Energy resolution of the Medipix3RX with a 500um silicon sensor

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bachelor thesis

Energy resolution of the Medipix3RX

with a 500µm silicon sensor

Robbert Geertsema 10757805

Report Bachelor Project Physics and Astronomy, size 15 EC Conducted between 03-04-2017 and 05-07-2017

at Nikhef, Amsterdam

Date of submission: 05-07-2017 Daily supervisor: dhr. Martin Fransen

Supervisor: mw. dr. Hella Snoek Second assessor: dhr. dr. Ivo van Vulpen

Faculteit der Natuurwetenschappen, Wiskunde en Informatica Universiteit van Amsterdam

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List of Figures

2 Een ’normale’ en een ’kleuren’ r¨ontgenfoto. . . vii 2.1 Illustration of bump bonding. The orange circles represent the solder and

the black squares the connection pads. . . 2 2.2 Illustration of the charge summing algorithm used in the Medipix3RX made

by Ballabriga et al. (2013). The red circle represents the electron cloud induced by a photon. The arrows point to the pixel that got the biggest part of the electron cloud. Here the total energy of the electron cloud is assigned to pixel C3. . . 4 2.3 Schematic overview of a pn-junction. The x-axis of the sketch corresponds to

the width of the sensor. The Fermi level is indicated with the dashed/striped line. . . 5 2.4 Part of the circuit of the Medipix3RX. This part of the circuit determines

the gain of the incoming signal (id). The current source only draws a current

when a signal is deposited in the capacitor. . . 6 2.5 The setup used to create a monochromatic energy spectrum. The beam

of the X-ray tube is aimed at the red target material. The fluorescence from this target material is emitted in all directions and measured by the Medipix3RX. . . 8 2.6 The threshold scan and the derived energy spectrum from this threshold scan. 9 2.7 Illustrations made by Schioppa(2014). This illustrates the model Schioppa

uses for the spectral response of the Medipix. This model is the same as the model used in this thesis. . . 10 2.8 In blue the photoelectric absorption for 500µm Si and in green the Compton

absorption. This data is retrieved from Berger et al. (2010). . . 10 2.9 The measured spectra with zirconium as the target material. All of these

measurements were performed with the Medipix3RX in SPM during the equalization. . . 11

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3.1 Energy calibration performed with the Medipix3RX in CSM and HGM mode. The error bars of the points are in the order of .01 and are therefore not shown in this figure. A linear line is fitted through the three calibration points. . . 13 3.2 An energy spectrum measured in the setup with zinc as the target in SPM.

The fluorescence peak of Zinc is visible around 27 THL. A single normal distribution is fitted on the data points on the right side of the peak and five percent left of the peak. This results in a position of 27.15 THL, a width of 2.306 THL and a height of 9302. . . 15 3.3 Two cases of four normal distributions positioned either at different positions

or at the same position. . . 16 3.4 Heatmap of the amount of hits for an energy level close to the energy of the

Kα emission line of zirconium. A brighter color represents more hits. There is a difference in the amount of hits for the four chips.. . . 17 3.5 The distribution of the center of the individual normal distributions and the

distribution of the width of the individual normal distributions for chip 0.. 18 3.6 The distribution of the width for chip 0 in LGM and SLGM and the

corre-sponding heatmap for LGM. . . 19 3.7 An energy spectrum of a measurement with zirconium. Two normal

distribu-tions are fitted to the energy spectrum. This resulted in the position for the first normal distribution at 55.2 THL and the position of the second normal distribution at 62.14 THL. . . 20 4.1 The difference in energy resolution for some operating modes compared to

each other. . . 23 A.1 The distribution of the widths for HGM, LGM, SLGM for the four chips of

the detector. . . 32 B.1 Both the C-V profile and the corresponding 1/C2_{-V graph of the 500µm}

silicon sensor on the used Medipix3RX. . . 34 C.1 The transmission spectra for copper (red), molybdenum (blue) and cadmium

(green). The energy bins used to assign rgb values to the picture are separated by dashed vertical lines. . . 35 C.2 Both a ’normal’ X-ray image and a ’color’ X-ray image. . . 37

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English abstract

To accurately determine the energy spectrum measured by the Medipix3RX the energy resolution is important. In this thesis the energy resolution for nine different operating modes of the Medipix3RX with either a bias voltage of 100V or 200V is determined using a X-ray fluorescence setup. The energy resolution is determined at three energies, namely 8.6KeV, 15.7KeV and 25.2KeV. From these results the best operating mode tested is determined by looking at the best energy resolution. The best operating mode tested is 200V bias, Single Pixel Mode equalization, Single Pixel Mode and Low Gain Mode. This operating mode resulted before a pixel-per-pixel calibration in an energy resolution of 1.51KeV at 8.6KeV and after a pixel-per-pixel calibration in an energy resolution of 0.98KeV at 8.6KeV.

Populaire samenvatting

Röntgenstraling wordt gebruikt om röntgenfoto’s te maken. Röntgenstraling is elektromag-netische straling met specifieke frequenties. De golflengte van röntgenstraling ligt tussen 30 petahertz (3 × 1016 _{Hz) en 30 exahertz (3 × 10}19 _{Hz). Deze frequenties komen overeen}

met een energie van 0.1 KeV tot 100 KeV. Röntgenstraling kan worden gemaakt door middel van een röntgenbuis. Deze röntgenbuis zendt röntgenstraling uit met verschillende frequenties. Tijdens het vastleggen van de uittredende straling (het maken van een normale röntgenfoto foto) wordt er normaal geen onderscheid gemaakt tussen de verschillende energieën röntgenstraling. Als er wél onderscheid kan worden gemaakt kunnen verschillende materialen beter zichtbaar worden dan dat ze op de normale röntgenfoto zouden zijn.

Om de energie van de r¨ontgenstraling precies te bepalen met een detector moet bekend zijn hoe groot de zogenoemde ‘energie resolutie’ is. De energie resolutie is de mate van nauwkeurigheid waarmee een detector kan meten. Een voorbeeld van zo’n detector is een detector met een Medipix3RX chip. Dit is een detector van 2.8 cm bij 2.8 cm die beschikt over meer dan 65 duizend pixels. Deze detector kan tot 1300 frames per seconde meten en hij is commercieel verkrijgbaar. In deze thesis is de energie resolutie bepaald van deze detector.

Met behulp van deze energie resolutie kan worden bepaald wat wél en wat niet gemeten kan worden. Een voorbeeld van een toepassing is het maken van onderscheid tussen verschillende materialen met behulp van de bepaling van de specifieke energieën. Figuur 2a laat een normale röntgenfoto zien zoals deze ook in een ziekenhuis wordt gemaakt. In deze röntgenfoto zijn vier verschillende plaatjes materiaal zichtbaar. Op deze röntgenfoto is niet zichtbaar welke plaatjes van hetzelfde materiaal zijn en welke van een ander materiaal. Maar als de specifieke energieën van de röntgenstraling gemeten worden met de Medipix3RX,

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kan de informatie van deze energie¨en worden gebruikt om figuur 2b te maken. In dit figuur is zichtbaar dat het om drie verschillende kleuren gaat. Hierdoor wordt duidelijk dat deze vier plaatjes uit drie verschillende materialen bestaan. Op basis van de gewone r¨ontgenfoto is dit onderscheid niet te bepalen.

