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

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370 Principles of Radiation Interaction in Matter and Detection

Rogers (1980)]), the NIEL deposition occurs with a limited cascade of displaced

silicon atoms (e.g., see Sect. 4.2.1.4).

4.2.2 Radiation Induced Defects

The radiation interaction in silicon semiconductors generates primary point defects,

i.e., vacancies (V ) and interstitials (I) as mentioned in Sects. 4.1.1.2 and 4.2.1. Pos-

sible structures for the silicon vacancy and interstitial are discussed in [Privitera,

Coﬀa, Priolo and Rimini (1998)], i.e., slightly diﬀerent conﬁgurations may result

depending on the charge state of the point defect.

At room temperature, these defects are mobile

with low activation energies for

their motion. For instance, the activation energies for vacancy migration are diﬀerent

for n- and p-type materials, depend on the resistivity and are about (18–45) meV

(e.g., see Section 3 in [Claeys and Simoen (2002)]). As a consequence, not all primary

defects will result in creating stable secondary defects or defect complexes, because a

non negligible fraction of them will anneal, for example, by an interstitial ﬁlling of a

vacancy. However, they can also interact with other point defects and impurities

‡‡

(interstitial and substitutional) to form more stable defects (e.g., see [Privitera,

Coﬀa, Priolo and Rimini (1998); Lazanu and Lazanu (2003)]), like for example i) the

divacancy referred to as “G7-center” (V -V , indicated also as V

, i.e., two adjacent

vacant lattice sites [Watkins and Corbett (1961a, 1965a,b); Cheng, Corelli, Corbett

and Watkins (1966)]) in various charge states

††

, ii) vacancy-oxygen

∗∗

(V -O) referred

to as “A-center” or “B1-center” [Watkins and Corbett (1961b); Watkins, Corbett,

Chrenko and McDonald (1961)] (see also [Li et al. (1992)] and references therein),

iii) vacancy-dopant impurity (for instance, V -P or V -As in n-type silicon) referred to

as “E-center” or “G8-center” [Watkins and Corbett (1964); Samara (1988);

Og˘utt

and Chelikowsky (2003)] and iv) others (e.g., see Sections 3–5 in Chapter II of

Part I of [Vavilov and Ukhin (1977)], Section 7.3 of [van Lint, Flanahan, Leadon,

Naber and Rogers (1980)], Sections 2.4 and 3.2.1 of [Claeys and Simoen (2002)],

Sections 2.2.1–2.2.4 of [Holmes-Siedle and Adams (2002)] and Sections 3.2.1–3.2.3

of [Kozlovski and Abrosimova (2005)]).

Radiation-induced defects, which are electrically active, are (and have been)

extensively studied by means of experimental techniques, for instance the Electron

One can see, for instance, Section 24 of [Seitz and Ko ehler (1956)], Chapters 4 and 5 of [Dienes

and Vineyard (1957)], Section 3 in Chapter II of Part I of [Vavilov and Ukhin (1977)] and [Privitera,

Coﬀa, Priolo and Rimini (1998); Hall´en, Keskitalo, Josyula and Svensson (1999)].

‡‡

Impurities (and vacancies) can diﬀuse (e.g., see Section 2 of [Ravi (1981)]) and, in addition, in-

troduce deep energy-levels in silicon, which can become recombination centers (e.g., see Chapters 2

and 6 of [Milnes (1973)].

††

The reader can also see [Kholodar and Vinetskii (1975); Borchi et al. (1989); Bosetti et al.

(1995); Bondarenko, Krause-Rehberg Feick and Davia (2004)] and references therein.

∗∗

EPR investigations have led to the observation of more complex-defects relating vacancies and

oxygen(s) (e.g., see [Lee and Corbett (1976)]).

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Radiation Environments and Damage in Silicon Semiconductors 371

Table 4.3 Energy levels (in eV) of electron (E

) and hole (H

) traps determined with the DLTS

technique between about 90 and 350 K. E

and E

are the energies (with respect to an arbitrary

level) of the conduction and valence band edges, respectively (from [Leroy and Rancoita (2007)]).

