Download Alpha Particle Attenuation in Matter Measurements

N2: Alpha Particle Attenuation in Matter
Measurements Using a Semiconductor
Detector
University of Sheffield
2nd Year Lab
February 18, 2005
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CAUTION: Health & Safety Advice
This experiment involves the use of a radioactive alpha particle emitter. Alpha particles
have a very short range in air, however they do still present a radiation risk. In the event
of any difficulties please consult a demonstrator, or the laboratory technician.
The alpha particle sources are described as “sealed sources for teaching laboratory use”,
and are of sufficiently low activity so as to pose no significant radiation risk to the user.
One of the aims of this experiment is for you to use radioactive sources safely, and with
good laboratory practice. Again, if you are in any doubt at all about the correct procedure
please consult a demonstrator, or the laboratory technician.
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1
Aims
This experiment involves the basic concepts and operations of alpha particle spectroscopy.
It is designed to give experience in calibrating and using a semiconductor detector; measuring alpha source spectra and measuring alpha particle attenuation in matter.
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Apparatus
• alpha particle source (241 Am)
• semiconductor detector device interfaced with a PC
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N2: α-Particle Spectroscopy
Figure 1: Alpha particle spectrum, and the associated nuclear energy level scheme.
• vacuum chamber with a vacuum pump and electronic manometer
• metallic foils for the attenuation measurements
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Alpha Particle Decay
Heavy nuclei tend to be unstable and to decay to a lighter element with a corresponding
emission of a helium nucleus (alpha particle). This can be shown schematically as,
A
ZX
4
−→A−4
Z−2 Y +2 α
(1)
A typical spectrum of alpha particles produced in a radioactive decay shows that they
occur in one or more energy groups that are mono-energetic to a first approximation. This is
because the energy is shared between the alpha particle and the recoil nucleus according to
quantum selection rules. Often an element is characterised by a single mono-energetic alpha
emission. Some elements have more than one transition energy, and then the alpha particles
appear in groups with differing relative intensities. The 241 Am alpha spectrum consists of
three principal components, corresponding to the three principal nuclear transitions, like
the example of plutonium (Pu) shown in figure 1.
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N2: α-Particle Spectroscopy
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Alpha Particle Interactions in a Semiconductor Detector
Semiconductor detectors based principally on silicon (Si) and germanium (Ge) have been
extensively used to make high resolution measurements of alpha particle and gamma ray
spectra. The short range of alpha particles (as little as 20 µm in silicon), allow relatively
thin detectors to be used which can be operated at room temperature.
A semiconductor detector is essentially a reverse biased diode. This consists of two
pieces of semiconductor material, an n-type (a material doped so that electrons are the
majority charge carrier) and a p-type (a material doped so that holes are the majority
carrier) material. At the junction between these two materials, the electrons can migrate
across the junction from n-type to p-type and annihilate with the holes, (i.e. they are
captured by one of the vacancies in the covalent bonds in the p-type material. Conversely
the holes can migrate from the p-type to the n-type material.)
The overall effect of this migration is that a net negative space charge is formed on
the p-type side of the interface, and a positive space charge formed on the n-type side.
An electric potential difference is therefore established across the junction, and hence an
electric field. This region is known as the depletion region.
The depletion region has excellent properties for detecting radiation. An incoming
alpha particle will excite and ionise a silicon atom. The ionisation results in an electronhole pair being produced, and these are separated by the electric field across the depletion
zone. The electrons created in the junction are attracted towards the n-type material, and
the holes to the p-type material. Once these charges are swept out from the depletion
region they can produce an induced current in the external circuit.
This current is integrated on the capacitor of a charge-integrating amplifier and the
output voltage of the charge amplifier is given by,
V0 =
Q
Cf
(2)
Where Q is the integrated charge on the feedback capacitor, and Cf is the value of the
feedback capacitor (1 pF for the TC170).
The output of the charge-integrating amplifier is fed into a shaping amplifier. This is
essentially a voltage amplifier with some pulse shaping to reduce the effect of pile-up and
noise. The output from this shaping amplifier is fed into the input of the MCA (Multi
Channel Analyser) card in the PC. The electronic circuit used in this experiment is shown
schematically in figure 2.
The MCA consists of an Analogue to Digital Converter (ADC) and a counter. Each
channel corresponds to a given pulse height (output voltage from the amplifier) and the
output is displayed as a pulse height spectrum on the PC. The pulse height can be calibrated
so that a given channel number corresponds to a given energy, giving the energy spectrum,
an example of which is seen in figure 3.
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N2: α-Particle Spectroscopy
Test Pulse In
Oscilloscope
Detector
MCA
Preamp
Amplifier
Figure 2: The circuit used in the alpha particle detector mechanism.
Figure 3: The output from the MCA is shown. The x-axis is the channel number, and
the y-axis is the number of alpha particles detected within any given channels
energy range.
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N2: α-Particle Spectroscopy
Figure 4: (a) Amplifier and pulse generator, (b) close up of pulse generator attenuator
settings.
5
Calibration, Control and Data Acquisition
The detector system should first be calibrated using the electric pulser to the right of the
amplifier rig, see figure 4. To do this, check the apparatus is set up as shown in figure 2.
