Characterization Studies of a CdTe Pixelated Timepix Detector for Applications in Medical Physics and Particle Physics
1. Université de Montréal
Characterization Studies of a CdTe Pixelated Timepix Detector for Applications in
Particle Physics and Medical Physics.
par
Constantine Papadatos
Département de physique
Faculté des arts et des sciences
Mémoire présenté à la Faculté des études supérieures
en vue de l’obtention du grade de Maître ès sciences (M.Sc.)
en physique
Août, 2016
c Constantine Papadatos, 2016.
2. Université de Montréal
Faculté des études supérieures
Ce mémoire intitulé:
Characterization Studies of a CdTe Pixelated Timepix Detector for Applications in
Particle Physics and Medical Physics.
présenté par:
Constantine Papadatos
a été évalué par un jury composé des personnes suivantes:
Pierre Bastien, président-rapporteur
Claude Leroy, directeur de recherche
Hugo Bouchard, membre du jury
Mémoire accepté le: . . . . . . . . . . . . . . . . . . . . . . . . . .
3. RÉSUMÉ
Un détecteur à pixels Timepix a été caractérisé en vue d’applications dans la physique
des particules et en imagerie médicale. Ce Timepix est fait d’une couche sensible de
CdTe d’une épaisseur de 1000 µm divisée en (256 × 256) pixels avec des contacts
ohmiques. Chaque pixel a une aire de (55 × 55) µm2.
L’effet de polarisation dans le détecteur Timepix-CdTe (TPX-CdTe) a été étudié dans
le but de déterminer si un détecteur aux contacts ohmiques démontre cet effet. Il a été
observé que le biais effectif du détecteur a diminué pendant une période de mesure de
38 heures, ce qui signifie que le détecteur est devenu polarisé.
Le détecteur a été exposé à des photons de 59,5 keV et de 662 keV émis par des
sources d’241Am et 137Cs respectivement et les énergies mesurées avec le TPX-CdTe
étaient précises à 1,18% et 0,03% respectivement. Un étalonnage global du détecteur
a été développé qui a été comparé à un étalonnage conventionel pixel par pixel sou-
vent utilisé. Les énergies (0,8 à 10 MeV) de protons ont été mesurées et les résolutions
en énergie obtenues par les deux étalonnages ont été comparées. L’étalonnage global a
montré une amélioration dans la résolution d’en moyenne 8,6% pour des protons.
La présence de pièges dans le matériau du CdTe et leur influence sur la collection
de charge ont été étudiées. La valeur du produit de la mobilité et du temps de vie des
porteurs de charge a été mesurée pour des protons de 1,4 MeV à partir de l’équation de
Hecht.
Mots clés: Timepix, CdTe, polarisation, mobilité des porteurs de charge, temps
de vie des porteurs de charge, résolution en énergie, équation de Hecht.
4. ABSTRACT
A Timepix pixel detector has been characterized for the purpose of applications in par-
ticle physics and medical imaging. This Timepix detector consists of a segmented CdTe
sensor layer with a thickness of 1,000 µm divided into 256 × 256 pixels and manufac-
tured with Ohmic contacts. Each pixel has an area of 55 × 55 µm2.
The polarization effect in the Timepix-CdTe (TPX-CdTe) was studied with the aim
of determining whether a detector possessing Ohmic contacts exhibits the said effect.
It has been observed that the effective bias of the detector decreased over a 38 hour
measurement period. This indicates that the detector became polarized.
The detector was exposed to photons with energies of 59.5 keV and 662 keV emitted
from 241Am and 137Cs sources, respectively. The energies measured with the TPX-CdTe
were accurate to within 1.18% and 0.03%, respectively. A global calibration of the
detector was implemented and compared to a conventionally used per-pixel calibration.
Proton energies (from 0.8 up to 10 MeV) have been measured and the energy resolutions
obtained by both calibrations have been compared. The global calibration improves the
energy resolution by 8.6% for protons.
The presence of traps in CdTe and their influence on charge collection have been
investigated. The mobility × lifetime product of charge carriers has been measured for
1.4 MeV protons based on the Hecht equation.
Keywords: Timepix, CdTe, polarization, carrier mobility, carrier lifetime, en-
ergy resolution, Hecht equation.
7. LIST OF TABLES
2.I The interaction cross sections for photoelectric absorption and for
Compton scattering in Si and in CdTe, taken from NIST XCOM.[15] 17
3.I Mobility values of common semiconductors at 300 K, expressed
in cm2V−1s−1.[21] . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.I The measured proton energies Em with the per-pixel calibration
compared to the expected energies after Rutherford backscattering
with their percent deviation %Dev. The FWHM and the resolu-
tions R are provided for each energy. . . . . . . . . . . . . . . . . 52
5.II The energies Em of photons emitted from 241Am (59.5 keV) and
137Cs (662 keV). The energy of 59.5 keV is measured using the
per-pixel calibration while the 662 keV photons were measured
with the global calibration. %Dev gives the percent deviation of
each measured energy from its expected value. The FWHM and
the resolution R are given for each. . . . . . . . . . . . . . . . . . 53
5.III Les énergies de protons mesurées Em avec l’étalonnage global
comparées aux énergies attendues après la rétrodiffusion de Ruther-
ford avec leur différence en pourcentage %Dev. Les FWHM et les
résolutions R sont donnés pour chacune des énergies. . . . . . . . 57
5.IV The µτ product of the TPX-CdTe detector for 1.4 MeV protons
with the corresponding range in µm[9] and the quality of the fit (R2). 58
5.V The µeτe values found in the literature. The errors on these values
are not given for these references. . . . . . . . . . . . . . . . . . 60
8. LIST OF FIGURES
2.1 The electronic (black) and nuclear (red) stopping powers for hy-
drogen ions in CdTe. The contribution of dE/dxnucl is small com-
pared to dE/dxelec. The plot is graphed based on data from the
SRIM program.[9] . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The stopping power of muons as a function of their energy in cop-
per. The Bethe-Bloch equation describes the stopping power in the
region of 0.08 - 800 MeV with the minimum ionization energy at
∼ 3.5 MeV.[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 The rate of average energy loss in various materials. The energy of
minimum ionization of each aligns roughly at the same value (3.5
MeV). Different particles (muon, pion and proton) become MIPs
at different momenta.[12] . . . . . . . . . . . . . . . . . . . . . . 9
2.4 The energy deposited as a function of the average range in water
for a 250 MeV proton is described by the Bragg curve (red). Note
that the variation of the deposited energy as a function of the depth
for photons (10 MeV) is described by an attenuation curve (see
2.2.4).[13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 The difference between the trajectories of heavy and light charged
particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 The energy loss per radiation length, X0 (see Eq. (2.8)) in lead as
a function of the electron or positron energy.[12] . . . . . . . . . 13
2.7 The cross sections of the three principle interactions of photons
with matter.[14] . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.8 The photoelectric process. . . . . . . . . . . . . . . . . . . . . . 15
2.9 The photoelectric interaction cross section in lead is given as a
function of the photon energy. The edges correspond to the L and
K shells, indicated on the graph.[10] . . . . . . . . . . . . . . . . 15
2.10 The Compton scattering process. . . . . . . . . . . . . . . . . . . 18
9. ix
2.11 The Compton edges corresponding to different energies.[10] . . . 19
2.12 The interaction cross section for Compton scattering.[10] . . . . . 20
2.13 The pair production process. . . . . . . . . . . . . . . . . . . . . 20
2.14 The pair production interaction cross section in lead. The thresh-
old effect at low energy is shown at 1.022 MeV.[10] . . . . . . . . 21
2.15 a) A Timepix detector (ATLAS-TPX) covered by a mosaic of con-
verters: (1) LiF (5 mg/cm2), (2) Polyethylene (PE) of 1.3 mm, (3)
PE (1.3 mm) + Al (100 µm, (4) Al (100 µm), (5) Al (150 µm),
(6)Uncovered Si. b) An X-ray radiogram of the converter layers.[16] 25
3.1 A unit cell showing a diamond lattice structure.[19] . . . . . . . . 27
3.2 A unit cell showing a cubic (zincblende) crystal structure which is
distinguishable from the diamond structure due to the presence of
a second type of atom.[20] . . . . . . . . . . . . . . . . . . . . . 27
3.3 The band structure of Silicon, showing the conduction band with
the valence band below it. The energy is graphed as a function of
the wave-vector k.[23] . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 A comparison between the position of the energy bands of a metal,
a semiconductor and an insulator with respect to the Fermi energy.