Level Energy level Energy level

from [Bosetti et al. (1995)] from [Li, Chen and Kraner (1991); Li et al. (1992)]

− (0.16 ± 0.01) E

− 0.17

− (0.25 ± 0.02) E

− 0.21

− (0.40 ± 0.02) E

− 0.41

− (0.54 ± 0.02) E

− 0.55

+ (0.30 ± 0.01) E

+ 0.30

+ (0.50 ± 0.02) E

+ 0.54

Paramagnetic Resonance

†

(EPR), Thermally Stimulated Current

∗

(TSC), Photo-

Luminescence

(PL) and Deep Level Transient Spectroscopy

(DLTS).

Examples of DLTS spectra for p

− n silicon junctions with n-type Fz (Float-

Zone) and MCz (Magnetic Czochralski) substrates are shown in Figs. 4.23 and 4.24,

respectively [Bosetti et al. (1995)] (see also [SICAPO Collab. (1994c)] for details

about MCz substrate). These detectors

with an active area of 0.5 × 0.5 cm

were

irradiated with a fast neutron

‡

ﬂuence of 3×10

n /cm

. In Figs. 4.23 and 4.24, four

energy-levels (E

, E

and E

) of electron-traps and two (only one in the case of

MCz sample) of hole-traps are observed between about 90 and 350 K. The measured

energy-levels of these (electron and hole) traps are in agreement with those deter-

mined in [Li, Chen and Kraner (1991); Li et al. (1992)] (see Table 4.3). Furthermore,

a complete discussion of the observed defects and their association to determined

energy-levels is presented in [Li, Chen and Kraner (1991); Li et al. (1992); Bosetti et

al. (1995)] and references therein. From an inspection of Figs. 4.23 and 4.24, we can

notice that the ratio (R

trap

) of the trap concentrations

‡‡

over donor concentration

depends on the type of substrate, as expected. This occurs because the concen-

trations of impurities in the Fz and MCz substrates are diﬀerent (see Table 4.4

and [Bosetti et al. (1995)], for electron-traps). The E

energy-level corresponds to

that of an A-center (vacancy-oxygen). The ratio R

trap

for this level is lower in Fz

†

In EPR spectroscopy, the electromagnetic radiation of microwave frequency is absorbed by

defects possessing a magnetic dipole moment of unpaired spins.

∗

The TSC technique consists of the measurement of diode currents, generated after ﬁlling trap

levels by bias pulses, while performing thermal scans [Weisberg and Schade (1968); Schade and

Herrick (1969); Bueheler (1972)] (see also Chapter 9 of [Milnes (1973)] and references therein).

A recent review on PL spectroscopy is done in [Davies (1989)].

The DLTS consists of the measurement of capacitance transients, generated by repetitive ﬁlling

and emptying of deep levels in the depleted region by bias pulses, while performing a thermal

scan [Lang (1974)].

Both types of detectors were manufactured by STMicroelectronics.

‡

The mean kinetic energy was about 1 MeV [Bosetti et al. (1995)].

‡‡

The trap concentrations were induced in the Fz and MCz detectors by irradiations with similar

fast neutron ﬂuence.

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372 Principles of Radiation Interaction in Matter and Detection

Fig. 4.23 DLTS spectrum as a function of temperature of a silicon detector with an asymmetrical

one-side junction and Fz n-type silicon substrate (about 400 µm thick) cut along the Si crystal

direction < 111 > (adapted from Nucl. Instr. and Meth. in Phys. Res. A 361, Bosetti, M. et al.,

DLTS measurement of energetic levels, generated in silicon detectors, 461–465, Copyright (1995),

with permission from Elsevier, e.g., for the list of the authors see [Bosetti et al. (1995)]). The

ordinate corresponds to the ratio of concentrations of traps after a fast neutron irradiation of

about 3 × 10

n/cm

divided by the donor concentration. The oxygen concentration of the Fz

bulk silicon is (1 ± 0.04) × 10

−3

and the resistivity is between 4–6 kΩ cm. Solid and dashed

lines are traps for electrons and holes, respectively.

