  \pgfdeclareimage[width=120mm]{samples}{pic/samples1}
  \pgfuseimage{samples}
  \begin{columns}
      \begin{column}{0.45\textwidth}
	    \begin{block}{\ru{Образцы} I \ru{по} III}
		  Frist the diploma thesis was based on these 3 samples. 
		  This work was announced for at least 2 years.
		\end{block}
      \end{column}
	  \begin{column}{2mm}
	  \end{column}
      \begin{column}{0.45\textwidth}
	    \begin{block}{\ru{Образцы} IV \ru{по} VI}
		  Further Samples Lennard Dudy brought from Moscow. Samples during
		  measurement destroyed.
		\end{block}
      \end{column}
  \end{columns}	
\end{frame}

\subsection{Crystal Quality Check by Laue Refraction}
\begin{frame}
  \frametitle{\ru{Проверка качества кристалов методом Лауэ}}
  \begin{columns}
    \begin{column}{0.5\textwidth}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{laue2}{pic/laue2}
		  \pgfuseimage{laue2}
		\end{center}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.45\textwidth}	
	  \begin{block}{Fringe rings}

          In this Laue transmission picture we see some rings
		  that are typical for the Debye-Scherrer powder method. 
		  Accordingly this shows that our sample IV is not of 
		  perfect crystal quality. Rather there are some 
		  polycrystallic parts included in the sample. By the brightness
		  of the other spots its amount can be assumed to be lower 
		  than 10 \%

	  \end{block}
	  %\vspace{10mm}
	\end{column}
  \end{columns}  	
\end{frame}

\subsection{Surface Preparation by Cleaving}
\begin{frame}
  \frametitle{Surface Preparation - Cleavage Mechanism 1}
  \begin{columns}
    \begin{column}{0.45\textwidth}
      \begin{block}{}
	    \begin{center}
          \pgfdeclareimage[height=60mm]{orlowski}{pic/orlowski}
		  \pgfuseimage{orlowski}\\
		  Norbert Orlowski 2000
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.45\textwidth}
      \begin{block}{}
	    \begin{center}
          \pgfdeclareimage[height=60mm]{cleave2}{pic/cleave2}
		  \pgfuseimage{cleave2}\\
		  Matthias Kreier 2006
		\end{center}
      \end{block}
	\end{column}
  \end{columns}  
\end{frame}

\begin{frame}
  \frametitle{Surface Preparation - Cleavage Mechanism 2}
  \begin{columns}
    \begin{column}{0.394\textwidth}
      \begin{block}{}
	    \begin{center}
          \pgfdeclareimage[height=60mm]{cleave3}{pic/cleave3}
		  \pgfuseimage{cleave3}\\
		  inside the cleavage chamber
		\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{First Surface Quality Check by SEM}
\begin{frame}
  \frametitle{First Surface Quality Check by SEM}
  \begin{columns}
    \begin{column}{0.53\textwidth}
      \begin{block}{SEM Image}
	    \begin{center}
          \pgfdeclareimage[width=0.95\textwidth]{sem}{pic/sem}
		  \pgfuseimage{sem}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.4\textwidth}
	  \begin{block}{SEM results}
	    %\begin{center}
		In front we see the predermined breaking point - a sawn 
		valley of 100 $\mu$m depth and the resulting cleavage.
		Already in this magnification a steplike surface structure 
		can be observed. No flat surface as Van-der-Waals crystals 
		show after cleavage.
  	    %\end{center}		
      \end{block}
	  \begin{exampleblock}{Improvement}
        By cooled cleavage the surface quality improved 
		tremendously. We used liquid Nitrogen to cool the 
		samples down to 80 K and performed the cleavage.
	  \end{exampleblock}
	\end{column}
  \end{columns} 
\end{frame}

\subsection{Recent SEM pictures}
\begin{frame}
  \frametitle{Recent SEM pictures}
  \begin{columns}
    \begin{column}{0.45\textwidth}
      \begin{block}{\ru{Успешный раскол}}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{sem2}{pic/sem2}
		  \pgfuseimage{sem2}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.45\textwidth}
	  \begin{block}{\ru{Неуспешный раскол}}
	    \begin{center}
          \pgfdeclareimage[width=\textwidth]{sem3}{pic/sem3}
		  \pgfuseimage{sem3}
  	    \end{center}		
      \end{block}
	\end{column}
  \end{columns} 
\end{frame}