[24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 The Fermi-Dirac distribution for a few values of kBT/EF. . . . . 30
3.6 a) A direct band gap, like for CdTe. b) An indirect band gap, like
for Si. The photon absorption process is illustrated for each case
with an arrow indicating the transition of an electron from the top
of the valence band to the bottom of the conduction band.[25] . . 32
3.7 A Timepix detector equipped with a FITPix interface.[27] . . . . 33
3.8 A Timepix detector. (A) is the semiconductor sensor layor. (B)
shows the readout chip and the electronic bump bonds.[27] . . . . 34
3.9 The electronics scheme of a single pixel in a Timpepix detector.[26] 34
10. x
3.10 A frame showing the tracks of 1.4 MeV protons in the TPX-CdTe
detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Band bending model near the semiconductor-metal interface, used
to calculate the depth of the depletion layer and the electric field.
l is the depletion layer’s thickness. W is the function describing
the band bending and whose value corresponds to the separation
between the deep acceptor energy (E) and the Fermi energy. V is
the applied potential, φ is the contact potential, λ is the region in
which the charges are accumulated and δ = l −λ.[8] . . . . . . . 37
4.2 Schematic plot of the electric field as a function of the position
in the situation shown in Figure 4.1. The slope of the electric
field changes abrubtly where the energy band intersects the Fermi
energy.[8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 A 38 hour measurement of the deposited energy by α particles
from an 241Am source at 150 V. . . . . . . . . . . . . . . . . . . 43
4.4 Measurements of the change in the cluster size as a function of
the applied voltage for α particles from an 241Am source. A lin-
ear fit around 150 V (120-180 V) gives the correspondance CS =
−0.110860V +44.8359. The R2 value of this fit is 0.994426. . . . 43
4.5 The influence of the bias on the radial diffusion of charges created
by 3.5 MeV protons at an incidence of 0◦ in a Si Timepix.[30] . . 44
4.6 A measurement in time of the cluster size of α particles over 38
hours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.7 The behaviour of the effective bias over the course of the 38 hour
measurement period with an initial applied voltage of 150 V. . . . 47
5.1 The dependence of the TOT on the X-ray energy for each pixel,
expressed by the calibration function f. The c
x−t term takes into
account the calibration’s non-linearity near the threshold.[31] . . . 49
11. xi
5.2 The photon energy spectrum of an 241Am source with a peak at
58.8 keV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 The energy spectrum of photons coming from a 137Cs source (662
keV photons) with a peak at 711,1 keV. . . . . . . . . . . . . . . 50
5.4 The calibration function for the heavy ionizing particles (3, 5 et 9
MeV protons and 20 MeV 6Li ions). . . . . . . . . . . . . . . . . 53
5.5 The energy spectrum for 662 keV photons emitted from a 137Cs
source processed with a global calibration. The measured energy
is 661.8 keV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.6 A comparison between the energy spectra for 10 MeV protons ob-
tained with the per-pixel (black) and global (red) calibrations. . . 56
5.7 The resolutions of each energy for the per-pixel (black) and global
(red) calibrations. Protons with energies from 0.8 to 10 MeV are
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.8 The calculation of the coefficient of determination. . . . . . . . . 59
5.9 The measured energy as a function of the bias for 1.4 MeV protons
with statistical error bars. The fit function (red) has an R2 value of
0.99914. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.1 A) A Timepix-CdTe irradiated by α-particles in 2008 with a large
quantity of localized trapping centres. B) A second Timepix-CdTe
irradiated by α-particles in 2015 displaying a more homogeneous
structure. The vertical lines correspond to columns of dead pixels
resulting from the implantation of the bump bonds during fabri-
cation. The scales indicate the number of α-particles registered
in each pixel. A) and B) comme from measurements taken at the
Tandem accelerator at the University of Montreal. . . . . . . . . . 62
12. LIST OF ABBREVIATIONS
ATLAS A Toroidal LHC Apparatus
CERN Conseil européen pour la recherche nucléaire
CMS Compact Muon Solenoid
CS Cluster Size
FWHM Full-Width at Half-Maximum
HPGe High-Purity Germanium
IEAP Institute of Experimental and Applied Physics
LHC Large Hadron Collider
MAFalda Medipix Analysis Framework
MIP Minimum Ionizing Particle
NIST National Institute of Standards and Technology
PET Positron Emission Tomography
SPECT Single Photon Emission Computed Tomography
SRIM Stopping and Range of Ions in Matter
ToA Time of Arrival
TOT Time Over Threshold
TPX Timepix
USB Universal Serial Bus
XRF X-Ray Fluorescence
13. NOTATION
Al Aluminium
241Am Americium-241
C Carbon
c Speed of light in vacuum. c = 3.00 × 108 m/s2.
CdTe Cadmium Telluride
137Cs Cesium-137
eV electronvolt
fC femtocoulomb
GaAs Gallium Arsenide
GaP Gallium Phosphide
Ge Germanium
h Planck constant. h = 4.14 ×10−15 eV s.
He Helium
InSb Indium Antimonide
keV kiloelectronvolt
6Li Lithium-6
6LiF Lithium Fluoride
MeV Megaelectronvolt
µm micrometre
Si Silicon
Sn Tin
99mTc Technetium-99m
ZnS Zinc Sulfide
15. ACKNOWLEDGMENTS
I would like to thank, first, my research supervisor, Claude Leroy, for having given
me the opportunity to work on this project. Your patience and advice were greatly ap-
preciated. Thanks to my research and office colleague, Thomas, for having shared his
knowledge, his company, and innumerable pints with me over the course of this mas-
ter’s project. I wish to also thank all my colleagues in the bunker, in the Groupe de
Physique des Particules, and at the IEAP in Prague for enriching these past two years
with discussions on physics and distractions from it.
Thanks to Chen for always having a solution to my computer problems. Thanks to
Louis Godbout for managing the Tandem, providing the particle beams and helping with
any technical problem encountered during our experiments.
Finally, I would like to thank my friends and family. In one way or another, each of
you has supported and encouraged me. I love you all.
16. PREFACE
My contributions to this master’s project are centred on the collection and analysis
of data. I participated in the experimental component of the spectroscopic characteriza-
tion of the Timepix-CdTe detector through the use of protons produced by the Tandem
accelerator at the University of Montreal and the Van der Graaf accelerator in Prague, of
γ-rays coming from 241Am and 137Cs sources and of α-particles emitted by the 241Am
source. In addition, I conducted a study on the polarization effect in the Timepix-CdTe
detector.
I wrote supplementary algorithms to the ones already included in the MAFalda anal-
ysis software which permitted the analysis of the measured data. Two calibrations of the
detector were performed. The per-pixel calibration was completed by Thomas Billoud
at the IEAP in Prague, while the global calibration was developed and implemented by
myself using protons and 6Li ions. The sum of my research activities and my results can
be found in chapters 3 and 4 of this thesis.
Additional research activity: I also participated in the luminosity analysis of data
from the ATLAS experiment at the LHC at CERN as part of the ATLAS-TPX collabo-
ration. I worked on reconstruction software validation for proton-proton collision events
in the context of "class 2 shifts" as a member of the ATLAS collaboration.
17. CHAPTER 1
INTRODUCTION
CdTe detectors are used in medical imaging and in particle physics in general because
their γ-ray detection efficiency is relatively high owing to their large atomic number
(ZCd = 48, ZTe = 52). Applications in SPECT and in PET are thus possible. The ability
to measure precisely the energies of photons from a few tens to hundreds of keV allows
the measurement of 140 keV photons emitted by 99mTc in SPECT imaging devices and
511 keV photons in PET imaging devices. CdTe is also a good candidate as a photon
detection material in particle physics, in accelerator experiments and in space, where its
high density gives it good radiation hardness.[1][2]
The development of CdTe as a particle detector had been hampered in favour of Si,
which has become the most well-studied material, historically. Nonetheless, the past 40
years have seen an increase in the research of CdTe as a photon detector.
It is important that CdTe detectors have a short electronic response time and can
therefore distinguish the signal from noise. Additionally, they must permit the charac-
terization and identification of γ-rays coming from unknown sources.
The energy resolution of a γ-ray detector is quantified by the full-width at half-
maximum (FWHM) of the energy peak divided by the mean measured energy (the
barycentre). The resolution is expressed as a percentage. High purity semiconductor
detectors, like HPGe (high purity Germanium) at 77 K, can have resolutions as good as
1% for 662 keV photons.[3]
When an ionizing particle interacts with the semiconductor, a charge cloud is created
made up of free charges possessing either negative (electrons) or positive (holes) charge.
A bias voltage applied across the electrodes provokes the drift of these two types of
charges in opposite directions. The speed with which each charge drifts towards the
electrode depends on the bias voltage and on the structure of the crystal lattice of the
material.[4]
These charge carriers can become trapped by impurities in the lattice. They can also
18. 2
recombine with each other. In both cases, the result is a loss in the collected charge. The
performance of a CdTe detector depends on the number and distribution of these traps
in the material. The quantity of traps can be inferred by measuring the product of the
mobility and the lifetime of charge carriers (µτ). A large amount of traps results in a
shorter lifetime and, therefore, a smaller µτ value.[5]
To reduce the leakage current, Schottky-type CdTe detectors have been made, the
result of which was a good energy resolution for γ-rays. For 59.5 keV and 662 keV
photons, the obtained resolutions were 2.5% and 1.5% respectively [1]. However, these
Schottky-type detectors displayed time-instability problems under an external bias volt-
age. In practice, time-stability is of great importance to the functioning of a detector.
This instability phenomenon is called "polarization". Polarization is characterized by a
decrease in the energy resolution as well as a decrease in charge collection with time,
shifting the measured photopeaks toward lower energies after applying an external bias.
The term polarization is used to describe any temporal instability in compound semi-
conductors. Previous research has shown that this phenomenon is the result of an accu-
mulation of negative charges at a deep acceptor level during the application of the bias
voltage. This results in the variation of the electric field inside the CdTe with time.[1]
To eliminate the polarization effect, detectors with Ohmic contacts were used, the
compromise being that the energy resolution is inferior. It is nonetheless possible that
an Ohmic-type detector may become polarized under certain conditions.
1.1 Objectives of this Project
The research activity presented in this thesis has been made possible by the use of a
Timepix-CdTe (TPX-CdTe) detector possessing Ohmic contacts. Data from 0.8 MeV to
10 MeV protons and 20 MeV 6Li ions have been taken at the Tandem accelerator of the
University of Montreal and 1 MeV protons at the Van der Graaf accelerator of the IEAP
in Prague. 137Cs and 241Am sources have also been used for photon measurements and
the same 241Am source has been used for measurements of α-particles. The prepara-
tion and analysis of the data was done using the Pixelman[6] and MAFalda[7] analysis
19. 3
softwares.