Fig. 4.24 DLTS spectrum as a function of temperature of a silicon detector with an asymmetrical

one-side junction and MCz n-type silicon substrate (about 525 µm thick) cut along the Si crystal

direction < 100 > (adapted from Nucl. Instr. and Meth. in Phys. Res. A 361, Bosetti, M. et al.,

DLTS measurement of energetic levels, generated in silicon detectors, 461–465, Copyright (1995),

with permission from Elsevier, e.g., for the list of the authors see [Bosetti et al. (1995)]). The

ordinate corresponds to the ratio of concentrations of traps after a fast neutron irradiation of

about 3 × 10

n/cm

divided by the donor concentration. The oxygen concentration of the MCz

bulk silicon is (1 ± 0.04) × 10

−3

and the resistivity is between 4–6 kΩ cm. Solid and dashed

lines are traps for electrons and holes, respectively.

(which contains less oxygen) than in MCz substrate. The E

energy-level is that

of a double negative charge state of a divacancy (V

−−

). While the E

energy-level

has two components with E

− (0.39 ± 0.01) [V

−

, divacancy in single negative

charge state] and E

−(0.42 ±0.02) eV [E-center, i.e., a vacancy-phosphorous com-

plex]. These two latter levels were resolved by an investigation employing the TSC

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Radiation Environments and Damage in Silicon Semiconductors 373

spectroscopy [Borchi et al. (1991)]. The E

energy-level has also shown two anneal-

ing stages around 150 and 300

◦

C [Borchi et al. (1989)]. The E

and E

centers have

smaller R

trap

ratios for MCz compared to Fz detectors, as expected by a getter ef-

fect [Li et al. (1992); Bosetti et al. (1995)] when oxygen is present at the A-centers,

thus avoiding the formation of deeper vacancy centers. In fact, more A-centers were

found in the MCz than in the Fz detectors. Furthermore for Fz substrates, R

trap

for the E

level was measured for fast neutron ﬂuences up to Φ

≈ 2 × 10

n/cm

and found to be linearly dependent on the ﬂuence [Borchi et al. (1989)]:

trap

) ≈ (2.12 ± 0.06) × 10

−12

× Φ

These data are in agreement with those found in [Bosetti et al. (1995)] for ﬂuences

up to ≈ 3 × 10

n/cm

. A linear dependence of R

trap

) as a function of the Kr-

ion ﬂuence was also observed up to a maximum ﬂuence of 10

Kr/cm

[Croitoru,

Rancoita, Rattaggi and Seidman (1999)].

DLTS peaks were also observed in the temperature range (10–90) K for irradia-

tions with neutrons, electrons, photons, Ar- and Kr-ions. Both non-irradiated and

irradiated samples show a peak related to an oxygen-related donor state, with an

energy level E

= E

− E

with E

= (0.11–0.12) eV [Walker and Sah (1973);

Brotherton and Bradley (1982); Jellison (1982); Kimerling and Benton (1982);

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

Rattaggi and Seidman (1999)]. It has been identiﬁed as an oxygen-carbon pairing

[Walker and Sah (1973); Jellison (1982)]. A few other (electron trap) levels were

also observed at energies . 0.1 eV below E

(e.g., see [Walker and Sah (1973);

Kimerling and Benton (1982); Croitoru, Rancoita, Rattaggi and Seidman (1999)])

Commonly observed defect levels in Fz, Cz (Czochralski) and MCz silicon inclu-

ding those after irradiations can be found in Table 9 at pages 155–157 of [Vavilov

and Ukhin (1977)] and also in [Konozenko, Semenyuk and Khivrich (1969); Milnes

(1973); Walker and Sah (1973); Borchi et al. (1989); Li et al. (1992); Borchi and

Bruzzi (1994); Bosetti et al. (1995); Levinshtein, Rumyantsev and Shur (2000); Lutz

(2001); Claeys and Simoen (2002)] (see also references therein); typical experimental

errors for energy levels of defects are about (0.5–2.5) meV (e.g., see [Walker and Sah

(1973); Jellison (1982); Li et al. (1992); Bosetti et al. (1995)] and Table 4.3).