(a) Een ’normale’ r¨ontgenfoto van vier verschil-lende plaatjes metaal. De drie verschilverschil-lende metalen kunnen niet van elkaar onderscheiden worden op alleen de basis van de grijstinten.

(b) Een ’kleuren’ r¨ontgenfoto van de vier ver-schillende plaatjes metaal. Door de verschil-lende kleuren wordt het duidelijk dat er 3 ver-schillende soorten metaal in de foto aanwezig zijn.

Figure 2: Een ’normale’ en een ’kleuren’ r¨ontgenfoto.

De energie resolutie van de Medipix3RX wordt be¨ınvloed door de instellingen. In dit onderzoek is de energie resolutie bepaald voor negen verschillende instellingen. De verschillen in energie resolutie tussen ’Charge Summing Mode’ en ’Single Pixel Mode’ worden in kaart gebracht bij een bias voltage van 100V en 200V. Tevens wordt de energie resolutie bepaald voor een energie van 8.6KeV, 15.7KeV en 25.2KeV voor alle negen instellingen. Op basis van de meetresultaten blijkt dat bij een bias voltage van 200V, SPM egalisatie, SPM en HGM de Medipix3RX de beste energie resolutie oplevert van de negen onderzochte instellingen.

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Chapter 1 Introduction

Currently, in hospitals for example, X-ray photos are used to visualize parts of the human body that are not visible for the naked eye. These X-ray photos consist of a map of the summed energy of the photons that arrive at the different locations of the photo. Therefore there is no information about the energy of the individual photons. If one could look at the energy of the photons, some of the components would be more visible in a certain energy domain (see appendix C). This means that the amount of information one could get out of these pictures will increase. This information could for example be useful for investigating old paintings. Sometimes reused canvasses have an older painting under the visible painting, which is therefore not visible anymore for the human eye. By determining the elements present on these canvasses these older painting can be digitally visualized (Dik et al., 2008). These elements can be determined by looking at the energy spectrum of the X-ray image. This kind of X-ray imaging is called spectral X-ray imaging. But to accurately distinguish different materials from each other, one needs to know the accuracy of the energy that is measured by the detector. This accuracy, the energy resolution, is determined in this thesis for the Medipix3RX by performing a threshold scan for multiple monochromatic energy sources.

Because the focus of this thesis is on the determination of the energy resolution of the Medipix3RX, side effects of the Medipix3RX are not investigated in this thesis. These side effects will be documented and can be investigated in further research.

In Chapter two the various operating modes of the Medipix3RX are discussed as well as the method of the threshold scan, from which the energy spectrum is derived. In Chapter three the energy and the pixel-per-pixel calibration is performed and the fitting procedure used in this thesis is explained The results for the various operating modes are shown in Chapter four. Finally, in Chapter five the various unexplained effects are discussed and the conclusion is drawn.

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Chapter 2 The Medipix3RX X-ray detector

2.1 The Medipix3RX readout chip

The Medipix3RX is a readout chip (ASIC) it is the successor of the Medipix3 and was released in 2012. Both of these ASICs are single-photon-processing hybrid pixel ASICs developed by the Medipix collaboration. These detectors can detect single photons and determine the energy. The Medipix3RX has a frame rate of 1300 frames/s, has a fairly big spatial resolution and is commercially available.

In this thesis a detector is used that consists of four Medipix3RX chips connected to a 500µm thick silicon sensor. A single chip is 14.1 by 14.1 mm. There are two versions of the Medipix3RX: a fine pitch module and a spectroscopic module. The fine pitch module consists of an array of 256 by 256 pixels with a size of 55µm. Each of these pixels is bump bonded to the chip. Bump bonding consists of small balls of solder that are bonded to connection pads at the semiconductor (silicon) sensor and the chip. Figure 2.1 illustrates this. This chip is connected to the read-out electronics via wire bonds.

Figure 2.1: Illustration of bump bonding. The orange circles represent the solder and the black squares the connection pads.

With the fine pitch module two thresholds per pixel can be set. With the spectroscopic module every cluster of two by two pixels has just one pixel bump-bonded to the chip.

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This allows for eight thresholds (2 × 4) to be set per pixel cluster. Therefore there are effectively 128 by 128 pixels, each with a size of 110µm. The detector used in this thesis consists of four spectroscopic Medipix3RX chips. The detector is used with the settings indicated in table 2.1 at a temperature between 30◦C and 34◦C. A few operating modes of the Medipix3RX are discussed below.

CRW freq (Hz) 100 Shutter open length 40000µs Shutter down length 10000µs Pixel depth 12 bits

LUT On

Trigger Mode Auto

Operation Mode Sequential R/W

Preamp 100

IKrum 5

Shaper 125

Disc 125

Disc LS 100

Table 2.1: The setting for the Medipix3RX used in this thesis.

2.1.1 Charge summing mode

Charge summing mode (CSM) is one of the two possible operating modes of the Medipix3RX, with the other mode being single pixel mode (SPM). If the Medipix3RX is operating in CSM the pixels alongside each other always communicate. When a photon creates an electron cloud in the detector material, this cloud is not just a single point. Therefore if a photon creates such a cloud on the edge of a pixel there is a chance that the adjacent pixels will also measure a part of this cloud. In SPM one will therefore measure two separate ’photons’ if the electron cloud spans two pixels. The combined energy of these two ’photons’

is equal to that of the real photon. In CSM these two pixels communicate and notice that both measure the same electron cloud. The pixels that measure the highest energy will then add the energy from the adjacent pixel to its own energy. This combined energy is then considered the energy of the original photon. An illustration of this process is shown in figure 2.2.

2.1.2 Bias voltage

The bias voltage applied to the silicon sensor determines the width of the depletion zone. In this zone the electrons in the silicon are forced away by the induced electric field in the silicon. This means that if the depletion width is smaller than the width of the silicon sensor not all electrons are forced to the edge of the silicon and are therefore not measured. Therefore it is preferred that the depletion zone covers the full width of the detection material. The width of the depletion zone is given by formula 2.1 if the concentration of acceptors (Na) is higher than the concentration of donors (Nd). In that case the depletion

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Figure 2.2: Illustration of the charge summing algorithm used in the Medipix3RX made by Ballabriga et al. (2013). The red circle represents the electron cloud induced by a photon. The arrows point to the pixel that got the biggest part of the electron cloud. Here the total energy of the electron cloud is assigned to pixel C3.

region primarily extends into the n-doped side. An n-doped material is a material in which impurities (donors) have been added with more electrons than the original material. This results in the Fermi level shifting closer to the conduction band due to the increased electron concentration. P-doping means that impurities (acceptors) have been added with less electrons than the original material. This results in the Fermi level shifting closer to the valance band.

w ≈ xn =

r 2ε0εrVb

eNd

(2.1)

The silicon sensor on the Medipix3RX has both p- and n-doped regions (pn-junction). In thermal equilibrium the Fermi level should be constant throughout the sensor. This means that in the pn-junction the valance bands are offset from each other and make a gradual transition from the p-region to the n-region (see figure 2.3). The difference between the p- and n-region gives rise to a potential difference which is a ’build in’ bias voltage. This voltage is given by formula 2.2.

