Merge branch 'augermanual' into 'master'

\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}.

  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},