Defect introduction rates were measured after irradiations with electrons of 1

and 12 MeV (e.g., see [Walker and Sah (1973); Brotherton and Bradley (1982)]). For

instance, the introduction rates for the A-center and divacancy were found to be

almost constant, although the data indicate a tendency for the rates to decrease

with increasing ﬂuence up to a maximum of 5.5 × 10

electrons/cm

[Brotherton

and Bradley (1982)].

Crystals containing defects induced by radiation are unstable, although they

tend to stabilize with time, and the concentrations of defects decrease with time

if the temperature is typically larger than zero degree Celsius. This mechanism is

sometimes referred to as self-annealing process. Furthermore, defect concentrations

have been studied as a function of the temperature (i.e., by annealing) to determine

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374 Principles of Radiation Interaction in Matter and Detection

the value at which each typ e of defect spontaneously dissociates (see Section 5

in Chapter II of Part I of [Vavilov and Ukhin (1977)], Section 3.2.1 of [Claeys

and Simoen (2002)], Section 3.2.8 of [Holmes-Siedle and Adams (2002)] and, for

instance, [Dannefaer, Mascher and Kerr (1993); Makarenko (2001); Poirier, Avalos,

Dannefaer, Schiettekatte, Roorda and Misra (2003)]).

Clusters of defects are generated in semiconductors when the incident particles

(e.g., fast neutrons) transfer enough energy to the recoil atoms for allowing large ca-

scades of displacements and, consequently, closely spaced lattice-defects. These clus-

ters introduce large local concentrations of energy-levels in the forbidden gap. For

instance (Fig. 4.14), a recoil atom with kinetic energy of 50 keV

generates clusters

with subclusters of defects which extend up to about (100–200)

A [van Lint, Leadon

and Colweel (1972)]. Typical cluster and subcluster size distributions resulting from

proton–, electron– and neutron–silicon interactions are rep orted in Table 7.2 of [van

Lint, Flanahan, Leadon, Naber and Rogers (1980)] (see also [van Lint, Leadon and

Colweel (1972)] and references therein). The most direct evidence for the existence

of clusters was given by Bertolotti (1968): his electron microscopy observations

have provided an excellent physical picture of clusters with a central (disordered)

region surrounded by a region attributed to space charge (e.g., see page 311 of [van

Lint, Flanahan, Leadon, Naber and Rogers (1980)]). Relevant eﬀects associated to

defect clusters are expected in semiconductors: for instance, a change of the type

of conductivity was observed in germanium by Cleland et al

in the mid of 1950s

[Cleland, Crawford and Pigg (1955a,b)]. It has to be noted that a change of the

type of conductivity was also observed in silicon (e.g., see Sects. 4.3.5 and 4.3.6,

and references therein).

The Gossick–Gregory–Leadon model for defect clusters assumes that, for a large

local concentration of defects generated by an incoming particle

∗∗

, the damage

consists of a disordered region (densely populated by defects) surrounded by an

almost undisturbed lattice. Thus, a potential well is created because the position of

the Fermi level relative to the energy bands is diﬀerent within the disordered region

from the outside. As a consequence, the model postulates that the core of the cluster

is capable to acquire a net charge by capturing majority-carriers. Furthermore, it

predicts a large short-term annealing and the eﬀect of the material resistivity on

annealing rate [Gossick (1959); Gregory (1969); Leadon (1970)] (see also Section 6 in

Chapter II of Part I of [Vavilov and Ukhin (1977)] and, in addition, [Gregory, Naik

and Oldham (1971); Litvinov, Ukhin and Oldham (1989)]). Under the assumption

of a spherical cluster, the core region of radius r

≈ (10–25) nm (e.g., [Borchi and

This is the average energy transferred by a neutron with a kinetic energy of about 0.76 MeV

(see Sect. 4.2.1.2).

