Commit fd3f0877 authored by Simon Spannagel's avatar Simon Spannagel
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Manual: add some contect to Auger recombination

(cherry picked from commit 60ee07ae)
parent 181db21f
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@@ -267,11 +267,20 @@ This model can be selected in the configuration file via the parameter \paramete

\subsection{Auger Recombination}

The charge carrier lifetime according to the Auger recombination model is calculated as:
At high doping levels exceeding $\SI{5e18}{\centi\metre^{-3}}$~\cite{FOSSUM1983569}, the Auger recombination model becomes increasingly important.
It assumes that the excess energy created by electron-hole recombinations is transferred to another electron (\textit{e-e-h process}) or another hole (\textit{e-h-h process}).
The total recombination rate is then given by~\cite{kerr}:

\begin{align*}
	R_{Auger} = C_n n^2p + C_p n p^2\textrm{,}
\end{align*}
where $C_n$ and $C_p$ are the Auger coefficients.
The first term corresponds to the e-e-h process and the second term to the e-h-h process.
In highly-doped silicon, the Auger lifetime for minority charge carriers can be written as:
\begin{equation}
    \tau(N) = \frac{1}{C_{a} \cdot N^2}
\end{equation}
where $C_{a}$ is the Auger coefficient, taken as $C_{a} = \SI{3.8e-31}{\cm^6 \per \s}$ from~\cite{dziewior}.
where $C_{a} = C_{n} + C_{p}$ is the ambipolar Auger coefficient, taken as $C_{a} = \SI{3.8e-31}{\cm^6 \per \s}$ from~\cite{dziewior}.

This recombination mode applies to minority charge carriers only, majority charge carriers have an infinite life time under this model and Equation~\eqref{eq:recomb:prob} will always evaluate to \emph{true}.

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  author = "A. {Haug}",
}

@article{kerr,
	author = {Kerr, Mark and Cuevas, Andres},
	year = {2002},
	month = {02},
	pages = {},
	title = {General parametrization of Auger Recombination in crystalline silicon},
	volume = {91},
	journal = {Journal of Applied Physics - J APPL PHYS},
	doi = {10.1063/1.1432476}
}

@article{dziewior,
  author = {Dziewior,J.  and Schmid,W. },
  title = {Auger coefficients for highly doped and highly excited silicon},