The characterization of the TPX-CdTe detector is separated in three parts. First,
an investigation into polarization was conducted in order to show that an Ohmic-type
detector can become polarized. This would prove that the electric field in the sensor layer
of the TPX-CdTe can become unstable with time under the application of a bias voltage.
Next, a study of the energy resolution of the detector has been completed comparing the
reliability of two calibrations (a per pixel calibration and a global calibration). Lastly,
the mobility-lifetime product was measured in order to determine the contribution of
traps within the detector to its charge collection.
1.2 Structure of the Thesis
In the first chapter, an overview of the interaction of particles with matter is pre-
sented. A particular emphasis is placed on the interaction of photons with matter via
the photoelectric effect and Compton scattering. The second chapter is dedicated to the
description of CdTe semiconductors and to the operation of the Timepix detector. The
polarization effect in CdTe detectors is described in chapter 3, extending the method in-
troduced by [8] for non-pixelated CdTe detectors. An investigation of this effect on the
TPX-CdTe is included here. Chapter 4 presents the spectroscopic properties of the TPX-
CdTe detector and its charge collection capabilities with a description of its calibration.
This chapter also reports the measurement of the mobility × lifetime product of the said
detector.
20. CHAPTER 2
INTERACTION OF PARTICLES WITH MATTER
2.1 Direct Ionization
Particles such as electrons, protons and α-particles (alphas) directly ionize the matter
through which they pass. They lose their kinetic energy over the course of their path
through collisions or radiative processes. The energy loss of these particles over the
distance travelled is quantified as the stopping power −dE/dx,
dE
dx
=
dE
dx col
+
dE
dx rad
=
dE
dx elec
+
dE
dx nucl
+
dE
dx rad
(2.1)
The collision stopping power, (−dE/dx)col, is composed of two parts. The first part
describes collisions between the particle and the atomic electrons, (−dE/dx)elec. The
second part describes nuclear collisions, (−dE/dx)nucl. The interaction cross-section
with electrons being much greater than that for nuclear interactions at high energy (E >
100 keV),
−dE
dx elec
−dE
dx nucl
, (2.2)
as is shown in Figure 2.1.
For heavy particles, such as protons and alphas, the energy loss by collisions is sub-
stantially greater than that by radiation. For light particles (electrons, positrons), radia-
tive losses become increasingly important at energies greater than 10 MeV. The energy
loss by collisions represents losses from excitation and ionization. Excitation is the pro-
cess that moves an electron from a given shell to a more energetic shell. Consequently,
an incident particle can lose energy without removing an electron from an atom. Ion-
ization removes one or more electrons from the atom. It creates electron-hole pairs in
a semiconductor and electron-ion+ pairs in a gas. The number of pairs created is given
21. 5
Figure 2.1 – The electronic (black) and nuclear (red) stopping powers for hydrogen ions
in CdTe. The contribution of dE/dxnucl is small compared to dE/dxelec. The plot is
graphed based on data from the SRIM program.[9]
22. 6
by the ratio (E/ε) of the energy, E, deposited by the particle in the material and ε, the
energy required to create a pair. ε varies from one material to another (εSi = 3.62 eV et
εArgas = 26.4 eV)[10].
2.1.1 The Bethe-Bloch Equation
The average rate of energy loss per unit lenght of a heavy charged particle is given
by the Bethe-Bloch equation which assumes i) that the mass of the incident particle is
greater than that of an atomic electron and ii) that the motion of the atomic electron is
negligible. If Tmax is defined to be the maximum energy transferred to an atomic electron
by a massive charged particle,
Tmax = 2mec2
β2
γ2
1+2γ
me
M
+
m2
e
M2
−1
(2.3)
γ2 = 1−β2 −1
is the Lorentz factor, me is the mass of the electron, M is the mass
of the incident particle and β = v/c (i.e., the speed of the particle in units of the speed
of light). When the mass of the incident particle is much greater than the mass of the
electron, M me and when γ is not very large, (2.3) becomes
Tmax ≈ 2mec2
β2
γ2
(2.4)
The Bethe-Bloch equation gives the average energy loss per unit length:
−
dE
dx
= 4πNAr2
emec2 Z
A
ρ
z2
β2
B (2.5)
where the factor B is given by
B ≡ ln
2mec2β2γ2Tmax
I2
−β2
−
δ
2
−
C
Z
. (2.6)
Z is the atomic number of the target atom, A is its atomic mass, NA is Avogadro’s
number, ρ is the atomic density and z is the electric charge of the incident particle. The
classical electron radius is defined as re = e2/mec2 = 2.82 × 10−13cm. I is the average
23. 7
ionization energy. The factor δ takes into account the shielding of atomic electrons
through density effects in the material. This is due to polarization of the atomic electrons
by the electric field created by the incident particle. Inner shell electrons are not sensitive
to this field and, as a consequence, contribute less to the energy loss. The C/Z term is
associated to the non-participation of inner shell electrons (primarily coming from the K-
shell) in the collision process at low energy[11]. This shielding effect is produced when
the incident particle has a speed that is, at its maximum, comparable to the orbital speed
of atomic electrons. It is at these speeds that the assumption of a stationary electron with
respect to the incident particle becomes invalid. On the whole, the contribution of this
correction is relatively small. As an example for muons (mµ = 105 MeV/c2), the region
of energy over which the Bethe-Bloch equation is valid is represented in Figure 2.2.
2.1.2 Minimum Ionizing Particles (MIPs)
Energy loss is not strongly dependent on the mass of the incident particle unless
its mass is much greater than that of an electron. The stopping power (−dE/dx) is
proportional to z2/β2 where z is the particle’s charge. The stopping power depends on
the absorber, according to Z/A. The quantity dE/dx is at a minimum when βγ ≈ 3.5, as
shown in Figure 2.3. Particles that undergo a minimal energy loss are called minimum
ionizing particles, or MIPs. The rate of average energy loss of particles in different
materials is shown in Figure 2.3.
For example, the proton, whose mass is close to the GeV scale (938 MeV/c2), must
have a kinetic energy of many GeV in order to become a MIP. For an electron, whose
mass is 0.511 MeV/c2, only a few MeV (∼ 2 MeV) are necessary. The stopping power’s
value at minimum ionization is roughly the same for all particle’s possessing the same
charge. However, each particle attains minimum ionization with a different momentum,
as is seen in Figure 2.3, which allows for its identification. A particle with a charge
z ≥ 2 (α-particle, z = 2) has a rate of loss that is larger because of the proportionality of
−dE/dx to the square of the charge. Such a particle can become a MIP for much higher
energies, as is the case with cosmic rays or in relativistic energy ion accelerators.
24. 8
Figure 2.2 – The stopping power of muons as a function of their energy in copper. The
Bethe-Bloch equation describes the stopping power in the region of 0.08 - 800 MeV with
the minimum ionization energy at ∼ 3.5 MeV.[12].
25. 9
Figure 2.3 – The rate of average energy loss in various materials. The energy of mini-
mum ionization of each aligns roughly at the same value (3.5 MeV). Different particles
(muon, pion and proton) become MIPs at different momenta.[12]
26. 10
2.1.3 Bragg Curve and Range
Due to the dependence of dE/dx on 1/β2 for heavy charged particles, these particles
lose the majority of their energy immediately before being completely stopped in the
medium. This is illustrated by the Bragg peak, represented in Figure 2.4. The range is
the distance travelled by a particle of a given energy in a given material. It is obtained
experimentally by sending a beam of energetically coherent particles across layers of
identical materials of different thickness. The current of particles transmitted across the
layer is compared to the initial intensity of the beam. Figure 2.5 illustrates the difference
between the ranges of heavy and light charged particles. Heavy particles are not subject
to strong deviations from their trajectories because only a small fraction of kinetic energy
is lost with each collision of the particle with an electron.
In practice, the statistical nature of the energy loss causes fluctuations in the value of
the range of the particle across a material. These fluctuations manifest themselves as lat-
eral and longitudinal straggling. Consequently, two identical particles having the same
initial energy and travelling through the same material will not lose the same amount
of energy along their trajectory and will therefore not have the same range values. The
range is expressed as a Gaussian distribution. The straggling effect diminishes with an
increase of the particle’s mass.
The CSDA 1 range is calculated by integrating the inverse of the Bethe-Bloch for-
mula.
R(E0) =
0
E0
1
−dE
dx
dE (2.7)
2.1.4 Electrons and Positrons
For electrons and positrons, whose mass is much smaller than that of a proton, the
radiative losses (bremsstrahlung) are much more significant at energies ≥ 10 MeV. 2 In
addition, (dE/dx)col, given by Bethe-Bloch is also modified because the incident particle
1. Continuous Slow Down Approximation
2. Bremsstrahlung is the radiation created by the acceleration of negative electric charges.
27. 11
Figure 2.4 – The energy deposited as a function of the average range in water for a
250 MeV proton is described by the Bragg curve (red). Note that the variation of the
deposited energy as a function of the depth for photons (10 MeV) is described by an
attenuation curve (see 2.2.4).[13]
28. 12
Figure 2.5 – The difference between the trajectories of heavy and light charged particles.
possesses the same mass as the atomic electron. It can then no longer be assumed that
the motion of the atomic electron is negligible compared to the incident electron. The
effects, including bremsstrahlung, that contribute to the total energy loss per radiation
length (X0) for electrons and positrons are presented in Figure 2.6. For electrons, the
radiation length is defined as,
X0 =
A
4αNAZ2r2
e
log183
Z1/3
, (2.8)
where α is the fine structure constant of the electromagnetic force.