A fast neutron is likely to generates ≈ 10

displaced atoms in a volume of approximately

−16

The experimental results (originally interpreted in the framework of the James–Lark-Horovitz

model [James and Lark-Horovitz (1951)]) have also motivated Gossick’s model for defect clusters

[Gossick (1959)].

∗∗

The model was originally proposed for studying the damage induced by fast neutrons.

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Radiation Environments and Damage in Silicon Semiconductors 375

Table 4.4 Ratio (R

trap

) of the trap concentrations over donor

concentrations for silicon detectors with Fz and MCz n-type

substrate, after irradiation with a fast neutron ﬂuence of

about 3 × 10

n /cm

(from [Leroy and Rancoita (2007)], see

also [Bosetti et al. (1995)]). R

trap

is given for the 4 energy levels

for electron traps shown in Table 4.3. The experimental errors

on R

trap

are about ±1%.

Level Fz substrate MCz substrate

0.0750 0.0850

0.0500 0.0150

0.5400 0.5000

0.0180 0.0007

Bruzzi (1994); Gossick (1959); Gregory (1969)] and references therein) is surrounded

by a semiconductor volume of radius r

from which majority-carriers have been

partially removed generating a region similar to that depleted in a p-n junction

with a potential hill (well) for majority (minority) carriers. The outer boundary

must exceed the Debye–H¨uckel length (L

) in the undisturbed lattice:

T ε

imp

, (4.118)

where e is the charge of the electron, k

is the Boltzmann’s constant, T is the

absolute temperature, ε is the silicon electric permittivity (e.g., see Appendix A.2)

and N

imp

is the concentration of impurities which contribute current carriers to the

undisturbed material. For a high resistivity silicon, L

is about 4 µm at ro om

temperature.

Since point defects are mobile at room temperature (e.g., see page 370), a re-

arrangement process can take place ([Gregory, Naik and Oldham (1971)] and re-

ferences therein), resulting in a decrease of cluster eﬀects on the semiconductor

electronic properties with time. Large annealing factors (& 50) at early times were

experimentally measured [Harrity and Mallon (1970)] and are consistent with the

fact that the induced damage depends on the cluster size. In Section 7.4 of [van

Lint, Flanahan, Leadon, Naber and Rogers (1980)], one ﬁnds a review of expe-

rimental data that can be explained by the presence of defect clusters pro duced

by neutron irradiations. These data regard carrier removal, lifetime degradation,

mobility changes and short-term thermal annealing. Calculations [Leadon (1970)]

based on the cluster model

††

have shown that i) the major features of short-term

annealing, ii) the shape of the annealing factor curve with time, iii) the eﬀect of

injection level and iv) the material resistivity on the lifetime degradation constants

††

Other cluster models have been proposed with cylindrical clusters [Holmes (1970)] and eﬀective

radii of the space-charge region larger than the range of the primary recoil atom [van Lint and

Leadon (1966)].

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376 Principles of Radiation Interaction in Matter and Detection

can be all reasonably explained by the cluster nature of the damage induced by fast

neutrons.

As discussed in Sects. 4.2.1.1–4.2.1.4 for NIEL processes, the amount of the

deposited energy (Sect. 4.2.1.5) and the size of the cascade depend on the type

of interaction and the energy of incoming particles. Thus, it is expected that the

extension of clusters and subclusters (when generated) can, in turn, depend on

the type of interaction between the incoming particle and the atom in the lat-

tice, i.e., the damage eﬀectiveness can be aﬀected by the prop erties of the defect

clusters (e.g., see also [Tsveybak, Bugg, Harvey and Walter (1992)] and references

therein). A comparative investigation carried out with Kr-ions, electrons and fast-

neutrons has conﬁrmed that the introduction rates of complex-defects normalized

to the total displacement cross-section depend on the type of incoming particle:

a factor of ≈ 18 for the divacancies and vacancy-doping impurity complexes was

found ([Mangiagalli, Levalois and Marie (1998)] and references therein).

