Department of Physical Electronics
Faculty of Science, Masaryk University, Brno
Physical laboratory 3
Task H Photomultiplier
Tasks
1. Determine the dependence of the secondary electron emission coeﬃcient on the energy of the
electrons impacting the dynode. Plot ln(σ/V ) = f(V ). Determine if the secondary electron
emission coeﬃcient σ depends on the light intensity on the photocathode.
2. Determine and plot the dependence of the integral photomultiplier sensitivity photomultiplier
ampliﬁcation on the multiplier voltage S = f(Ua) a M = f(Ua).
3. Determine the integral sensitivity of the photocathode k = If /Φ.
4. Determine the eﬀect of the dark current on the measurement.
Theory
The photomultiplier is an electro-optical device used for measuring very low-intensity light (e.g.
optical spectra). Photomultipliers are used, for example, in scintillating detectors to regulate the
brightness and exposure in some x-ray devices or in the sensitive measurement devices of light
and luminous ﬂux. Its working principle lies in a combination of two electron emission types –
photoemission and secondary emission.
Fotoemise
The photoemission, also called the external photoelectric eﬀect, is characterised by the emission
of electrons from the surface of an illuminated body. Its essence is the conversion of the light
quantum into the work function and the kinetic energy of an electron realising the electrical
conductivity by its ﬂight from one electrode to another. The following laws describe the external
photoeﬀect:
1. The number of electrons emitted per one time unit is proportional to the intensity of the
light, i.e. the number of incident photons. Such a formulation of Stoletov’s law is valid if
the spectral composition of the light does not change with the changing light intensity and
that the photocathode is not saturated.
2. The velocity of the electrons emitted from the surface of the photocathode is independent
of the light intensity.
3. The initial velocity v0 of the electrons leaving the photocathode increases with increasing
radiation frequency as per Einstein’s law:
hν = w +
mv2
0
2
, (1)
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where hν is the energy of the quantum of monochromatic light of the frequency ν and w is
the eﬀective work function of the electrons from the photocathode material.
Einstein’s law leads to the red limit of the photoeﬀect. If we select such lowest frequency of the
incident radiation with the frequency ν0, for which we can write
hν0 = w , (2)
the electrons from the photocathode are emitted with the velocity v0 = 0. If the eﬀective work
function is w > hν, no electrons can be emitted from the photocathode because the energy of
the light quantum is insuﬃcient for their release from the material. The frequency ν0 is called
the red limit of the photoeﬀect, and it is dependent on the material of the photocathode. It is in
the ultraviolet region for most metals, and only alkaline metals have the red limit in the visible
region.
Stoletov’s law deﬁnes the number of the emitted electrons – the magnitude of the photocurrent
from the photocathode due to the eﬀect of photocathode irradiation by spectrally constant light
as
If = k(λ)Φ. (3)
The proportionality constant k(λ) depends on the wavelength of the incident light. If is the
current of the primary electrons emitted from the photocathode and Φ is the luminous ﬂux
irradiating the photocathode. The k(λ) = f(λ) dependence is called the spectral characteristic of
the photocathode.
Secondary emission
Electrons can also be emitted from an electrode by the impact of fast electrons with their energy
higher than the work function of that electrode. Such secondary electrons include newly emitted
electrons and electrons backscattered from the surface of the electrode. If the energy of the
primary incident electrons is high enough (usually several times the work function of the electrode
material), the number of the secondary electrons can be larger than the number of primary
electrons. The ratio of the secondary electrons Isec to the primary electrons Iprim is called the
secondary electron emission coeﬃcient σ.
σ =
Isek
Iprim
(4)
and its magnitude depends on the electrode material and the electron acceleration according to
σ = A E · exp(−µE) , (5)
where A and µ are electrode (so called dynode) material constants, E is the energy of the electrons
incident on the electrode that can be set by the voltage between two neighbouring dynodes (V ).
Photomultiplier’s principle of operation
A simpliﬁed diagram of the principle of the photomultiplier operation is shown in ﬁgure 1. The
main parts of a photomultiplier are the photocathode FK, a series of dynodes Di and an anode
A. The voltage between the electrodes is set to gradually increase from the cathode over the
individual dynodes up to the anode.