\subsection{Surface Quality Check by AFM}
\begin{frame}
  \frametitle{\ru{Исследование поверхности с} AFM}
  AFM - Atomic Force Microscope (\ru{АСМ Атомный Силовый Микроскоп})
  \begin{columns}
    \begin{column}{0.48\textwidth}
      \begin{block}{height measurement}
	    \begin{center}
          \pgfdeclareimage[width=57mm]{afm1}{pic/afm1}
		  \pgfuseimage{afm1}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.48\textwidth}
      \begin{block}{lateral deflection}
	    \begin{center}
          \pgfdeclareimage[width=57mm]{afm2}{pic/afm2}
		  \pgfuseimage{afm2}
		\end{center}
      \end{block}
	\end{column}
  \end{columns} 
\end{frame}

\begin{frame}
  \frametitle{3D-\ru{Исследование поверхности}, AFM}
  \begin{center}
    \pgfdeclareimage[width=120mm]{afm3}{pic/afm3}
    \pgfuseimage{afm3}
  \end{center}
\end{frame}

\begin{frame}
  \frametitle{3D-\ru{Исследование поверхности образец № 3}}
  \begin{center}
    \pgfdeclareimage[width=112mm]{afm4}{pic/afm4}
    \pgfuseimage{afm4}
  \end{center}
\end{frame}

\begin{frame}
  \frametitle{3D-\ru{Исследование поверхности образец № 5}}
  \begin{center}
    \pgfdeclareimage[height=70mm]{afm5}{pic/5-2}
    \pgfuseimage{afm5}
  \end{center}
\end{frame}

\subsection{Surface Quality Check by LEED}
\begin{frame}
 \frametitle{\ru{Обследование качества поверхности} LEED}
  \begin{columns}
    \begin{column}{0.5\textwidth}
      \begin{block}{LEED image at 156 eV}
	    \begin{center}
           \pgfdeclareimage[width=\textwidth]{leed}{pic/leed}
           \pgfuseimage{leed}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.45\textwidth}
      \begin{block}{LEED method}
        The LEED method is very sensitive to overstructures - but
		we see a clean surface with constant periodicity. By the 
		Laue formulae and the de Broglie relation
		\begin{center}
		$\vec{a_1}(\vec{k}-\vec{k_0})=2\pi h$\\
		$\vec{a_2}(\vec{k}-\vec{k_0})=2\pi k$\\
		$\lambda_{deBroglie} = \frac{h}{p} = \frac{h}{\sqrt{2mE}}$
		\end{center}
		with given Electron energy we get the lattice constants\\[2mm]
		\centerline{a = 3.5 \AA ~~~ b = 2.4 \AA}
		\vspace{1mm}
		of the observed sample.
      \end{block}
	\end{column}
  \end{columns} 
\end{frame}

% *************************************************************************** [4]
\section{ARPES Results on CdHgTe}
\subsection{Brillouin Zone of ZnS Crystals}
\begin{frame}
 \frametitle{Brillouin Zone of ZnS Crystals}
  \begin{columns}
    \begin{column}{0.55\textwidth}    
	    \begin{center}	   
          \pgfdeclareimage[width=\textwidth]{brillouin}{pic/brillouin}
		  \pgfuseimage{brillouin} 
		\end{center}		
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.4\textwidth}	
	  \begin{block}{Dispersion perpendicular}
	    %\begin{center}	   
          Volumen-Brillouin-Zone des fcc-Gitters mit hochsymetrischen Punten sowie 
		  die Oberflächen-Brillouin-Zonen der idealen (001) und (110)-Oberfläche.
		  Die hochsymmetischen Richtungen Delta, Sigma und Lambda, die den Richtungen 
		  [001], [110] und [110] entsprechen, sind ebenfalls eingezeichnet.
 	    %\end{center}
	  \end{block}
	  \vspace{10mm}
	\end{column}
  \end{columns}  
\end{frame}


\subsection{Expected Bandstructure}
\begin{frame}
 \frametitle{\ru{Ожидаемая структура зоны}}
   \begin{columns}
    \begin{column}{0.48\textwidth}
      \begin{block}{CdTe}
	    \begin{center}
          \pgfdeclareimage[width=50mm]{cdte}{pic/CdTeTheorie}
		  \pgfuseimage{cdte}
		\end{center}
      \end{block}
    \end{column}
	\begin{column}{1mm}
	\end{column}
    \begin{column}{0.48\textwidth}
      \begin{block}{HgTe}
	    \begin{center}
          \pgfdeclareimage[width=50mm]{hgte}{pic/HgTeTheorie}
		  \pgfuseimage{hgte}
		\end{center}
      \end{block}
	\end{column}
  \end{columns} 
\end{frame}

