Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

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490 Principles of Radiation Interaction in Matter and Detection

and the bias voltage achieving full depletion is:

q |N

eﬀ

2²

. (6.102)

The so-called body capacitance per unit length for a depletion depth x is given by

Eq. (6.28), i.e., in the present case we have

= ²

, (6.103)

thus, for V

< V

, c

∝ 1/

√

and for V

≥ V

, c

= ²p/d.

The relative dimensions of the pitch “p” (p) and strip width “w” (w) (w/p < 1

in practice) contribute a term which increases the full depletion voltage [Eq. (6.102)]

to the depletion voltage, V

, for the strip [Barberis et al. (1994)]

= V

1 + 2

¶¸

q |N

eﬀ

2²

+ 2 p d f

¶¸

, (6.104)

and decreases the strip body capacitance, c

, per unit length for a depletion depth

x [Barberis et al. (1994)]:

= ²

x + pf

= ²

+ V

´i

. (6.105)

At full depletion depth d, we obtain:

= ²

d + pf

= ²

1 +

. (6.106)

The function f

is given [Barberis et al. (1994)] by:

= −0.00111

−2

+ 0.0586

−1

+ 0.240

−0.651

+ 0.355

. (6.107)

The total capacitance, C

tot

, has a dominant contribution to the readout electro-

nic noise. The total capacitance has a linear dependence on the strip width, for a

given pitch. In the range 0.1 ≤ w/p ≤0.55, for a detector 300 µ m thick [Sonnenblick

et al. (1991)]:

tot

0.8 + 1.6

[pF/cm], (6.108)

for p = 100 µm. The interstrip capacitance, C

int

, can be calculated from:

int

= C

tot

− c





0.8 + 1.6

− ²

d + p f





[pF/cm], (6.109)

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Solid State Detectors 491

where c

is given by Eq. (6.106). As an example for w/p = 0.5, d = 300 µm,

p = 100 µm, one ﬁnds f

= 0.116, p/d = 1/3 and c

= 0.35 pF/cm,

tot

= 1.6 pF/cm, and C

int

= 1.25 pF/cm. This example illustrates the impor-

tant contribution of C

int

to the total capacitance. In fact for d = 300 µm and

0.18 ≤ w/p ≤ 0.36 and 50 µm≤ w/p ≤ 200 µm, Eq. (6.109) can be replaced in very

goo d approximation (better than 10%) by the formula [Braibant et al. (2002)]:

int

∼

0.1 + 1.6

w + 20 µm

[pF/cm]. (6.110)

The electronics noise of the charge sensitive ampliﬁer expressed as an equivalent

noise charge (ENC) can be parametrized similarly to Eq. (6.79):

ENC = a + b C

tot

[pF/cm], (6.111)

where a and b are constants depending on the preampliﬁer. Typical value of ENC

in peak mode is [Braibant et al. (2002); Jones (1999)]:

ENC = 246 + 36 C

tot

[pF/cm]. (6.112)

Using Eq. (6.108) with w/p = 0.4, one ﬁnds C

tot

= 1.44 pF/cm which gives ENC ≈

300, comparable to the contribution of 300 electrons reported in [Nygard et al.

(1991)] with another preampliﬁer. One should also consider the contributions of

leakage current and bias resistor to the equivalent noise charge. The noise due to

the leakage current (typically, 1 nA per strip) is given by Eq. (6.80). For θ = 250 ns

and I

= 1 nA in Eq. (6.80), one obtains a noise of about 40 electrons. The equivalent

noise charge due to bias resistor (EN C

) is given by:

ENC

2θkT

, (6.113)

where q is the electronic charge, e is the base of natural logarithm, T is the tempe-

rature, k is the Boltzmann constant (kT = 0.0259 eV at T = 300 K) and R is the

biasing resistance. For R = 2 MΩ, one ﬁnds ENC

∼ 550 electrons.

