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+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics II}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ SS 2011\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 1}
+\end{center}
+
+\section{Indirect band gap of silicon}
+
+Some facts about silicon:
+\begin{itemize}
+ \item Lattice constant: $a=5.43 \cdot 10^{-10} \, m$.
+ \item Silicon has an indirect band gap.
+       \begin{itemize}
+        \item The minimum of the conduction band is located at
+             $k=0.85 \frac{2 \pi}{a}$.
+       \item The maximum of the valance band is located at $k=0$.
+       \item The energy gap is $E_g=1.12 \, eV$.
+       \end{itemize}
+\end{itemize}
+\begin{enumerate}
+ \item Calculate the wavelength of the light necessary to lift an electron from
+       the valence to the conduction band.
+       What is the momentum of such a photon?
+ \item Calculate the phonon momentum necessary for the transition.
+       Compare the momentum values of phonon and photon.
+ \item Draw conclusions concerning optical applications.
+\end{enumerate}
+
+\section{Charge carrier density of semiconductors}
+
+Calculate the charge carrier densities $n$ and $p$ for $E_{\text{c}}-\mu_{\text{F}} >> k_{\text{B}}T$ and $\mu_{\text{F}}-E_{\text{v}} >> k_{\text{B}}T$.\\\\
+{\bf Hint:}
+Consider the influence of these two conditions for the energy of the states, which are situated in the conduction and valence band.
+The parabolic approximation of the density of states of electrons in the conduction and holes in the valence band with the effective masses $m_n$ and $m_p$ is given by
+$D_c(\epsilon)=\frac{1}{2\pi^2}(\frac{2m_n}{\hbar^2})^{3/2}(\epsilon-E_c)^{1/2}$ and
+$D_v(\epsilon)=\frac{1}{2\pi^2}(\frac{2m_p}{\hbar^2})^{3/2}(E_v-\epsilon)^{1/2}$.
+If you do not calculate the non-simplified Fermi-integral the substitutions $x=(\epsilon - E_{\text{c}})/k_{\text{B}}T$ and $x=(E_{\text{v}}-\epsilon)/k_{\text{B}}T$ can be used. Furthermore use the equality $\int_0^{\infty} x^{1/2} e^{-x} dx = 1/2 \sqrt{\pi}$.
+
+\end{document}