2.2 Indirect Ionization
Photons interact indirectly with matter according to three principle interaction pro-
cesses. These interactions are photoelectric absorption, Compton scattering and pair
production. The dependence on the energy and on the atomic number of the absorber
dictates which process dominates. This is illustrated in Figure 2.7.
29. 13
Figure 2.6 – The energy loss per radiation length, X0 (see Eq. (2.8)) in lead as a function
of the electron or positron energy.[12]
Figure 2.7 – The cross sections of the three principle interactions of photons with
matter.[14]
30. 14
2.2.1 The Photoelectric Effect
Photoelectric absorption occurs when an incident photon of energy Eγ interacts with
an atomic electron. The photon is converted into a photoelectron with kinetic energy
KE = Eγ − BEi, where BEi is the binding energy of the electron to the i shell. An
illustration of this is given in Figure 2.8. This is the dominant effect for low energy
photons, typically less than ∼ 50 keV. The resulting photoelectrons also possess low
energies. The binding energy depends on the atomic number Z and on the electronic
shell. The binding energies of the K, L and M shells are given by,
BEK = Ry(Z −1)2
eV (2.9)
BEL =
Ry
4
(Z −5)2
eV (2.10)
BEM =
Ry
9
(Z −13)2
eV (2.11)
where Ry = 13.62 eV is the Rydberg constant.
When the photon energy increases, the photon can penetrate the electron cloud more
profoundly, which permits it to attain an electron of an internal shell. The photoelectron
is emitted, creating a vacancy that can be occupied by the transition of an electron on an
external shell. This transition is accompanied by the emission of an X-ray.
A photon with a lower energy can only attain the external shells, producing an edge.
An edge corresponds to the minimum photon energy necessary to eject an electron in a
given shell. This threshold effect is characteristic to each atom. As an example, Figure
2.9 presents the photoelectric interaction cross section in lead as a function of the photon
energy, indicating the edge effect.
The photoelectric interaction cross section of low energy photons for the K edge is
given by
31. 15
Figure 2.8 – The photoelectric process.
Figure 2.9 – The photoelectric interaction cross section in lead is given as a function
of the photon energy. The edges correspond to the L and K shells, indicated on the
graph.[10]
32. 16
σK
pe =
8
3
2
mec2
Eγ
7 1/2
4πr2
eα4
Zn
(2.12)
where n is a number that varies between 4 and 5. For n = 5, the photoelectric cross
section displays a general dependence of
σK
pe ∼
Z5
E
7/2
γ
(2.13)
For Eγ mec2 (so Eγ/mec2 1),
σK
pe =
mec2
Eγ
4πr2
eα4
Z5
(2.14)
showing the following dependence:
σK
pe ∼
Z5
Eγ
(2.15)
Table 2.I compares the interaction cross sections of the photoelectric effect and of
Compton scattering for photons from 20 keV to 2 MeV in Si and CdTe.
2.2.2 Compton Scattering
Compton scattering dominates for photons with energies greater than a few hun-
dred keV to a few MeV. The incident photon transfers a part of its energy to an atomic
electron. The resulting products of the Compton interaction are a recoil electron and a
scattered photon. This is illustrated in Figure 2.10. In the laboratory reference frame,
for an incident photon with an energy Eγ, the scattered photon has an energy Eγ,
Eγ = h
c
λ
=
Eγ
1+
Eγ
mec2 (1−cosθ)
(2.16)
The energy of the recoil electron is
33. 17
Table 2.I – The interaction cross sections for photoelectric absorption and for Compton
scattering in Si and in CdTe, taken from NIST XCOM.[15]
34. 18
Figure 2.10 – The Compton scattering process.
ER = Eγ −Eγ = Eγ
Eγ
mec2 (1−cosθ)
1+
Eγ
mec2 (1−cosθ)
(2.17)
For a forward collision, θ = 0, Eγ = Eγ and ER = 0. For a backward collision, θ = π
and,
Eγ =
Eγ
1+2
Eγ
mec2
(2.18)
ER = Eγ
2Eγ
mec2
1+
2Eγ
mec2
(2.19)
which corresponds to a Compton edge, illustrated in Figure 2.11.
The interaction cross section as a function of the atomic number of the absorber and
the energy of the photon is
σC = σs +σa ∼
Z
Eγ
, (2.20)
where σs and σa are the scattering and absorption cross sections, respectively. These
two contributions are represented in Figure 2.12 as a function of the photon energies.
35. 19
Figure 2.11 – The Compton edges corresponding to different energies.[10]
The cross sections of Si and CdTe are given in Table 2.I.
2.2.3 Pair Production
If the photon energy is Eγ ≥ 2mec2 = 1.022MeV, and approaches the atomic nucleus
or an electron, the photon can be converted into an electron-positron pair. This process
is shown in Figure 2.13. The created positron is annihilated immediately with the nearby
electron, which causes the emission of two photons with equal energies (0.511 MeV).
The dependence of the pair production interaction cross section on the atomic num-
ber of the absorber and on the photon energy is
σPP ∼ Z2
logEγ (2.21)
and is graphically represented in Figure 2.14 where the threshold effect can be ob-
served (Eγ = 1.022 MeV).
36. 20
Figure 2.12 – The interaction cross section for Compton scattering.[10]
Figure 2.13 – The pair production process.
37. 21
Figure 2.14 – The pair production interaction cross section in lead. The threshold effect
at low energy is shown at 1.022 MeV.[10]
The photon energy is
Emin
γ = 2mec2
1+
2mec2
2Mc2
(2.22)
If the mass M of the target particle is much greater than me, for example if it is an
atomic nucleus, this enables pair production to occur. If the target is an electron, M = me,
and a triplet is produced. The kinetic energy available is
T = hν −1,022MeV (2.23)
for pair production (2mec2 = 1,022 MeV). It is
T = hν −2,044MeV (2.24)
for triplet production (4mec2 = 2.044 MeV).
38. 22
2.2.4 Photon Attenuation and Total Absorption
When photons travel through matter, their numbers decrease exponentially with the
distance. This gives
I (x) = I0e
− µ
ρ ρx
, (2.25)
where ρ is the density of the material through which the photon travels, x is the
distance travelled and µ is the total absorption coefficient. This quantity is proportional
to the inverse of the mean free path of photons in that material.
The total interaction probability of a photon in the material is the sum of all possible
interactions: photoelectric, Compton, pair production, Rayleigh scattering and photonu-
clear interactions. 3 The total cross section, σ, multiplied by the density of atoms, N,
gives the interaction probability per unit of length, with the total absorption coefficient,
µ, given by
µ = σN = σNA
ρ
A
, (2.26)
where A is the molar mass and σ = σpe + σC + σPP. Thus, the probability that a
photon interacts with the material is given by
P = 1−e
− µ
ρ ρx
. (2.27)
2.3 Neutrons
Neutrons interact with matter via elastic and inelastic scattering and nuclear reac-
tions. These interactions allow for their detection. The neutron interaction probability in
matter depends on the neutron energy.
3. Rayleigh scattering and photonuclear interactions don’t play a big role in the context of this study.
39. 23
2.3.1 Thermal Neutrons
Thermal neutrons undergo certain nuclear reactions which cause the emission of
charged particles which are used for their detection.
A practical application that is used by the ATLAS-TPX silicon pixel detectors oper-
ated in the ATLAS experiment is to cover a portion of the detector’s chip with a layer
of 6LiF that acts as a thermal neutron converter [16]. The resulting neuclear reaction
caused by the thermal neutrons on the 6LiF is the following:
n+6
3Li → α +3
1H. (2.28)
The interaction cross section of this reaction is 940 barns. The α-particles and the tri-
tium emitted have energies of 2.73 MeV and 2.05 MeV respectively and can be detected
in Si.
2.3.2 Fast Neutrons
Fast neutrons are those whose kinetic energy is typically greater than 100 keV. These
neutrons are detected thanks to nuclei that recoil from a converter. The recoil energy of
a nucleus in an elastic collision with a fast neutron is
EA = En
4A
(A+1)2
cos2
θ, (2.29)
where En is the energy of the incident neutron, A is the atomic mass of the nucleus
and θ is the scattering angle in the laboratory reference frame. The maximum recoil
energy of the nucleus is obtained for θ = 0.
EA
En
=
4A
(A+1)2
. (2.30)
This relation makes evident the fact that these materials possessing small atomic
numbers are more favourable for the detection of fast neutrons. Consequently, polyethy-
lene (CH2) is used for this purpose.
40. 24
The mosaic of neutron converters used on the ATLAS-TPX detectors in the ATLAS
experiment is shown in Figure 2.15.
41. 25
Figure 2.15 – a) A Timepix detector (ATLAS-TPX) covered by a mosaic of converters:
(1) LiF (5 mg/cm2), (2) Polyethylene (PE) of 1.3 mm, (3) PE (1.3 mm) + Al (100 µm,
(4) Al (100 µm), (5) Al (150 µm), (6)Uncovered Si. b) An X-ray radiogram of the
converter layers.[16]
42. CHAPTER 3
SEMICONDUCTORS
The applications of semiconductors as particle detection instruments are varied. In
medical physics, the use of semiconductors, in particular CdTe, whose atomic number is
high, is generally associated with imaging via SPECT 1 and PET 2 applications [1] [17].
They are primarily used in particle physics as dosimeters and trackers, as in the ATLAS
and CMS experiments at the Large Hadron Collider (LHC) at CERN [16].
3.1 Classification of Semiconductors and Band Structure
Semiconductors can be classified into three large families corresponding to their po-
sition on the periodic table. Group IV materials display a tetragonal binding structure,
with four valence electrons. These are referred to as elemental semiconductors [C, Si,
Ge, α-Sn] and their crystal lattice is characterized by a diamond structure.
