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\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}

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