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Verified Commit 6ddd1384 authored by Simon Josef Thür's avatar Simon Josef Thür
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rm useless section, use only sss instead of ss2

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......@@ -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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