The second family of materials occupies the III-V group and possesses a cubic crystal
(zincblende) structure, again with tetragonal bonds. Being composites, the bonds of
this group of semiconductors are covalent and ionic, which induces polarity within the
material (i.e., possessing an intrinsic electric polarity). They are made up of one trivalent
atom (3 valence electrons) and one pentavalent atom (5 valence electrons). The members
of this group are GaAs, InSb, GaP, etc. Finally, there is also the II-VI group, of which
CdTe and ZnS are members. These semiconductors also possess cubic (zincblende)
structures. The bonds of these materials are also covalent and ionic, but are even more
ionic than those of group III-V [18].
At temperature T=0, a semiconductor contains energy bands that are either empty
or full. The electrons occupy the valence band completely while the conduction band
remains empty. Between the valence and conduction bands exists a band gap.
Figure 3.4 illustrates the differences between metals, semiconductors and insulators
1. Single Photon Emission Computed Tomography
2. Positron Emission Tomography
43. 27
Figure 3.1 – A unit cell showing a diamond lattice structure.[19]
Figure 3.2 – A unit cell showing a cubic (zincblende) crystal structure which is distin-
guishable from the diamond structure due to the presence of a second type of atom.[20]
44. 28
Figure 3.3 – The band structure of Silicon, showing the conduction band with the valence
band below it. The energy is graphed as a function of the wave-vector k.[23]
in the context of energy bands. The conduction and valence bands are indicated in blue
and red respectively. The position of these bands with respect to the Fermi level dictates
how charges are conducted within the material. For conduction to occur, electrons are
displaced from the valence band to the conduction band. For metals, the two bands
overlap, thus the energy required to excite an electron is small. For these materials,
conduction can result simply by thermal excitation. In the case of insulators, the large
separation between the bands prohibits electrons from jumping from the valence band to
the conduction band.
The bands of a semiconductor are neither overlapping, as they are for metals, nor are
they as far as they are for insulators. Their band gap is on the order of a few eV, which
significantly limits conduction by thermal excitation but also allows for conduction by
virtue of the energy transferred by radiation entering the material.
It is important to note that the density of charge carriers in a semiconductor is much
lower than it is for metals and is highly temperature dependent. Furthermore, the bands
below the valence band and above the conduction band do not play a role in the con-
ductivity of the material [18]. The number of charge carriers varies as a function of the
45. 29
temperature according to the Fermi-Dirac distribution [21].
f(E) =
1
e
E−EF
kBT +1
(3.1)
3.2 Electrical Conductivity and Mobility
The current density of a semiconductor is given by [18] [21]
j = σ|E| (3.2)
The electric field causes charge carriers to drift with a velocity
vde,h = µe,hE (3.3)
with a mobility, expressed in cm2V−1s−1,
µe,h =
qe,hτe,h
me,h
, (3.4)
me,h and τe,h are the mass and the lifetime of the electron or the hole. The lifetime
represents the elapsed time prior to which the charge carrier is captured by a trap in the
crystal lattice [4]. The product of the mobility and the lifetime is a parameter that char-
acterizes the spectroscopic quality of a detector. It is the only parameter of the material
which describes the dependence of the charge collection efficiency on an applied bias.
This µτ product will be evaluated in section 5.2 of this study.
A few mobility values for common materials are presented in Table 3.I.
Material Electrons Holes
Si 1350 480
CdTe 1100 100
GaAs 8000 300
Ge 3600 1800
Table 3.I – Mobility values of common semiconductors at 300 K, expressed in
cm2V−1s−1.[21]
46. 30
Figure 3.4 – A comparison between the position of the energy bands of a metal, a semi-
conductor and an insulator with respect to the Fermi energy. [24].
Figure 3.5 – The Fermi-Dirac distribution for a few values of kBT/EF.
47. 31
3.3 Properties of CdTe
3.3.1 Fundamental Absorption
CdTe possesses a direct band gap, meaning that the trough of the conduction band
lies directly above the peak of the valence band. The band width is the difference in
energy between these two points. Figure 3.6 compares direct and indirect band gaps.
The property of having a direct band gap grants CdTe with the ability to be used as
an optoelectronic instrument [18]. In fundamental absorption, an electron absorbs an
incident photon and jumps from the valence band to the conduction band. This photon
must have an energy greater or equal to the energy of the band gap. Its frequency must
therefore be
ν ≥
Eg
h
(3.5)
where Eg is the energy of the band gap (Eg = 1.52 eV for CdTe)[21]. For a material
possessing an indirect band gap, like Si (Eg = 1.12 eV)[21], the electron cannot make
the transition between bands in the same way. In this case, the process takes two steps.
The electron absorbs a photon and a phonon 3 simultaneously. The photon provides the
energy necessary to make the jump while the phonon provides the momentum required
to transition to the bottom of the conduction band.
3.3.2 Applications of CdTe
CdTe has a high atomic number (ZCd = 48. ZTe = 52), a high density (ρ = 5.85
g/cm3) and a wide band gap (Eg = 1.52 eV). Its electron-hole pair creation energy (ε)
is 4.43 eV and its resistivity is 109 Ωcm[22]. The band gap of CdTe is relatively large
compared to other semiconductors (Eg = 1.12 eV for Si), which allows it to be oper-
ated at relatively high temperatures (up to 100◦C) [5]. Beyond 100◦, the value of Eg
decreases significantly with the temperature. Its high atomic number endows it with a
3. A phonon is a quasi-particle corresponding to an excitation of the vibrational energy of the crystal
lattice
48. 32
Figure 3.6 – a) A direct band gap, like for CdTe. b) An indirect band gap, like for Si.
The photon absorption process is illustrated for each case with an arrow indicating the
transition of an electron from the top of the valence band to the bottom of the conduction
band.[25]
high detection efficiency for γ-rays due to their interactions with matter through pho-
toelectric absorption (σPE ∼ Z4−5), Compton scattering (σC ∼ Z) and pair production
(σPP ∼ Z2). In medical imaging, this high sensitivity to γ-rays is crucial for SPECT
and PET [1] [17]. In particle physics experiments, CdTe’s high density gives it good
radiation hardness[2] and its high photon detection efficiency allows it to be used as a
γ-ray detector in high radiation fields produced by particle collisions where photons are
present in large quantities.
The performance of CdTe is limited by the existence of traps within the material.
These traps capture charge carriers and are a result of impurities in the crystal lattice or
crystal fabrication defects.
3.4 The TIMEPIX Detector
The Timepix (TPX) detector [26], illustrated in Figure 3.7, is a pixelated semicon-
ductor detector. In this study, the detector used is made up of a sensor layer of 1 mm
which is connected by bump-bonding to a readout chip. The CdTe chip is equipped with
a common backside electrode and with a matrix of electrodes (256 × 256 pixels squared,
each with an area of 55 × 55 µm2) on the front side. Figure 3.8 shows the different
49. 33
components of the TPX. Each pixel contains its own amplification circuit, composed of
a preamp, a discriminator and a counter. The Timepix electronics scheme is shown in
Figure 3.9.
The device can be connected with a USB FITPix interface (for Silicon) or a Canpix
interface (for the TPX-CdTe)[28], which is then connected to a computer via USB cable.
The data acquisition and device control is done using the Pixelman[6] software.
The charges produced from electron-hole pair creation migrate towards the elec-
trodes under the influence of an electric field induced by the bias voltage applied across
the detector. At the cathode of each pixel, the charge is collected and the signal is ampli-
fied by the current amplifier. This signal is then compared to a threshold. If it is superior
to the threshold, the counter increments by 1, otherwise it stays at 0. A frame is produced
indicating the state of each pixel during the data acquisition period (Figure 3.10). The
adjacent pixels that also have counter values greater than 0 are collectively called a clus-
ter or a track, whose shape depends upon the type of interaction of the incident particle
with the detector’s active layer. The shape varies according the the energy, the incidence
and the species of the particle. It is by studying these shapes that particle identification
is possible.
The measurement of events can be accomplished using one of three possible modes
of operation: 1) tracking and counting mode, 2) TOT (Time-over-Threshold) mode and
3) ToA (Time of Arrival) mode. In TOT mode, an internal clock counts the time during
which the signal is above the threshold. This clock operates at a defined frequency of
9.6, 24, 48 or 96 MHz for FITPix interfaces. Thus, the TOT values obtained are simply
Figure 3.7 – A Timepix detector equipped with a FITPix interface.[27]
50. 34
Figure 3.8 – A Timepix detector. (A) is the semiconductor sensor layor. (B) shows the
readout chip and the electronic bump bonds.[27]
Figure 3.9 – The electronics scheme of a single pixel in a Timpepix detector.[26]
51. 35
Figure 3.10 – A frame showing the tracks of 1.4 MeV protons in the TPX-CdTe detector.
the clock frequency multiplied by the measured time. It is therefore, possible to measure
energy values of incident particles using an appropriate TOT-energy calibration. ToA
mode allows one perform coincidence measurements with the aim of measuring time of
flight (ToF).
52. CHAPTER 4
POLARIZATION EFFECTS IN COMPOUND SEMICONDUCTORS
The so-called "polarization effect" contributes towards the reduction of the charge
collection efficiency of the studied CdTe detector. Polarization in the TPX-CdTe detector
has been observed and studied in this chapter.
