From 231dfbc53dad8c88281f78185c06010be3973e95 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20Th=C3=BCr?= <thuer.simon@hotmail.com>
Date: Fri, 7 Apr 2023 23:08:41 +0200
Subject: [PATCH] make tex friendlyer

---
 02_carrier_transport.tex | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/02_carrier_transport.tex b/02_carrier_transport.tex
index 963e45b..cccd15b 100644
--- a/02_carrier_transport.tex
+++ b/02_carrier_transport.tex
@@ -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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