Physics and Engineering of Radiation Detection

388 Chapter 6. Scintillation Detectors and Photodetectors

whereδidenotes the gain of theith dynode and

∏

stands for the product.

Example:

The multiplication structure of a PMT is composed of 10 dynodes. The

gain of the first 4 dynodes is such that each of them produces 3 secondary

electrons. The rest of the dynodes produce 4 secondary electrons. Compute

the gain of the PMT.

Solution:

Given the gains of the first 4 dynodes as 3 and the remaining 6 dynodes as 4,

the overall gain as calculated from equation 6.5.18 is

μ =

[ 4

∏

i=1

δi

][ 10

∏

i=5

δi

]

=

(

34

)(

46

)

=3. 3 × 105.

The strong dependence of gain on the applied voltage implies that the output of
a PMT is highly susceptible to changes in the voltage. To quantify the variation
of gain with change in applied voltage, let us differentiate both sides of equation
6.5.16. This gives

dμ=

Anαn

(n+1)αn

Vαn−^1 dV. (6.5.18)

The relation for the relative change in gain can be obtained by dividing this equation
with equation 6.5.16. Hence we have

dμ

μ

=αn

dV

V

, (6.5.19)

which can also be written as

μ

μ

=

αn V

V

. (6.5.20)

For a PMT with 10 dyno des we haveαn≈7. For such a tube the relative change
in gain would be about 7 times the relative change in applied voltage. Hence, if the
applied voltage changes by 2%, the gain will change by about 14%. The effect is less
dramatic for tubes constructed with lower number of dynodes. However, since the
gain depends on the number of dynodes as well, the sensitivity of such a tube will
also be lower. Fig.6.5.17 shows the dependence of the number of dynodes on gain
for a PMT operatedunder the nominal voltage of 2000 volts.

A.11SpatialUniformity

In most applications it is desirable that the PMT is capable of covering as large an
area as possible. This requires, above all, a large area photocathode. A uniformly
built photocathode should have essentially same quantum efficiency throughout its
entire coverage. Achieving a high degree of uniformity is, however, not an easy task