4.1 Polarization in CdTe Detectors
When an external bias of the order of a few tens to a few hundreds of Volts is applied
on a detector, an electric field is produced under whose influence charge carriers drift
towards the electrodes, where they are collected. It has been observed that, at room
temperature (T = 25◦C), the collected charges decrease as a function of time after the
application of an initial bias. This has led to the consensus that there is a reduction in the
electric field intensity across the detector thickness, implying a reduction in the effective
internal voltage[1]. The result of this is the partial depletion of the detector. The depleted
zone is partially lost near the electrodes and is considered to be polarized, leading to the
reduction of the applied voltage.
An accumulation of charges is produced at the interface of the electrode and of the
material which provokes the diminished performance of the detector. A model explain-
ing this effect considers the energy band bending in the region of the electrode contacts.
In addition to this bending, hole detrapping by deep acceptor levels creating a charge
accumulation is proposed as the physical phenomenon responsible for polarization[8].
Such deep acceptor levels can cross the Fermi level when the bands are bent at a close
proximity to the electrode contacts, as is shown in Figure 4.1. This bending translates to
the behaviour of the electric field observed in Figure 4.2.
The temporal dependence of this behaviour is a result of the high activation energy
associated with the ionization of deep acceptor levels [5]. These deep acceptors are
ionized in a time τI, on the order of
53. 37
Figure 4.1 – Band bending model near the semiconductor-metal interface, used to cal-
culate the depth of the depletion layer and the electric field. l is the depletion layer’s
thickness. W is the function describing the band bending and whose value corresponds
to the separation between the deep acceptor energy (E) and the Fermi energy. V is the
applied potential, φ is the contact potential, λ is the region in which the charges are
accumulated and δ = l −λ.[8]
Figure 4.2 – Schematic plot of the electric field as a function of the position in the
situation shown in Figure 4.1. The slope of the electric field changes abrubtly where the
energy band intersects the Fermi energy.[8]
54. 38
τI =
1
N0 v σ
eE/kT
(4.1)
where N0 is the density of states of deep acceptors, σ is the acceptor capture cross-
section, v is the average thermal velocity of charge carriers and E is the depth, in
energy, of the traps. It is immediately seen that, since E kT, τI is large. In the case of
detrapping, the time becomes shorter and is given by
τD =
1
NV v σ
(4.2)
where NV is the electronic density of states at the top of the valence band.
Solving the Poisson equation for the potential V as a function of the position x gives
the form of the band bending at equilibrium (without an applied bias). The space is
characterized by two regions:
d2V
dx2
= −(p+N)
e
ε
, 0 < x < λ, (4.3)
d2V
dx2
= −p
e
ε
, λ < x < l, (4.4)
where p is the equilibrium hole concentration, ε is the dielectric constant, e is the unit
of electronic charge, l is the total depletion thickness of the detector and N is the number
of ionized deep acceptors. The λ region is the region in which charges are accumulated.
Solving (4.3) and (4.4), an expression describing the λ region can be obtained[8].
λ =
2ε
e(N + p)
1
2
V0 −
N
N + p
W
1
2
−
p
N + p
δ, (4.5)
where
δ = l −λ =
2Wε
ep
1
2
(4.6)
The potential V0 is the sum of the applied potential V and the contact potential 1 φ
1. The contact potential is the difference between the electrostatic potentials of two metals in contact
55. 39
and W is the separation between the deep acceptor and the Fermi level. These quantities
are all indicated in Figure 4.1.
At t = 0, N = 0. In general, we can assume
N = N0 1−e−t/τI
(4.7)
When N0 p and W V0, we get
p
N0
1−e−t/τI
=
λ0
λ
2
−1, (4.8)
where λ0 is the final value (t → ∞) of λ:
λ0 =
2ε
e(N0 + p)
1
2
V0 −
N0
N0 + p
W
1
2
−
p
N0 + p
δ. (4.9)
Then, for short time periods, t τI, we obtain:
λ0
λ
2
−1 =
t
τI
p
N0
, (4.10)
so when t τI, (4.8) becomes
λ0
λ
2
−1 =
p
N0
. (4.11)
4.2 Polarization Reduction Techniques
There have been many different methods traditionally used to eliminate or, at the
very least, strongly reduce the effects of polarization in CdTe detectors.
One method reinitializes the applied bias to a value of 0 V, thus dissipating the spa-
tial charge that is collected at the electrodes. The procedure consists of periodically
removing the bias during the measurement to induce depolarization. This is done over
the course of a charge collection measurement for a long period of time. This technique
with each other. It is determined by the difference in the work functions of each metal.
56. 40
exploits the fact that τI > τD. In practice, for example when a detector is used in dosime-
try, its detection efficiency is reduced whenever the applied bias is reset to 0 V. Even if
the overall stability of the detector is improved, periodically, a fraction of the particles
penetrating the material is not detected.
A more effective technique is to use electrodes with high work functions. In doing
so, the contact potential at the electrode-semiconductor interface is modified to prevent
the deep acceptor level from crossing the Fermi level. This is accomplished by using a
p-type metal that behaves like an Ohmic contact. Gold and platinum have been conven-
tionally used as contact metals.
4.2.1 Schottky and Ohmic Contacts
It has been mentioned that the type of contact used in CdTe devices influences the de-
gree of polarization of the semiconductor. A description of Schottky and Ohmic contacts
is therefore necessary.
A Schottky contact is a metal-semiconductor contact whose contact potential is large
and whose dopant concentration is small (i.e., a concentration which is less than the
electronic density of states in the valence or in the conduction band). In this scenario,
the conduction band is bent away from the Fermi energy and the semiconductor becomes
intrinsic in this region. There are now fewer mobile charge carriers and the depletion
layer is produced.
An Ohmic contact is a metal-semiconductor contact that is characterized by a negli-
gible contact resistance with respect to that of CdTe. In the case of the TPX-CdTe, the
contact is made of Pl [28]. There exists an unimpeded majority carrier transfer going
from the semiconductor to the contacts. This means that the contact does not limit the
current [29]. In this case, the conduction band energy is less than the Fermi energy close
to the interface. The semiconductor behaves electrically like a metal in this region, the
result being the formation of an Ohmic contact.
57. 41
4.3 Polarization Studies with the Timepix-CdTe Detector
A study of the possible effects of polarization in the TPX-CdTe detector were under-
taken at the University of Montreal. Previous studies on this topic primarily used diodes
and their results were principally taken from charge or deposited energy measurements
from photons in the active layer. For detectors possessing Schottky contacts, this type of
analysis based on collected charge measurements was adequate for such studies. How-
ever, when the same procedures were applied to Ohmic-type detectors, the polarization
effect was sufficiently reduced, the result being that the charge collection within the
detector was reliable for long periods of time.
This does however raise the question of whether the electric field inside the detector
is truly unchanged after a long measurement period. The advantage of using a Timepix
detector is that it allows for the measurement of the deposited energy or charge as well as
the position of particles, permitting the measurement of charge sharing between pixels.
By using the charge sharing effect, a small weakening of the electric field can be deduced
from an increase in the size of certain clusters.
The TPX-CdTe detector has been exposed to an 241Am source during a 38 hour
period inside a vacuum chamber set at 5 × 10−7 Torr with an external bias of 150 V
which was fixed for the duration of the experiment. The 241Am source is placed at
a distance of 1.5 cm from the TPX-CdTe. The α particles reached the detector at an
average angle of incidence of 0◦. The energy of the emitted α particles was measured
in increments of an hour and is represented as a function of time in Figure 4.3. As is
expected from a detector with Ohmic contacts, the results show no significant reduction
in the measured energy, indicating the absence of polarization. The average α particle
energy measured over the 38 hour period was 4920 keV, as is shown in Figure 4.3.
It is important to note that this energy is less than that expected from an 241Am
source, 5.48 MeV. This is due to the CdTe thickness being only partially depleted at 150
V. Consequently, a fraction of the energy is not converted into charge carriers and, thus,
does not contribute to the signal. The measured energy being practically unchanged over
38 hours, a method using the cluster size as a variable was developed. It is for this reason
58. 42
that the value of 150 V was chosen as the reference bias voltage. This assures that the
variation in the size of clusters is sufficiently large to observe the weak variations in the
bias. To illustrate this, Figure 4.4 shows the variation of the cluster size as a function of
the bias. It is clear that operating at a reference bias of 300 V or 400 V would not reveal
a significant increase in the cluster size after a long measurement period if the reduction
in the voltage is weak. This then makes the task of determining any variation in effective
voltage with time difficult.
The behaviour seen in Figure 4.4 can be explained in the following manner. An
incident particle creates a column of charges (electrons and holes) so these charges drift
towards their respective electrodes under the influence of the electric field created by the
applied voltage across the detector thickness. At the same time, there exists a lateral or
radial drift, caused in part by the diffusion due to the density gradient which leads this
charge column to grow radially before each carrier is collected at the electrode. If the
voltage increases, the intensity of the field increases as well. This accelerates the drift
towards the electrodes and subsequently reduces the lateral drift. The result of this is that
the cluster size becomes smaller, which is illustrated in Figure 4.5 for 3.5 MeV protons
at an angle of incidence normal to a Silicon Timepix detector, where the radial diffusion
at 40 V and 7 V are compared.
For the same measurement period, the average cluster size of α particles has been
plotted in the same way as for the energy, showing the evolution of this variable in
time. Its behaviour is shown in Figure 4.6. In the absence of polarization caused by
an electric field, there would not be any change in the size of clusters over the course
of the measurement. Figure 4.6 shows that this is not the case. There is an increase
in the cluster size as of the beginning of the measurement until the end, indicating a
weakening of the electric field across the layer of CdTe. Such a weakening slows the
longitudinal drift of carriers, increasing their drift time. This enables a longer radial drift
and, therefore, a larger cluster size.
