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

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410 Principles of Radiation Interaction in Matter and Detection

Fig. 4.34 (a) Resistivity (ρ) in Ωcm, (b) absolute value of the Hall coeﬃcient [R

, see Eqs. (4.166, 4.169)] in cm

/C and (c) Hall mobility [µ

, see

Eqs. (4.171, 4.172)] in cm

−1

as a function of the temperature from 300 down to 11 K (in 1000/T, where T is in K) for n-type silicon samples

with resistivities of ≈ 56 Ωcm before irradiation with fast neutrons: the experimental data are from [Consolandi, Pensotti, Rancoita and Tacconi

(2008)]. R

was observed to be negative before (e.g., for n-type silicon) and after irradiations, i.e., there was no change of the Hall-coeﬃcient sign.

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Radiation Environments and Damage in Silicon Semiconductors 411

and Rattaggi (1998); Croitoru, Gubbini, Rancoita, Rattaggi and Seidman (1999a,b);

Mangiagalli, Levalois, Marie, Rancoita and Rattaggi (1999)]). At very large ﬂu-

ences of fast-neutrons (i.e., above

‡

n/cm

), Kr-ions (i.e., above 10

Kr/cm

[Croitoru, Gubbini, Rancoita, Rattaggi and Seidman (1999a,b)]) and Ar-ions (i.e.,

above 10

Ar/cm

[Mangiagalli, Levalois, Marie, Rancoita and Rattaggi (1998)])

the resistivity is roughly that of the intrinsic silicon.

After irradiation with fast neutrons, the resistivity temperature-dependence

[Fig. 4.34(a)] from 300 down to 11 K was investigated for n-type silicon samples

with a resistivity of ≈ 56 Ωcm before irradiation [Consolandi, Pensotti, Rancoita

and Tacconi (2008)]. From 300 (1000/T ' 3.3) down to ≈ 60 K (1000/T ' 16.7)

and for a neutron ﬂuence up to 3 × 10

n/cm

, the temperature dependence does

not exhibit a signiﬁcant variation with regard to that before irradiation. However,

for temperatures lower than ≈ 50 K (1000/T = 20) and for a neutron ﬂuence up

to 1.3 × 10

n/cm

, the resistivity values are lower than the corresponding non-

irradiated ones. For neutron ﬂuences above 1.1 ×10

n/cm

a large departure from

the behavior of the non-irradiated sample is observed.

For both n- and p-type silicon, the Hall coeﬃcient was measured after ir-

radiations with diﬀerent type of particles. At large ﬂuences of photons emit-

ted by a

Co-radioactive source, it was found that, while p-type silicon main-

tains the same conductivity type [i.e., the Hall coeﬃcient remains positive;

see Eqs. (4.165, 4.169, 4.170)], the n-type silicon may change conductivity

type, i.e., from negative the Hall coeﬃcient may become positive ([Konozenko,

Semenyuk and Khivrich (1969)] and references therein). In irradiations with fast-

neutrons and 3.8 MeV electrons, the Hall coeﬃcients were observed to show a sim-

ilar behavior for n-type Fz and p-type silicon [Lugakov, Lukashevich and Shusha

(1982)], while no change of conductivity type [e.g., see Figs. 4.34(b)] occurred for

the n-type Cz

†

and oxygen enriched silicon samples with ρ = (56–157) Ωcm [Lu-

gakov, Lukashevich and Shusha (1982); Consolandi, Pensotti, Rancoita and Tacconi

(2008)]. Other experimental data conﬁrmed that n-type silicon with high-resistivity

may change type of conductivity with irradiations, for instance, with fast-neutrons

and Kr-ions (e.g., see [Borchi and Bruzzi (1994); Biggeri, Borchi, Bruzzi and Lazanu

(1995); Biggeri, Borchi, Bruzzi, Pirollo, Sciortino, Lazanu and Li (1995); Croitoru,

Dahan, Rancoita, Rattaggi, Rossi and Seidman (1997); Croitoru, Gubbini, Ran-

coita, Rattaggi and Seidman (1999a,b); Mangiagalli, Levalois, Marie, Rancoita and

Rattaggi (1999); Consolandi, Pensotti, Rancoita and Tacconi (2008)] and references

therein). In low resistivity samples, no change in conductivity type was observed

in irradiations with Ar-ions [Mangiagalli, Levalois, Marie, Rancoita and Rattaggi

(1998)].