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Figure 2.3: Schematic overview of a pn-junction. The x-axis of the sketch corresponds to the width of the sensor. The Fermi level is indicated with the dashed/striped line.

Vbi = EF n− EF p = kT e ln N_aNd n2 i (2.2)

ni stands for the intrinsic carrier concentration. For silicon the intrinsic carrier

concen-tration is given by formula 2.3 (Misiakos & Tsamakis, 1993).

ni(T ) = 5.28 · 1019 T 300 2.54 exp −6726 T (2.3)

For a temperature of 306.15K (32◦C) the intrinsic carrier concentration is 1.599·1010cm−3. The concentration of acceptors (Na) is assumed to be around 1015cm−3 and the concentration

of donors is 8.88057 · 1011_cm−3 _{(see appendix} _B_{). This results in a ’build in’ bias voltage of}

0.3973V. The externally applied bias voltage necessary to deplete a semiconductor with a width of w is given by formula 2.4 (Spieler, 2005).

Vd=

eNdw2

2ε0εr

− Vbi (2.4)

Vd is the externally applied bias voltage. The silicon sensor used in this thesis is 500µm

thick. This means that with an externally applied voltage of 171.58V the wafer is fully depleted.

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Both an externally applied bias voltage of 100V and 200V are used in this thesis. With 100V the depletion layer is calculated to be 381µm thick and with 200V the depletion layer is calculated to be 539µm thick.

2.1.3 Gain Modes

The Medipix3RX offers four different gain modes, namely Super High Gain Mode (SHGM), High Gain Mode (HGM), Low Gain Mode (LGM) and Super Low Gain Mode (SLGM). These different gain modes select the value of the preamplifier’s (A) feedback capacitance (Cf, figure 2.4). The capacitance is 7fF, 14fF, 21fF or 24fF respectively. The value of

this capacitor determines the gain of the initial electrical signal via formula 2.5. If the capacitance is bigger this will result in a smaller gain.

Gain = 1 Cf

. (2.5)

Figure 2.4: Part of the circuit of the Medipix3RX. This part of the circuit determines the gain of the incoming signal (id). The current source only draws a current when a signal is

deposited in the capacitor.

2.1.4 Threshold equalization of the Medipix3RX

A threshold equalization, or in short equalization, can be performed on the Medipix3RX. This equalization is a build-in function of the software that is used to control the Medipix3RX. During this equalization the software tries to align the thresholds of the different pixels as best as possible. This is done by determining the threshold level at which the noise floor starts for all the pixels individually. The spread in this threshold value for the different

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pixels is minimized by the software by changing the threshold offsets for certain pixels. The equalization is finished when the spread of the threshold levels is minimized.

Because the noise floor changes for example as a result of temperature fluctuations, this equalization is not able to align all pixels perfectly. Therefore small differences in the threshold levels between different pixels remain.

2.2 X-ray source

X-rays are electromagnetic radiation just like visible light. Both light and X-rays are photons, but the terminology arises due to the different energies the photons can have. Photons with an energy around 1 eV are called light while the typical energy for photons that will be called X-rays is between 100 eV and 100 KeV. X-rays are commonly used to make X-ray pictures in for example hospitals. In this thesis X-rays (photons) are used to determine the energy resolution of the Medipix3RX.

A monochromatic source of X-rays is used to determine the energy resolution of the detector. This is because the energy resolution is defined as the spread of the distribution of X-rays that the detector measures. By using a monochromatic source the spread of the X-rays is due to the detector and not due to the initial distribution of the X-rays.

For this thesis a fluorescence setup is used to create the ’monochromatic’ X-rays. The X-ray beam produced by the X-ray tube is directly aimed at a metal foil that is under an angle with respect to the beam (see figure2.5). The X-rays that hit this foil excite electrons in the atoms of this foil. These excited electrons eventually fall back to a lower state in the atom and this produces fluorescence photons (X-rays) with a certain energy. The energy of these transitions is well documented and therefore the energy spectrum of the fluorescence of these materials is known.

These energy spectra have several peaks (table 2.2). Zinc, zirconium and tin will be used in this thesis. Only the Kα- and the Kβ-emission lines of these materials are substantial enough to be visible during the measurements. These materials have their Kα line at respectively 8.6KeV, 15.7KeV and 25.2KeV. Zirconium and tin both show two peaks and zinc one peak. For zinc, the Kα and the Kβ peak can not be separated due to the limited resolution of the detector. With these materials the energy resolution in the range of 8KeV-25KeV can be determined.

The lower limit is selected to be just above the noise floor at HGM. The silicon sensor on top of the detector becomes mostly transparent above 20KeV (see figure 2.8). Therefore the upper limit of 25.2KeV is chosen to ensure that the measurements do not take days.

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Figure 2.5: The setup used to create a monochromatic energy spectrum. The beam of the X-ray tube is aimed at the red target material. The fluorescence from this target material is emitted in all directions and measured by the Medipix3RX.

Kα Kβ

Zinc (Zn) 8.6KeV 9.6KeV Zirconium (Zr) 15.7KeV 17.8KeV

Tin (Sn) 25.2KeV 28.6KeV

Table 2.2: The energy of the Kα- and Kβ-emission lines of the material used in this thesis.

The beam of the X-ray source is not focused perfectly and therefore a background is present during the measurements. The background of this setup is determined by measuring one minute without the target material in front of the beam. The amount of counts is then compared to a measurement of one minute with the target material in front of the beam. From this it is concluded that the background is less then 10% of the data.

2.3 Threshold scan

To determine the energy spectrum of the Medipix3RX a so called threshold scan is performed. This scan consists of performing a measurement of the X-ray spectrum for a range of threshold levels. For each of these threshold levels the Medipix3RX outputs the counts above that threshold level (figure2.6a). This corresponds to the amount of photons counted above the threshold level. The threshold scan is then converted into an energy spectrum by differentiating the counts with respect to the threshold level and inverting the y-axis (figure2.6b). This differentiation is performed using the two-point numerical differentiation

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df dx =

f (x − h) − f (x)

h . (2.6)

Figure 2.7a illustrates the energy spectrum for a perfect detector. But this is not the reality. The monochromatic peak is broadened by the resolution of the Medipix3RX chip. This results in a normal distribution centered at the energy of the monochromatic peak, as shown in figure 2.7b.

(a) The raw data output by the Medipix3RX from a measurement on tin. This corresponds to the integrated energy spectrum.

(b) The energy spectrum from the data shown in figure 2.6a. The Kα (25.2KeV) and Kβ (28.6KeV) peaks are shown in red.

Figure 2.6: The threshold scan and the derived energy spectrum from this threshold scan.

