5.1. Calorimetric Capabilities of the Neo Scmos
The camera response to
,
and
source radiation is examined in order to determine the Neo sCMOS’ calorimetric measurement capabilities. Background data obtained with no source present is used as well for this analysis.
Figure 7 shows cluster charge spectra measured for these sources. To create these, the analysis procedures detailed in
Section 4 are applied to the raw frames and a cluster size larger than two pixels is required for all entries in the plots.
The contribution of the source radiation to the spectra has to be disentangled from the contribution of the background radiation. To this end, spectra obtained with radioactive sources and the background spectrum are normalised to the same live-time and then the background spectrum is subtracted from the source spectra. The results are shown in
Figure 7b–d.
:
The cleanest spectrum is obtained with the
source, which has an activity of
as of at the time the measurement. The uncertainty on the initial source activity is not known, therefore a 5% error is assumed. Americium-241 decays via an
-decay to
. There are many possible
-decays with different
Q values from 5000
to 5500
[
23], where the most probable (85%) decay has an energy of 5485
. These
-decays occur together with
-ray emission and X-ray emission by the
atom [
23].
Table 2 lists the two
energies with the largest yield per decay as well as X-ray lines measured in
spectra elsewhere. The CMOS chip of the Neo sCMOS camera is housed behind a glass window, with an assumed thickness of 1
—therefore the
-particles will not reach the sensor, since the range of
s of this energy is less than 100
[
24]. The energy deposits measured with the
source are thus for the most part due to
- and X-rays. Attenuation lengths for different
- and X-ray energies are given in
Table 3.
:
Iron-55 decays via electron capture to
[
23]. After the decay, the electron shell re-arranges to match the levels of
and to fill the hole from the electron capture. By doing so, Auger-Meitner electrons with an energy of up to 6
are released as well as X-rays of
and
. For these X-ray energies the yield per decay is 16.6% and 7%, respectively. Although the source used has a rate of
, the background subtracted spectrum in
Figure 7c is compatible with zero. For low charge values, that is, low energy deposits, the spectrum is more erratic—however, no clear peak can be identified. For photon energies
we estimate a lower limit for the photon absorption in glass with the data from Reference [
25], assuming 10
photon energy and a glass density of
/
. For a window of 1
and 2
, at least 97% and 99.04% of the X-rays are absorbed in the glass before they reach the chip, respectively. Therefore, the non observation of any clear peak is most likely due to the X-ray absorption in the Neo sCMOS window.
:
Lead-210 decays via
decay to
as mentioned in
Section 1.1. The most probable
decay (84%) results in an excited state of
, whilst emitting an electron with an average decay energy of
. The nucleus de-excites by emitting a
of
with a 4% yield per decay. The de-excitation is accompanied by the emission of X-rays from approximately 9
to 16
with a yield of 22% per decay. The second most probable decay (16%) is a
decay with an electron mean energy of
to
in the ground state [
23]. The
source used has a rate of
. It holds the lead diluted in nitric acid in a small glass vial. It is not likely that any of the low energy
-radiation is detected by the Neo sCMOS, given that the decay electrons have to traverse the liquid, the glass of the vial and of the Neo sCMOS before it can be detected by the CMOS chip. Therefore, similarly to the
source, only the X-rays and
-rays are measured.
The
spectrum in
Figure 7d contains fewer counts than the
spectrum (
Figure 7b). There are several factors contributing to this: First, the activity of the
source is a factor of 1.85 lower than the activity of the
source. The latter source has also a significantly smaller extent—compared to the CMOS sensor it can be considered as a point source, while the lead source extends over a vial of more than 1
length and
diameter. Next, the
yield for the two sources differs greatly—comparing
to
for the
-ray and the
-ray. In order to establish whether the
and
spectra are consistent with each other, we first need to establish the overall energy scale and compare peaks at a known energy directly.
5.1.1. Energy Response Calibration
All the spectra presented so far are shown with
analogue-to-digital units as unit of the deposited energy in the detector. The Neo sCMOS’s manuals consulted during this work do not state a conversion factor from
to energy in
. However, the report [
27] specifies a gain of either
or
according to the supplier. These gain values translate to a conversion factor of either
/ADU or
/ADU, respectively, accounting for the
W factor in Si of
to create an electron-hole-pair [
28]. In order to establish the exact energy scale, the known energies of radioactive sources from literature are matched to the
values at which peaks are observed. All large peaks in the cluster charge spectra are fitted with a Gaußian curve and their mean energy,
, and
is extracted.
Table 4 lists all peaks used for this analysis and the result of the fits. The Gaußians are furthermore plotted in
Figure 7b,d and
Figure 8a. The fits are done locally—in the ranges from
to
as specified in
Table 4—and where necessary a polynomial of order one is added to the Gaußian curve to account for the floor due to other radiation. For the peaks at the high energy end of the
and
spectrum an error-function is used instead of a polynomial.