4.2.3 Ionization Energy-Loss and NIEL Processes

As mentioned at page 346, charged particles heavier than electrons (or positrons)

traversing (or being stopped inside) a silicon medium lose energy predominantly

by collision energy-losses

, i.e., by the excitation and ionization of atoms close

to the particle path. For electrons and positrons, the collision energy-loss is the

dominant process at energies below the so-called critical energy (see Sect. 2.1.7.4)

while, above, the main mechanism is the so-called radiation energy-loss, i.e., by

emitting photons. Photon interactions in matter

†

allow the energy of photons to

be partially or fully absorbed in matter, as a consequence of the interaction inside

the medium of the scattered (emitted) electrons or of the created electron–positron

pairs. As discussed in Sect. 4.2.1.3, light ions (i.e., protons and α-particles) can be

regarded as charge invariant over most of the energy region, while heavier isotopes

only with velocities largely exceeding the orbital velocities of their electrons can be

fully ionized

‡

and lose energy predominantly by electronic energy-loss [Northcliﬀe

(1963); Leroy and Rancoita (2004)], i.e., by the excitation or ionization of atomic

electrons of the medium. The energy-loss processes (by collision and radiation) and

partial or complete absorption of photons in matter were reviewed in the chapter on

Electromagnetic Interaction of Radiation in Matter.

Displaced silicon atoms can also undergo both electronic and nuclear energy-

losses (see Sect. 4.2.1.1) to dissipate their energy inside the medium. Consequently,

neutrons can also deposit energy via the interaction of the recoil silicon with the

The energy-loss formula describing the energy deposited in a medium is that called restricted

energy-loss formula; see, for instance, Eq. (2.27).

†

The dominant processes of photon interaction in matter are photoelectric eﬀect, Compton scatte-

ring and pair production (e.g., see chapter on Electromagnetic Interaction of Radiation in Matter ).

‡

At low energy the isotope becomes partially ionized and the electronic stopping power is modiﬁed

to account for it (see [Northcliﬀe (1963)]). Furthermore, the collisions with nuclei of the medium

cannot be neglected anymore (see Sect. 4.2.1.3).

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Radiation Environments and Damage in Silicon Semiconductors 377

atoms of the medium through ionization and excitation.

4.2.3.1 Imparted Dose in Silicon

When there is no nuclear transformation, the absorbed dose

in (silicon) devices

accounts for the energy deposited by the energy-loss processes of primary particles,

those of recoil atoms (i.e. the PKAs generated in the semiconductor medium) and

by NIEL processes (discussed in Sect. 4.2.1) resulting in the deposition of damage

energy (for instance for creating PKAs, lattice vibrations, . . . ).

For fast neutrons from nuclear reactors, the contribution (D

NIEL

) of NIEL pro-

cesses to the absorbed dose can be estimated using Eq. (4.81), i.e.

NIEL

dis

6.24 × 10

× ρ

(4.119)

≈

dis

1.45 × 10

[Gy], (4.120)

where E

dis

is in MeV/cm

and ρ

= 2.33 g/cm

is the density of the silicon

medium. For example in the case of the Triga reactor RC:1 at Casaccia (Rome)

[Codegoni et al. (2004b); Consolandi, D’Angelo, Fallica, Mangoni, Modica, Pen-

sotti and Rancoita (2006)], a ﬂuence 2.33 ×10

n/cm

of fast neutrons with kinetic

energies above 10 keV creates a concentration of Frenkel-pairs

∗

of about 10

−3

and, by NIEL processes, deposits a dose

NIEL

≈ 4.3 Gy. (4.121)

The dose deposited by ionization (D

Ion

) with this ﬂuence of neutrons can be estima-

ted by considering that the elastic scattering is the dominant interaction mechanism

for fast reactor neutrons on silicon up to (3–4) MeV

. In addition neutrons with ki-

netic energy up to a few MeV (see, Chapter 2 in [van Lint, Flanahan, Leadon,

Naber and Rogers (1980)]) are isotropically (or almost isotropically) scattered and,

ﬁnally, the fraction of energy deposited by ionization was also estimated (e.g., see

for instance [Smith, Binder, Compton and Wilbur (1966)]) for neutrons with larger

kinetic energies, i.e., when the elastic scattering is a relevant, but not dominant,

interaction in silicon. D

Ion

can be calculated by replacing E

dis

with the energy de-

posited by ionization (in MeV) per cm

in Eq (4.119) [or in Eq (4.120)]. For the

Triga reactor neutrons, within 5 %, we have

Ion

≈ 4.8 Gy. (4.122)

Thus, ionization and non-ionization processes result in depositing amounts of

energy, which diﬀer by ≈ (10–11) %.