Due to charge sharing in the detector some of the electron clouds induced by photons are detected by two pixels and thus will be counted as two individual photons with a combined energy of the single photon. This effect results in spectrum shown in figure 2.7c. With the charge summing mode that was discussed in section 2.1.1 this effect should be corrected.

Compton scattering could also produce an effect that looks like the charge sharing effect shown in figure2.7c. The Compton absorption of 500µm silicon as well as the corresponding photoelectric absorption is shown in figure 2.8. From this figure the conclusion is drawn that the Compton absorption is about 0.018 times the photoelectric absorption in the energy range from 0KeV to 25KeV.

This means that the area of the plateau in figure 2.7c is 0.018 times the area of the peak that is due to the photoelectric effect. This is such a small fraction that this effect is not noticeable in our our measurements and cannot explain the plateau.

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(a) Monochromatic input (spectrum of X-ray source).

(b) Effect of the energy reso-lution of the detector.

(c) Effect of charge sharing in the detector.

Figure 2.7: Illustrations made by Schioppa (2014). This illustrates the model Schioppa uses for the spectral response of the Medipix. This model is the same as the model used in this thesis.

Figure 2.8: In blue the photoelectric absorption for 500µm Si and in green the Compton absorption. This data is retrieved from Berger et al. (2010).

The different operating modes show different energy resolutions, but the position of a specific energy should not shift for these operating modes (except for the different gain modes). So if in one operating mode the peak at 8.6 KeV is positioned at 53 THL, the position of the peak should also be positioned at 53 THL in any other operating mode. By checking this position for different operating modes it can be examined if there are no effects that change the THL value during these measurements. Figure2.9 shows such a plot for four different operating modes for a single pixel. Because the position of the peak does not change it can be confirmed that the measurements taken for different operating modes do not differ. There is also no difference in the low energy region between CSM and SPM.

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This suggests that CSM is not working properly. However, the results show a decreased energy resolution if the Medipix3RX is operating in CSM, therefore it is concluded that CSM does operate to some extend, but it does not decrease the tail.

Figure 2.9: The measured spectra with zirconium as the target material. All of these measurements were performed with the Medipix3RX in SPM during the equalization.

2.4 Definition of the energy resolution

In this thesis we use the definition for the energy resolution as given by the paper by Frojdh et al. (2014). The energy resolution is defined as the Full-Width-at-Half-Maximum (FWHM) of the normal distribution that arises in the energy spectrum of the detector due

to monochromatic photons.

The distribution that is found can be fitted. The fitting procedure used in this thesis is discussed in section 3. The fit returns a width for the distribution. This width is converted to a FWHM using formula 2.7.

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Chapter 3 Calibration and measurement

To determine the energy resolution of the Medipix3RX, the threshold scan needs to be analyzed. First an energy calibration, discussed in section 3.1 and section 3.2, is performed. The fitting procedure that is used in this thesis is described in section 3.3. The method to determine the energy resolution is described in section 3.4.

3.1 Energy calibration

The Medipix3RX has the ability to set the threshold level (THL) in a range of 0 and 511. These threshold levels correspond to an energy in electron volt. To link the different threshold values to their corresponding energy in KeV an energy calibration is performed. During this calibration the threshold level of the position of the peak of monochromatic photons is determined for multiple energies. With these points a relation between threshold level and energy in KeV is determined. This means that the determined energy resolution in threshold level can be converted to an energy resolution in KeV. This calibration is performed for each operating mode of the Medipix3RX.

The Medipix3RX is designed to have a linear relation between threshold level and energy over the complete threshold range. The energy calibration on the three points from zinc, zirconium and tin their Kα lines (in the range 8 to 25 KeV) is performed with the CSM and HGM modes and with a bias voltage of 100V. This calibration is shown in figure 3.1 for all four chips of the detector. A linear curve fit is then fitted for each individual pixel of all four chips (4 times 128×128, 65536, individual spectrum analyses). A maximum of two hundred pixels for each fit did not converge. The linear curve fit is shown in the same figure.

The threshold level per energy is linear in this range and therefore it is assumed that the response of the electronics and the sensor itself is linear within this energy range for

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Figure 3.1: Energy calibration performed with the Medipix3RX in CSM and HGM mode. The error bars of the points are in the order of .01 and are therefore not shown in this figure. A linear line is fitted through the three calibration points.

all settings. If this is not the case, this is revealed by a poor linear fit through these three points. If one of these three points deviates visibly from the fit the response is not linear.

3.2 Pixel-per-pixel calibration

After performing an equalization of the Medipix3RX, the response of the pixels is still not uniform. This is due to fluctuations in for example temperature during the equalization that typically takes multiple hours. The THL/KeV and the THL for a certain energy value are varying between the pixels. This problem can be solved by post processing the data to achieve a perfectly equalized grid. This is done by calculating the energy/THL conversion ratio for all the pixels by performing an energy/THL calibration per pixel. After the energy calibration one will end up with the slope (THL/KeV) of the energy conversion ratio including the intersect point with the y-axis. With these two variables every pixel is scaled to match one chosen central pixel. This process is called a pixel-per-pixel calibration.

Because the pixel-per-pixel calibration aligns each pixel, the initial spread in the found position of the individual normal distributions is zero. This improves the energy resolution of the detector. After the pixel-per-pixel calibration, the energy resolution depends only on the width of the individual normal distributions and thus the overall energy resolution

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is the average of these widths. The spread of these individual widths is two orders of magnitude smaller than the individual widths itself. Because other variations in for example the temperature during the measurements, result in a larger error this spread is neglected in this thesis.

3.3 The energy spectrum fit

As discussed before, a threshold scan is performed in order to determine the energy spectrum. This energy spectrum is analyzed to determine the energy resolution for the various gain modes and energies.

The individual photons of the monochromatic source are measured as an energy close to the energy of the monochromatic source with a random deviation (as discussed in section2.3). Because the deviations are random, a normal distribution is visible in the spectrum centered about the energy of the monochromatic source. The FWHM (Full-Width-at-Half-Maximum) of this normal distribution is called the energy resolution.

Formula 3.1 represents this normal distribution. This formula is fitted to the obtained energy spectrum to retrieve the height (a), the position (b) and the width (c) of the distribution.

dN/dT HL = a · e−(T HL−b)22c2 (3.1) A typical spectrum is shown in figure 3.2. The fluorescence peak is visible around 27 THL. On the left of the peak some sort of noise is visible that will be called the ’tail’. This spectrum looks like a spectrum with charge sharing effects, but the measured spectra in charge summing mode also exhibit this tail. This could suggest that the charge summing mode is not working perfectly. The tail cannot be due to the Compton effect. Figure 2.8 shows the photoelectric absorption and the Compton absorption for 500µm silicon. As discussed in section 2.3, Compton scattering will contribute an area of 0.018 times the area of the photoelectric effect. As is visible in figure 3.2, this area of the tail is about the same size as the area of the peak. Therefore it is concluded that the tail is not due to Compton scattering in the silicon sensor.

At this point it is not known what else causes this tail. But the main focus during this thesis is to determine the energy resolution. By assuming that every point on the right side of the peak and five percent left follows the normal distribution, it is still possible to determine the energy resolution for this spectrum. Because this tail does not influence the capability of determining the energy resolution, this tail is not further investigated in this thesis. This should be investigated in a further study about the performance of the Medipix3RX.

