6.5. Photodetectors 393
A.14EnergyResolution
The pulse height at the anode of a PMT depends on the number of secondary
electrons. Since we know the overall gain of the tube we might conclude that it
would have a very good energy resolution. Unfortunately this is not really true
since we have not considered the fact that the number of electrons produced at
each step of the multiplication chain fluctuates around a mean value. We had noted
earlier that the emission of secondary electrons is Poisson distributed, which implies
that at each dynode the spread in the number of electrons can be written as
σNi
Ni=
√
Ni
Ni=
1
√
Ni, (6.5.23)
whereNiis the average number of secondary electrons produced by dynodei.
Since the spread depends inversely on the square root of the number of elec-
trons therefore the first dynode, producing the least number of secondary electrons,
introduces the largest uncertainty. As the multiplication progresses the overall un-
certainty increases but at a slower rate after each step due to the increase in the
number of electrons. The end result is a fairly broad peak at the anode and poor
energy resolution. The only way out of this problem is to somehow increase the
number of electrons at each stage. This can be done by using dynodes with a very
large value of gainδsince it would guarantee emission of large number of electrons
even at the first stage of multiplication. The PMTs designed to deliver good energy
resolution are actually constructed with such dynodes. In general, however, PMTs
have poor energy resolution.
If the PMT is used to detect the photons coming from a scintillator, the overall
energy resolution will have a component due to scintillator alone as well. Generally,
scintillators by themselves have good energy resolution and the largest uncertainty
is introduced by the PMTs. This is one of the reasons why semiconductor photode-
tectors are now sometimes preferred over conventional PMTs.
A.15ModesofOperation
A PMT can be operated in two distinct modes: digital and analog. Digital mode,
also called the photon counting mode, is the one that actually utilizes the potential
of PMT design to its fullest. In this mode the PMT is used to count the number
of light photons that strike the photocathode, something that is extremely difficult,
if not impossible, with other types of detectors. The caveat, of course, is that this
does not work very well when the incoming photon intensity is very high and the
associated electronics is not fast enough. This technique works best in situations
when the incident photons are well separated in time.
When the photon intensity is low, a small number of photoelectrons are generated
in the photocathode. Consequently the output pulses at the anode are well separated
in time. The proportionality of the number of these pulses to the incident light
forms the basis of the photon counting mode of operation. Fig.6.5.21 shows the
pulse counting process in the digital operation mode of a PMT. It is evident that
all of the photons incident on the photocathode do not generate photoelectrons.
The ones that do, can reach the first dynode and initiate the electron multiplication
process leading to a measurable pulse at the anode. Of course if the photoelectron
goes astray and does not reach the first dynode, there will not be any pulse at the