‡

The reader can see [Croitoru, Dahan, Rancoita, Rattaggi, Rossi and Seidman (1997); Croitoru,

Gubbini, Rancoita, Rattaggi and Seidman (1999a,b)].

†

These are samples grown by the Czochralski (pulled) method (e.g., see page 296) and contain

oxygen and carbon in higher concentrations with respect to those grown by the vacuum ﬂoat-zone

(Fz) method.

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412 Principles of Radiation Interaction in Matter and Detection

As already mentioned, from combined measurements of the resistivity and Hall

coeﬃcient we can determine the Hall mobility. The Hall mobility was observed

to decrease with increasing particle ﬂuence (e.g., see [Borchi and Bruzzi (1994);

Biggeri, Borchi, Bruzzi, Pirollo, Sciortino, Lazanu and Li (1995); Croitoru, Dahan,

Rancoita, Rattaggi, Rossi and Seidman (1997, 1998); Mangiagalli, Levalois, Marie,

Rancoita and Rattaggi (1998); Croitoru, Gubbini, Rancoita, Rattaggi and Seidman

(1999b); Mangiagalli, Levalois, Marie, Rancoita and Rattaggi (1999); Consolandi,

Pensotti, Rancoita and Tacconi (2008)] and references therein). For low ﬂuence of

fast-neutrons (≈ 9.9 × 10

n/cm

), the electron-mobility, which diﬀers from the

Hall mobility by the Hall factor [e.g., see Eq. (4.172)], is given by:

e,irr

∝ T

−α

where α ≈ 2.6 and 200 < T < 300 K [Croitoru, Gubbini, Rancoita, Rattaggi and

Seidman (1999b)]. The coeﬃcient α was about 2.3, before irradiation [e.g., see

Eq. (4.174)].

Furthermore since one of the primary eﬀects of irradiation is to cause displa-

cement damage (e.g., see Sect. 4.2.1) and, as a consequence, to generate deep

complex-defects (e.g., see Sect. 4.2.2), it is convenient to show the value of Hall

mobility as a function of the concentration of Frenkel-pairs (FP ) created in the

samples. In Figs. 4.35 and 4.36, the Hall mobility

‡

[Eq. (4.171)] is shown as a func-

tion of the particle ﬂuence and FP, respectively, for irradiations with i) fast-neutrons

[Croitoru, Gubbini, Rancoita, Rattaggi and Seidman (1999a,b); Consolandi, Pen-

sotti, Rancoita and Tacconi (2008)], ii) 1.5 MeV electrons [Mangiagalli, Levalois,

Marie, Rancoita and Rattaggi (1999)], iii) 60 MeV/amu Kr-ions

††

[Croitoru, Gub-

bini, Rancoita, Rattaggi and Seidman (1999a,b)] and iv) 6.7 MeV/amu Ar-ions

[Mangiagalli, Levalois, Marie, Rancoita and Rattaggi (1998)]. The concentrations

of Frenkel-pairs for the irradiations with Ar- and Kr-ions were computed using

the SRIM-2003 code [Ziegler, Biersack and Littmark (1985a); Ziegler (2006)], for

those with electrons by means of the data reported in Sect. 4.2.1.5 and for those

with fast-neutrons by combining their spectral-ﬂuence and the data reported in

Sect. 4.2.1.5. The experimental data show that i) there is more similarity in the

trend of data as a function of FP than as a function of the particle ﬂuence [i.e.,

compare Figs. 4.35 and 4.36], ii) at low FP the Hall mobility diﬀers slightly from

the electron Hall mobility expected in a non-irradiated and weakly doped n-typ e

silicon [e.g., see Eq. (4.172)], iii) a large decrease of the Hall mobility is observed for

FP & 2 × 10

−3

, iv) in high-resistivity samples, a ﬁrst change of conductivity

type may occur for FP & 10

−3

(i.e., for fast neutrons and Kr-ions) and v) a

second change of conductivity type occurs for Kr-ions for FP & 2 × 10

−3

After irradiation with fast neutrons, the temp erature-dependence of the Hall co-

eﬃcient and mobility [Figs. 4.34(b) and (c)] from 300 down to 11 K was investigated

‡

In Figs. 4.35 and 4.36, the Hall mobility is shown maintaining the sign of the Hall coeﬃcient,

instead of using its absolute value [see Eqs. (4.171–4.173)], and at room temperature.