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The reason it is assumed that the selected data points are solely due to the fluorescence peak is because these are the most energetic photons. All other processes, such as different interaction processes, will always result in a measurement with an energy lower than the most energetic photons (that originate from the fluorescence target).

Figure 3.2: An energy spectrum measured in the setup with zinc as the target in SPM. The fluorescence peak of Zinc is visible around 27 THL. A single normal distribution is fitted on the data points on the right side of the peak and five percent left of the peak. This results in a position of 27.15 THL, a width of 2.306 THL and a height of 9302.

3.4 Chip-wide versus per-pixel energy resolution

There are two possible ways to determine the spread, and thus the energy resolution, of a spectrum. A chip-wide fit can be performed or the individual pixels can be fitted separately. Both possibilities are discussed below.

The chip-wide fitting procedure consists of summing the spectra of the individual pixels. This results in one spectrum for the entire detector on which the fitting procedure is performed. This procedure then returns the width corresponding to the normal distribution. If in the individual spectra a lower second peak is visible from the Kβ lines, this second peak is not visible in the summed spectrum. The Kβ peak will be included in the Kα peak due to the variation of the centers of the normal distribution for each single pixel. The energy resolution that is found is therefore worse then the actual energy resolution of the individual pixels. Figure 3.3 shows this effect of broadening the energy resolution if the position differs per pixel. This procedure is also used by Frojdh et al. (2014) to determine the energy resolution of the Medipix3RX.

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(a) Four separate normal distributions are shown that do not have the same position. The total of these normal distributions (pur-ple) will have a smaller resolution then the individual distributions.

(b) The four normal distributions shown in figure 3.3acorrected to be at the same po-sition (47 THL). Because the four distribu-tions overlap, just one distribution is visible. The total distribution (purple) now has the same energy resolution as the individual dis-tributions.

Figure 3.3: Two cases of four normal distributions positioned either at different positions or at the same position.

The second method to determine the spread of the spectrum involves analyzing the spectra of the individual pixels. This method involves fitting one or two normal distributions to the energy spectrum of each pixel depending on the energy spectrum involved. After the fitting procedure for every pixel, a distribution can be made for both the position of the normal distributions and the widths of these distributions. The average width of the individual normal distributions is then determined (σ1). If a second normal distribution

is fitted to the distribution of the positions, a spread (σ2) for this distribution is found.

The width of the energy spectrum of the total chip (σtot) is then a combination of the two

widths found. These two widths can be quadratically added to find the total width of the energy spectrum: σtot = pσ12+ σ22. σtot is then converted to a FWHM via formula 2.7.

Due to the individual fits the second peak is fitted separately and therefore the FWHM from this method is more precise. The second method is used in this thesis to determine the energy resolution of the Medipix3RX.

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The detector consists of four separate chips in a two-by-two grid. In figure 3.4 it is visible that the chips itself are not calibrated that well compared to each other. The lower left chip has between 30000 and 50000 counts while the upper left chip almost has no counts. If the chips were calibrated perfectly they should show the same amount of counts for every chip due to the uniform exposure of the detector. The analyses is therefore performed for each of the four chips separately. This means that there will be an energy resolution determined for each chip. Otherwise a superposition of four normal distributions would be visible instead of just one normal distribution.

Figure 3.4: Heatmap of the amount of hits for an energy level close to the energy of the Kα emission line of zirconium. A brighter color represents more hits. There is a difference in the amount of hits for the four chips.

3.5 Determination of the energy resolution

The energy spectrum of each of the 256×256 individual pixels needs to be analyzed to determine the energy resolution of the whole detector. The fits on the pixels returns the height (a), the mean (b) and the width (c) of the normal distribution. The values for the mean and the width are plotted in a histogram (respectively figures 3.5a and 3.5b). This represents the distribution of the values of the chip. Because of random deviations in the

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chip, these distributions are expected to also follow a normal distribution. By fitting a normal distribution on this histogram an average mean for the chip is found as well as the width (σ1) of this distribution. From the distribution of widths an average width (σ2) is

found. The combination of these two determines the energy resolution: pσ2

1+ σ22· 2 ln 2.

In this case this results in an energy resolution of√2.952_{+ 2.39}2 _{= 5.26 THL.}

(a) Distribution of the mean of the indi-vidual normal distributions for chip 0 with HGM. The center is located at 31.1 THL with a spread of 2.95 THL.

(b) Distribution of the width of the indi-vidual normal distributions for chip 0 with HGM. The center is located at 2.39 THL with a spread of 0.21 THL.

Figure 3.5: The distribution of the center of the individual normal distributions and the distribution of the width of the individual normal distributions for chip 0.

In some cases the distribution of the widths does not follow a normal distribution as visible in figure3.6a. A heatmap is made for the four chips of the detector with the width that is found per pixel. This heatmap is shown in figure 3.6b. Here it is visible that the widths show a gradient over the chip. This is due to the hardware of the ASIC and therefore cannot be remedied. The gradient is also visible in the distributions of the width that did not show this deviation from the normal distribution. In these cases the differences between the widths are small. The strength of the gradient also depends on the gain mode. For HGM the difference is not visible in the distribution of the width (see figure3.5b), for LGM this is a bit visible (figure3.6a) and for SLGM this is clearly visible (figure3.6c). To give a impression of how the shape of the distribution changes for the different gain modes four figures are made. The different distributions for each chip with HGM, LGM and SLGM are shown in appendix A. In these figures it is visible that the position of the highest peak for SLGM moves away from the position of the peaks at HGM and LGM.

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(a) The distribution of the width for chip 0 with LGM. Chip 0 is the chip on the bottom left of the heatmap in figure3.6b. It is visible that this is not a single normal distribution.

(b) The heatmap of the width for the whole detector corresponding to the measurement shown in figure3.6a. The distribution shown belongs to the chip on the bottom left side.

(c) The distribution of the width for chip 0 with SLGM.

Figure 3.6: The distribution of the width for chip 0 in LGM and SLGM and the corresponding heatmap for LGM.

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The width of the distribution of the widths is in the order of 0.2 THL. This is small compared to the width and therefore it is assumed that the average of the distribution is a correct indication for the width of the individual pixels. This however could be investigated in another study of the Medipix3RX.

For zirconium and tin the Kβ emission line is visible in the energy spectrum. This results in a spectrum with a superposition of two normal distributions (figure 3.7). A fit is set up with two normal distributions superposed (formula 3.2) to describe this data. Again a fitting region is defined from five percent left of the Kα peak until the last data point. The statistics for the Kβ peak are worse then the statistics for the Kα peak due to the lower counts, therefore the Kβ peak will not be used for determining the energy resolution. The Kβ peak is included in the fit to avoid a bias in the Kα peak.

dN/dT HL = a1· e −(T HL−b1)2 2c2 1 + a₂· e −(T HL−b2)2 2c2 2 (3.2)

Figure 3.7: An energy spectrum of a measurement with zirconium. Two normal distributions are fitted to the energy spectrum. This resulted in the position for the first normal distribution at 55.2 THL and the position of the second normal distribution at 62.14 THL. At this point the energy resolution is still expressed in terms of THL. This THL can be converted to KeV by applying an energy calibration with the procedure described in 3.1. In this case the slope for the energy calibration is 3.192 THL/KeV. This results in a measured energy resolution of 5.26/3.192 = 1.65KeV for this particular setting at this energy. This procedure is repeated for every operating mode that is examined.

