Merge branch '10-Qss' into main

10_mos.tex

@@ -173,12 +173,33 @@ Notes:
     \item Higher inner doping level, higher $V_T$.
     \item Thinner oxide, lower $V_T$.
 \end{enumerate}
+
+
 \subsubsection{Body effect}
 In the case of a non-zero $V_{SB}$, we have to adjust the threshold voltage:
 \begin{equation}
     V_{TH} = V_{TH0} + \gamma\left(\sqrt{|2\phi_F + V_{SB}|} - \sqrt{|2\phi_F|}\right) \qquad \text{where}\quad \Phi_F = \frac{k T}{q} \ln\left(\frac{N_{sub}}{n_i}\right)
 \end{equation}
 
+\subsection{Effective fixed charge density $Q_{ss}$}
+At the interface Si-SiO$_2$, there are fixed charges due to lattice mismatch.
+This affects the threshold and flatband voltage.
+
+\begin{minipage}[t]{.5\textwidth}
+    Ideal case:
+    \begin{align}
+        V_{FB} & = \Phi_{ms}                    \\
+        V_T    & = \Phi_{ms} - 2\Phi_p + V_{ox}
+    \end{align}
+\end{minipage}
+\begin{minipage}[t]{.5\textwidth}
+    Non-ideal case:
+    \begin{align}
+        V_{FB}' & = \Phi_{ms}-\frac{Q_{ss}}{C_{ox}}                      \\
+        V_T'    & = \Phi_{ms} - 2\Phi_p + V_{ox} - \frac{Q_{ss}}{C_{ox}}
+    \end{align}
+\end{minipage}
+
 \subsection{Strong inversion}
 \begin{equation}
     V_{GB} > V_T