6.5. Photodetectors 369
energy. Hence we have0=
hc
λmax−Φ
⇒λmax =hc
Φ=(
6. 63 × 10 −^34
)(
2. 99 × 108
)
2 × 1. 602 × 10 −^19
=6. 187 × 10 −^7 m
= 618. 7 nm.Looking at equation 6.5.1 it is apparent that choosing a material with low work
function is advantageous in terms of delivering energy to the outgoing electrons.
However this is not the only criterion for selecting a photocathode for use in a
PMT. for example if the PMT is to be used to detect scintillation photons then
the most important factor is the conversion efficiency of the material at the most
probably wavelength of the scintillation light. If the material does not have high
enough efficiency at that wavelength then even a very low work function would not
matter much. Since the realization of this problem, a number of extensive stud-
ies have been carried out to find the optimum photocathode materials at different
scintillation wavelengths. Most of these efforts have gone into understanding the
spectral response of the materials. By spectral response we mean the efficiency of
the production of photoelectrons as a function of light wavelength. This efficiency
is generally referred to as photocathode quantum efficiency and is simply defined as
the ratio of the number of emitted photoelectrons to the number of incident photons,
that is
QE=Ne
Nγ, (6.5.2)
whereNeis the number of electrons emitted andNγ is the number of incident
photons. Quantum efficiency can also be expressed in terms of more convenient
quantities, such as incident power and photoelectric current. To do that we first
note that the incident power can be defined as
Pγ=nγhν, (6.5.3)wherenγrepresents the number of photons of frequencyνincident on the detector
per unit time. The expression for quantum efficiency can then be written as
QE =ne
Pγ/hν=
Ipehν
ePγ. (6.5.4)
Hereneis the number of photoelectrons ejected per unit time andIpe=eneis the
photoelectric current. This equation can be used to determine the photoelectric
current for a particular value of the incident power (see example below).