The pulser should be set to output electronic (square) pulses for a chosen voltage, which
can be fed directly into an oscilloscope and calibrated on the oscilloscope scale. This should
be done for a range of values of output voltages as given below. These pulses can then be
used to calibrate the MCA.
The MCA is essentially a counting device, in which each channel number corresponds
to a very small voltage range, hence each channel number can be assigned a voltage.
When setting up the circuit, set the bias supply on the Farnell power source to positive
and adjust its value to the recommended value for this detector (approximately 70 V). Set
the input polarity of the amplifier to positive and the output from the amplifier to the
MCA should be UNIPOLAR.
To start the MCA, switch on the computer and when Windows is loaded select Multi
Channel Analyser. Set the output of the pulse generator to 100/1000 (1 Mev), where
100=pulse height and 1 000=frequency (Hz). In order to verify that the pulser is properly
calibrated it is necessary to adjust its output such that 100/1000 = 1 MeV in alpha particle
energy.
Start collecting data in the MCA — to do this click GO on the toolbar menu. To
terminate collecting, click on STOP (the MCA should collect into 1000 channels). Use the
LIVE time counter to record the time of data acquisition. The screen can be cleared at
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N2: α-Particle Spectroscopy
Figure 5: View of the experimental chamber from above.
anytime (except when data is being collected) by selecting CLEAR from the ACQUIRE
menu.
You should now set up the system as shown schematically in figure 5. Place the 241 Am
source approximately 1–2 cm away from the detector with no foil in place. Now pump
down the chamber. To do this ensure that the rotary pump is switched on at the mains,
and then open the pump down valve (the long thin valve).
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It is imperative that the bias supply should be turned OFF whenever you
are pumping the chamber up or down — not doing this could damage the
detector.
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Switch on the electronic pressure meter. You should find that after approximately
2 minutes the chamber will not pump down anymore — at this point the chamber is
as evacuated as the vacuum pump used can achieve. Leave the pump down valve open
throughout the period you take measurements.
Now start the MCA. You should see a single peak — this is the energy peak of the
241
Am source. The peak energy is 5.484 MeV, set the pulser to 548/1000 and adjust the
attenuation of the pulser such that the peak of the alpha particle energy conincides with the
electronic pulses generated. If you are unable to do this exactly consult the lab technician
so that he can adjust the pulser.
You should now apply a series of different pulse voltages — you are recommended to
use 100/1000 (1 MeV), 200/1000 (2 Mev), 300/1000 (3 Mev) up to 600/1000 (6 Mev).
Check the pulse output with the oscilloscope, and note the corresponding channel number
for each different voltage. The scale obtained will be linear, so plotting the results in a
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N2: α-Particle Spectroscopy
Figure 6: Measuring the Full Width Half Maxima.
spreadsheet and using a trend line will give an equation which relates the value of the
voltage of the applied pulse to the channel number. Hence you will know the energy that
corresponds to each channel number.
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Resolution of the Detector System
The next stage is to determine the intrinsic resolution of the detector system. The alpha
particles produced by the sample will have a range of energy values centred on the peak
value, so they fall into a range of channels in the MCA instead of a single channel. The
resolution of the system is conventionally obtained by measuring the Full Width at Half
Maximum (FWHM) of the signal on the MCA, as shown in figure 6.
The resolution, R, of the system is defined as,
R=
FWHM
H0
(3)
Where H0 is the location of the centre of the peak. More information can be found on this
in “Radiation Detection and Measurement” by G.F. Knoll, pages 114–117 (in the lab).
To measure the resolution of the detector system you should switch off the pulser, clear
the MCA and begin taking new readings. You should see a single peak. Using figure 6 you
should be able to calculate its FWHM and hence the resolution of the detector system.
The MCA software program can also do this for you. To analyse a recorded spectrum
the cursor can be moved by the mouse over the channels, and the number of counts in each
channel will be displayed.
To analyse the peaks in a spectrum, the REGION OF INTEREST (ROI) facility should
be used. First move the cursor to the lower limit of the peak under investigation and select
the option MARK from the ROI menu. Then put the cursor at the upper limit of the peak
and click MARK again. The whole peak (the ROI) will then be coloured purple.
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N2: α-Particle Spectroscopy
Double click the mouse in the coloured region and the computer will fit a Gaussian
function to the selected peak and will display information such as the Centroid (Centre
of the Peak)and the Full Width at Half Maximum (FWHM). To clear an ROI select the
region, and then use the CLEAR option from the ROI menu.
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Measurement of Alpha Particle Energy Attenuation in Matter
The system can now be used to measure how alpha particles are attenuated in matter.
Place the 241 Am source close to the detector and pump down the system.
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Ensure the detector bias is switched off when pumping.
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Select GO in the menu and the detected alpha particles will appear on the computer
screen as counts in the MCA. Change the gain of the amplifier so that the 5.31 MeV alpha
particles from the 241 Am source are in approximately channel 800. Then use the pulse
generator as described earlier to recalibrate the system, i.e. produce a new keV/channel
graph and calculate the slope.
