  The results of a 1-D Monte-Carlo program, which simulates the avalanche
multiplication in diodes with depths of the order of 1 $\mu$m based on the
method proposed in Ref.1, are presented. The aim of the study is to achieve a
deeper understanding of silicon photo-multipliers. It is found that for a given
over-voltage, $\mathit{OV}$, the maximum of the discharge current is reached at
the breakdown voltage, $U_\mathit{bd}$, and that the avalanche stops when the
voltage drops to $U_\mathit{bd} - \mathit{OV}$. This is completely different to
the generally accepted understanding of SiPMs, which has already been noted in
Ref.1.
  Simulated characteristics of the avalanche breakdown, like the time
dependence of the avalanche current, over-voltage dependence of the
Geiger-breakdown probability and the gain for photons and dark counts, are
presented and compared to the expectations from silicon photo-multipliers.