Photoelectrons emitted from the photocathode by, e.g. white light, impact the ﬁrst dynode
when its potential accelerates them to a high enough energy. Secondary emission takes place
on the ﬁrst dynode, and I1 = σIf secondary electrons leave the ﬁrst dynode. These secondary
electrons of the ﬁrst dynode become primary electrons of the second dynode, where the same
process is repeated. The geometry and the potential distribution around the dynodes are so that
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Figure 1: Photomultiplier with 6 dynodes and the coeﬃcient of secondary emission σ = 2. Φ is
the luminous ﬂux, FK is the photocathode, D1 ∼ D6 are the individual dynodes, A is the anode.
The electrode potentials suﬃce the condition UA > UD6 > · · · > UD1 > UFK.
nearly all the electrons ejected from the nth dynode are accelerated by the ﬁeld of the (n + 1)th
dynode and impact it. Electrons from the last dynode then impact the anode.
The whole ampliﬁcation process, in a simpliﬁed manner, can be described by the following
equations. The ﬂux of the electrons from the photocathode If depends on the luminous ﬂux
incident on the photocathode according to Stoletov’s law for white light:
If = k · Φ, (6)
where the proportionality constant k corresponds to the sensitivity of the photocathode to white
light containing photons of all wavelengths. Therefore, it is known is integral sensitivity of the
photocathode. The studied photomultiplier keeps the same voltage V between each dynode pair.
If no electron losses in the photomultiplier are considered, the ﬁnal anode current can be written
as
Ia = σn
· If , (7)
where n is the number of dynodes. The photomultiplier ampliﬁcation M is given by the ratio of
the anode current to the photocurrent according to
M = σn
=
Ia
If
. (8)
Mutually substituting these expressions, we obtain the relations between the ampliﬁcation, the
luminous ﬂux and the ﬁnal anode current:
Ia = Mk Φ = S Φ, S = Mk, (9)
where S is the integral sensitivity of the photomultiplier and k is the integral sensitivity of the
photocathode. The dependence of the ampliﬁcation on the voltage over the photomultiplier M =
f1(Ua) and the dependence of the integral sensitivity on the voltage over the photomultiplier
S = f2(Ua) are the crucial properties of any photomultiplier.
The photomultiplier produces an unwanted current even without any light – the so-called dark
current. Its origin is mostly in the thermoemission from the photocathode, and it can be reduced
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1 2 3 5 6
b
a
4
Figure 2: Measurement setup (1) Anode current Ia source. (2) Safety resistor. (3) Microammeter
for the anode current measurement. (4) Photomultiplier chamber: a) Socket for electrical connection
of the photomultipler. b) Rotating screw of the graded grey plate. (5) Light source. (6)
High-voltage source Ua.
by cooling the photocathode. Generally, the dark current needs to be taken into account, and it
needs to be subtracted from the measured currents.
Experimental procedure
Figure. 3 shows the diagram of the photomultiplier’s connection. All the measurements will be
done with this connection. There are 14 dynodes. Most of the dynodes are permanently connected,
just connect microammeters to the voltage divider between the 10th and 12th dynode to measure
the current on the dynodes (for the determination of the secondary emission coeﬃcient). The high
voltage DC power source supplies 400 – 1000 V to the voltage divider between the photocathode
and the 14th dynode. A safety resistor, microammeter with the 100 µA range and an acceleration
DC source set to 80 V and the polarity towards the anode are connected between the anode and
the 14th dynode.
The photocathode illumination needs to be done with care in order not to damage it. The
light ﬂux can be changed by a graded grey plate placed in front of the light entrance of the
photocathode. The description of the grey plate control, including a graph for estimation of
the luminous ﬂux Φ are available on-site. The light-sensitive layer on the photocathode can be
damaged by light overexposure, and the cathode will then permanently lose its sensitivity. The
photocathode may not be under any circumstances exposed to ambient sunlight when the voltage
Ua between the photocathode and the anode is connected.
The assembled apparatus allows for the control of the voltage on the multiplier (Ua) and the
luminous ﬂux on the photocathode (Φ). You can measure the anode current (Ia), the current
through the 10th (I10) and 12th (I12) dynode and the voltage on the multiplier (Ua).
For 3 diﬀerent luminous ﬂux values, measure all the parameters needed to calculate the dependence
of the secondary electron emission coeﬃcient, integral sensitivity of the photomultiplier
and the photomultiplier ampliﬁcation on the voltage on photomultiplier. Determine the inﬂu-
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Figure 3: Photomultiplier electrical connection diagram: The photomultiplier voltage Ua is divided
by a voltage divider between the individual dynodes. Only the highlighted parts (further
speciﬁed by the teacher) need to be connected at the start of the task. Other parts are connected
permanently.
ence of the dark current on the measurement while the light source is turned oﬀ. Determine if
the secondary electron emission coeﬃcient (σ) depends on the intensity of the irradiation of the
photocathode. You can do this by measuring the secondary electron emission coeﬃcient for all
the diﬀerent grey plate settings Φ1, . . . , Φ7 at a constant voltage on the multiplier. Do so for 2
diﬀerent multiplier voltages.