The absorbed dose is deﬁned as the mean energy imparted by ionizing radiation per unit mass

[ICRUM (1980b, 1993b)] (see also Sect. 2.3.5). It accounts for the net diﬀerence of kinetic energies

of particle entering and leaving from the medium volume and nuclear transmutations changing

the rest masses in the medium volume.

∗

The concentration of Frenkel-pairs can be calculated using Eq. (4.83) with E

≈ 25 eV.

For the Triga reactor RC:1, the neutron ﬂuence above 3.7 MeV is about 2 % of the neutron

ﬂuence above 10 keV. These high-energy fast neutrons deposit less than about 8% of the damage

energy.

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378 Principles of Radiation Interaction in Matter and Detection

Table 4.5 D

Ion

and particle ﬂuence (from [Leroy and Rancoita (2007)]) for

fast reactor neutrons (i.e., for the Triga reactor RC:1 energy spectrum), heavy

ions (i.e.,

Ar and

Kr, see page 378), protons and electrons (see

page 379). These values refer to similar NIEL energy deposition, i.e., that

needed to generate a concentration of Frenkel-pairs of about 10

−3

Particle Kinetic Energy Fluence (part./cm

) D

NIEL

Ion

(Gy) (Gy)

n > 10 keV 2.33 × 10

4.3 ≈ 4.8

C 95.0 MeV/amu 8.10 × 10

4.3 ≈ 2.7 × 10

C 11.1 MeV/amu 9.30 × 10

4.3 ≈ 1.7 × 10

Ar 13.6 MeV/amu 1.40 × 10

4.3 ≈ 1.8 × 10

Kr 60.0 MeV/amu 1.60 × 10

4.3 ≈ 2.6 × 10

p 1 GeV 1.92 × 10

4.3 ≈ 5.2 × 10

e 9.1 MeV 2.58 × 10

4.3 & 6.3 × 10

In case of incoming ions, like for instance in the space radiation environ-

ment (see Sect. 4.1.2), the energy deposited by ionization largely exceeds that

by NIEL processes. Let us examine, as an example, the energy

depositions by

the four ions used for the investigation reported in [Codegoni et al. (2004b); Con-

solandi, D’Angelo, Fallica, Mangoni, Modica, Pensotti and Rancoita (2006)]:

accelerated at 95 MeV/amu,

C at 11.1 MeV/amu,

Ar at 13.6 MeV/amu and

Kr at 60 MeV/amu. In a silicon bulk depth

∗∗

down to about 20 µm, a dose

NIEL

≈ 4.3 Gy

††

is deposited by NIEL-processes [e.g. see Eq. (4.121)] with ion

ﬂuences of about 8.1 ×10

, 9.3 ×10

, 1.4 ×10

and 1.6 ×10

ions/cm

, respec-

tively. With these ion ﬂuences, the corresponding doses deposited by ionization

are about 2.7 × 10

, 1.7 × 10

, 1.8 × 10

and 2.6 × 10

Gy, respectively. Thus, the

ionization doses are larger by almost 4 orders of magnitude with respect to that

for NIEL processes, while D

NIEL

and D

Ion

diﬀer slightly for neutrons, as discussed

above.

Protons are the most abundant particles in cosmic rays and are among the

particles populating the radiation belts in the space near the Earth. Protons are

commonly used as beam particles in experiments of particle physics. As already men-

tioned in Sect. 4.2.1.5, for protons with kinetic energies above 10 MeV, the damage

function was found to be slightly dependent on E

(see [Summers, Burke, Shapiro,

Messenger and Walters (1993)], for instance). Furthermore, by an inspection of

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

∗∗

This is the part of the silicon substrate relevant for VLSI components and located in front of

the incoming ion beam.