6.5 Pixel Detector Devices

Most of the pixel detector devices in operation nowadays are based on silicon tech-

nology, although such devices based on GaAs, CdTe and CdZnTe are also used. The

pixels are small detector elements or cells of a two-dimensional array, organized into

rows and columns. One often uses the expression “pixellated silicon detector”. The

pixels of present generation are usually of squared area with dimensions ∼ 50 µm ×

50 µm. Practically, the silicon pixel detector is of the hybrid-type. It is made up of

two superimposed layers. The top layer is the detecting or sensor layer, the bottom

layer is the readout electronics layer which deﬁnes the segmentation of the sensor

material and the size of the pixels. Each cell and its corresponding readout chip are

connected via conductive bumps (i.e., a drop of solder between two metals pads per

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492 Principles of Radiation Interaction in Matter and Detection

pixel) using the so-called bump-bonding and ﬂip-chip technique. This metal bump

allows the transfer of the pulse generated in a pixel in the sensor layer to the readout

chip. The pixel sensor layer is a p −n diode operated in reverse bias mode. Incident

particles on the detector creates electrons and holes in the sensor by ionization. The

movement of the separated charges in the applied electric ﬁeld induces a signal on

the pixel electrode and possibly its neighbors. This signal is transmitted to the chip

periphery after ampliﬁcation, discrimination and digitization by the electronic cir-

cuitry in the pixel cell of the chip. The amount of ionization charge collected by

a series of cells allows the reconstruction of the track of a particle incident on the

detector. The track length depends on the incidence angle as particles of large inci-

dence angle (close to or along the normal to the sensor plane create tracks covering

a pixel or just a few whereas tracks of particles of low incidence angle cover a larger

numb er of pixels. Obviously, the number of pixel covered by a track also depends

on the incident particle type and energy. One should observe that pixels detectors

provide large signal-to-noise ratios since the ionization charge Q is collected on a

very small area typically ∼ 2500 µm

. Therefore, the capacitance at the ampliﬁer

input is about C = 88 fF for a silicon thickness of 300 µm, leading to very small

noise ∼ 100 e

−

r.m.s., as this noise is dominated by capacitance. Also, the signal

is high as V = Q/C. The signal typically consists of the order of ∼ 10, 000 e

−

charges, and in a segmented matrix with ∼ 50 µm size pixels, one can process

∼ 1000 e

−

signals with a noise as low as 100 e

−

r.m.s [Heijne (2007)]. The small

size of a pixel also helps the limitation of the leakage current. A leakage current as

high as 1 mA cm

−2

only represents 25 nA for a 50 µm × 50 µm pixel, if the current

is evenly distributed [Heijne (2007)]. A further progress in pixel detector technol-

ogy is to build a pixel detector device which could store the image data in each

pixel until readout rather than transmit and process particle signal oﬀ-chip. Using

a comparator,i.e., setting a threshold, this enables a 1 bit analog-to-digital conver-

sion and accurate analog performance can be achieved by combining linear ampliﬁer

and tunable threshold. Examples of such devices are the MediPix-type devices.

6.5.1 The MediPix-type Detecting Device

This hybrid silicon pixel device was developed in the framework of the Medipix

Collaboration [Medipix Collab. (2008)] and originally designed for position sensi-

tive single X-ray photon detection. In a ﬁrst version, the device called MediPix1,

consists of a silicon detector chip (sensor) bonded to a readout chip. The sensor

chip is equipp ed with a single common backside electrode and a front side matrix

of 64 ×64 squared pixels is deﬁned with a pixel size of 170 µm × 170 µm allowed by

a 1 µm CMOS process. Usually the silicon thickness is 300 µm thick, although other

thicknesses are possible. Each pixel is connected to its respective readout chain in-

tegrated on a readout chip. When a quantum of radiation is absorbed in the sensor

layer, the generated charge is transferred through the bump bond to the correspon-

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Solid State Detectors 493

ding electronic chip where after preampliﬁcation the charge is fed to a discriminator

