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32 {\LARGE {\bf Materials Physics I}\\}
37 {\Large\bf Tutorial 6 - proposed solutions}
40 \section{Indirect band gap of silicon}
44 \item Photon wavelength:\\
45 $E_g=\hbar\omega=\hbar\frac{2\pi}{T}=\hbar 2\pi v
46 \stackrel{c=v\lambda}{=}\hbar 2\pi\frac{c}{\lambda}$
47 $\Rightarrow \lambda=\frac{\hbar 2\pi c}{E_g}
48 =\frac{hc}{E_g}=\ldots=1.11 \, \mu m$
49 \item Photon momentum:\\
50 $p=\hbar k=\hbar\frac{2\pi}{\lambda}=\frac{h}{\lambda}
51 =\ldots=5.97 \cdot 10^{-28} \, kg\frac{m}{s}$
53 \item Phonon momentum necessary for transition:\\
54 $p=\hbar \cdot \Delta k=\hbar \cdot 0.85 \, \frac{2\pi}{a}
55 =\frac{0.85 \, h}{a}=\ldots=1.04 \cdot 10^{-24} \, kg\frac{m}{s}$\\
56 $\rightarrow$ Phonon momentum 3 orders of magnitude below
57 the momentum necessary for transition!