Electron Multiplication in a Photomultiplier

The quantity e depends on the geometry. The quantity d depends on the voltage between two successive dynodes and on the material of which the dynode is made. The dependence of 6 on voltage is of the form 

Equation 6.6 indicates that the value of M increases with the voltage V and the number of stages n. The number of dynodes is limited, because as n increases, the charge density between two dynodes distorts the electric field and hinders the emission of electrons from the previous dynode with the lower voltage. In commercial photomultipliers, the number of dynodes is 10 or more. If one takes = 10 and ed = 4, typical value, the value of M becomes equal to 10 . 

To apply the electric field to the dynodes, a power supply provides a voltage adequate for all the dynodes. A voltage divider, usually an integral part of the preamplifier, distributes the voltage to the individual dynodes. When reference is made to phototube voltage, one means the total voltage applied. For example, if 1100 V are applied to a phototube with 10 dynodes, the voltage between any two dynodes is 100 V. 

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