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Commit 98cbd78c authored by Simon Josef Thür's avatar Simon Josef Thür
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Merge branch '04-addon' into 'main'

04 pn junction update

See merge request !3
parents f1973ccc d63a4b72
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1 merge request!304 pn junction update
......@@ -13,7 +13,7 @@ resulting in a new equilibrium (\autoref{label:fig:pn_carrier_profile_equilibriu
\hfill
\begin{subfigure}[b]{.45\textwidth}
\includegraphics[width=\textwidth]{imgs/pn_fermi_level_band_bending.png}
\caption{Resulting carrier profile in thermal equilibrium}
\caption{Energy band diagrams of pn-junction in thermal equilibrium}
\label{label:fig:pn_fermi_level_band_bending}
\end{subfigure}
\end{figure}
......@@ -27,7 +27,7 @@ the energy levels for conduction and valence bands bend, whereas the fermi level
We assume p and n regions quasi-neutral,
and the intermediate space charge region to be completely depleted of carriers.
We further assume all transitions are expressed as step-functions.
This allows the following simplified equations:
This allows the following simplified equations: (depicted in \autoref{label:fig:space-charge-region})
\begin{align}
\rho(x) & = \begin{dcases}
0 & x<-x_p \\
......@@ -62,6 +62,21 @@ Where $\phi_B$ is the built-in potential (see \autoref{label:eq:boltzman:phi_B})
Also, it is the less heavily doped region that defines the junction width.
It is also in the less heavily doped region that the depletion zone extends farther.
Therefore we get the total width of space charge region:
\begin{equation}
W_{dep} = x_{d} = x_n + x_p = \sqrt{\frac{2 \varepsilon \phi_B (N_a+N_d)}{q N_a N_d }}
\end{equation}
and the maximal electric field: (at metallurgical junction)
\begin{equation}
\left|E_0\right| = \sqrt{\frac{2 q \phi_B N_a N_d}{\varepsilon(N_a+N_d)}}
\end{equation}
\begin{figure}[H]
\centering
\includegraphics[width=.4\textwidth]{imgs/space_charge_region.pdf}
\caption{Charge density, electric field and the potential in the space charge region.}\label{label:fig:space-charge-region}
\end{figure}
\subsection{Contact potential}
Although there is a potential accross the diode, it cannot be measured because there are the metal semi-conductor junctions for both p and n regions.
\begin{equation}
......
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