added parts of tutorial and proposed solutions 6

diff --git a/solid_state_physics/tutorial/1_06.tex b/solid_state_physics/tutorial/1_06.tex
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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 I}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ WS 2007/08\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 6}
+\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{\ldots}
+
+\ldots
+
+\begin{enumerate}
+ \item \ldots
+ \item \ldots
+\end{enumerate}
+
+\end{document}

diff --git a/solid_state_physics/tutorial/1_06s.tex b/solid_state_physics/tutorial/1_06s.tex
new file mode 100644 (file)
index 0000000..f3d6992
--- /dev/null
+++ b/solid_state_physics/tutorial/1_06s.tex
@@ -0,0 +1,70 @@
+\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 I}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ WS 2007/08\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 6 - proposed solutions}
+\end{center}
+
+\section{Indirect band gap of silicon}
+
+\begin{enumerate}
+ \item \begin{itemize}
+        \item Photon wavelength:\\
+             $E_g=\hbar\omega=\hbar\frac{2\pi}{T}=\hbar 2\pi v
+                 \stackrel{c=v\lambda}{=}\hbar 2\pi\frac{c}{\lambda}$
+             $\Rightarrow \lambda=\frac{\hbar 2\pi c}{E_g}
+                                 =\frac{hc}{E_g}=\ldots=1.11 \, \mu m$
+       \item Photon momentum:\\
+             $p=\hbar k=\hbar\frac{2\pi}{\lambda}=\frac{h}{\lambda}
+               =\ldots=5.97 \cdot 10^{-28} \, kg\frac{m}{s}$
+       \end{itemize}
+ \item Phonon momentum necessary for transition:\\
+       $p=\hbar \cdot \Delta k=\hbar \cdot 0.85 \, \frac{2\pi}{a}
+         =\frac{0.85 \, h}{a}=\ldots=1.04 \cdot 10^{-24} \, kg\frac{m}{s}$\\
+       $\rightarrow$ Phonon momentum 3 orders of magnitude below
+                     the momentum necessary for transition!
+ \item 
+\end{enumerate}
+
+\section{\ldots}
+
+\ldots
+
+\begin{enumerate}
+ \item \ldots
+ \item \ldots
+\end{enumerate}
+
+\end{document}