  Impact ionization in silicon devices has been extensively studied and several
models for a quantitative description of the impact ionization coefficients
have been proposed. We evaluate those models against gain measurements on Low
Gain Avalanche diodes (LGADs) and derive new parameterizations for the impact
ionization coefficients optimized to describe a large set of experimental data.
We present pulsed IR-laser based gain measurements on 5 different types of
$50\mu m$-thick LGADs from two different producers (CNM and HPK) performed in a
temperature range from $-15^oC$ to $40^oC$. Detailed TCAD device models are
conceived based on SIMS doping profiles measurements and tuning of the device
models to measured C-V characteristics. Electric field profiles are extracted
from the TCAD simulations and used as input to an optimization procedure (least
squares fit) of the impact ionization model parameters to the experimental
data. It is demonstrated that the new parameterizations give a good agreement
between all measured data and TCAD simulations which is not achieved with the
existing models. Finally, we provide an error analysis and compare the obtained
values for the electron and hole impact ionization coefficients against
existing models.