Assuming all the dynodes in the multiplier are of the same material and that the voltage
between every two neighbouring dynodes is equal, the secondary electron emission coeﬃcient can
be determined from the I10 and I12 currents according to:
σ =
I12
I10
(10)
Using the calculated value of σ we can determine the photocurrent If . All of the remaining
unknown parameters can be determined from the available quantities. According to the magnitude
of the dark current on the dynodes I10, I12 and the anode Ia at zero luminous ﬂux on the
photocathode Φ = 0 determine if a correction of the measured values with non-zero luminous ﬂux
need to be corrected to the dark current.
Report tips: The results will be clearer when all the analogical dependencies measured for
diﬀerent photocathode illumination levels are plotted in a single graph. Diﬀerent symbols mark
the diﬀerent dependencies. If a theoretical expression for a given measured dependence exists, it
is appropriate to plot also the theoretical dependence based on the said expression.
• You will be using voltages of around 1 000 V during your measurements, be careful!
• The anode current Ia may never exceed 100 µA. Higher currents can cause photocathode
damage.
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Practical use
Photomultipliers are a part of elementary particle detection systems practically used in many
ﬁelds, from light industry through medicine to particle physics and astrophysics.
From its principle of operation, a photomultiplier itself can be used only as a detector of visible
light or in near-UV or near-IR light. In detectors of diﬀerent elementary particles diﬀerent from
photons of said frequency interval (typically X-ray photons or electrons), a scintillation material
is put in front of the photomultiplier. Interaction of the particles with the scintillating material
will cause the emission of photons typically from the visible range. These are detected by the
photomultiplier and pass the information about the particles impacting the scintillator.
Detectors of light, UV and IR radiation equipped by a photomultiplier
Photomultipliers are used as light detectors in spectrometers (absorption and emission) used for
chemical analysis.
Measurements of light by a photomultiplier is also used while monitoring the environment.
For example, the optical transmission of the environment can be measured, and the amount
of dust in the air can be calculated from such measurements. Also, gas molecule excitation
and consecutive measurement of the light emitted during the deexcitation is often used. The
concentration of pollutants such as sulphur oxides or nitrogen oxides can be measured in such a
manner. Photomultipliers are also used in biology and biotechnology. They are used to detect light
emitted by or reﬂected from the investigated biological structures in devices such as cytometers,
confocal laser microscopes or DNA sequencers.
In the ﬁeld of experimental physics, photomultipliers are used as detectors of the Cherenkov
radiation caused by the deceleration of particles created, e.g. by diﬀerent collision processes in
particle accelerators. A special device containing several thousand photomultipliers is the neutrino
detector in Kamiokande in Japan.
Detectors combining a scintillator and a photomultiplier
In medicine, scintillator-photomultiplier detectors are used in diﬀerent X-ray diagnostic devices
such as gamma cameras or positron emission tomography.
Particle physics utilises such detectors in experimental devices such as TOF counters or
calorimeters used for energy and trajectory determination of elementary particles.
Scintillator-photomultiplier detectors placed on satellites detect extraterrestrial X-ray radia-
tion.
The combination of a scintillator and a photomultiplier is also used in radiation dose measurements.
Areas around nuclear reactors or goods during customs check are measured this way.
In the industry, the combination of an X-ray radiation source and a scintillator-photomultiplier
detector is used, for example, to measure oil content in the soil or to measure material thickness,
e.g. in paper manufacturing.
The combination of a scintillator and a photomultiplier is used for electron detection in electron
microscope imaging.
Semiconductor detectors are replacing photomultipliers in many of the aforementioned ﬁelds.
This is due to miniaturisation as well as lowering the price of the device. We can nowadays ﬁnd
PIN diodes in backscattered electron detectors in electron microscopy. The avalanche Photo-Diode
(APD) is now often used as a visible light detection in some applications.
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References
[1] Chudoba T. a kol.: Fyzikální praktikum III. , skripta Přír. fak. UJEP v Brně (MU v Brně),
SPN Praha 1986.
[2] Čečik, Fajnštejn, Lifšic: Elektronnyje umnožitěli, Moskva 1954.
[3] Ondráček Z. : Elektronika pro fyziky, Skriptum Přír. fak. MU, Brno 1998