From 6ddd1384535f0e4ee9e13885212480cdd646e11d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Simon=20Th=C3=BCr?= <thuer.simon@hotmail.com>
Date: Fri, 7 Apr 2023 23:07:28 +0200
Subject: [PATCH] rm useless section, use only sss instead of ss2
---
02_carrier_transport.tex | 17 +++++++----------
1 file changed, 7 insertions(+), 10 deletions(-)
diff --git a/02_carrier_transport.tex b/02_carrier_transport.tex
index eb80b64..963e45b 100644
--- a/02_carrier_transport.tex
+++ b/02_carrier_transport.tex
@@ -26,11 +26,8 @@ Which gives us the useful relation:
n_i = \sqrt{N_cN_v}e^{-(E_c-E_v)/2kT} = \sqrt{N_cN_v}e^{-E_g/2kT}
\end{equation}
-\subsubsection{Temperature dependance}
-Looking at the equations in \autoref{label:sec:fermi} we see that the higher the temperature or the lower the band-gap, the more electrons and holes are created.
-\subsection{Carrier transport}
-\subsubsection{Thermal equilibrium}
+\subsection{Behaviour in thermal equilibrium}
\begin{align}
\lambda & \equiv \text{mean free path} [cm] \\
\tau_c & \equiv \text{mean time between collisions} [s^{-1}] \\
@@ -39,7 +36,7 @@ Looking at the equations in \autoref{label:sec:fermi} we see that the higher the
\end{align}
-\subsubsection{Drift velocity}
+\subsection{Drift velocity}
Quick electromag recap: (for holes use + and $m_p$)
\begin{align}
F & = -qE \\
@@ -51,7 +48,7 @@ Average drift velocity:
v_d = \pm \frac{qE\tau_c}{2m_{n,p}}
\end{equation}
-\subsubsection{Mobility}
+\subsection{Mobility}
For the sake of simplicity, let's define mobility for both holes and electrons.
(These values are usually found in diagrams.)
\begin{align}
@@ -61,7 +58,7 @@ For the sake of simplicity, let's define mobility for both holes and electrons.
\mu_n & >_mu_p
\end{align}
-\subsubsection{Drift current}
+\subsection{Drift current}
For the net drift current density slap together velocity, density and charge.
\begin{equation}
label{eq:drift_current}
@@ -79,7 +76,7 @@ Which gives us different resistances for n and p type semiconductors.
\end{align}
-\subsubsection{Diffusion current}
+\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.
\begin{align}
F_n & = -D_n\frac{\mathrm{d} n}{\mathrm{d} x} \\
@@ -94,12 +91,12 @@ Which gives us the diffusion current density:
\end{align}
-\subsubsection{Einstein relation between mobility and diffusion coefficient}
+\subsection{Einstein relation between mobility and diffusion coefficient}
\begin{equation}
\frac{D_n}{\mu_n} = \frac{D_p}{\mu_p} = \frac{kT}{q^2}
\end{equation}
-\subsubsection{Total current}
+\subsection{Total current}
\begin{alignat}{2}
J_{total} & =J_n+J_p & & \\
J_n & =J_n^{drift}+J_n^{diff} & & =qn\mu_nE+qD_n\frac{\mathrm{d} n}{\mathrm{d} x} \\
--
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