(comparator) which compares the received signal to a preset threshold. If the signal

is above that threshold, the counter of this pixel is incremented by one. This opera-

tion is done in each pixel independently. After completion of the data acquisition,

the counters of all pixels are read out to obtain an image (a frame). The single lower

global threshold for the discriminator allows the rejection of very low energy X-ray

photons, so helping the image contrast and provides at the same time suppression

against electronic noise or dark current of the active layer, reducing the background

in the image. The counter depth of 15-bit in each pixel limits the dynamic range and

image contrast. The electronic chip of the MediPix1 device only works for positive

charges (holes). Then, heavy semiconductors such as GaAs, CdTe and Cd(Zn)Te

having low hole mobility are not the best choice for sensor material of MediPix1.

The MediPix2 hybrid silicon pixel-detector [Llopart et al. (2002)] is the successor

of MediPix1. Most of the content of this chapter will be now about the MediPix2 de-

vice as it represents the most powerfull detector of the type, for the time being. The

MediPix2 has a front side matrix of 256 × 256 electrodes. Each pixel has an area

of 55 µm × 55 µm. The use of 0.25 µm CMOS process has allowed this small pixel

size. The silicon thickness is 300 µm, although larger thicknesses (700 µm and 1 mm,

for instance) are also possibly utilized. The use of heavy semiconductors like GaAs,

CdTe, Cd(Zn)Te is better adapted to MediPix2 compared to MediPix1 as MediPix2

works for electrons and holes. The MediPix2 has additional features compared to

MediPix1. The MediPix2 detector has a preampliﬁer, two discriminators (window

discriminator) and a 14-bit counter in each readout pixel cell chain. The presence of

a second discriminator allows one to set an energy window with a lower and a upper

threshold. The pixel counter is incremented only when the energy of the interacting

quantum of radiation falls within this preset energy window. The assembled hybrid

pixel device is glued on a printed circuit board (motherboard). There is an inter-

face board between the MediPix2 hybrid pixel device and a Universal Serial Bus

(USB), which is presently the most widespread PC interface [Vykydal, Jakubek and

Pospisil (2006)]. All necessary detector support, including the detector bias source

(up to 100 V), is integrated into one compact system (64 × 50 × 20 mm

). Power

supplies are internally derived from the voltage provided by the USB connection,

so no power source on the device is required and the bus provides the communica-

tion lines (signals, etc.). The interface board has been designed for connection to

motherboards carrying one or four MediPix2 pixel devices, permitting, in the latter

case, an increased sensitive area. The MediPix2 motherboard connected to the USB

interface represents a volume of about 142 × 50 × 20 mm

for the MediPix2-USB

device. The MediPix2-USB device is controlled by the pixelman software package

using a PC via USB cables [Holy, Jakubek, Pospisil, Uher, Vavrik and Vykydal

(2006)]. This software provides a set of plugin’s which are used to control diﬀerent

features of the chip or of the experimental environment. The pixelman control can

be extented up to 50 Medipix-USB devices, operating simultaneously.

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494 Principles of Radiation Interaction in Matter and Detection

An additional signiﬁcant advantage of the USB interface is the support of back-

side pulse processing. This feature enables the possibility to determine not only the

position but also the energy deposited by the interacting particle. Each particle of

ionizing radiation interacting in the depleted region of the MediPix2 sensor pro-

duces a speciﬁc amount of electron-hole pairs proportional to the energy lost by

the particle in the sensor. If the total charge is large enough, it can b e measured

by a charge sensitive preampliﬁer and, after shaping, sampled by a fast ADC. This

feature also allows the generation of a trigger pulse. Particle signals detected by the

MediPix2 device can either be integrated in the pixel counters, or the pixel matrix

can be read-out at such a frame rate that visualization of single particle events be-

comes possible. Hence, this circuit can process these signals in various mo des either

counting or tracking. The counting mode is usable for high detection rates (above