%\subsection{ARPES Results on CdTe and HgTe}
%\begin{frame}
% \frametitle{ \ru{Резултаты} ARPES \ru{на} CdTe \ru{и} HgTe }
%  ARPES Results on CdTe and HgTe
%\end{frame}

\subsection{ARPES on CdHgTe}
\begin{frame}
 \frametitle{\ru{Результаты} ARPES \ru{на} BESSY, $\hbar\omega = 125$ eV}
    \pgfdeclareimage[width=123mm]{cdhgte1}{pic/cdhgte2}
    \pgfuseimage{cdhgte1}
\end{frame}

\begin{frame}
 \frametitle{Core levels of Te$_{5/2}$ and Te$_{3/2}$} %
   \begin{center}
    \pgfdeclareimage[height=75mm]{corete}{pic/CoreTe}
    \pgfuseimage{corete}
   \end{center}
\end{frame}

\begin{frame}
 \frametitle{Core levels of Cd$_{5/2}$, Cd$_{3/2}$, Hg$_{5/2}$ and Hg$_{3/2}$} %
   \begin{center}
    \pgfdeclareimage[height=75mm]{corehg}{pic/CoreHg}
    \pgfuseimage{corehg}
   \end{center}
\end{frame}

\begin{frame}
 \frametitle{Valence band and core levels of Hg and Cd} %
   \begin{center}
    \pgfdeclareimage[height=75mm]{valence}{pic/valence}
    \pgfuseimage{valence}
   \end{center}
\end{frame}

\subsection{K perpendicular - Dispersion on CdHgTe}
\begin{frame}
 \frametitle{\ru{К-перпендикуляр: Дисперсия на} CdHgTe}
  \begin{columns}
    \begin{column}{0.48\textwidth}    
	    \begin{center}	   
          \pgfdeclareimage[height=75mm]{disp1}{pic/071130-3}
		  \pgfuseimage{disp1} 
		\end{center}
    \end{column}
	\begin{column}{2mm}
	\end{column}
    \begin{column}{0.48\textwidth}	
	    \begin{center}	   
          \pgfdeclareimage[height=75mm]{disp2}{pic/071130-2}
		  \pgfuseimage{disp2} 
		\end{center}
	\end{column}
  \end{columns}  
\end{frame}



\begin{frame}
  \frametitle{Core level shift depending on composition}
  \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}{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}
	\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}
  \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}

\subsection{Recent EPR results - explanation needed!}
\begin{frame}
 \frametitle{\ru{Результаты} EPR \ru{в Москве}}
   \begin{center}
    \pgfdeclareimage[height=75mm]{epr}{pic/epr}
    \pgfuseimage{epr}
   \end{center}
\end{frame}




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

\subsection{Summary}
\begin{frame}
  \frametitle{\ru{Выводы}}
  \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 complicated surface preparation
     \item successfull cooled cleavage
     \item bulk crystallity is to question
     \item dispersion in angle resolved measurements
    \end{itemize}
   \end{block}
  \end{column}
 \end{columns}  
\end{frame}

\subsection{Outlook}
\begin{frame}
  \frametitle{\ru{Перспективы}}
  \begin{columns}
    \begin{column}{0.6\textwidth}   
      \begin{block}{\ru{Исследования в Москве}}
        \begin{itemize}
			\item Determination of electron and hole mass
			\item Completed dispersion analysis
			\item Heat capacity measurement
			\item EPR on samples, SQUID
		\end{itemize}
	  \end{block}
      \begin{block}{\ru{Обратно в Берлине}}
		\begin{itemize}
		   \item Hall measurement of the samples in our workgroup by Dr. Dwelk
		   \item Measurements at BESSY training beamline with syncrotron light and new Scienta
		   \item Surface preparation by sputtering and annealing
		\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 \ru{Спасибо за внимание!}}\\
	\vspace{5mm}
	%further information can be found at\\
	\ru{подробную информацию смотрите на}\\
	\vspace{5mm}	
	\textcolor{blue!70!black}{http://people.physik.hu-berlin.de/$\sim$kreier/}
  \end{center}
\end{frame}

\end{document}

\end{document}