††

This damage-energy deposition allows one to generate a concentration of Frenkel-pairs of about

−3

for E

≈ 25 eV.

At these energies, the electronic energy-loss is far larger than the nuclear energy-loss and deter-

mines the corresponding ionization dose.

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Radiation Environments and Damage in Silicon Semiconductors 379

Fig. 4.20, we can note that there is a good agreement

‡‡

among the diﬀerent calcu-

lations for the NIEL deposition of protons with kinetic energy of about 1000 MeV

(βγ ≈ 1.81); the deposition of a damage energy corresponding to D

NIEL

≈ 4.3 Gy

[e.g. see Eq. (4.121)] requires a ﬂuence of about 1.92 × 10

protons/cm

. In a sub-

strate (500–900) µm thick, the probability of p–Si strong interactions is small

†

and,

to a ﬁrst approximation, does not aﬀect the amount of energy deposited by ioni-

zation processes induced by the incoming proton in the silicon absorber. Since fast

δ-rays can escape from the medium, the deposited energy has to be estimated by the

so-called restricted energy-loss formula. For 900 µm thick Si detectors, the restricted

energy-loss (based on measured values, see Sect. 2.1.1.3) is about 394 eV/µm and,

as a consequence, for such a ﬂuence of protons we have

Ion

≈ 5.2 × 10

Gy. (4.123)

Electrons with a kinetic energy larger than about (250–260) keV can induce

initial displacement damages with a very small (if at all) subsequent cascade, while

above a few MeV, displacements result also from a small cascade development. Let

us examine, for instance, the energy deposition of electrons with 9.1 MeV kinetic

energy used for the investigation reported in [Codegoni et al. (2006)]. In Fig. 4.22,

we can see that electrons with a kinetic energy of 9.1 MeV (βγ ≈ 18.8) have a NIEL

of about 2.42×10

−4

MeV/cm. Thus, a ﬂuence of about 2.58 ×10

electrons/cm

required to deposit D

NIEL

≈ 4.3 Gy

∗

[e.g. see Eq. (4.121)]. To a ﬁrst approximation,

since the fastest δ-rays can escape from a silicon medium (500–900) µm thick, the

collision (i.e. ionization) energy-losses of such electrons are properly described by the

restricted energy-loss

‡

deposition, which amounts to about 355 eV/µm. A ﬂuence

of about 2.58 × 10

electrons/cm

with kinetic energy of 9.1 MeV deposits an

ionization dose

Ion

coll

≈ 6.3 × 10

Gy, (4.124)

to account for the collision-loss processes. Furthermore, in silicon absorbers, the

energy-loss by collisions of these electrons accounts for about 86% of the total

energy-loss (i.e., collision and radiative). As a consequence, the overall dose for

ionization process, D

Ion

, is slightly larger because it has also to account for the

energy deposition (by ionization) of the secondary electrons emitted by the intera-

ctions of radiated photons.

‡‡

These calculations assume diﬀerent values [(20–21) eV] for the displacement energy and, as a

consequence, the estimated concentrations of Frenkel-pairs may diﬀer up to ≈ 20 % for E

= 25 eV.

†

The collision length in silicon is about 30.3 cm (see Table 3.4) and the probability of interaction

is about 0.3% in a silicon medium 900 µm thick.

∗

The NIEL calculations, reported in Sect. 4.2.1.5, show that the deposited damage-energy slightly

depends on the displacement energy. For E

= 25 eV and a ﬂuence of 2.58 × 10

electrons/cm

the concentration of Frenkel-pairs is about 10

−3

‡

The restricted energy-loss for massive (i.e., protons) particles and electrons are described by

similar equations {see Sects. 2.1.1.4 and 2.1.2.3 (or see Sections 2.1.1.3 and 2.1.5.2 of [Leroy and

Rancoita (2004)])}.