††

The reader can ﬁnd the deﬁnition of kinetic energies per amu in Sect. 1.4.1.

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Radiation Environments and Damage in Silicon Semiconductors 413

Fig. 4.35 Hall mobility (in cm

−1

) at room temperature for n-type silicon as a function of the particle ﬂuence in particles/cm

(adapted

from [Leroy and Rancoita (2007)]): 60 MeV/amu Kr-ions (◦, high-resistivity) [Croitoru, Gubbini, Rancoita, Rattaggi and Seidman (1999a,b)],

6.7 MeV/amu Ar-ions (♦, for high-resistivity, and ¨, for low-resistivity) [Mangiagalli, Levalois, Marie, Rancoita and Rattaggi (1998)], 1.5 MeV

electrons (N, high-resistivity) [Mangiagalli, Levalois, Marie, Rancoita and Rattaggi (1999)], fast-neutrons (¥, high-resistivity) [Croitoru, Gubbini,

Rancoita, Rattaggi and Seidman (1999a,b)], fast neutrons (J, F and ¤ for 2500, 157 and 56 Ωcm before irradiation, respectively) [Consolandi,

Pensotti, Rancoita and Tacconi (2008)]. For the above data, before irradiation the resistivities of the high-resistivity samples are in the range

1 . ρ . 7 kΩcm, while . 100 Ωcm for low-resistivity samples. The sign of the Hall mobility is the sign of the measured Hall coeﬃcient. The lines are

to guide the eye.

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414 Principles of Radiation Interaction in Matter and Detection

Fig. 4.36 Hall mobility (in cm

−1

) at room temperature for n-type silicon as a function of the concentration of the Frenkel-pairs in cm

−3

(adapted from [Leroy and Rancoita (2007)]): the experimental data and corresponding symbols are the same of those shown in Fig. 4.35. The sign

of the Hall mobility is the sign of the measured Hall coeﬃcient. The lines are to guide the eye.

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Radiation Environments and Damage in Silicon Semiconductors 415

for n-type silicon samples with a resistivity of ≈ 56 Ωcm before irradiation [Con-

solandi, Pensotti, Rancoita and Tacconi (2008)]. No change of the Hall-coeﬃcient

sign was observed after irradiation, i.e., the Hall-coeﬃcient was negative before

(e.g., for n-type silicon) and after irradiation. From 300 (1000/T ' 3.3) down to

≈ 60 K (1000/T ' 16.7) and for a neutron ﬂuence up to 1.1 × 10

n/cm

, it is

observed a gradually reduction of the temperature-region extension in which the

Hall coeﬃcient is almost constant [Figs. 4.34(b)]. This region is absent for samples

irradiated with ﬂuences above 4.5×10

n/cm

. For temperatures lower than ≈ 50 K

(1000/T = 20) and for a neutron ﬂuence up to 1.3 × 10

n/cm

, the Hall coeﬃ-

cient values are lower than the corresponding non-irradiated ones. In addition, the

experimental determinations [Figs. 4.34(c)] indicate i) at all temperatures the Hall

mobility of the non-irradiated sample is larger than that of irradiated ones and ii) for

these latter samples it gradually decreases with increasing ﬂuence and temperature,

except at the largest ﬂuence where it increases with increasing temperature.

As discussed in Sect. 4.2.2, the displacement damage generated by the inco-

ming particles results in the formation of defects with deep levels in the forbidden

energy gap. These investigations conﬁrm that large concentrations of deep complex-

defects (e.g. see [Konozenko, Semenyuk and Khivrich (1969); Lugakov, Lukashevich

and Shusha (1982)] and references therein) are introduced in the silicon and, then,

at very large ﬂuences the Fermi level is expected to approach the middle of the

forbidden gap

irrespective of the incoming particle type and initial kind of con-

ductivity. At the initial stage of irradiation, complex-defects, for instance vacancies

with impurity-atoms (donors or acceptors), are introduced that decrease the eﬀec-

tive dopant concentration, while, at a later stage, divacancies and other intrinsic

defects (e.g, di-interstitial, four-vacancies) become predominant [Konozenko, Se-

menyuk and Khivrich (1969); Lugakov, Lukashevich and Shusha (1982)]. These

defects can be introduced as primary by the cascade mechanism or as secondary by

the diﬀusion of the primary defects. The introduction rate of complex-defects may

