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Commit f047ea30 authored by T. van der Sar's avatar T. van der Sar
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Update 13_semiconductors.md - fix

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...@@ -62,6 +62,9 @@ A completely filled band is very similar to a completely empty band. ...@@ -62,6 +62,9 @@ A completely filled band is very similar to a completely empty band.
In a filled band $n(E)=1$ because $|E - E_F| \gg kT$. In an empty band $n(E)=0$. In a filled band $n(E)=1$ because $|E - E_F| \gg kT$. In an empty band $n(E)=0$.
Heat capacity $C_v = \tfrac{d}{dT}\int_{-\infty}^\infty E\times g(E) \times dE\times n_F(E, T) = 0$. Heat capacity $C_v = \tfrac{d}{dT}\int_{-\infty}^\infty E\times g(E) \times dE\times n_F(E, T) = 0$.
A completely filled band carries no electric current:
$$
j = 2e \frac{1}{2\pi} \int_{-\pi/a}^{\pi/a} v(k) dk = 2e \frac{1}{2\pi \hbar} \int_{-\pi/a}^{\pi/a} \frac{dE}{dk})\times dk = \\ j = 2e \frac{1}{2\pi} \int_{-\pi/a}^{\pi/a} v(k) dk = 2e \frac{1}{2\pi \hbar} \int_{-\pi/a}^{\pi/a} \frac{dE}{dk})\times dk = \\
2e \frac{1}{2\pi \hbar} [E(-\pi/a) - E(\pi/a)] = 0 2e \frac{1}{2\pi \hbar} [E(-\pi/a) - E(\pi/a)] = 0
\end{align} \end{align}
......
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