This behaviour can then be compared to the values of the cluster size obtained during
an analysis at multiple biases, as in Figure 4.4. We can then assume that, for small
variation in bias, a linear relation between the bias and the cluster size is valid. By
59. 43
Figure 4.3 – A 38 hour measurement of the deposited energy by α particles from an
241Am source at 150 V.
Figure 4.4 – Measurements of the change in the cluster size as a function of the ap-
plied voltage for α particles from an 241Am source. A linear fit around 150 V (120-180
V) gives the correspondance CS = −0.110860V + 44.8359. The R2 value of this fit is
0.994426.
60. 44
Figure 4.5 – The influence of the bias on the radial diffusion of charges created by 3.5
MeV protons at an incidence of 0◦ in a Si Timepix.[30]
61. 45
Figure 4.6 – A measurement in time of the cluster size of α particles over 38 hours.
assuming that the change in cluster size is linear around the 150 V point (Figure 4.4), a
linear approximation over the 120-180 V interval is taken and a fit function is produced:
CS = −0.110860V +44.8359, (4.12)
where CS is the cluster size.
Evaluating the fit function for the cluster size at the end of the measurement, ex-
tracted from Figure 4.6, the effective bias can be calculated. In fact, the behaviour of
the bias and, as a consequence, that of the electric field can be obtained for the entire
measurement period. An expression describing the behaviour of the effective bias for
small deviation from 150 V can be obtained.
V = −9.02039CS+404.437 (4.13)
From (4.13), the effective bias is calculated for each point in Figure 4.6. Each cal-
culated voltage corresponds to an hour during the measurement. Together, they show
the behaviour of the effective bias as a function of time during the 38 hour period. This
is illustrated in Figure 4.7. During the 38 hours, the effective bias does not vary by
62. 46
more than 15 V. Furthermore, the majority of its variation occurs in the first 17 hours,
after which, the bias seems to stabilize for a time. As of the 29 hour mark, a weakly
decreasing trend resumes.
This proves that an Ohmic-type detector can become weakly polarized. The reason
for this is that the resistivity of the Pl contact is larger than that of the CdTe, which
causes a very small deviation from Ohm’s law and, therefore, a small quantity of deep
acceptors can be produced near the electrodes.
63. 47
Figure 4.7 – The behaviour of the effective bias over the course of the 38 hour measure-
ment period with an initial applied voltage of 150 V.
64. CHAPTER 5
CHARACTERIZATION OF THE TIMEPIX-CDTE DETECTOR
5.1 Energy Resolution
A study of TPX-CdTe’s energy resolution has been completed using data from pro-
tons and photons. The measured energies were obtained from a per-pixel calibration
conducted at the IEAP in Prague and are compared to those obtained with a global cali-
bration using protons and 6Li ions performed in Montreal.
5.1.1 Per-Pixel Energy Calibration
A calibration by X-ray fluorescence (XRF)[31] has been performed for each pixel in
the TPX-CdTe detector. The detector has been irradiated by monoenergetic X-rays in
order to limit to a single pixel the propagation of charge carriers created by an incident
photon. The necessary cluster size for this calibration is one pixel. Events producing
larger cluster sizes are rejected. Such events can be caused by a photon that interacts
with the detector at the boundary of multiple pixels or by charges that diffuse from one
pixel to its neighbour. Each pixel registers an energy spectrum whose peak is fitted with
a Gaussian function. This step is repeated for at least three other X-ray energies in order
to produce an adequate calibration function of the form
f(x) = ax+b−
c
x−t
(5.1)
where the c
x−t term takes into account the non-linear TOT response at low energy.
The a, b, c, and t parameters are calculated for the function f and at least five least
squares fit tests are performed for each pixel. The function f is shown in Figure 5.1,
where seven calibration points have been used.
This calibration method is applicable for per-pixel energies less than ∼ 500 keV. To
demonstrate this, the TPX-CdTe has been exposed to a 59.5 keV photon 241Am source.
A 3.2 mm Al plate was positioned between the source and the detector in order to stop
65. 49
Figure 5.1 – The dependence of the TOT on the X-ray energy for each pixel, expressed by
the calibration function f. The c
x−t term takes into account the calibration’s non-linearity
near the threshold.[31]
the 5.48 MeV α particles also emitted. The source has been placed on a mounted support
at a distance of 1.5 cm from the detector, at an angle of 0◦ with respect to its surface.
The detector was operated at a bias of 400 V. Figure 5.2 shows the peak at 58.8 keV in
the spectrum produced by the X-rays.
The energy difference between the observed peak and the expected energy of 59.5
keV is 1.18%.
If this calibration is applied to higher energy photons, the same precision is not repro-
duced. Figure 5.3 illustrates the energy spectrum of a 137Cs source of 662 keV photons.
Once again, a 3.2 mm Al plate was placed between the source and the detector to stop
the emitted electrons 1. The distance between the source and the detector was 1.2 cm.
The measured energy of these photons is 711.1 keV, a difference of 7.4% from its
expected value of 662 keV. It is clear that the measurement of higher energy photons and
particles would be poorly served by this calibration.
Energy measurements of 0.796 - 9.949 MeV protons have been taken at the Van
der Graaf accelerator at the University of Montreal and the measurement of 0.995 MeV
1. Electrons of 514 keV emitted from 137Cs are stopped in 0.84 mm of Al.
66. 50
Figure 5.2 – The photon energy spectrum of an 241Am source with a peak at 58.8 keV.
Figure 5.3 – The energy spectrum of photons coming from a 137Cs source (662 keV
photons) with a peak at 711,1 keV.
67. 51
protons have been taken at the IEAP in Prague with the goal of measuring the energy
resolution of the TPX-CdTe detector. We describe here the experimental setup used
in Montreal which makes use of Rutherford backscattering. The TPX-CdTe is placed
inside a vacuum chamber under a pressure of ∼10−7 Torr. A proton beam (0.8 up to 10
MeV) has been backscattered off a gold foil with a thickness of 0.12 µm. The detector
is bombarded by backscattered protons. It is placed at a scattering angle of 90◦ after the
gold foil. The gold foil is placed in an adjacent chamber, at 45◦ with respect to the beam
direction.
Table 5.I gives the resolutions for each energy with percent differences between the
measured and expected energies.
The resolution is calculated and expressed as a percentage according to
R =
FWHM
Em
×100, (5.2)
where FWHM is the full-width at half-maximum of the Gaussian distribution fitted
to the spectrum for each energy and Em is the measured energy.
The accuracy of the calibration is quantified in terms of the percent deviation %Dev
of the measured and expected energy of the backscattered proton from the gold foil. It is
observed that the calibration is accurate for energies between 3 to 7 MeV but becomes
less so outside of this energy interval.
5.1.2 Global Energy Calibration
Due to the per-pixel calibration’s limitations, it was necessary to calibrate the TPX-
CdTe detector using some other method in order to measure the energy resolution. The
method employed uses protons of different energies as calibration points. Henceforth,
this method will be called "global calibration".
The detector was operated at a bias of 300 V and was exposed to a flux of heavy
ionizing particles of known energies. 3, 5, and 9 MeV protons have been used as well
as 20 MeV 6Li ions. The mean TOT value measured for each spectrum is illustrated
as a function of the backscattered energy in Figure 5.4. A curve has been fitted on the
68. 52
E (keV) Em (keV) FWHM (keV) R (%) % Dev
795.95 430.898 73.095 16.96 45.86
895.44 585.320 84.712 14.47 34.63
994.94 718.528 135.200 18.82 28.13
1,094.43 873.908 112.458 12.87 20.15
1,193.92 981.923 132.357 13.48 17.76
1,293.42 1,116.610 134.320 12.03 13.67
1,392.91 1,239.910 155.245 12.52 10.98
1,492.41 1,411.620 74.230 12.36 5.41
1,989.87 1,919.320 112.352 13.76 3.55
2,984.81 3,021.590 151.194 11.76 1.23
3,979.75 3,997.160 206.310 12.13 0.44
4,974.68 4,954.210 253.156 12.01 0.41
5,969.62 5,966.670 261.112 10.28 0.05
6,964.56 6,952.300 298.755 10.10 0.18
8,954.43 8,502.680 395.129 10.92 5.04
9,949.37 9,055.420 450.306 11.69 8.98
Table 5.I – The measured proton energies Em with the per-pixel calibration compared to
the expected energies after Rutherford backscattering with their percent deviation %Dev.
The FWHM and the resolutions R are provided for each energy.
four points producing a quadratic function. Inverting this function gives the calibration
function,
E = −1,3848.7 −0.000144418(TOT +8.6129)+6.01324−2.45219 . (5.3)
Reprocessing the 662 keV proton data shown in Figure 5.3 with the global calibration
gives the spectrum illustrated in Figure 5.5. The accuracy in energy is visibly improved.
The photopeak is now located at 661.8 keV. Table 5.II provides the measured photon
energies.
Figure 5.6 compares two energy spectra measured with both calibrations for 10 MeV
protons. The expected energy after backscattering is 9,949 keV. The per-pixel calibra-
tion gives a value of 9,055 keV, which corresponds to a difference of 8.98% from the
expected value. The measured energy using the global calibration is 9,737 keV, corre-
69. 53
Figure 5.4 – The calibration function for heavy ionizing particles (3, 5 et 9 MeV protons
and 20 MeV 6Li ions).
E (keV) Em (keV) FWHM (keV) R (%) % Dev
59.5 58.8 14.994 25.50 1.18
662 661.8 85.515 13.22 0.03
Table 5.II – The energies Em of photons emitted from 241Am (59.5 keV) and 137Cs (662
keV). The energy of 59.5 keV is measured using the per-pixel calibration while the 662
keV photons were measured with the global calibration. %Dev gives the percent devia-
tion of each measured energy from its expected value. The FWHM and the resolution R
are given for each.
