add SOI

12_nanometric_mos.tex

-\section{Nanometric MOS}
\ No newline at end of file
+\section{Nanometric MOS}
+\subsection{Strained silicon}
+For N-MOS, increase distance between atoms,
+for P-MOS, decrease the distance.
+this improves mobility.
+
+\subsection{Velocity saturation}
+In the case of high electric fields, the velocity of the electrons saturates (Short-Channel-Effect).
+\begin{equation}
+    I_D = \begin{cases}
+        W Q_I(x)v_x(x)                              & : v=\mu E           \\
+        W C_{ox} \mu v_{sat}\left(V_{GS}-V_T\right) & : \text{saturation}
+    \end{cases}
+\end{equation}
+With the `new' saturation voltage
+\begin{equation}
+    V_{D,sat} = \left(V_{GS}-V_T\right)/m \to \sqrt{2v_{sat}L/m\mu}
+\end{equation}
+where $m$ is a non-ideality constant.
+Note that we completely lose the dependence on L for the current.
+
+Essentially $\alpha=1$ for complete saturation and $\alpha=2$ for long channel:
+\begin{equation}
+    I_D\bigg|_{V_{DS}=V_{DD}} \sim (V_{GS}-V_T)^\alpha \qquad :\    1< \alpha <2
+\end{equation}
+
+
+
+\subsection{Silicon-On-Insulator (SOI)}
+PD SOI:
+\begin{itemize}
+    \item Body thicker than channel depletion width
+    \item Body voltage floating
+    \item Depends on charge injected into bulk
+    \item History effect changes $V_T$
+\end{itemize}
+FD SOI:
+\begin{itemize}
+    \item Body thinner than channel depletion width
+    \item Fixed body charge
+    \item Fixed body voltage
+    \item Hard to manufacture
+    \item Not used yet
+\end{itemize}
+\subsubsection{Partially depleted SOI}
+\begin{itemize}
+    \item[+] simolar to bulk-Si
+    \item[+] no coupling
+    \item[-] SCE
+    \item[-] floating body
+    \item[-] kink effect
+    \item[-] dynamic over- undershoots
+    \item[-] self heating
+\end{itemize}
+\paragraph{Floating body effect}
+Kink effect because of impact ionization near the drain.
+Holes are swept into the neutral body, collecting at the source junction.
+\begin{equation}
+    T_{SOI}> \sqrt{\frac{2\varepsilon_{si}\cdot2\phi_F}{qN_{Body}}}
+\end{equation}
+
+
+\subsubsection{Fully depleted SOI}
+\begin{itemize}
+    \item[+] Excellent ctrs of SCE
+    \item[+] no floating body
+    \item[+] Less parasitic capacitance
+    \item[+] less junction leakage
+    \item[+] Quasi-ideal subthreshold swing
+    \item[-] $V_T$ sensitive to SOI thickness
+    \item[-] Self heating
+\end{itemize}
+
+\subsubsection{Why bother with SOI}
+By reducing the thickness of the channel, we reduce the SCE,
+since the gate can better control the channel.
+
+\todo[inline]{Subthreshold swing}
\ No newline at end of file

format.tex

@@ -45,6 +45,11 @@
     within=section,
 ]{circuit}
 
+
+\usepackage{enumitem}
+
+\setlist[itemize]{noitemsep}
+
 \usepackage{url}
 \usepackage[pdfusetitle]{hyperref}
 \hypersetup{

semiconductor_summary.tex

@@ -31,7 +31,8 @@
 
     The aim of this summary is to provide a denser overview of the course material.
     Specifically, it is intended to be used as a reference for the exam,
-    which is why it has only few remarks and focuses mainly on equations with little regard for how they were derived.
+    which is why it has only few remarks and focuses mainly on equations with little regard for how they were derived,
+    unless I found it noteworthy.
 
 
 \end{titlepage}