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Verified Commit 231dfbc5 authored by Simon Josef Thür's avatar Simon Josef Thür
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make tex friendlyer

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......@@ -2,7 +2,8 @@
\subsection{Fermi distribution}
\label{label:sec:fermi}
Fermions are weird particles, see QM II.
Not sure if needed for this course, but heres the probability distribution:
Not sure if needed for this course,
but heres the probability distribution:
\begin{equation}
f(E) = \frac{1}{1+e^{(E-E_F)/kT}}
\end{equation}
......@@ -77,14 +78,17 @@ Which gives us different resistances for n and p type semiconductors.
\subsection{Diffusion current}
If there is a concentration gradient, the carriers will diffuse to equalize the concentration. Here flux $F \ [cm^{-2}s^{-1}]$ is the number of electrons/holes per unit area per unit time.
If there is a concentration gradient,
the carriers will diffuse to equalize the concentration.
Here flux $F \ [cm^{-2}s^{-1}]$ is the number of electrons/holes per unit area per unit time.
\begin{align}
F_n & = -D_n\frac{\mathrm{d} n}{\mathrm{d} x} \\
F_p & = -D_p\frac{\mathrm{d} p}{\mathrm{d} x}
\end{align}
Which gives us the diffusion current density:
(Defined as density times charge, ergo the double negative for electron diffusion.)
(Defined as density times charge,
ergo the double negative for electron diffusion.)
\begin{align}
J_n^{diff} & = qD_n\frac{\mathrm{d} n}{\mathrm{d} x} \\
J_p^{diff} & =- qD_p\frac{\mathrm{d} p}{\mathrm{d} x}
......
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