∼ 5 ×10

events per second per cm

) when the number of interactions in individual

pixels is determined at diﬀerent thresholds yielding the fraction of radiation with

the corresponding ionizing power. By setting thresholds high enough, this mode

allows one to diﬀerentiate the signal from ionizing particles with poor detection

eﬃciency compared to electrons or low energy X-rays, for instance. Calibration of

the devices enables the conversion of the individual counts measured into ﬂuxes of

respective types of radiation and dose rates. The tracking mode is applicable at

low detection rates. It permits an analysis of individual tracks or traces (with their

pattern recognition) of interacting quanta of radiation. In this mode, the threshold

is set just above noise level and short time acquisitions are done with the aim to

avoid the overlap of characteristic tracks from diﬀerent particles which then can be

separately distinguished. So the tracking mode is based on electronic visualization

of tracks and traces of individual quanta of radiation in the sensitive silicon volume.

MediPix2 devices have demonstrated speciﬁc capabilities for particle identiﬁ-

cation relying on pattern recognition techniques. In a single frame, diﬀerent pat-

terns, that can be associated to diﬀerent types of particles can be identiﬁed with

a great level of accuracy. However, the MediPix2 device cannot do a direct study

of the energy deposition. This can be achieved with the newly developed TimePix

device [Medipix Collab. (2008)]. From its time over threshold (TOT) mode of ope-

ration, the TimePix device can count the amount of charge being deposited in a

given pixel element, among the 256 × 256 pixels available, and these counts can be

translated into energy with a proper calibration. This added to the pattern recog-

nition capabilities already available from MediPix2, it is possible to measure the

amount of a certain type of radiation at a given position.

6.5.2 Examples of Application: Particle Physics

Images of MediPix2-USB device responses are characteristic of illuminations by

speciﬁc radiation, resulting from diﬀerent charge deposition mechanisms. Then, the

MediPix2-USB device makes possible the detection in counting and tracking mode of

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Solid State Detectors 495

Fig. 6.23 The silicon sensor is covered on the upper half with a CH

layer (orange) to detect

fast neutrons and part of the lower half with a

LiF layer (green) to detect thermal and very

slow neutrons [Holy et al. (2006)]. Are seen: the long and thick tracks (Bragg-peak energy depo-

sition) of recoiled protons and big tracks and clusters generated by nuclear products in LiF and

via

Si(n,α)

Mg and

Si(n,p)

Al nuclear reactions in silicon. Electrons and photons (always

accompanying neutrons) are also seen.

Fig. 6.24 Measurement of muons (mip’s) at the CERN SPS with a MediPix2-USB device operated

with a 20 V bias voltage [Idarraga (2008)]. The muons are striking the MediPix2 along a direction

parallel to the device surface.

a variety of particles produced by collisions in the case of an accelerator [Campbell,

Leroy, Pospisil and Suk (2006); Holy et al. (2006)] or subsequent interactions with

matter of particles produced by a source. These capabilities can be exploited for

real-time measurement of the composition and spectroscopic characteristics of a

given radiation ﬁeld.

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496 Principles of Radiation Interaction in Matter and Detection

MediPix2-USB devices have been intensively and successfully used for detection

of single X-ray photons, electrons, minimally ionizing particles (mip’s), energetic

ions (protons, alpha particles, and other heavy charged ions such as carbon and oxy-

gen) and neutrons. Furthermore, the applications for medical imaging are discussed

in Sect. 11.4.

