Allpix Squared implements charge multiplication via impact ionization models. These models are only used by propagation
modules which perform a step-by-step simulation of the charge carrier motion.
The gain $`g`$ is calculated for all models as exponential of the model-dependent impact ionization coefficient $`\alpha`$ and
The per-step gain $`g`$ is calculated for all models as exponential of the model-dependent impact ionization coefficient $`\alpha`$ and
the length of the step $`l`$ performed in the respective electric field. If the electric field strength stays below a
configurable threshold $`E_{\text{thr}}`$, unity gain is assumed:
@@ -21,6 +21,22 @@ g (E, T) = \left\{
\right.
```
The impact ionization coefficient $`\alpha`$ is calculated depending on the selected impact ionization model. The models themselves are described below.
The number of additional charge carriers generated per step $`n`$ is determined via a stochastic approach by applying the following equation dependent on a random number drawn from a uniform distribution $`u(0,1)`$
```math
n = \frac{\ln(u)}{\ln(1-1/g)} = \frac{1}{\log_u(1-1/g)}
```
This distribution is applied e.g. in Garfield++\[[@garfieldpp]\] and represents a microscopic simulation of Yule processes.
The number of secondary charge carriers generated from impact ionization is calculated for every individual charge carrier within a group of charge carriers and summed per propagation step. Additional charge carriers are then added to the group (same-type carriers) or deposited (opposite-type) at the end of the corresponding step.
This algorithm results in a mean number of secondaries generated equal to
