Merge branch 'materials_doc' into 'materials' (019cd1d6) · Commits · XRFLab109 / Allpix Squared

doc/usermanual/chapters/models.tex

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		@@ -26,21 +26,21 @@ The sources for the chosen default values are provided in the table.
		\caption{List of default sensor material properties implemented in \apsq}
		\label{tab:material_properties}
		\centering
		\begin{tabular}{lll}
		\begin{tabular}{llll}
		\toprule
		\textbf{Material} & \textbf{Charge Creation Energy [eV]} & \textbf{Fano factor} \\
		\textbf{Material} & \shortstack[l]{\textbf{Charge Creation}\\\textbf{Energy [eV]}} & \textbf{Fano factor} & \textbf{Sources} \\
		\midrule
		Silicon & 3.64~\cite{chargecreation} & 0.115~\cite{fano} \\
		Silicon & 3.64 & 0.115 & \cite{chargecreation}, \cite{fano} \\
		\midrule
		Gallium Arsenide & 4.2 & 0.14~\cite{GaAs_Fano} \\
		Gallium Arsenide & 4.2 & 0.14 & \cite{GaAs_Fano} \\
		\midrule
		Cadmium Telluride & 4.43~\cite{DABROWSKI1974531} & 0.24~\cite{SAMMARTINI2018168} \\
		Cadmium Telluride & 4.43 & 0.24 & \cite{DABROWSKI1974531}, \cite{SAMMARTINI2018168} \\
		\midrule
		Cadmium Zinc Telluride \ce{Cd_{0.8}Zn_{0.2}Te} & 4.6~\cite{CdZnTe_Creation} & 0.14~\cite{cdznte} \\
		Cadmium Zinc Telluride \ce{Cd_{0.8}Zn_{0.2}Te} & 4.6 & 0.14 & \cite{CdZnTe_Creation}, \cite{cdznte} \\
		\midrule
		Diamond & 13.1~\cite{Diamond_Creation_Fano} & 0.382~\cite{Diamond_Creation_Fano} \\
		Diamond & 13.1 & 0.382 & \cite{Diamond_Creation_Fano}, \cite{Diamond_Creation_Fano} \\
		\midrule
		Silicon Carbide (4H-SiC) & 7.6~\cite{SiC_Creation} & 0.1~\cite{SiC_Fano} \\
		Silicon Carbide (4H-SiC) & 7.6 & 0.1 & \cite{SiC_Creation}, \cite{SiC_Fano} \\


		\bottomrule
		@@ -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 field 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}

		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 and their references 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} & $v_{sat,300} [\si{cm \per s}]$ & \num{1.02e7} & \num{0.72e7} & \cite{quay} \\
		& $A$ & 0.74 & 0.37 & \cite{quay} \\
		& $M [\si{\cm^2K}^\gamma \si{\per V \per s}]$ & \num{1.43e9} & \num{1.35e8} & \cite{jacoboni} \\
		& $\gamma$ & 2.42 & 2.2 & \cite{jacoboni} \\
		\midrule
		\multirow{4}{*}{Germanium} & $v_{sat,300} [\si{cm \per s}]$ & \num{0.7e7} & \num{0.63e7} & \cite{quay} \\
		& $A$ & 0.45 & 0.39 & \cite{quay} \\
		& $M [\si{\cm^2K}^\gamma \si{\per V \per s}]$ & \num{5.66e7} & \num{1.05e9} & \cite{omar}, \cite{LandoltBornstein} \\
		& $\gamma$ & 1.68 & 2.33 & \cite{omar}, \cite{LandoltBornstein} \\
		\midrule
		\multirow{4}{*}{\shortstack[l]{Gallium\\Arsenide}} & $v_{sat,300} [\si{cm \per s}]$ & \num{0.72e7} & \num{0.9e7} & \cite{quay} \\
		& $A$ & 0.44 & 0.59 & \cite{quay} \\
		& $M [\si{\cm^2K}^\gamma \si{\per V \per s}]$ & \num{2.5e6} & \num{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 $\mu = \textrm{const}$.

doc/usermanual/references.bib

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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},