6.5.2.1 Electrons and Photons

X-rays or low energy signals generally produce hits in 1 or 2 pixels only (depending

on their energy, on the pixel threshold set and other parameters at the base of the

charge sharing mechanism (see later)). Beta particles can be identiﬁed through their

erratically longer, curved tracks. The length of the electron tracks are consistent

with the average energy transferred by photons per interaction (dominance of the

photoelectric eﬀect for energies lower than 50 keV, while Compton dominates for

energies above 100 keV) [Fiederle et al. (2008)]. The direction of a particle beam

can be determined from the measurement of impinging angles. Particles along a

direction parallel or very close to being parallel to the surface of the MediPix2

device have long tracks inside the sensor material, i.e., tracks covering a number

of pixels given by the particle range divided by 55 µm. Particle impinging on the

pixels at larger angle leave shorter tracks. With the low signal threshold setting one

observes adjacent hits when the particle is near to the b order between pixels. This

allows one to determine the direction of the particle, and provide coordinates. It

is possible to determine the beam direction using the intensity decrease in the

MediPix [Fiederle et al. (2008)]. The use of the interaction probability in silicon

∗

for photons of energies from 10 keV up to 160 keV produced by X-ray sources allows

the measurement of the photon detection eﬃciency that is found to range from ∼ 1

at 10 keV and 10

−2

at 160 keV (threshold set at 8 keV) [Fiederle et al. (2008)].

6.5.2.2 Neutrons

The MediPix2 device can be used for neutron detection. For detection of thermal or

very slow neutrons, the silicon sensor is partially or totally covered with a neutron

absorbing material which converts the energy into radiation detectable in silicon

(see Sect. 6.7). A ﬁlm of

LiF is often used and exploits the reaction

n +

Li → α (2.05 MeV) +

H (2.72 MeV)

to detect thermal neutrons. The thermal neutron detection eﬃciency is ≤ 5% for a

converter 7 mg/cm

thick (see Sect. 6.7). For fast neutrons (or neutrons with kinetic

energy higher than hundreds of keV) detection, the silicon sensor is partially or

totally covered with a ﬁlm of hydrogen-rich material, such as polyethylene (CH

1.3 mm thick - see Sect. 6.7). The neutrons are detected by recoil protons in the

elastic scattering of neutrons on nuclei in CH

. In practice, the sensitive area of the

∗

The probability is equal to 1 − exp(−µx), where x is the traversed silicon depth and µ is the

sum of photon attenuation coeﬃcients for the photoelectric and Compton eﬀects, mainly.

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Solid State Detectors 497

Fig. 6.25 Measurement of pions at the CERN SPS with a MediPix2-USB device operated with

a 20 V bias voltage [Idarraga (2008)]. One can see for non-mip pions, the interaction pattern

featuring large energy deposition around a vertex with recoil fragments remaining in the sensitive

volume of the detector. δ-rays are also visible.

Fig. 6.26 Signature of 10 MeV protons measured at the Van de Graaﬀ tandem of the University

of Montreal with a MediPix2-USB device operated with a 20 V bias voltage. The protons after

being Rutherford back-scattered on a gold foil are striking the MediPix2 postionned at paral-

lel incidence angle [RBS (2008)]. The proton tracks show an energy deposition characteristic of

standard asymmetric feature of a Bragg curve. The threshold was set at 13.3 keV.

MediPix2-USB device is divided in several regions: regions covered with one layer or

combination of layers of

LiF, polyethylene, aluminium materials (aluminium for low

energy electrons absorption) and one region is uncovered. A simple example is shown

in Fig. 6.23 for a silicon sensor covered on the upper half with a CH

layer (orange)

to detect fast neutrons and part of the lower half with a

LiF layer (green) to detect

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498 Principles of Radiation Interaction in Matter and Detection

thermal and very slow neutrons. One can see long and rather thick tracks (Bragg

peak energy deposition) of recoiled protons and big tracks and clusters generated by

nuclear products in LiF and via

Si(n,α)

Mg and

Si(n,p)

Al nuclear reactions

in the body of the silicon detector. Electrons and photons are also seen. However,

the huge background of photons which always accompany neutrons can be highly

suppressed via threshold setting. Another example can be found with the MediPix2-

USB devices used in the ATLAS detector at the CERN-LHC [Campbell, Leroy,

Pospisil and Suk (2006); Holy et al. (2006)]. These devices will be exposed, in

particular, to a neutron ﬁeld and accompanying photon ﬁeld. By comparing the

responses from the diﬀerent regions of a device, uncovered and covered by speciﬁc

ﬁlm and foils of given thicknesses, one can determine, in real-time, the spectral

composition of the neutron ﬁeld if one uses the calibration obtained from known

sources of neutrons with speciﬁc energy, E

, such as neutron beams from Van

de Graaﬀ accelerators (E

= 14–17 MeV), ﬁssion sources (E

= 25 meV),

252

∼ 2 MeV) and AmBe (E

∼ 4 MeV) sources.

