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}] \\
...
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@@ -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}
...
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@@ -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}
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...
@@ -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}\\
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...
@@ -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}