add 1st part of chap 2

02_carrier_transport.tex

-\section{Carrier transport}
+\section{Carrier transport}
\ No newline at end of file
+\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:
+\begin{equation}
+    f(E) = \frac{1}{1+e^{(E-E_F)/kT}}
+\end{equation}
+
+Electron concentration in conductance band:
+\begin{equation}
+    n=N_ce^{-(E_c-E_f)/kT}
+\end{equation}
+Hole concentration in valence band:
+\begin{equation}
+    p=N_ve^{-(E_f-E_v)/kT}
+\end{equation}
+
+In intrinsic silicon ($n=p=n_i$) we have ($E_i$ somewhere in the middle of the bandgap)
+\begin{equation}
+    E_i=E_f=\frac{E_c+E_v}{2}-\frac{kT}{q}\ln{\frac{N_c}{N_v}}
+\end{equation}
+
+Which gives us the useful relation:
+\begin{equation}
+    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}
+\begin{align}
+    \lambda & \equiv \text{mean free path} [cm]                   \\
+    \tau_c  & \equiv \text{mean time between collisions} [s^{-1}] \\
+    v_{th}  & \equiv \text{thermal velocity} [cm/s]               \\[1em]
+    \lambda & = v_{th}\cdot\tau_c
+\end{align}
+
+
+\subsubsection{Drift velocity}
+Quick electromag recap: (for holes use + and $m_p$)
+\begin{align}
+    F    & = -qE             \\
+    v(t) & =-\frac{qE}{m_n}t
+\end{align}
+
+Average drift velocity:
+\begin{equation}
+    v_d = \pm \frac{qE\tau_c}{2m_{n,p}}
+\end{equation}
+
+\subsubsection{Mobility}
+\begin{align}
+    \mu_{n,p} & = \frac{q\tau_c}{2m_{n,p}} \equiv \text{mobility}\ [cm^2/Vs] \\
+    amhere
+\end{align}
\ No newline at end of file

semiconductor_summary.tex

@@ -32,6 +32,6 @@
 \tableofcontents
 
 \include{01_fundamentals}
-\include{02_carrier_transport.tex}
+\include{02_carrier_transport}
 
 \end{document}