depend on the incoming particle type (e.g, see Table 9 at pages 155–157 of [Vavilov

and Ukhin (1977)] and [Konozenko, Semenyuk and Khivrich (1969); Mangiagalli,

Levalois and Marie (1998); Mangiagalli, Levalois, Marie, Rancoita and Rattaggi

(1999)] and references therein) and, also, may not be linearly dependent on ﬂuence,

as sometimes observed for secondary defects. For example, in irradiations with pho-

tons emitted by a

Co-radioactive source, the divacancy concentration (interpreted

as a secondary defect [Konozenko, Semenyuk and Khivrich (1969)]) was determined

to be

d−v

= 5 × 10

× Φ

0.6

[cm

−3

where Φ

(in γ/cm

) is the photon ﬂuence ([Konozenko, Semenyuk and Khivrich

(1969)] and references therein).

Many authors have experimentally determined that the Fermi level approaches the middle of

the forbidden gap after irradiation (e.g., see [Konozenko, Semenyuk and Khivrich (1969); Lugakov,

Lukashevich and Shusha (1982); Biggeri, Borchi, Bruzzi and Lazanu (1995); Mangiagalli, Levalois,

Marie, Rancoita and Rattaggi (1999)] and references therein).

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416 Principles of Radiation Interaction in Matter and Detection

After irradiation with large ﬂuences, the measurement of the Hall coeﬃ-

cient allows one to determine the approximate free-carrier concentration

using

Eqs. (4.165, 4.169, 4.170). As a consequence, the resistivity

can be estimated from

Eq. (4.168). It has to be noted that, for large fast-neutron ﬂuences, the measured

resistivity was found to disagree with that derived by the combined measurement

of the Hall coeﬃcient

∗∗

on the same sample [Croitoru, Dahan, Rancoita, Rattaggi,

Rossi and Seidman (1997)]. This indicates that a further understanding (as well as

investigations) of transport mechanism in irradiated semiconductors is needed.

4.3.6 AFM Structure Investigation in Irradiated Devices

Using optical and Atomic Force Microscopy (AFM) techniques along with micro-

hardness studies, the characteristics of p −n silicon detectors were widely investiga-

ted after fast neutron irradiations for ﬂuences ranging from 10

n/cm

up to above

n/cm

(e.g., see [Golan et al. (1999, 2000, 2001)] and references therein). It

has to be noted that, above these fast-neutron ﬂuences, the Hall coeﬃcient was

observed to change sign in n-type substrate with resistivity of (4–6) kΩ cm (e.g., see

Sect. 4.3.5 and [Croitoru, Dahan, Rancoita, Rattaggi, Rossi and Seidman (1997);

Croitoru, Gubbini, Rancoita, Rattaggi and Seidman (1999a); Mangiagalli, Levalois,

Marie, Rancoita and Rattaggi (1999)]).

The physical change in the irradiated detector seems to be inﬂuenced by the

type of defects and their distribution in the bulk material (e.g., [Golan et al. (1999)]

and references therein). Investigations have shown morphological changes in silicon

detectors. High neutron ﬂuences result in vacancy accumulations and large quanti-

ties of interstitial atoms creating dislocation accumulations, which increase the local

value of the micro-hardness. For instance, in Fig. 4.37 (left side) the AFM surface

topography [Golan et al. (2001)] of a cleaved sample along the p

− n doping-

distribution and substrate is shown for (I) a non-irradiated device, (II) a device

irradiated with a fast neutron ﬂuence of 5. 28 ×10

n/cm

and (III) a device irradi-

ated with a fast neutron ﬂuence of 3.12 × 10

n/cm

. For a non-irradiated sample

[left side of Fig. 4.37 (I)], the defects are homogeneously distributed on the surface

of the detector. At large neutron ﬂuences [left side of Figs. 4.37 (II) and 4.37 (III)],

accumulations of defects are more observable. An additional set of measurements

was carried out on these devices in order to scan the Contact Potential Diﬀerence

(CPD) along the substrate depth (right side of Fig. 4.37). A sensitivity of less than

10 mV was achieved at an applied bias voltage of 5 V. For the non-irradiated sam-

To determine the free carrier concentration (e.g., see [Konozenko, Semenyuk and Khivrich

(1969); Lugakov, Lukashevich and Shusha (1982)]), r

= r

' 1 and b ≈ 3 (e.g., see [Lugakov,

Lukashevich and Shusha (1982)]) is assumed in Eq. (4.165), or, the temperature dependence of

the Hall factor in Eqs. (4.169, 4.170) is that one given in [Messier and Merlo-Flores (1963)].