The second, independent, dataset to obtain the energy scale calibration uses measurements where the CMOS is irradiated by an X-ray tube, described in
Section 3. For the spectra obtained with the X-ray tube using only Gaußian fits with a local background is not sufficient (
Figure 8a): The two characteristic peaks of the molybdenum X-ray tube are expected to be located on top of the
bremsstrahlung spectrum of the tube. For low X-ray energies the camera has negligible calorimetric capabilities as seen in the measurements with the
source (previous section,
Figure 7c). Hence, the Neo sCMOS should become efficient for X-rays of the molybdenum X-ray tube somewhere after
– from that point onwards there should be an increasing number of counts due to
bremsstrahlung and eventually the molybdenum
and
peaks at
and
, respectively.
Figure 8a shows the spectrum, the fit to the spectrum, and the fit’s components. An onset of counts is observed at
however, no clear double peak structure is observed. As there is no clear expected functional shape for the bremsstrahlung contribution, we model it as the minimal functional addition (
) needed so
fits the data well.
In these equations
is the cluster charge (or energy deposited in the chip) in
. The parametrisation (
8) for the bremsstrahlung contribution yields the lowest
of 4.62 for the total fit of
to the data, whilst all fit parameters are free. The extracted parameters of the two
K lines (
,
) are listed in
Table 4.
Using a Cu or a Zr foil to filter the molybdenum X-rays results in the spectra shown in
Figure 8b. The absorption edges of those two elements for energies higher than
are at
(Cu) and at 18
(Zr). The shape of the spectrum recorded with the Cu filter does not feature a drop which can be identified with an absorption edge—the edge is thus placed in the energy range where the Neo sCMOS is not sensitive to allow X-ray calorimetry. There is a larger reduction of counts for energies
, relative to the not filtered spectrum and the one with the Zr filter. After, the number of counts increases again. Starting from low energies, the shape of spectrum with the zirconium filter matches the un-filtered spectrum, until the edge at
. This drop is identified with the Zr absorption edge. The
value at which the amplitude reaches the 50% value between maximal peak height and the floor in the spectrum is taken as its energy position (
Table 4). The uncertainty on the edge’s position is taken to be half of the
range between the edge’s 10% and 90% value.
Figure 9a displays the measured charge values plotted against their expected energies for all peaks and edges in
Table 4. Fitting a linear function without an axis intercept to these points yields the conversion factor from
to
(and vice versa) to be
ADU/
(
/ADU). For this fit
is
while using a function with an intercept results in a
of 0.56, an intercept of −
, and a slope of
/ADU (
ADU/
). These values are compatible with the conversion factor mentioned before, although slightly different from an intercept of zero. In the next sections the conversion factor without an intercept is favoured over the conversion with an intercept, since the low
in the latter case indicates over-fitting.
The measured conversion factors matches well with the higher of the two gain values discussed before, that is, ADU/ which is located between the two different fit values. This agreement is taken as another reason to use in the following the conversion factor determined without an intercept, given the supplier does not specify an offset.
5.1.2. Energy Resolution
In
Figure 9b the energy resolution is shown as
divided by the peak positions
(
Table 4). As the uncertainty on
the uncertainty of the fit is used while
itself is used as the uncertainty of the peak position
. The uncertainty on the energy resolution,
includes both of these contributions. For the most part the resolution is better than 2%. Outliers from this trend are the two molybdenum X-ray lines and the Np,
line (at
). The two X-ray lines are extracted from a more complicated fit with the worst
and the uncertainty on their
values is likely to be underestimated.
The energy resolution is determined by several factors. The full containment of all electrons produced during the photon conversion and their subsequent readout will play an important role. Furthermore their can be pixel-to-pixel variations of each pixels’ amplifier gain. An increasing trend in cluster size with increasing energy has been observed, as stated in
Section 4.2.4, but the good linearity of the
to
relation suggests that all electrons produced by a photon interaction are read out. The pixel-to-pixel amplifier gain variations for the Neo sCMOS are not known. Typical values are in the few % range—for example, Reference [
29] shows a variation of about
[
29]. Such a variation would be consistent with the energy resolution shown here. Note that the energy measurements in
Figure 9b are the result of summing the energy measured in each pixel of a cluster. If the per-pixel amplifier variation would be the dominating factor for the energy resolution, the Neo sCMOS would have variations slightly larger than
.
5.3. Geant4 Simulations of the Neo Scmos Detector
To extend the limited knowledge of the sensor geometry beyond the estimations based on the toy MC simulations, a Geant4 MC simulation study is carried out to estimate the impact of the window, the micro lens array and sensor thickness on the - and X-ray absorption.
Geant4 [
16,
32,
33] version 10.5 patch 1 is used to simulate the primary particles and the production of the resulting secondary particles, for the tracking of all particles through the detector geometry, and to assess the energy deposition in the sensitive detector parts. This work employs physics lists which follow mainly the
Shielding physics list of the above mentioned Geant4 version with one physics modification; namely
.
is used instead of
, because the former is more accurate for low-energy electromagnetic interactions.