70. 54
sponding to a difference of 2.13% from the expected value. The shift in the peak of the
global calibration shows how it can correct for the energy loss observed by the per-pixel
calibration, caused by saturation effects in the pixels that measure energies greater than
500 keV.
The values presented in Table 5.I are calculated once again in Table 5.III using the
global calibration. On average, the global calibration improves the resolution by 8.6%
compared to that of the per-pixel calibration. This improvement is shown in Figure 5.7.
It is also observed that the accuracy of the measured energy decreases for low ener-
gies, quantified by %Dev. Alternatively, by increasing the proton energy, the quantity of
charge carriers increases as well. This means that the relative fraction of trapped carriers
decreases with increasing energy.
There are, however, limitations to the global calibration. It can only be applied to
data taken at the bias used during calibration measurements.
5.2 µτ Studies
The CdTe material contains impurities and defects which are caused by fabrication
limitations and by the presence of two types of atoms within the crystal lattice[4]. These
imperfections manifest themselves in the form of traps that prevent charge carriers from
freely moving through the material.
One way of determining how the TPX-CdTe detector is affected by these traps is to
measure the product of the charge carriers’ mobility and their lifetime (µτ). In section
3.2, the importance of this parameter was mentioned in relation to the spectroscopic
characterization of a detector. The lifetime varies depending on the trap concentration in
the detector. The more traps there are, the higher is the possibility that a charge carrier
can become captured and, thus, τ becomes smaller.
To calculate the µτ product for charge carriers in the detector, measurements of
deposited energy in the TPX-CdTe detector at multiple bias voltages have been taken.
A curve was fitted to these points. By assuming that the electric field is uniform and
by neglecting detrapping, one obtains an expression for the charge collection efficiency,
71. 55
Figure 5.5 – The energy spectrum for 662 keV photons emitted from a 137Cs source
processed with a global calibration. The measured energy is 661.8 keV.
CCE, given by the Hecht Equation[4],
CCE =
Q
Q0
=
µeτeE
d
1−e
−(d−x0)
µeτeE +
µhτhE
d
1−e
−x0
µhτhE
. (5.4)
where Q is the measured charge, Q0 is the charge created near the cathode, d is the
detector thickness and x0 is the distance between the cathode and the charge carrier. The
pixels, which are located on the anode side, collect electrons. In an Ohmic detector, the
signal is induced only by electrons. If the penetration of an incident particle is small
enough, i.e., corresponding to a small range compared to the thickness of the detector
(1,000 µm), the x0 term becomes negligible (x0 ∼ 0) and the Hecht Equation becomes
Q(V) = Q0
µeτe(V −V0)
d2
1−e
−d2
µeτe(V−V0)
, (5.5)
where V0 takes into account the imprecision of the bias while the Canpix interface
applies a bias of 0 V.
72. 56
Figure 5.6 – A comparison between the energy spectra for 10 MeV protons obtained
with the per-pixel (black) and global (red) calibrations.
Figure 5.7 – The resolutions of each energy for the per-pixel (black) and global (red)
calibrations. Protons with energies from 0.8 to 10 MeV are shown.
73. 57
E (keV) Em (keV) FWHM (keV) R (%) % Dev
795.95 464.10 71.33 6.54 41.69
895.44 615.56 79.91 5.52 31.26
994.94 789.69 98.07 5.28 20.63
1,094.43 898.01 94.14 4.46 17.95
1,193.92 1,001.42 104.31 4.43 16.12
1,293.42 1,136.33 109.49 4.10 12.15
1,392.91 1,254.65 121.53 4.12 9.93
1,492.41 1,422.860 128.50 3.83 4.66
1,989.87 1,912.720 198.50 4.42 3.88
2,984.81 3,014.020 277.75 3.92 0.98
3,979.75 4,001.590 352.70 3.75 0.55
4,974.68 5,023.260 474.21 4.02 0.98
5,969.62 6,100.430 463.00 3.23 2.19
6,964.56 7,216.970 564.18 3.33 3.62
8,954.43 9,078.090 786.33 3.69 1.38
9,949.37 9,737.610 897.28 3.92 2.13
Table 5.III – The measured proton energies Em with the global calibration compared to
the expected energies after Rutherford backscattering with their percent deviation %Dev.
The FWHM and the resolutions R are provided for each energy.
The µeτe, Q0 and V0 factors are treated as free parameters and are extracted from the
fit. The values of Q and Q0 are obtained in fC by dividing the measured energies with the
per-pixel calibration by the mean energy required for electron-hole pair creation in CdTe
(4.43 eV). The measurements were made at the Tandem accelerator at the University
of Montreal. The incident particles were 1.4 MeV protons to reduce the penetration in
the TPX-CdTe as well as to limit the energy lost inside the platinum contact material.
Figure 5.9 shows the Hecht fit calculated using the Minuit2 software package. The result
is summarized in Table 5.IV 2 with the average range of protons in CdTe, giving an idea
as to how precise the approximation is with respect to the 1,000 µm thickness of the
TPX-CdTe. Due to the τe factor, the electron lifetime, a low µeτe value would indicate
2. The coefficient of determination is given by
R2
= 1−
Σn
i=1(yi − fi)2
Σn
i=1(yi − ¯y)2
, (5.6)
where yi are measured energy values, fi are the predicted values based on the fit and ¯y is the average of
the measurements. The code that was used to calculate this value is shown in Figure 5.8.
74. 58
that trapping contributes significantly to the decrease of the charge collection efficiency.
It should be noted that the charge collected (Q0 = 45.37 fC) is 11% less than the
expected charge, Q, given by
Q =
1.39291×106eV
4.43eV
×1.602×10−19
C = 50.37 fC, (5.7)
which means that there is a significant quantity of charges that are trapped in the
material.
This µeτe value is in agreement with those measured by other researchers. A list of
values taken from the literature can be found in Table 5.V.
Proton Energy Range (µm) µτ ×10−3 cm3
V R2
1,393 keV 14.21 1.32 ± 0.43 0.99914
Table 5.IV – The µτ product of the TPX-CdTe detector for 1.4 MeV protons with the
corresponding range in µm[9] and the quality of the fit (R2).
75. 59
Figure 5.8 – The calculation of the coefficient of determination.
Figure 5.9 – The measured energy as a function of the bias for 1.4 MeV protons with
statistical error bars. The fit function (red) has an R2 value of 0.99914.
76. 60
Reference µeτe ×10−3 cm3
V
Mandal et al.[32] 2
Sato et al.[33] 2.8
Takahashi et al[34]. 1-2
Armantrout et al. [35] ∼ 1
Value measured in Montreal 1.32
Table 5.V – The µeτe values found in the literature. The errors on these values are not
given for these references.
77. CHAPTER 6
CONCLUSION
The possibility of using CdTe detectors for medical and particle physics applications
has motivated this study, made possible with the use of a Timepix-CdTe detector. CdTe
offers the advantage of a high atomic number, which allows for an improved γ-ray de-
tection efficiency. Its high radiation hardness [2] endows it with the ability to be used in
space as well as in high energy physics accelerator physics experiments.
There has been considerable progress in the fabrication of CdTe detectors by manu-
facturers. Consequently, companies that make these detectors are interested in knowing
precisely their properties and their characterization for radiation detection. Within a
7-year interval, data was taken under the same experimental conditions with two dif-
ferent TPX-CdTe detectors produced by the same company [28]. Figure 6.1 shows the
improvement in homogeneity between these two detectors.
In this work, a spectroscopic characterization of a TPX-CdTe detector was completed
with the aim of evaluating its energy resolution for particles (protons and photons) of
different energies, its charge collection and the precision of its calibration. Of particular
interest was its response to 59.5 keV and 662 keV photons, demonstrating its suitability
for applications in SPECT and PET, where the typical detected photon energies are 140.5
keV 1 and 511 keV respectively. The TPX-CdTe detector mesures energies at 59.5 keV
and 662 keV with a precision of 1.18% (with the per-pixel calibration) and 0.03% (with
the global calibration) respectively.
The reliability of the per-pixel calibration has been compared to that of the global
calibration. It is shown that the per-pixel calibration becomes less precise as measured
energies increase. Alternatively, the global calibration allows for the extension of the
measurable energy range for protons by the TPX-CdTe and improves the energy resolu-
tion by 8.6%, on average.
A study of polarization effects has been done showing the behaviour of the effective
1. Photons with energies of 159 keV (123In), 171 keV (111In) and 245 keV (99mTc) are also used.
78. 62
Figure 6.1 – A) A Timepix-CdTe irradiated by α-particles in 2008 with a large quan-
tity of localized trapping centres. B) A second Timepix-CdTe irradiated by α-particles
in 2015 displaying a more homogeneous structure. The vertical lines correspond to
columns of dead pixels resulting from the implantation of the bump bonds during fab-
rication. The scales indicate the number of α-particles registered in each pixel. A)
and B) comme from measurements taken at the Tandem accelerator at the University of
Montreal.
79. 63
bias in the TPX-CdTe as a function of time. It is shown that a TPX-CdTe fabricated
with Ohmic contacts exhibits relatively moderate polarization effects. The decrease in
the bias reproduces the results observed by other researchers who used Schottky type
detectors. However, this decrease is comparatively weak, not exceeding 15 V during the
38 h measurement.
Finally, the mobility-lifetime product of electrons has been measured. The obtained
value has been calculated from the Hecht equation and is in agreement with those found
in the literature.
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