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Chapter 4 Results

The energy resolution is determined for a selection of operating modes of the Medipix3RX. To check some results with the results of Frojdh et al. (2014), HGM is selected as the primary gain mode to investigate. The energy resolution for a lower gain mode is determined to get an impression of the performance of the Medipix3RX in such a lower gain mode. Therefore both LGM and SLGM are examined at least once.

Another goal is to determine the effects of the charge summing mode. Therefore the energy resolution of the Medipix3RX is checked in both CSM and SPM to compare these two. Furthermore the difference between the two equalization modes (CSM or SPM) is examined. The energy resolution could also change by varying the bias voltage such that the depletion width of the silicon sensor on top of the Medipix3RX changes. Therefore both a bias voltage of 100V and a bias voltage of 200V are examined to compare these two bias voltages.

For all of these combinations the energy resolution in KeV is determined for each chip. This results in a separate table for each chip. For chip 0 the table is shown in table A.1. The error on the resolution is also determined with formula 4.1.

∆E = σ/√N (4.1)

This error is in the range of 0.01KeV to 0.03KeV and is the same for all the measurements. This corresponds to a THL of about 0.1. The error on the energy energy/THL conversion ratio is 1σ of the normal distribution of the slopes (see section 3.1).

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From these tables the following is concluded:

• The resolution for the entire chip (if a pixel-per-pixel calibration is not performed) is decreasing with increasing energy. This is the case for every operating mode that is used except for 100V bias, CSM equalization, CSM and HGM. The energy resolution if a pixel-per-pixel calibration is performed on the other hand is constant for increasing energy. From this it is concluded that the decreasing resolution is due to the spread of the conversion ratio that is present if a pixel-per-pixel calibration is not performed. • The energy resolution is better after a pixel-per-pixel calibration for all operating

modes. The difference between the pixel-per-pixel calibration and one without the pixel-per-pixel calibration is shown in figure 4.1a. In this figure two operating modes are compared: 200V, SPM equalization, SPM with HGM for chip 0.

• The increase in resolution after a pixel-per-pixel calibration depends on the operating mode. With a bias voltage of 200V, SPM equalization, CSM with HGM the energy resolution after the pixel-per-pixel calibration is 1.32KeV at 8.6KeV. For a bias voltage of 200V, SPM equalization, SPM with HGM the energy resolution is 1.06KeV at 8.6KeV. For these two operating modes the energy resolution is shown in figure 4.1b. In CSM the noise of four pixels is always added. This explains why the energy resolution for CSM is always worse than the energy resolution for SPM.

• While operating with a bias voltage of 200V the resolution is slightly increased compared to a bias voltage of 100V. This is shown in figure 4.1c. In this figure the energy resolution of chip 0 is shown for two operating modes with SPM equalization, SPM and HGM with a bias of either 100V or 200V.

• A lower gain mode slightly increases the resolution before and after a pixel-per-pixel calibration is performed. This increase is due to the decreased energy bin size (higher energy resolving power) of the detector in a lower gain mode .

• The energy/THL conversion ratio with HGM is independent of bias voltage and CSM/SPM. For LGM the energy/THL conversion ratio is also independent of bias voltage and CSM/SPM. From this it is concluded that the conversion ratio of the chip is independent of the operating mode (except for different gain modes).

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(a) The energy resolution for 200V, SPM equal-ization, SPM with HGM for chip 0. Both the energy resolution without a pixel-per-pixel bration (Chip) and with a pixel-per-pixel cali-bration (Pixel) are shown.

(b) The energy resolution without a pixel-per-pixel calibration with 200V, SPM equalization, CSM, HGM for chip 0 is shown in red and for the same operating mode but with SPM instead of CSM is shown in blue.

(c) The energy resolution for a bias voltage of 100V and SPM equalization, SPM and HGM for chip 0 is shown in red and for a bias voltage of 200V the energy resolution is shown in blue.

Figure 4.1: The difference in energy resolution for some operating modes compared to each other.

In section 3.5 it is already concluded that the spread of the widths of the individual pixels show a gradient across the chip. In HGM this gradient is not noticeable, but in LGM this is noticeable and in SLGM a significant deviation is observed from a normal distribution.

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Chapter 5 Conclusion and discussion

The energy resolution of the Medipix3RX is determined for several operating modes with and without a pixel-per-pixel calibration. This resulted in four tables for the four separate chips on the detector. The results are shown in tables A.1, A.2, A.3 and A.4. It is also confirmed that the energy/THL conversion ratio is linear in the range energy range of 8KeV-25KeV for all the examined operating modes.

The resolution is smallest if the equalization used is performed with CSM. This suggests that the equalization should not be performed in CSM but only in SPM. The energy resolution is also better if the bias voltage is 200V instead of 100V.

Due to the spread in the energy/THL conversion ratio an extra blurriness of the high energy photons arises. This means that the higher the energies the smaller the resolution is. By performing a pixel-per-pixel calibration this extra spread can be reduced to zero. This results in the same energy resolution for every energy and therefore increasing the energy resolution. For higher energies a pixel-per-pixel calibration is therefore recommended. By performing a pixel-per-pixel calibration the spread in the energy/THL conversion ratio is removed.

It can be concluded that with a bias voltage of 200V, an equalization performed in SPM and operating in SPM and LGM results in the highest energy resolution.

The energy resolution of two operating modes is compared with the energy resolution found by Frojdh et al. (2014) for these operating modes. These two operating modes are SPM with HGM and CSM with HGM. The energy resolution found in this paper for 200V, SPM equalization, CSM and HGM for chip 0 at 8.6KeV is 1.80KeV while Frojdh et al. (2014) found an energy resolution of 2.2KeV at an energy of 10KeV. And for CSM with the same settings the energy resolution found at 8.6KeV is 1.65KeV while Frojdh et al. (2014) found an energy resolution of 1.43 at 10KeV. This difference could be due to the different fitting methods used in this thesis and the paper.

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The main objective of this thesis is determine the energy resolution performance of the Medipix3RX chip with a 500µm silicon sensor for a selected set of operating modes. Several unexpected effects have been observed. However, this thesis focuses only on the understanding of effects that impact the energy resolution. There are several effects that we suggest to be further investigated.

The tail at low energy, which is briefly discussed in section 3, is such an effect. It is assumed that the most energetic photons are solely due to the fluorescence of the target material and therefore the energy resolution can still be determined. But if one was to determine the energy spectrum of two monochromatic photon sources that differ more then 2KeV this tail would interfere with the energy spectrum, because the lowest energy photons would create a superposition with the tail of the highest energy photon source. Therefore this tail should be addressed if one was to measure energy spectrum’s with photons with different energies. Charge sharing and Compton scattering in the detector as a potential origin of this effect have already been ruled out. This tail could be due to the CSM not working properly, but this has not yet been confirmed.

