Document Massey Optimized

  doi = {10.1016/j.nima.2022.166491},

  author = {R. Ballabriga and J. Braach and E. Buschmann and M. Campbell and D. Dannheim and K. Dort and L. Huth and I. Kremastiotis and J. Kröger and L. Linssen and M. Munker and P. Schütze and W. Snoeys and S. Spannagel and T. Vanat},

}

@article{rd50ionization,

  title={Study of impact ionization coefficients in silicon with Low Gain Avalanche Diodes},

  author={Esteban Curras Rivera and Michael Moll},

  year={2022},

  eprint={2211.16543},

  archivePrefix={arXiv},

  primaryClass={physics.ins-det}

}

 No newline at end of file

B(T) = C + D \cdot T.

```

### Original publication

The parameter values implemented in Allpix Squared are taken from Section 3 of \[[@massey]\] as:

```math

This model can be selected in the configuration file via the parameter `multiplication_model = "massey"`.

### Optimized parameters

An optimized parametrization of the Massey model based on measurements with an infrared lased TCT setup is implemented in Allpix Squared, based on Table 2 of \[[@rd50ionization]\] with the values:

```math

\begin{aligned}

    A_{e} &= 1.186\times 10^{6} \,\text{/cm}\\

    C_{e} &= 1.020\times 10^{6} \,\text{V/cm}\\

    D_{e} &= 1.043\times 10^{3} \,\text{V/cm/K}\\

\\

    A_{h} &= 2.250\times 10^{6} \,\text{/cm}\\

    C_{h} &= 1.851\times 10^{6} \,\text{V/cm}\\

    D_{h} &= 1.828\times 10^{3} \,\text{V/cm/K}\\

\end{aligned}

```

for electrons and holes, respectively.

This model can be selected in the configuration file via the parameter `multiplication_model = "massey_optimized"`.

## Van Overstraeten-De Man Model

[@massey]: https://doi.org/10.1109/TED.2006.881010

[@rd50ionization]: https://arxiv.org/abs/2211.16543

[@overstraeten]: https://doi.org/10.1016/0038-1101(70)90139-5

[@okuto]: https://doi.org/10.1016/0038-1101(75)90099-4

[@bologna]: https://doi.org/10.1109/SISPAD.1999.799251