Model descriptions

Two simple mathematical models were developed for the multiplication register gain stages of the L3Vision CCDs. In both cases the number of additional charge carriers generated from each input electron through impact ionisation was treated as an independent random variable with a probability distribution which remained fixed for the duration of each simulation. The gain stages were assumed to have perfect charge transfer efficiency, so the input electrons were always passed to the output of the gain stage regardless of whether or not impact ionisation took place. The two linear models of a single gain stage which were considered can be summarised as follows:

Model 1

For the first model, for each input electron the number of additional electrons generated by impact ionisation within the gain stage was selected from a Poisson distribution. This corresponds to the case where impact ionisation is an instantaneous process, and an input electron can generate multiple charge carriers within a single gain stage. Impact ionisation events triggered by secondary electrons generated within that gain stage were not considered.

Model 2

For the second model, a maximum of one additional electron could be generated through impact ionisation within one gain stage. This corresponds to the case where the generation of additional electrons by impact ionisation cannot occur twice within the time taken to transfer the charge from one gain stage to the next.

It is unlikely that either model perfectly describes the real operation of a gain stage, but the models considered here cover a reasonably broad spectrum of possible properties.