W1

01_fundamentals.tex

-\section{Fundamentals of semiconductor physics}
+\section{Basics of semiconductor physics}
+\subsection{Notation}
+We only care about free electrons and define
+\begin{equation}
+    \begin{split}
+        n &= \text{electron concentrations density}\ [cm^{-3}]\\
+        p &= \text{hole concentrations density}\ [cm^{-3}]\\
+    \end{split}
+\end{equation}
+
+\subsection{Band gap}
+If an electron energy $E$ is large enough to overcome the bandgap $E_g$,
+it can escape the valence band into the conduction band.
+It then leaves behind a hole.
+\begin{figure}[h]
+    \centering
+    \includegraphics[width=.6\textwidth]{imgs/band_gap_electorn_holes.png}
+\end{figure}
+
+\subsection{Generation and recombination}
+Generation is the breakup of covalent bonds,
+which creates free electrons and holes.
+This requires energy, either thermal or optical.
+Assuming the atom density far larger than n or p (and thus bonds can be split defacto infinitely),
+we have:
+\begin{align}
+    G & = G_{th} + G_{opt} \\
+    R & \sim  n\cdot p
+\end{align}
+
+
+In thermal equilibrium, the generation and recombination rates are equal:
+\begin{align}
+    G_0                & = f(T)=R_0 \\
+    \Rightarrow n_0p_0 & =n_i^2(T)
+\end{align}
+
+
+\subsection{Doping}
+Doners are in the 5th shell (V), usually As,P,Sb.
+Acceptors are in the 3rd shell (III), usually B,Al,Ga,In.
+For doners we have:
+\begin{align}
+    n_0 & = N_d               \\
+    p_0 & = \frac{n_i^2}{N_d}
+\end{align}
+
+\subsection{Charge neutrality}
+Every semiconductor is neutral,
+which imposes the following condition:
+\begin{equation}
+    P_0-n_0+N_d + N_a = 0
+\end{equation}
+where $p_0n_0=n_i^2$.
\ No newline at end of file

02_carrier_transport.tex

+\section{Carrier transport}
\ No newline at end of file

format.tex

@@ -50,3 +50,7 @@
 \rhead{\today}
 \lhead{}
 \cfoot{\thepage}
+
+
+
+\numberwithin{equation}{subsection}

semiconductor_summary.tex

@@ -32,5 +32,6 @@
 \tableofcontents
 
 \include{01_fundamentals}
+\include{02_carrier_transport.tex}
 
 \end{document}