Now turn off the bias and vent the system again. Place the thinnest copper foil between
the 241 Am source and the detector.
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BE CAREFULL!!! The foils are very delicate and are easily broken — they
are also very expensive!!!
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Now pump down the system and put the bias back on. From the calibration curve
determine the energy of the alpha particles and record this value.
Now turn off the bias and vent the chamber SLOWLY, in order to avoid damage to the foil. Put the next thinnest foil in (at the same point in the chamber) and
repeat the above. This should be repeated for all the copper foils in the set, and the
measured alpha particle energy should be recorded for each one. You should find that as
the foil thickness increases the alpha particle energy will decrease, and also the full width
half maxima of the peaks will widen.
Now produce a graph of the energy loss as a function of foil thickness. Calculate the
theoretical energy loss for the alpha particles — this is done with the following method:When an alpha particle passes through a thin foil, the foil on average has a “stopping
power” for the particle due to the interactions with the atoms in the foil. This stopping
power can be conveniently quantified in terms of the alpha particle energy loss for a given
length of the attenuating material — dE/dx. So the stopping power of the foil varies with
the energy of the particles interacting in the foil, this is shown in figure 7.
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N2: α-Particle Spectroscopy
α
Energy
¡ dE ¢ = E0-
Energy
¡ dE ¢ = Ef- α
dx E0
dx Ef
¾ -
∆x
Figure 7: Energy change of an alpha particle in matter.
The value of (dE/dx)E0 at the incident energy, and of (dE/dx)Ef at the final alpha
particle exit energy is given for a range of materials in table 1.
Energy
(MeV)
0.050
0.080
0.128
0.201
0.400
0.500
0.640
0.800
1.000
1.600
2.000
2.401
2.800
3.200
4.000
5.000
6.400
8.000
Cu
0.311
0.401
0.670
0.643
0.764
0.780
0.781
0.770
0.740
0.660
0.630
0.580
0.550
0.520
0.460
0.410
0.360
0.320
N
0.564
0.684
0.817
0.956
1.303
1.442
1.604
1.734
1.816
1.776
1.640
1.458
1.292
1.152
0.949
0.792
0.655
0.556
O
0.530
0.644
0.777
0.930
1.262
1.389
1.546
1.665
1.748
1.688
1.561
1.385
1.227
1.098
0.900
0.756
0.626
0.530
Ne
0.471
0.576
0.710
0.865
1.201
1.327
1.466
1.574
1.632
1.529
1.396
1.238
1.098
0.982
0.802
0.672
0.561
0.479
Table 1: dE/dx in MeV/mg/cm2 for various materials.
Since the foil is fairly thin, it is reasonable to assume that dE/dx changes linearly across
the foils. Hence calculate an average value of dE/dx which will give the average energy
loss. Hence,
¡ dE ¢
¡ ¢
µ ¶
+ dE
dE
dx E0
dx Ef
(4)
=
dx average
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N2: α-Particle Spectroscopy
The theoretical energy loss is given by,
µ
∆E =
dE
dx
¶
× ∆x
(5)
average
Calculate ∆E for the range of foil thicknesses used. Compare these values with the
ones obtained by direct measurement and calculate a percentage difference. Explain any
inconsistencies.
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Measure the Attenuation of Alpha Particles in Air
This simple experiment allows the range of alpha particles in air to be measured.
First, place the 241 Am source 2–3 cm from the detector and close the chamber. Switch
off the bias and then pump down the chamber. When it is evacuated re-apply the bias
to the detector and check that the calibration obtained in section 5 is still valid. Also
check that the gain is set so that the 5.31 MeV alpha particles in a vacuum correspond to
approximately Channel 800 in the MCA. If this is not the case recalibrate the detector.
Now with the chamber fully pumped out, take a good reading (3000 or so counts),
and measure the peak channel number. Hence calculate the corresponding peak channel
energy.
Increase the pressure in the chamber by 50–60 mbar (5–6 kPa), using the needle valve in
the pumping line, and again measure the peak energy. This should be repeated increasing
the pressure each time until atmospheric pressure or a statistically good alpha spectrum
(even for long exposures) can no longer be obtained. Record the pressures. Note that
the pressure meters are differentials so the pressure values they give out are the pressures
relative to atmospheric pressure — hence you will need to correct the read out values to
get the absolute pressure.
For each recorded pressure use the ideal gas equation (P V = nRT ) to calculate the
path thickness of air (in mg/cm2 ). From your energy/channel calibration curve, you should
calculate the final energies (Ef ) for each “gas thickness”. Hence calculate the energy loss
for each gas thickness, and present this as a graph.
Now calculate the theoretical energy loss — do this using the same method as described
in section 6. Use the values of dE/dx for oxygen and nitrogen in table 1. Given that the
atmosphere is approximately 80% nitrogen and 20% oxygen, you should take a weighted
average of the dE/dx values. Hence plot a graph of these and fit a curve to the values. Then
using equation 5 and values for (dE/dx)f read from the graph, calculate the theoretical
energy losses for alpha particles at the various pressures.
Compare these with the ones measured and explain any discrepancies.
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