A chip-wide gradient in the energy resolution is noticed. The strength of this gradient is increasing with decreasing gain mode (lower gain mode). This gradient is shown in figure 3.6b, but it is not visible in the distribution of the position of the individual normal distributions. It is also visible for the width in CSM and SPM with both a bias voltage of 100V and 200V. This suggest this might be caused by the design of the chip. This has not yet been confirmed and should be investigated further.

The energy calibrations performed in this thesis are all in the range of 8KeV to 25KeV. In this range the energy/THL conversion ratio is linear for all operating and gain modes. It could be that at higher energies the energy/THL conversion ratio is not linear anymore. If one was to use a gallium arsenide sensor instead of a silicon sensor this can quickly be determined due to the higher photoelectric absorption of gallium arsenide compared to silicon at higher energies. A benefit of using gallium arsenide as the sensor material is that higher energy photon can be measured compared to a silicon sensor.

In this thesis only the bias voltage, calibration modes, charge summing mode and gain modes have been varied. But there are much more variables that could possibly influence the energy resolution like Ikrum and the value of the pre-amplifier. The behaviour that is observed with the examined operating modes could be different if one of the other variables is changed. This could also be examined.

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Abbreviations

CSM: Charge Summing Mode

FWHM: Full-Width-at-Half-Maximum HGM: High Gain Mode

LGM: Low Gain Mode

SHGM: Super High Gain Mode SLGM: Super Low Gain Mode SPM: Single Pixel Mode THL: Threshold level

Acknowledgements

I would like to thank Nikhef (Nationaal instituut voor subatomaire fysica) to give me the opportunity to complete my bachelor thesis. I have received excellent support from Martin Fransen on a daily basis which was very valuable to me and I would like to extend my sincere gratitude to Martin for all his efforts. Next to Martin I would like to thank Hella Snoek as well. After I approached Hella to discuss the possibilities for a bachelor thesis in an area of my preference, Hella arranged for me to work on this particular subject at Nikhef. Also I want to thank Hella for her guidance during the writing of my bachelor thesis. Last but not least Amsterdam Scientific Instruments B.V. supported me and I want to thank Navrit Bal for all technical support on the Medipix3RX.

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Appendix A

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Configuration

FWHM(KeV)

Con

v

ersion

ratio

(THL/KeV)

8.6KeV

15 .7KeV

25.2KeV

Bias

Equalization

Op

era

ting

Chip

Pixel

Chip

Pixel

Chip

Pixel

100V

CSM

HGM

2.18

1.

25

2.07

1.17

2.32

1.38

3.21 ±

0.09 LGM

1 .67

1.18

1.68

1.22

1.82

1.20

4.47 ±

0.12 SPM

CSM

HGM

1.93

1.

38

1.94

1.34

2.09

1.39

3.18 ±

0.09 LGM

1 .59

1.16

1.62

1.10

1.84

1.20

4.42 ±

0.18 SPM

HGM

1.83

1.24

1.85

1 .17

2.00

1.25

3.23 ±

0.08 200V

SPM

CSM

HGM

1.80

1.19

1.81

1.19

1.88

1.21

3.22 ±

0.09 SPM

HGM

1.65

1.

04

1.72

0.99

1.82

1.05

3.19 ±

0.08 LGM

1 .51

0.98

1.47

0.91

1.57

1.01

4.25 ±

0.12 SLGM

1.38

1.21

1.41

1.18

1.59

1.20

6.82 ±

0.18

T able A .1 : Mea su red energy resolution and energy/T H L con v ersion ratio for chip 0. The v arious mo des of op eration are indicated. The column chip indicates the energy resolution witho ut a pixel-p er-pixel calibration and pixel in dicates the energy resolu tion after a pixel-p er-pixel calibration.

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Configuration

FWHM(KeV)

Con

v

ersion

ratio

(THL/KeV)

8.6KeV

15 .7KeV

25.2KeV

Bias

Equalization

Op

era

ting

Chip

Pixel

Chip

Pixel

Chip

Pixel

100V

CSM

HGM

2.17

1.

27

2.10

1.20

2.26

1.26

3.14 ±

0.08 LGM

1 .71

1.22

1.73

1.29

1.92

1.30

4.39 ±

0.12 SPM

CSM

HGM

1.89

1.

25

1.90

1.19

2.03

1.27

3.11 ±

0.09 LGM

1 .66

1.22

1.69

1.20

1.91

1.29

4.42 ±

0.17 SPM

HGM

1.87

1.27

1.95

1 .23

2.03

1.30

3.17 ±

0.08 200V

SPM

CSM

HGM

1.92

1.24

1.94

1.26

1.97

1.27

3.16 ±

0.08 SPM

HGM

1.73

1.

04

1.86

1.00

1.93

1.06

3.14 ±

0.07 LGM

1 .58

0.99

1.56

0.93

1.63

1.04

4.19 ±

0.12 SLGM

1.33

1.18

1.43

1.18

1.57

1.19

6.77 ±

0.19

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Configuration

FWHM(KeV)

Con

v

ersion

ratio

(THL/KeV)

8.6KeV

15 .7KeV

25.2KeV

Bias

Equalization

Op

era

ting

Chip

Pixel

Chip

Pixel

Chip

Pixel

100V

CSM

HGM

2.12

1.

27

2.12

1.20

2.36

1.32

3.086 ±

0.09 LGM

1 .66

1.22

1.67

1.25

1.83

1.29

4.32 ±

0.12 SPM

CSM

HGM

1.72

1.

22

1.74

1.28

2.04

1.29

3.03 ±

0.09 LGM

1 .70

1.20

1.75

1.17

1.83

1.29

4.43 ±

0.16 SPM

HGM

1.90

1.22

1.91

1 .18

2.00

1.27

3.16 ±

0.08 200V

SPM

CSM

HGM

1.90

1.14

1.88

1.13

1.92

1.17

3.15 ±

0.09 SPM

HGM

1.78

1.

00

1.82

0.95

1.92

1.03

3.15 ±

0.07 LGM

1 .55

0.96

1.52

0.87

1.57

1.00

4.16 ±

0.12 SLGM

1.25

1.07

1.31

1.05

1.47

1.09

6.73 ±

0.17

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Configuration

FWHM(KeV)

Con

v

ersion

ratio

(THL/KeV)

8.6KeV

15 .7KeV

25.2KeV

Bias

Equalization

Op

era

ting

Chip

Pixel

Chip

Pixel

Chip

Pixel

100V

CSM

HGM

1.90

1.

28

1.74

1.18

1.97

1.17

3.41 ±

0.09 LGM

1 .66

1.27

1.64

1.30

1.83

1.29

4.67 ±

0.13 SPM

CSM

HGM

1.60

1.

