Physics:Single electron peak

Distribution of the total charge observed at the anode of a photomultiplier, resulting from a single electron leaving the cathode. For the single electron peak the spread in transit time can be assumed to be independent of the gain fluctuations.

The single electron peak is useful in studying the mean gain and the statistical properties of a photomultiplier. The gain is given by the abscissa of the centre of gravity in units of the electron charge, and the relative variance can be approximated by

where v_di is the relative variance of the gain at the ith dynode, and g_i is the average gain at the ith dynode (100% interstage collection efficiency is assumed).

In practice, the single electron peak is measured by illuminating the photocathode by a triggered light source attenuated by suitable filters, and electrons leaving the cathode are Poisson distributed with an average

where is the averaged conversion efficiency of the photocathode.

The contribution of zero electrons, therefore, is

contributing only the dark current integrated over the gate length of the analogue-to-digital Converter.

For the contribution of more than one electron is given by

At low flux ( ) one finds

To evaluate the gain of the photomultiplier one has to correct for the collection efficiency of the first dynode. To evaluate the photon flux reaching the cathode the quantum efficiency of the photocathode must also be considered (up to 25% and dependent on the wavelength).