Fig. 6.27 Signature of 5.4 MeV α-particles from an

241

Am source measured with a MediPix2-USB

device operated with a 20 V bias voltage. The α-particles are striking the MediPix2 positioned at

perpendicular incidence angle. The threshold was set at 5.6 keV. The α-source was ﬁt into a vacuum

chamber of the Van de Graaﬀ Tandem accelerator of the University of Montreal.

6.5.2.3 Muons, Pions and Protons

The capability of MediPix2-USB to allow the real-time measurement of microscopic

details of muons trajectories, and pions interactions from an hadronic beam has been

demonstrated at CERN-SPS [Field and Heijne (2007)] for a MediPix2-USB device

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Solid State Detectors 499

placed parallel to the beam [Field and Heijne (2007)]. The muons resulting from

the decay of pions produce typical minimum ionizing particle (mip) trails in the

sensor. In absence of nuclear interactions the tracks of these mips in MediPix2 are

continuous, crossing the rows of pixels of the detector matrix with regular stretches

of overlapping rows (Fig. 6.24). Incoming non-mip pions produce interaction pat-

terns characterized by large energy deposition around a vertex with recoil fragments

traveling in the detector sensitive volume and leaving long tracks or short tracks

depending on recoil angles (Fig. 6.25). δ-rays are also observed. It should be ob-

served that mip pions and muons will leave the same long trails and cannot b e

distinguished, possibly causing mis-tagging. The same type of measurement can be

performed with protons. Dedicated measurements with protons of low energies have

been performed with a MediPix2-USB device [RBS (2008)]. An example of 10 MeV

protons hitting this MediPix2-USB device along a direction parallel to its surface

is shown in Fig. 6.26. Protons of that energy have a total range of up to ∼ 742 µm

(including the longitudinal straggling) in silicon which represents a track length of

742/55 = 14 pixels in the device.

6.5.2.4 α-Particles and Heavier Ions

Alpha particles and heavier ions deposit large amounts of energy in a very conﬁned

space. Therefore, the signature of this type of particle corresponds to a rather

symmetric cluster of adjacent pixels.

The example of 5.4 MeV α-particles (from a

241

Am source) measured with a

MediPix2-USB device is shown in Fig. 6.27.

The measurement with a MediPix2-USB device of carbon and oxygen ions pro-

duced from Rutherford back-scattering of 30 MeV carbon and 35 MeV oxygen beams

on gold are shown in Fig. 6.28 [RBS (2008)]. Small dots can be observed in these ﬁ-

gures. Their origin is explained by the Au X-rays (Kα and Kβ). They are generated

via proton induced X-ray emission.

6.5.2.5 Charge Sharing

The shape of a track in a MediPix2-USB device depends on the nature of the

interaction in the detector sensitive volume and is inﬂuenced by the charge sharing

eﬀect. This eﬀect among adjacent pixels takes its origin from the lateral spreading

of charges from the interaction of an ionizing particle in the silicon detector. This

response to single particle hit is taking the form of a cluster of adjacent pixels. The

charge deposited in an adjacent pixel is counted if higher than the threshold set for

the comparator. The charge sharing eﬀect can be used as an advantage allowing

the improvement of the spatial resolution of the incident particle and exploited for

tracking. One can take advantage of heavily ionizing particles (α-particles, carbon,

oxygens ions, . . . ) to understand the eﬀect.

Heavy charged particles produce dense carrier tracks in silicon detectors, as