One makes the assumption that µ

is slightly aﬀected by the irradiation and b ≈ 3

(e.g., see [Croitoru, Dahan, Rancoita, Rattaggi, Rossi and Seidman (1997)]).

∗∗

b was assumed to vary in the range 1 < b < 3.3 (e.g., see [Croitoru, Dahan, Rancoita, Rattaggi,

Rossi and Seidman (1997)]).

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Radiation Environments and Damage in Silicon Semiconductors 417

Fig. 4.37 (left side) Atomic Force Microscope (AFM) surface topography of a cleaved sample

along the p

− n doping-distribution and substrate; (right side) Contact Potential Diﬀerence

(CPD), in units of V, as a function of the depth in µm of silicon detector junctions with n-type

silicon substrate and resistivity of about 6 kΩ cm (before irradiation) (reprinted from Microelect.

Reliab. 41, Golan, G. et al., Inversion phenomenon as a result of junction damages in neutron

irradiated silicon detectors, 67–72, Copyright (2001), with permission from Elsevier, e.g., for the

list of the authors see [Golan et al. (2001)]: (I) for a non-irradiated device, (II) for a device

irradiated with a fast-neutron ﬂuence of 5.28 × 10

n/cm

and (III) for a device irradiated with

a fast neutron ﬂuence of 3.12 × 10

n/cm

ple [right side of Fig. 4.37 (I)], the behavior of the contact potential follows that

expected in the junction region. In this region, the maximum potential of 0.165 mV

is approximately in agreement with that predicted by mean of Eq. (6.12) when the

free carrier concentrations of the n-type substrate and p

-region are taken into ac-

count. In addition the width of the depleted region is ≈ 20 µm, i.e., in agreement

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418 Principles of Radiation Interaction in Matter and Detection

with that expected from Eq. (6.26). For samples irradiated with the largest ﬂuence

(i.e., 3.12×10

n/cm

), the contact potential seems to exhibit an inverted behavior

[right side of Fig. 4.37 (III)]. Other measurements of CPD as a function of the depth

position (Figure 2 in [Golan et al. (2001)]) have provided values lower than those

shown in Figs. 4.37 (II) and 4.37 (III) (right side). These later data might indicate

a reduced space-charge region.

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Chapter 5

Scintillating Media and Scintillator

Detectors

The conversion of the energy deposited by incoming particles or radiation into

photons can lead to particle detection, energy determination and discrimination

between particles of diﬀerent masses. Therefore, the use of scintillating materials,

or the construction of detectors enhancing the

Cerenkov or the transition radiation

eﬀects, can be of great use in many application ﬁelds, such as high-energy physics

or medical imaging. The photons emitted in such detectors must be transported,

by light guides, to photosensitive devices, e.g., photomultipliers, in order to be

collected. In this chapter, the organic and inorganic scintillators will be reviewed,

as well as the

Cerenkov and transition radiation detectors, with many examples. A

section will also be devoted to the description of the light transport and detection

techniques.

5.1 Scintillators

Scintillators are materials in which large fractions of incident energy carried by

striking particles or radiation are absorbed and transformed into detectable pho-

tons (visible or near visible light), later converted into an electric signal. They are

used in many applications, e.g., as detecting elements of calorimeters or in medical

imaging. This section will put an emphasis on calorimetric applications. Medical

applications will be discussed in the chapter devoted to medical physics.

There are two types of light emission: ﬂuorescence and phosphorescence. Fluo-

rescence corresponds to prompt light emission (ns → µs) in the visible wavelength

range and is temperature independent. Phosphorescence corresponds to light emis-

sion over a longer period of time (µs → ms, even hours dep ending on the material)

with longer wavelengths compared to ﬂuorescence and is temperature dependent. In

practice, only ﬂuorescence, characterized by fast light emission, is useful for the de-

tection of particle or nuclear radiation.

Inorganic and organic scintillators are used for radiation detection (e.g., see [Hof-

stadter (1974); Knoll (1999)] and references therein). As will be seen later, diﬀerent

mechanisms are at the origin of light production in these two types of scintillators.

419