21

1.75

1.31

1.84

1.29

3.32 ±

0.10 LGM

1 .53

1.25

1.56

1.22

1.85

1.30

4.64 ±

0.20 SPM

HGM

1.71

1.32

1.68

1 .25

1.83

1.32

3.40 ±

0.09 200V

SPM

CSM

HGM

1.64

1.24

1.67

1.26

1.79

1.28

3.41 ±

0.09 SPM

HGM

1.49

1.

06

1.52

1.00

1.66

1.07

3.37 ±

0.08 LGM

1 .39

1.00

1.38

0.94

1.55

1.03

4.47 ±

0.12 SLGM

1.33

1.21

1.15

0.98

1.53

1.18

7.15 ±

0.19

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(a) The distribution of the width for the individual normal distributions of chip 0. The fit was performed on a tin fluorescence spectrum with HGM.

(b) The distribution for the width for the individual normal distributions of chip 1. The fit was performed on a tin fluorescence spectrum with LGM.

(c) The distribution for the width for the individual normal distributions of chip 2. The fit was performed on a tin fluorescence spectrum with HGM.

(d) The distribution for the width for the individual normal distributions of chip 3. The fit was performed on a tin fluorescence spectrum with LGM.

Figure A.1: The distribution of the widths for HGM, LGM, SLGM for the four chips of the detector.

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Appendix B

C-V Profiling

C-V profiling provides information about the growth of the depletion region by profiling the capacitance as a function of the applied bias voltage. From this C-V profile the average doping concentration can be determined.

The capacitance of the semiconductor depends on the width of the depletion region. This relation is given by formula B.1 (Bosma, 2012). With A as the area of the semiconductor.

C = εrε0A Wdep = A s qεrε0N 2 (Vbi+ Vbias) ≈ Ar qεrε0N 2Vbias (B.1)

By differentiating 1/C2 _{with respect to the bias voltage the following equation is}

obtained: d (1/C2₎ dVbias = 2 qεrε0A2N (W ) . (B.2)

With N (W ) representing the doping concentration. Because of the linear dependence of the doping concentration on d (1/C2_{) /dV}

bias the C-V profile is often represented as

a 1/C2_{-V graph. In this representation the slope can be used to determine the doping}

concentration (formula B.2).

A C-V profile is made for the 500µm silicon sensor on top of the Medipix3RX with the readout chip switched off. This C-V profile is shown in figure B.1a. In figure B.1b the same data is shown as in figure B.1a but now as a 1/C2-V graph. Through this data a linear line in the range of 15V to 30V is fitted. This fit returned a slope of 1.643 · 1017_.

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With this slope and the area of the silicon sensor (3.0160cm by 3.0160cm: 9.096cm2_{), the}

doping concentration is determined to be 8.88057 · 1011_cm−3_{. If the readout chip is turned}

on during this C-V measurement, only noise is visible.

(a) The C-V profile of the 500µm silicon sensor on the used Medipix3RX.

(b) The 1/C2_{-V graph of the C-V profile shown}

in figure B.1a. From a linear fit in the range 15V-30V the doping concentration is deter-mined to be 8.88057 · 1011_cm−3_.

Figure B.1: Both the C-V profile and the corresponding 1/C2-V graph of the 500µm silicon sensor on the used Medipix3RX.

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Appendix C

Distinction between different

materials

The transmission of different materials differs per material and per energy. All elements have a feature in their transmission spectrum called a K-edge. The position of this K-edge corresponds to the binding energy of the K-shell electron. At the energy of this K-edge and a little above this energy a sudden increase in the transmission is visible. The transmission spectra for copper, molybdenum and cadmium is shown in figure C.1.

Figure C.1: The transmission spectra for copper (red), molybdenum (blue) and cadmium (green). The energy bins used to assign rgb values to the picture are separated by dashed

vertical lines.

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will also get smaller. This effect only scales the curves that are shown in figure C.1. By choosing energy bins around the K-edges for the different materials the transmission of that energy bin can be determined. By determining the transmission in that energy bin, a distinction can be made between the materials. The spectroscopic Medipix3RX allows four different threshold levels to be set. These four threshold are set between the K-edges of copper, molybdenum and cadmium (dashed lines in figureC.1). With the results in table A.1 the energy in KeV can be converted to a value for the desired THL.

By performing two measurements the transmission of objects in front of the Medipix3RX can be determined. An ’open beam’ measurement must be performed first. This measure-ment corresponds to the amount of photons that enter each bin if there is no object in front of the Medipix3RX. After this a measurement is performed with the object in front of the Medipix3RX. By dividing the data with the object in front of the Medipix3RX by the open beam data one will get the transmission.

If one was to make a ’normal’ X-ray image of the four foils, no spectral information would be acquired. Such an image is shown in figure C.2a. A variation in gray is visible. With this picture one can not conclude that these foils consists of three separate materials because this variation could be due to a different thickness instead of other materials.

On the other hand, if one was to make the same image but with spectral information these materials can be distinguished. Such an image can be made by assigning the energy bin of 7KeV to 14.5KeV to the color red, the energy bin of 14.5KeV to 23KeV to the color green and the energy bin of 23KeV to 29KeV to the color blue. If a pixel has an absorption in the first bin of .3 this pixel will get a red value of 1 - 0.3 = 0.7. If this same has complete transmission in the second bin this pixel will get a green value of 1 - 1 = 0 and if this pixel has a transmission of .1 in the third bin this will correspond to a blue value of 1 - 0.1 = 0.9. This pixel will then have the rgb value of 0.7, 0.0, 0.9. This rgb value (color) is dependent of the material due to the different transmission spectra. Therefore copper, molybdenum and cadmium have different colors. An image of these three materials that is made by this process is shown in figure C.2b. There are three different color visible in this picture. The two red squares are copper foils with a thickness of 0.04mm and 0.06mm. The ticker foil is the foil at the coordinates (50, 50). The pink foil corresponds to 0.1mm molybdenum and the orange/white foil corresponds to 0.14mm cadmium. With this method all three different materials can be distinguished from each other which is not possible with the ’normal’ X-ray image.

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(a) A ’normal’ X-ray image of three different materials. Almost no difference is visible be-tween the triangle and the square in the top left corner.

(b) A ’color’ X-ray image of three different mate-rials. The three materials can be distinguished from each other.

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Bibliography

Ballabriga, R., Alozy, J., Blaj, G., et al., 2013, Journal of Instrumentation, 8, C02016 Berger, M., Hubbell, J., Seltzer, S.M., C.J., et al., 2010, Xcom: Photon cross section

database (version 1.5): http://physics.nist.gov/xcom [18.05.2017] Bosma, M., 2012, On the Cutting Edge of Semiconductor Sensors

Dik, J., Janssens, K., Van Der Snickt, G., et al., 2008, Analytical chemistry, 80, 6436 Frojdh, E., Ballabriga, R., Campbell, M., et al., 2014, Journal of Instrumentation, 9, C04028 Misiakos, K. & Tsamakis, D., 1993, Journal of applied physics, 74, 3293

Schioppa, E.J., 2014, The color of X-rays. Ph.D. thesis, PhD thesis, UvA, Amsterdam, 2014. XIII

Energy resolution of the Medipix3RX with a 500um silicon sensor