Physics and Engineering of Radiation Detection

398 Chapter 6. Scintillation Detectors and Photodetectors

HereIbgis the background current, which is the average anode current mea-

sured without the incident light and can be computed from

Ibg=Nγ,bge(QE)(CE), (6.5.28)

whereNγ,bgis the number of background photons incident on the photocathode

per unit time.


Dark Current: This is the term used to describe the average noise current

due to a number of sources. Dark current is dominated by thermionic emission

of electrons from the photocathode. Other sources of dark current include

current produced by ionization of residual gases inside the tube and leakage

current between electrodes. The presence of dark current in any practical PMT

is unavoidable but it can be minimized by proper designing and construction.

A constant dark current in itself is not a problem as far as measurements are

concerned since one can always subtract it out from the anode current. However

the fluctuations of the dark current can introduce significant uncertainty in the

final measurements. These fluctuations can be characterized by the shot noise

current, which for the average dark currentIdcan be estimated from

σd=μ

√

2 eIdFB. (6.5.29)

whereμ,F,andBrepresent the same parameters as described above. It is

apparent from this equation that decreasing the dark current has the merit of

decreasing the noise associated with it as well. Hence, keeping the dark current

to the minimum possible value is highly desirable.


Johnson Noise: Measurement of anode current requires that an amplifier

be connected to the PMT load. The equivalent impedance of this circuit is

subject to thermal variations causing injection of thermal orJohnsonnoise in

the system. The Johnson noise for an amplifier having noise figureFampcan

be expressed as

σamp=

√

4 FampkBTB

Reqv

. (6.5.30)

HerekBis the Botzmann’s constant,Tis the absolute temperature, andReqv

is the equivalent circuit impedance.

As Johnson noise depends explicitly on temperature, it is instructive to see how

it changes with changes in temperature. For that, let us differentiate equation

6.5.30 with respect to temperature. This gives

dσamp

dT

= A

1

√

T

, (6.5.31)

where A =

√

FkB

R

.

This shows that the effect is more dramatic at lower temperatures. Note that

here we are talking about the change in the Johnson noise and not the noise

itself. The noise is larger at higher temperatures according to equation 6.5.30

but the variation in the noise level with respect to change in temperature is

higher at lower temperatures.