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} -- GitLab