Commit bc72e6cf authored by Paul Schütze's avatar Paul Schütze
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Materials: add doc for quay mobility model

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@@ -292,6 +292,58 @@ for electrons and holes, respectively.
This model can be selected in the configuration file via the parameter \parameter{mobility_model = "ruch_kino"}.


\subsection{Quay Model}

The Quay mobility model describes the mobility of electron and holes in a large range of semiconductor materials.
In the original publication~\cite{quay}, the saturation velocity is modeled via the relation
\begin{align}
  \label{eq:mob:quay_vs}
  v_{sat}\left(T\right) &= \frac{v_{sat,300}}{(1-A) + A\cdot\left( T/300 \right)} ,
\end{align}
with the saturation velocity at $T=\SI{300}{K}$ and the free parameter $A$.

In \apsq  the mobility is determined according to a model published in~\cite{omar} as a function of the saturation velocity $v_{sat}$, the electrical field $E$ and the critical field $E_C$:
\begin{align}
  \label{eq:mob:quay_mob}
  \mu_e\left(E\right) &= \frac{v_{sat}}{E_C \cdot \sqrt{ 1 + \left( E/E_C \right)^2 }} .
\end{align}

The critical temperature in turn is defined as the saturation velocity divided by the mobility at zero field, where the zero-field mobility scales with temperature according to~\cite{omar}:
\begin{align}
  \label{eq:mob:ec}
  E_C(T) = \frac{v_{sat}}{M T^{-\gamma}} .
\end{align}

To date, the model has been implemented for silicon, germanium and gallium arsenide.
Parameters for several other compound semiconductors are given in~\cite{quay} and~\cite{LandoltBornstein}.
The parameters implemented in \apsq are listed in Table~\ref{tab:mob:quay}
\begin{table}[tbp]
\caption{List of parameters for the Quay mobility model.}
\label{tab:mob:quay}
\centering
\begin{tabular}{lllll}
  \toprule
\textbf{Material} & \textbf{Parameter} & \textbf{Electrons} & \textbf{Holes} & \textbf{Sources} \\
  \midrule
  \multirow{4}{*}{Silicon} & $v_{sat,300}$ [\SI{}{cm \per s}] & \SI{1.02e7}{} & \SI{0.72e7}{} & \cite{quay} \\
                  & $A$            & 0.74 & 0.37 & \cite{quay} \\
                  & $M$ [\SI{}{\cm^2K^{\gamma}\per V \per s}] & \SI{1.43e9}{} & \SI{1.35e8}{} & \cite{jacoboni} \\
                  & $\gamma$     & 2.42 & 2.2 & \cite{jacoboni} \\
  \midrule
  \multirow{4}{*}{Germanium} & $v_{sat,300}$ [\SI{}{cm \per s}] & \SI{0.7e7}{} & \SI{0.63e7}{} & \cite{quay} \\
                  & $A$            & 0.45 & 0.39 & \cite{quay} \\
                  & $M$ [\SI{}{\cm^2K^{\gamma}\per V \per s}] & \SI{5.66e7}{} & \SI{1.05e9}{} & \cite{omar}, \cite{LandoltBornstein} \\
                  & $\gamma$     & 1.68 & 2.33 & \cite{omar}, \cite{LandoltBornstein}  \\
  \midrule
  \multirow{4}{*}{\shortstack[l]{Gallium\\Arsenide}} & $v_{sat,300}$ [\SI{}{cm \per s}] & \SI{0.72e7}{} & \SI{0.9e7}{} & \cite{quay} \\
                  & $A$            & 0.44 & 0.59 & \cite{quay} \\
                  & $M$ [\SI{}{\cm^2K^{\gamma}\per V \per s}] & \SI{2.5e6}{} & \SI{6.3e7}{} & \cite{LandoltBornstein} \\
                  & $\gamma$     & 1.0 & 2.1 & \cite{LandoltBornstein} \\
\bottomrule
\end{tabular}
\end{table}


\subsection{Constant Mobility}

Some simulations require constant charge carrier mobility values $\mu = \textrm{const}$.
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@@ -763,6 +763,16 @@ doi = {10.1109/TNS.2004.839096}
    keywords = "Saturation velocity, Modeling, Temperature, Device simulation"
}

@Misc{LandoltBornstein,
editor="Madelung, O. and R{\"o}ssler, U. and Schulz, M.",
title="Landolt-B{\"o}rnstein - Group III Condensed Matter {\textperiodcentered} Volume 41A1$\beta$: ``Group IV Elements, IV-IV and III-V Compounds. Part b - Electronic, Transport, Optical and Other Properties''",
publisher="Springer-Verlag Berlin Heidelberg",
note="Copyright 2002 Springer-Verlag Berlin Heidelberg",
note="Part of SpringerMaterials",
note="accessed 2022-03-23",
doi="https://doi.org/10.1007/b80447"
}

@ARTICLE{cdznte,
  author={Niemela, A. and Sipila, H.},
  journal={IEEE Transactions on Nuclear Science},