5.3.1. Detector Geometry and Simulated Particles
The sensor is modelled as a silicon CMOS layer, behind a glass layer to represent the entrance window, behind an acrylic layer to represent the micro lens array. For this simulation, the material of the window is chosen to be
. The camera specifications indicate an organic material for the micro lens. Thus, for the material of this volume element, acrylic
is chosen. For the thicknesses of each volume element, values in the range of
are used. This study varies the thicknesses of the silicon and glass window. As discussed in
Section 5.1,
decays either by a combined
- and
-decay (84(3)%), where the
-ray has an energy of
and an average
energy of
, or by a pure
-decay (16(3)%) with an average
energy of
. When simulating electrons of this energy impinging on the detector with a 200
glass window and 5
of Si thickness, there are zero hits on the active region out of
simulated events. Since the energy of the other
is even lower, the signature
-ray of
is the main focus of this simulation work whereas
-particles are not included.
The simulated particle source is located from the outermost layer of the surface, and fires mono-energetic - and X-rays directly at the detector.
To construct the energy variable used to compare with data, the simulated ionisation energy deposition in the Si layer is recorded for each incident particle, and then smeared according to the energy resolution function
fitted to the data in
Figure 9b.
5.3.2. Analysis of the Simulated Spectra
A set of different thicknesses for the silicon layer and the glass window are simulated for comparison with the data. The list of thicknesses simulated ranges from 2–5
for the Si, and 200–2000
for the window, listed in
Table 6.
Figure 14 shows example spectra of the energy deposition in the Si layer for 200
(
Figure 14a), 1000
(
Figure 14b) and 2000
(
Figure 14c) glass thickness and a constant 4
micro lens thickness. Colours represent different thicknesses of the silicon layer varying in between 2
and 5
while the thickness of other volume elements is kept constant. There are two visible differences between each simulated template:
The total number of events registered in the silicon layer increases with Si thickness which is caused by more particles being absorbed by a thicker Si layer.
The number of events in the photo-peak and Compton continuum increases and decreases, respectively, as the silicon thickness increases. This is because the fraction of events for which the incident photons’ energy is fully contained in the Si rises as the thickness increases.
The information regarding the number of events in the photo-peak can be used to characterise the thickness of the silicon layer in conjunction with the amount of events in the Compton continuum. The ratio
is used as a variable to compare the simulated templates with data:
where
stands again for the energy of the photo-peak,
for the peak’s standard deviation and
for the number of events. The exact value of the photo-peak and the energy resolution of the detector need to be known, to precisely define the integration limits in (
15). We take
to be
[
23] and calculate
from the energy resolution for this energy using Equation (
14) to be
.
-values for different silicon layer and window thickness calculated from the simulation results can be found in
Table 6.
5.3.3. Comparison of Simulation with the Experimental Data
The thickness of the Neo sCMOS active layer, assuming Si as material, is estimated by comparing the spectra in
Figure 14 and the photopeak ratio
with the data.
When this variable is calculated for the data (black line in
Figure 14), it is found to be
. Comparing
with the values calculated from simulated templates (
cf. Table 6), it can be seen clearly that a combination of 4
silicon layer and 1000
glass window comes closest to this value with
.
As another check, one can investigate the spectral shape of simulation with respect to experimental data. Above 30 , the spectral shape of the data are closest to the spectrum of the 2 Si thickness simulation. Below that, the shape matches of the measured spectrum lies between the spectrum simulated for a 3 and 4 thick Si layer. All templates except for the 4 and 5 ones show a discontinuity before the photo-peak as the energies of the particles increase, which is an expected result due to thinner silicon layers being less efficient in stopping -rays and containing the particles energy.
5.3.4. Closing Remarks
The close match of
-values and the spectral shape between the data and the Geant4 simulation suggest a silicon thickness between 2
and 4
for a window of 1000
, where the comparison to
places the thickness at the high end of this range.
Table 6 shows that for this geometry only
of the
-rays of
are fully absorbed in the silicon layer, that is, contribute to the photo-peak. In
Section 5.2.3 the intrinsic efficiencies for the
and
-peak are determined to be
and
, respectively. The efficiency for the
-line is compatible with the value simulated here for
-rays. Given the fact that the measured value is at a higher energy than the
of the simulated
-rays, the Geant4 simulation most likely underestimates the Neo sCMOS detection efficiency at
slightly or the actual Si thickness is larger than 4
. This is, because the efficiency to detect
photons is expected to be larger than the one for higher energy photons.
Both the Geant4 simulation of
-rays and the toy MC simulation of
photons place the silicon layer thickness in the range between 2
and 4
,
cf. Section 5.2.4,
Figure 12b. While the full Geant4 simulation gives more parameters to compare between the data and the simulation, the toy MC simulation is significantly faster as it runs in an instant. The agreement between the two gives confidence to use the less sophisticated toy MC simulation in instances where a full fledged Geant4 simulation is not easily accessible.